wiki.fine.cz - User contributions [en]

Formula Specification in Templates

2024-12-20T14:30:57Z

PetrDlask: /* Informative */

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''{X⇕}''');120;-1) ⇒ 120''

''IF(MAX('''{X⇓2:⇓3}''')>'''{X⇓7}''';MAX('''{X⇓2:⇓3}''');'''{X⇓7}''')) ⇒ 6''

''IF(MAX('''1;2''')>'''6''';MAX('''1;2''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''{Coordinate Z}''''' ''= 210''';{GWT}''' = 180''

''IF('''{Coordinate Z}'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''{GWT}'''<'''{Coordinate Z}''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''{GWT}''''' ''= 15''
''IFS('''{GWT}'''>8;10;'''{GWT}'''>6;9;'''{GWT}'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

''CEILING(-10.4;2;0) ⇒ -10''

''CEILING(-10.4;2;1) ⇒ -12''
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''{X⇓2:⇓5}''') ... SUM('''1; 2; 3; 4''') ⇒ 10''

''SUM('''{X⇕}''') ⇒ 21''
|-
|SUMIF
|
|Returns the sum of all the values that meet a given criteria
|''SUMIF('''{X_Coor⇕}''';">2";'''{Y_Coor⇕}''')''
|-
|SUMIFS
|
|Returns the sum of all the values that meet the given criterias
|
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RADIANS
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''{GWTb}''' = 15''

''CONCAT('''{GWTb}''';" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|-
|TEXT
|
|Converts number to text
|
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''{X⇓3:⇓5}''') ... AVERAGE('''2; 3; 4''') ⇒ 3''
|-
|AVERAGEIF
|
|Returns the average (arithmetic mean) of all the values that meet a given criteria
|
|-
|AVERAGEIFS
|
|Returns the average (arithmetic mean) of all the values that meet the given criterias
|
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''{X⇓3:⇓5}''') ... AVERAGE('''2; 3; 4''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''{X⇓3:⇓5}''') ... AVERAGE('''2; 3; 4''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE('''{X⇕}''';0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC('''{X⇕}''';1) ⇒ NAN''

''PERCENTILE.INC('''{X⇕}''';0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC('''{X⇕}''';1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV('''{X⇕}''') ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P('''{X⇕}''') ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S('''{X⇕}''') ⇒ 1.581''
|-
|TRIMMEAN
|
|Returns the mean of the interior of a data set
|
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE(('''{X⇕}''') ⇒ NAN''

''MODE(('''{X⇕}''';3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''{Y⇓}''';2) ⇒ 16''

''INDEX('''{Y⇓}''';4) ⇒ 27''

''INDEX('''{Y⇓}''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''MATCH(11;'''{Y⇕}''') ⇒ 3''

''MATCH(27;'''{Y⇕}''') ⇒ 4''

''MATCH(999;'''{Y⇕}''') ⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FILTERTABLE
|''FILTERTABLE(Coordinates X;Coordinates Y)''
|Filters repeating values and keeps the last one of them
Returns matrix with 2 columns:

Column 1: X - Filtered X

Column 2: Y - Filtered Y
|''Inputs linked to data''
''FILTERTABLE('''{X-value⇕}''';'''{Y-value⇕}''')''

(<s>2.000</s> ... ignored value, '''2.000''' ... saved value)
{| class="wikitable"
|+
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|'''''1'''''
|'''0.000'''
|'''17.000'''
|-
|<s>2</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|<s>3</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|'''4'''
|'''2.000'''
|'''25.000'''
|-
|<s>5</s>
|<s>4.000</s>
|<s>32.000</s>
|-
|'''6'''
|'''4.000'''
|'''32.000'''
|-
|<s>7</s>
|<s>6.000</s>
|<s>24.000</s>
|-
|'''8'''
|'''6.000'''
|'''24.000'''
|}
|⇒⇒⇒⇒
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|0.000
|17.000
|-
|2
|2.000
|25.000
|-
|3
|4.000
|32.000
|-
|4
|6.000
|24.000
|}
|}
|[[File:Filtertable function.png|center|thumb|360x360px|Filtertable function]]
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND('''{X⇕}''';'''{Y⇕}''')''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND('''{X⇕}''';'''{Y⇕}''')''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC('''{X⇕}''';'''{R⇕}''')''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS('''{X⇕}''';'''{R⇕}''')''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS('''{X-Input⇕}''';'''{Y-Input⇕}''';2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE('''{X-Input⇕}''';'''{Y-Input⇕}''';[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

=== Informative ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|ISIMPERIAL
|''ISIMPERIAL()''
|Returns TRUE if project is calculated in imperial units
|''If the project is in imperial [ft, in, ...] units:''
''ISIMPERIAL() ⇒ TRUE; ⇒ 1''

''ISMETRIC() ⇒ FALSE; ⇒ 0''
|
|-
|ISMETRIC
|''ISMETRIC()''
|Returns TRUE if project is calculated in metric units
|''If the project is in metric [m, mm, ...] units:''
''ISMETRIC() ⇒ TRUE; ⇒ 1''

''ISIMPERIAL() ⇒ FALSE; ⇒ 0''
|
|-
|ISNUMBER
|''ISNUMBER()''
|Returns TRUE if argument is number
|ISNUMBER(15) ''⇒ TRUE; ⇒ 1''
ISNUMBER(15e2) ''⇒ TRUE; ⇒ 1''

ISNUMBER(1/4) ''⇒ TRUE; ⇒ 1''

ISNUMBER(aaa) ''⇒ FALSE; ⇒ 0''
|
|-
|ISTEXT
|''ISTEXT()''
|Returns TRUE if argument is text
|ISTEXT(123)
ISTEXT("123")

ISTEXT(abc)

ISTEXT("abc")
|
|-
|LANG
|''LANG()''
|LANG([ Application = False ])
|''If the application is in English and output language is Spanish:''
''LANG(FALSE()) ⇒ EN; LANG(0) ⇒ EN''

''LANG(TRUE()) ⇒ ES; LANG(1) ⇒ ES''
|
|}

=== Geotechnic ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FINESOILCLASSIFICATION
|''FINESOILCLASSIFICATION(Plasticity Index [-];Moisture [-];''
''Method 0 = EN ISO 14688-2 (2018); 1 = EN ISO 14688-2 (2013);''

''2 = ČSN 73 6133)''

For classification we can use these standards for plasticity diagram:[[File:Standards for plasticity diagram.png|thumb|Possible standards for plasticity diagram]]
|Returns the classification of fine soil according to selected method
For inputs use number from interval (0;1)

''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''

or percetage

''FINESOILCLASSIFICATION(13.7/100;33.3/100;0) ⇒ ClL''

or inputs linked to data according to unit

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]}/100;{LiqLimit⇓ [-]}/100;0)''

or inputs linked to data with unit setup

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]};{LiqLimit⇓ [-]};0)''[[File:Unit setup for input.png|thumb|Unit setup for input]]
|''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''[[File:Fine Soil Classification ISO 14-688-2 (2018).png|thumb|Fine Soil Classification EN ISO 14-688-2 (2018)|center|302x302px]]''FINESOILCLASSIFICATION(0.137;0.333;1) ⇒ ClL''[[File:Fine Soil Classification EN ISO 14-688-2 (2013).png|center|thumb|Fine Soil Classification EN ISO 14-688-2 (2013)]]
|-
|SOILCLASSIFICATION
|''SOILCLASSIFICATION(Size [mm];Fall [-];Method 0 = EN ISO 14688-2 (2018))''
|Returns the classification of soil according to selected method
|
{| class="wikitable"
|Číslo
|Průměr zrn
|Propad
|-
|
|[mm]
|[%]
|-
|1
|32,000
|100,00
|-
|2
|16,000
|100,00
|-
|3
|8,000
|100,00
|-
|4
|4,000
|99,76
|-
|5
|2,000
|98,76
|-
|6
|1,000
|97,52
|-
|7
|0,500
|95,52
|-
|8
|0,200
|91,52
|-
|9
|0,100
|85,02
|-
|10
|0,063
|79,02
|-
|11
|0,057
|76,40
|-
|12
|0,042
|70,70
|-
|13
|0,030
|67,50
|-
|14
|0,019
|65,00
|-
|15
|0,011
|60,50
|-
|16
|0,008
|57,40
|-
|17
|0,006
|55,00
|-
|18
|0,003
|51,20
|-
|19
|0,001
|46,10
|}
|}
=== Date and Time ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|DATE
|''DATE(Year;Month;Day)''
|Returns the serial number of a particular date
|''DATE(1899;12;30) ⇒ 0''
''DATE(2024;10;31) ⇒ 45596''

''Inputs linked to data''

'''''{MyYear}'''=2024;'''{MyMonth}'''=10;'''{MyDay}'''=31''

''DATE('''{MyYear}''';'''{MyMonth}''';'''{MyDay}''') ⇒ 45596''

|-
|NOW
|''NOW()''
|Returns the serial number of the current date and time
|''For date and time 20.12.2024 13:48:04 is''
''NOW() ⇒ 45646.5750510648''

''For date and time 01.01.1900 00:00:00 is''

''NOW() ⇒ 1.00''
|-
|TIME
|''TIME(Hour;Minute;Second)''
|Returns the serial number of a particular time
|''TIME(0;0;0) ⇒ 0''
''TIME(18;15;20) ⇒ 0.760648''

''Inputs linked to data''

'''''{MyHour}'''=10[hour];'''{MyMinute}'''=15[min.];'''{MySecond}'''=25[sec.]''

''TIME('''{MyHour}''';'''{MyMinute}''';'''{MySecond}''') ⇒ 0.42737''
|-
|TODAY
|''TODAY()''
|Returns the serial number of the current date
|''For date 20:12:2024''
''TODAY() ⇒ 45646''

''For date 1.1.1900''

''TODAY() ⇒ 1''
|}

Formula Specification in Templates

2024-12-20T13:03:51Z

PetrDlask: /* Date and Time */

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''{X⇕}''');120;-1) ⇒ 120''

''IF(MAX('''{X⇓2:⇓3}''')>'''{X⇓7}''';MAX('''{X⇓2:⇓3}''');'''{X⇓7}''')) ⇒ 6''

''IF(MAX('''1;2''')>'''6''';MAX('''1;2''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''{Coordinate Z}''''' ''= 210''';{GWT}''' = 180''

''IF('''{Coordinate Z}'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''{GWT}'''<'''{Coordinate Z}''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''{GWT}''''' ''= 15''
''IFS('''{GWT}'''>8;10;'''{GWT}'''>6;9;'''{GWT}'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

''CEILING(-10.4;2;0) ⇒ -10''

''CEILING(-10.4;2;1) ⇒ -12''
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''{X⇓2:⇓5}''') ... SUM('''1; 2; 3; 4''') ⇒ 10''

''SUM('''{X⇕}''') ⇒ 21''
|-
|SUMIF
|
|Returns the sum of all the values that meet a given criteria
|
|-
|SUMIFS
|
|Returns the sum of all the values that meet the given criterias
|
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RADIANS
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''{GWTb}''' = 15''

''CONCAT('''{GWTb}''';" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|-
|TEXT
|
|Converts number to text
|
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''{X⇓3:⇓5}''') ... AVERAGE('''2; 3; 4''') ⇒ 3''
|-
|AVERAGEIF
|
|Returns the average (arithmetic mean) of all the values that meet a given criteria
|
|-
|AVERAGEIFS
|
|Returns the average (arithmetic mean) of all the values that meet the given criterias
|
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''{X⇓3:⇓5}''') ... AVERAGE('''2; 3; 4''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''{X⇓3:⇓5}''') ... AVERAGE('''2; 3; 4''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE('''{X⇕}''';0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC('''{X⇕}''';1) ⇒ NAN''

''PERCENTILE.INC('''{X⇕}''';0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC('''{X⇕}''';1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV('''{X⇕}''') ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P('''{X⇕}''') ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S('''{X⇕}''') ⇒ 1.581''
|-
|TRIMMEAN
|
|Returns the mean of the interior of a data set
|
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE(('''{X⇕}''') ⇒ NAN''

''MODE(('''{X⇕}''';3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''{Y⇓}''';2) ⇒ 16''

''INDEX('''{Y⇓}''';4) ⇒ 27''

''INDEX('''{Y⇓}''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''MATCH(11;'''{Y⇕}''') ⇒ 3''

''MATCH(27;'''{Y⇕}''') ⇒ 4''

''MATCH(999;'''{Y⇕}''') ⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FILTERTABLE
|''FILTERTABLE(Coordinates X;Coordinates Y)''
|Filters repeating values and keeps the last one of them
Returns matrix with 2 columns:

Column 1: X - Filtered X

Column 2: Y - Filtered Y
|''Inputs linked to data''
''FILTERTABLE('''{X-value⇕}''';'''{Y-value⇕}''')''

(<s>2.000</s> ... ignored value, '''2.000''' ... saved value)
{| class="wikitable"
|+
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|'''''1'''''
|'''0.000'''
|'''17.000'''
|-
|<s>2</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|<s>3</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|'''4'''
|'''2.000'''
|'''25.000'''
|-
|<s>5</s>
|<s>4.000</s>
|<s>32.000</s>
|-
|'''6'''
|'''4.000'''
|'''32.000'''
|-
|<s>7</s>
|<s>6.000</s>
|<s>24.000</s>
|-
|'''8'''
|'''6.000'''
|'''24.000'''
|}
|⇒⇒⇒⇒
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|0.000
|17.000
|-
|2
|2.000
|25.000
|-
|3
|4.000
|32.000
|-
|4
|6.000
|24.000
|}
|}
|[[File:Filtertable function.png|center|thumb|360x360px|Filtertable function]]
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND('''{X⇕}''';'''{Y⇕}''')''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND('''{X⇕}''';'''{Y⇕}''')''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC('''{X⇕}''';'''{R⇕}''')''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS('''{X⇕}''';'''{R⇕}''')''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS('''{X-Input⇕}''';'''{Y-Input⇕}''';2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE('''{X-Input⇕}''';'''{Y-Input⇕}''';[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

=== Informative ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|ISIMPERIAL
|''ISIMPERIAL()''
|Returns TRUE if project is calculated in imperial units
|''If the project is in imperial [ft, in, ...] units:''
''ISIMPERIAL() ⇒ TRUE; ⇒ 1''

''ISMETRIC() ⇒ FALSE; ⇒ 0''
|
|-
|ISMETRIC
|''ISMETRIC()''
|Returns TRUE if project is calculated in metric units
|''If the project is in metric [m, mm, ...] units:''
''ISMETRIC() ⇒ TRUE; ⇒ 1''

''ISIMPERIAL() ⇒ FALSE; ⇒ 0''
|
|-
|ISNUMBER
|
|Returns TRUE if argument is number
|
|
|-
|ISTEXT
|
|Returns TRUE if argument is text
|
|
|-
|LANG
|''LANG()''
|LANG([ Application = False ])
|''If the application is in English and output language is Spanish:''
''LANG(FALSE()) ⇒ EN; LANG(0) ⇒ EN''

''LANG(TRUE()) ⇒ ES; LANG(1) ⇒ ES''
|
|}

=== Geotechnic ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FINESOILCLASSIFICATION
|''FINESOILCLASSIFICATION(Plasticity Index [-];Moisture [-];''
''Method 0 = EN ISO 14688-2 (2018); 1 = EN ISO 14688-2 (2013);''

''2 = ČSN 73 6133)''

For classification we can use these standards for plasticity diagram:[[File:Standards for plasticity diagram.png|thumb|Possible standards for plasticity diagram]]
|Returns the classification of fine soil according to selected method
For inputs use number from interval (0;1)

''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''

or percetage

''FINESOILCLASSIFICATION(13.7/100;33.3/100;0) ⇒ ClL''

or inputs linked to data according to unit

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]}/100;{LiqLimit⇓ [-]}/100;0)''

or inputs linked to data with unit setup

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]};{LiqLimit⇓ [-]};0)''[[File:Unit setup for input.png|thumb|Unit setup for input]]
|''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''[[File:Fine Soil Classification ISO 14-688-2 (2018).png|thumb|Fine Soil Classification EN ISO 14-688-2 (2018)|center|302x302px]]''FINESOILCLASSIFICATION(0.137;0.333;1) ⇒ ClL''[[File:Fine Soil Classification EN ISO 14-688-2 (2013).png|center|thumb|Fine Soil Classification EN ISO 14-688-2 (2013)]]
|-
|SOILCLASSIFICATION
|''SOILCLASSIFICATION(Size [mm];Fall [-];Method 0 = EN ISO 14688-2 (2018))''
|Returns the classification of soil according to selected method
|
{| class="wikitable"
|Číslo
|Průměr zrn
|Propad
|-
|
|[mm]
|[%]
|-
|1
|32,000
|100,00
|-
|2
|16,000
|100,00
|-
|3
|8,000
|100,00
|-
|4
|4,000
|99,76
|-
|5
|2,000
|98,76
|-
|6
|1,000
|97,52
|-
|7
|0,500
|95,52
|-
|8
|0,200
|91,52
|-
|9
|0,100
|85,02
|-
|10
|0,063
|79,02
|-
|11
|0,057
|76,40
|-
|12
|0,042
|70,70
|-
|13
|0,030
|67,50
|-
|14
|0,019
|65,00
|-
|15
|0,011
|60,50
|-
|16
|0,008
|57,40
|-
|17
|0,006
|55,00
|-
|18
|0,003
|51,20
|-
|19
|0,001
|46,10
|}
|}
=== Date and Time ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|DATE
|''DATE(Year;Month;Day)''
|Returns the serial number of a particular date
|''DATE(1899;12;30) ⇒ 0''
''DATE(2024;10;31) ⇒ 45596''

''Inputs linked to data''

'''''{MyYear}'''=2024;'''{MyMonth}'''=10;'''{MyDay}'''=31''

''DATE('''{MyYear}''';'''{MyMonth}''';'''{MyDay}''') ⇒ 45596''

|-
|NOW
|''NOW()''
|Returns the serial number of the current date and time
|''For date and time 20.12.2024 13:48:04 is''
''NOW() ⇒ 45646.5750510648''

''For date and time 01.01.1900 00:00:00 is''

''NOW() ⇒ 1.00''
|-
|TIME
|''TIME(Hour;Minute;Second)''
|Returns the serial number of a particular time
|''TIME(0;0;0) ⇒ 0''
''TIME(18;15;20) ⇒ 0.760648''

''Inputs linked to data''

'''''{MyHour}'''=10[hour];'''{MyMinute}'''=15[min.];'''{MySecond}'''=25[sec.]''

''TIME('''{MyHour}''';'''{MyMinute}''';'''{MySecond}''') ⇒ 0.42737''
|-
|TODAY
|''TODAY()''
|Returns the serial number of the current date
|''For date 20:12:2024''
''TODAY() ⇒ 45646''

''For date 1.1.1900''

''TODAY() ⇒ 1''
|}

Formula Specification in Templates

2024-12-20T10:52:18Z

PetrDlask: /* Mathematical */

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''{X⇕}''');120;-1) ⇒ 120''

''IF(MAX('''{X⇓2:⇓3}''')>'''{X⇓7}''';MAX('''{X⇓2:⇓3}''');'''{X⇓7}''')) ⇒ 6''

''IF(MAX('''1;2''')>'''6''';MAX('''1;2''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''{Coordinate Z}''''' ''= 210''';{GWT}''' = 180''

''IF('''{Coordinate Z}'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''{GWT}'''<'''{Coordinate Z}''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''{GWT}''''' ''= 15''
''IFS('''{GWT}'''>8;10;'''{GWT}'''>6;9;'''{GWT}'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

''CEILING(-10.4;2;0) ⇒ -10''

''CEILING(-10.4;2;1) ⇒ -12''
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''{X⇓2:⇓5}''') ... SUM('''1; 2; 3; 4''') ⇒ 10''

''SUM('''{X⇕}''') ⇒ 21''
|-
|SUMIF
|
|Returns the sum of all the values that meet a given criteria
|
|-
|SUMIFS
|
|Returns the sum of all the values that meet the given criterias
|
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RADIANS
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''{GWTb}''' = 15''

''CONCAT('''{GWTb}''';" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|-
|TEXT
|
|Converts number to text
|
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''{X⇓3:⇓5}''') ... AVERAGE('''2; 3; 4''') ⇒ 3''
|-
|AVERAGEIF
|
|Returns the average (arithmetic mean) of all the values that meet a given criteria
|
|-
|AVERAGEIFS
|
|Returns the average (arithmetic mean) of all the values that meet the given criterias
|
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''{X⇓3:⇓5}''') ... AVERAGE('''2; 3; 4''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''{X⇓3:⇓5}''') ... AVERAGE('''2; 3; 4''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE('''{X⇕}''';0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC('''{X⇕}''';1) ⇒ NAN''

''PERCENTILE.INC('''{X⇕}''';0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC('''{X⇕}''';1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV('''{X⇕}''') ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P('''{X⇕}''') ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S('''{X⇕}''') ⇒ 1.581''
|-
|TRIMMEAN
|
|Returns the mean of the interior of a data set
|
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE(('''{X⇕}''') ⇒ NAN''

''MODE(('''{X⇕}''';3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''{Y⇓}''';2) ⇒ 16''

''INDEX('''{Y⇓}''';4) ⇒ 27''

''INDEX('''{Y⇓}''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''MATCH(11;'''{Y⇕}''') ⇒ 3''

''MATCH(27;'''{Y⇕}''') ⇒ 4''

''MATCH(999;'''{Y⇕}''') ⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FILTERTABLE
|''FILTERTABLE(Coordinates X;Coordinates Y)''
|Filters repeating values and keeps the last one of them
Returns matrix with 2 columns:

Column 1: X - Filtered X

Column 2: Y - Filtered Y
|''Inputs linked to data''
''FILTERTABLE('''{X-value⇕}''';'''{Y-value⇕}''')''

(<s>2.000</s> ... ignored value, '''2.000''' ... saved value)
{| class="wikitable"
|+
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|'''''1'''''
|'''0.000'''
|'''17.000'''
|-
|<s>2</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|<s>3</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|'''4'''
|'''2.000'''
|'''25.000'''
|-
|<s>5</s>
|<s>4.000</s>
|<s>32.000</s>
|-
|'''6'''
|'''4.000'''
|'''32.000'''
|-
|<s>7</s>
|<s>6.000</s>
|<s>24.000</s>
|-
|'''8'''
|'''6.000'''
|'''24.000'''
|}
|⇒⇒⇒⇒
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|0.000
|17.000
|-
|2
|2.000
|25.000
|-
|3
|4.000
|32.000
|-
|4
|6.000
|24.000
|}
|}
|[[File:Filtertable function.png|center|thumb|360x360px|Filtertable function]]
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND('''{X⇕}''';'''{Y⇕}''')''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND('''{X⇕}''';'''{Y⇕}''')''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC('''{X⇕}''';'''{R⇕}''')''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS('''{X⇕}''';'''{R⇕}''')''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS('''{X-Input⇕}''';'''{Y-Input⇕}''';2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE('''{X-Input⇕}''';'''{Y-Input⇕}''';[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

=== Informative ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|ISIMPERIAL
|''ISIMPERIAL()''
|Returns TRUE if project is calculated in imperial units
|''If the project is in imperial [ft, in, ...] units:''
''ISIMPERIAL() ⇒ TRUE; ⇒ 1''

''ISMETRIC() ⇒ FALSE; ⇒ 0''
|
|-
|ISMETRIC
|''ISMETRIC()''
|Returns TRUE if project is calculated in metric units
|''If the project is in metric [m, mm, ...] units:''
''ISMETRIC() ⇒ TRUE; ⇒ 1''

''ISIMPERIAL() ⇒ FALSE; ⇒ 0''
|
|-
|ISNUMBER
|
|Returns TRUE if argument is number
|
|
|-
|ISTEXT
|
|Returns TRUE if argument is text
|
|
|-
|LANG
|''LANG()''
|LANG([ Application = False ])
|''If the application is in English and output language is Spanish:''
''LANG(FALSE()) ⇒ EN; LANG(0) ⇒ EN''

''LANG(TRUE()) ⇒ ES; LANG(1) ⇒ ES''
|
|}

=== Geotechnic ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FINESOILCLASSIFICATION
|''FINESOILCLASSIFICATION(Plasticity Index [-];Moisture [-];''
''Method 0 = EN ISO 14688-2 (2018); 1 = EN ISO 14688-2 (2013);''

''2 = ČSN 73 6133)''

For classification we can use these standards for plasticity diagram:[[File:Standards for plasticity diagram.png|thumb|Possible standards for plasticity diagram]]
|Returns the classification of fine soil according to selected method
For inputs use number from interval (0;1)

''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''

or percetage

''FINESOILCLASSIFICATION(13.7/100;33.3/100;0) ⇒ ClL''

or inputs linked to data according to unit

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]}/100;{LiqLimit⇓ [-]}/100;0)''

or inputs linked to data with unit setup

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]};{LiqLimit⇓ [-]};0)''[[File:Unit setup for input.png|thumb|Unit setup for input]]
|''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''[[File:Fine Soil Classification ISO 14-688-2 (2018).png|thumb|Fine Soil Classification EN ISO 14-688-2 (2018)|center|302x302px]]''FINESOILCLASSIFICATION(0.137;0.333;1) ⇒ ClL''[[File:Fine Soil Classification EN ISO 14-688-2 (2013).png|center|thumb|Fine Soil Classification EN ISO 14-688-2 (2013)]]
|-
|SOILCLASSIFICATION
|''SOILCLASSIFICATION(Size [mm];Fall [-];Method 0 = EN ISO 14688-2 (2018))''
|Returns the classification of soil according to selected method
|
{| class="wikitable"
|Číslo
|Průměr zrn
|Propad
|-
|
|[mm]
|[%]
|-
|1
|32,000
|100,00
|-
|2
|16,000
|100,00
|-
|3
|8,000
|100,00
|-
|4
|4,000
|99,76
|-
|5
|2,000
|98,76
|-
|6
|1,000
|97,52
|-
|7
|0,500
|95,52
|-
|8
|0,200
|91,52
|-
|9
|0,100
|85,02
|-
|10
|0,063
|79,02
|-
|11
|0,057
|76,40
|-
|12
|0,042
|70,70
|-
|13
|0,030
|67,50
|-
|14
|0,019
|65,00
|-
|15
|0,011
|60,50
|-
|16
|0,008
|57,40
|-
|17
|0,006
|55,00
|-
|18
|0,003
|51,20
|-
|19
|0,001
|46,10
|}
|}
=== Date and Time ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|DATE
|''DATE(Year;Month;Day)''
|Returns the serial number of a particular date
|''DATE(1899;12;30) ⇒ 0''
''DATE(2024;10;31) ⇒ 45596''

''Inputs linked to data''

'''''{MyYear}'''=2024;'''{MyMonth}'''=10;'''{MyDay}'''=31''

''DATE('''{MyYear}''';'''{MyMonth}''';'''{MyDay}''') ⇒ 45596''

|-
|NOW
|
|Returns the serial number of the current date and time
|
|-
|TIME
|''TIME(Hour;Minute;Second)''
|Returns the serial number of a particular time
|''TIME(0;0;0) ⇒ 0''
''TIME(18;15;20) ⇒ 0.760648''

''Inputs linked to data''

'''''{MyHour}'''=10[hour];'''{MyMinute}'''=15[min.];'''{MySecond}'''=25[sec.]''

''TIME('''{MyHour}''';'''{MyMinute}''';'''{MySecond}''') ⇒ 0.42737''
|-
|TODAY
|
|Returns the serial number of the current date
|
|}

Formula Specification in Templates

2024-12-20T10:43:04Z

PetrDlask: /* Mathematical */

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''{X⇕}''');120;-1) ⇒ 120''

''IF(MAX('''{X⇓2:⇓3}''')>'''{X⇓7}''';MAX('''{X⇓2:⇓3}''');'''{X⇓7}''')) ⇒ 6''

''IF(MAX('''1;2''')>'''6''';MAX('''1;2''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''{Coordinate Z}''''' ''= 210''';{GWT}''' = 180''

''IF('''{Coordinate Z}'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''{GWT}'''<'''{Coordinate Z}''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''{GWT}''''' ''= 15''
''IFS('''{GWT}'''>8;10;'''{GWT}'''>6;9;'''{GWT}'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''{X⇓2:⇓5}''') ... SUM('''1; 2; 3; 4''') ⇒ 10''

''SUM('''{X⇕}''') ⇒ 21''
|-
|SUMIF
|
|Returns the sum of all the values that meet a given criteria
|
|-
|SUMIFS
|
|Returns the sum of all the values that meet the given criterias
|
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RADIANS
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|-
|TEXT
|
|Converts number to text
|
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|AVERAGEIF
|
|Returns the average (arithmetic mean) of all the values that meet a given criteria
|
|-
|AVERAGEIFS
|
|Returns the average (arithmetic mean) of all the values that meet the given criterias
|
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|TRIMMEAN
|
|Returns the mean of the interior of a data set
|
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FILTERTABLE
|''FILTERTABLE(Coordinates X;Coordinates Y)''
|Filters repeating values and keeps the last one of them
Returns matrix with 2 columns:

Column 1: X - Filtered X

Column 2: Y - Filtered Y
|''Inputs linked to data''
''FILTERTABLE({'''X-value⇕'''};{'''Y-value⇕'''})''

(<s>2.000</s> ... ignored value, '''2.000''' ... saved value)
{| class="wikitable"
|+
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|'''''1'''''
|'''0.000'''
|'''17.000'''
|-
|<s>2</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|<s>3</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|'''4'''
|'''2.000'''
|'''25.000'''
|-
|<s>5</s>
|<s>4.000</s>
|<s>32.000</s>
|-
|'''6'''
|'''4.000'''
|'''32.000'''
|-
|<s>7</s>
|<s>6.000</s>
|<s>24.000</s>
|-
|'''8'''
|'''6.000'''
|'''24.000'''
|}
|⇒⇒⇒⇒
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|0.000
|17.000
|-
|2
|2.000
|25.000
|-
|3
|4.000
|32.000
|-
|4
|6.000
|24.000
|}
|}
|[[File:Filtertable function.png|center|thumb|360x360px|Filtertable function]]
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

=== Informative ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|ISIMPERIAL
|''ISIMPERIAL()''
|Returns TRUE if project is calculated in imperial units
|''If the project is in imperial [ft, in, ...] units:''
''ISIMPERIAL() ⇒ TRUE; ⇒ 1''

''ISMETRIC() ⇒ FALSE; ⇒ 0''
|
|-
|ISMETRIC
|''ISMETRIC()''
|Returns TRUE if project is calculated in metric units
|''If the project is in metric [m, mm, ...] units:''
''ISMETRIC() ⇒ TRUE; ⇒ 1''

''ISIMPERIAL() ⇒ FALSE; ⇒ 0''
|
|-
|ISNUMBER
|
|Returns TRUE if argument is number
|
|
|-
|ISTEXT
|
|Returns TRUE if argument is text
|
|
|-
|LANG
|''LANG()''
|LANG([ Application = False ])
|''If the application is in English and output language is Spanish:''
''LANG(FALSE()) ⇒ EN; LANG(0) ⇒ EN''

''LANG(TRUE()) ⇒ ES; LANG(1) ⇒ ES''
|
|}

=== Geotechnic ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FINESOILCLASSIFICATION
|''FINESOILCLASSIFICATION(Plasticity Index [-];Moisture [-];''
''Method 0 = EN ISO 14688-2 (2018); 1 = EN ISO 14688-2 (2013);''

''2 = ČSN 73 6133)''

For classification we can use these standards for plasticity diagram:[[File:Standards for plasticity diagram.png|thumb|Possible standards for plasticity diagram]]
|Returns the classification of fine soil according to selected method
For inputs use number from interval (0;1)

''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''

or percetage

''FINESOILCLASSIFICATION(13.7/100;33.3/100;0) ⇒ ClL''

or inputs linked to data according to unit

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]}/100;{LiqLimit⇓ [-]}/100;0)''

or inputs linked to data with unit setup

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]};{LiqLimit⇓ [-]};0)''[[File:Unit setup for input.png|thumb|Unit setup for input]]
|''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''[[File:Fine Soil Classification ISO 14-688-2 (2018).png|thumb|Fine Soil Classification EN ISO 14-688-2 (2018)|center|302x302px]]''FINESOILCLASSIFICATION(0.137;0.333;1) ⇒ ClL''[[File:Fine Soil Classification EN ISO 14-688-2 (2013).png|center|thumb|Fine Soil Classification EN ISO 14-688-2 (2013)]]
|-
|SOILCLASSIFICATION
|''SOILCLASSIFICATION(Size [mm];Fall [-];Method 0 = EN ISO 14688-2 (2018))''
|Returns the classification of soil according to selected method
|
{| class="wikitable"
|Číslo
|Průměr zrn
|Propad
|-
|
|[mm]
|[%]
|-
|1
|32,000
|100,00
|-
|2
|16,000
|100,00
|-
|3
|8,000
|100,00
|-
|4
|4,000
|99,76
|-
|5
|2,000
|98,76
|-
|6
|1,000
|97,52
|-
|7
|0,500
|95,52
|-
|8
|0,200
|91,52
|-
|9
|0,100
|85,02
|-
|10
|0,063
|79,02
|-
|11
|0,057
|76,40
|-
|12
|0,042
|70,70
|-
|13
|0,030
|67,50
|-
|14
|0,019
|65,00
|-
|15
|0,011
|60,50
|-
|16
|0,008
|57,40
|-
|17
|0,006
|55,00
|-
|18
|0,003
|51,20
|-
|19
|0,001
|46,10
|}
|}
=== Date and Time ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|DATE
|''DATE(Year;Month;Day)''
|Returns the serial number of a particular date
|''DATE(1899;12;30) ⇒ 0''
''DATE(2024;10;31) ⇒ 45596''

''Inputs linked to data''

'''''{MyYear}'''=2024;'''{MyMonth}'''=10;'''{MyDay}'''=31''

''DATE('''{MyYear}''';'''{MyMonth}''';'''{MyDay}''') ⇒ 45596''

|-
|NOW
|
|Returns the serial number of the current date and time
|
|-
|TIME
|''TIME(Hour;Minute;Second)''
|Returns the serial number of a particular time
|''TIME(0;0;0) ⇒ 0''
''TIME(18;15;20) ⇒ 0.760648''

''Inputs linked to data''

'''''{MyHour}'''=10[hour];'''{MyMinute}'''=15[min.];'''{MySecond}'''=25[sec.]''

''TIME('''{MyHour}''';'''{MyMinute}''';'''{MySecond}''') ⇒ 0.42737''
|-
|TODAY
|
|Returns the serial number of the current date
|
|}

Formula Specification in Templates

2024-12-20T10:41:41Z

PetrDlask:

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''{X⇕}''');120;-1) ⇒ 120''

''IF(MAX('''{X⇓2:⇓3}''')>'''{X⇓7}''';MAX('''{X⇓2:⇓3}''');'''{X⇓7}''')) ⇒ 6''

''IF(MAX('''1;2''')>'''6''';MAX('''1;2''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''{Coordinate Z}''''' ''= 210''';{GWT}''' = 180''

''IF('''{Coordinate Z}'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''{GWT}'''<'''{Coordinate Z}''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''{GWT}''''' ''= 15''
''IFS('''{GWT}'''>8;10;'''{GWT}'''>6;9;'''{GWT}'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|SUMIF
|
|Returns the sum of all the values that meet a given criteria
|
|-
|SUMIFS
|
|Returns the sum of all the values that meet the given criterias
|
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RADIANS
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|-
|TEXT
|
|Converts number to text
|
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|AVERAGEIF
|
|Returns the average (arithmetic mean) of all the values that meet a given criteria
|
|-
|AVERAGEIFS
|
|Returns the average (arithmetic mean) of all the values that meet the given criterias
|
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|TRIMMEAN
|
|Returns the mean of the interior of a data set
|
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FILTERTABLE
|''FILTERTABLE(Coordinates X;Coordinates Y)''
|Filters repeating values and keeps the last one of them
Returns matrix with 2 columns:

Column 1: X - Filtered X

Column 2: Y - Filtered Y
|''Inputs linked to data''
''FILTERTABLE({'''X-value⇕'''};{'''Y-value⇕'''})''

(<s>2.000</s> ... ignored value, '''2.000''' ... saved value)
{| class="wikitable"
|+
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|'''''1'''''
|'''0.000'''
|'''17.000'''
|-
|<s>2</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|<s>3</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|'''4'''
|'''2.000'''
|'''25.000'''
|-
|<s>5</s>
|<s>4.000</s>
|<s>32.000</s>
|-
|'''6'''
|'''4.000'''
|'''32.000'''
|-
|<s>7</s>
|<s>6.000</s>
|<s>24.000</s>
|-
|'''8'''
|'''6.000'''
|'''24.000'''
|}
|⇒⇒⇒⇒
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|0.000
|17.000
|-
|2
|2.000
|25.000
|-
|3
|4.000
|32.000
|-
|4
|6.000
|24.000
|}
|}
|[[File:Filtertable function.png|center|thumb|360x360px|Filtertable function]]
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

=== Informative ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|ISIMPERIAL
|''ISIMPERIAL()''
|Returns TRUE if project is calculated in imperial units
|''If the project is in imperial [ft, in, ...] units:''
''ISIMPERIAL() ⇒ TRUE; ⇒ 1''

''ISMETRIC() ⇒ FALSE; ⇒ 0''
|
|-
|ISMETRIC
|''ISMETRIC()''
|Returns TRUE if project is calculated in metric units
|''If the project is in metric [m, mm, ...] units:''
''ISMETRIC() ⇒ TRUE; ⇒ 1''

''ISIMPERIAL() ⇒ FALSE; ⇒ 0''
|
|-
|ISNUMBER
|
|Returns TRUE if argument is number
|
|
|-
|ISTEXT
|
|Returns TRUE if argument is text
|
|
|-
|LANG
|''LANG()''
|LANG([ Application = False ])
|''If the application is in English and output language is Spanish:''
''LANG(FALSE()) ⇒ EN; LANG(0) ⇒ EN''

''LANG(TRUE()) ⇒ ES; LANG(1) ⇒ ES''
|
|}

=== Geotechnic ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FINESOILCLASSIFICATION
|''FINESOILCLASSIFICATION(Plasticity Index [-];Moisture [-];''
''Method 0 = EN ISO 14688-2 (2018); 1 = EN ISO 14688-2 (2013);''

''2 = ČSN 73 6133)''

For classification we can use these standards for plasticity diagram:[[File:Standards for plasticity diagram.png|thumb|Possible standards for plasticity diagram]]
|Returns the classification of fine soil according to selected method
For inputs use number from interval (0;1)

''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''

or percetage

''FINESOILCLASSIFICATION(13.7/100;33.3/100;0) ⇒ ClL''

or inputs linked to data according to unit

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]}/100;{LiqLimit⇓ [-]}/100;0)''

or inputs linked to data with unit setup

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]};{LiqLimit⇓ [-]};0)''[[File:Unit setup for input.png|thumb|Unit setup for input]]
|''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''[[File:Fine Soil Classification ISO 14-688-2 (2018).png|thumb|Fine Soil Classification EN ISO 14-688-2 (2018)|center|302x302px]]''FINESOILCLASSIFICATION(0.137;0.333;1) ⇒ ClL''[[File:Fine Soil Classification EN ISO 14-688-2 (2013).png|center|thumb|Fine Soil Classification EN ISO 14-688-2 (2013)]]
|-
|SOILCLASSIFICATION
|''SOILCLASSIFICATION(Size [mm];Fall [-];Method 0 = EN ISO 14688-2 (2018))''
|Returns the classification of soil according to selected method
|
{| class="wikitable"
|Číslo
|Průměr zrn
|Propad
|-
|
|[mm]
|[%]
|-
|1
|32,000
|100,00
|-
|2
|16,000
|100,00
|-
|3
|8,000
|100,00
|-
|4
|4,000
|99,76
|-
|5
|2,000
|98,76
|-
|6
|1,000
|97,52
|-
|7
|0,500
|95,52
|-
|8
|0,200
|91,52
|-
|9
|0,100
|85,02
|-
|10
|0,063
|79,02
|-
|11
|0,057
|76,40
|-
|12
|0,042
|70,70
|-
|13
|0,030
|67,50
|-
|14
|0,019
|65,00
|-
|15
|0,011
|60,50
|-
|16
|0,008
|57,40
|-
|17
|0,006
|55,00
|-
|18
|0,003
|51,20
|-
|19
|0,001
|46,10
|}
|}
=== Date and Time ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|DATE
|''DATE(Year;Month;Day)''
|Returns the serial number of a particular date
|''DATE(1899;12;30) ⇒ 0''
''DATE(2024;10;31) ⇒ 45596''

''Inputs linked to data''

'''''{MyYear}'''=2024;'''{MyMonth}'''=10;'''{MyDay}'''=31''

''DATE('''{MyYear}''';'''{MyMonth}''';'''{MyDay}''') ⇒ 45596''

|-
|NOW
|
|Returns the serial number of the current date and time
|
|-
|TIME
|''TIME(Hour;Minute;Second)''
|Returns the serial number of a particular time
|''TIME(0;0;0) ⇒ 0''
''TIME(18;15;20) ⇒ 0.760648''

''Inputs linked to data''

'''''{MyHour}'''=10[hour];'''{MyMinute}'''=15[min.];'''{MySecond}'''=25[sec.]''

''TIME('''{MyHour}''';'''{MyMinute}''';'''{MySecond}''') ⇒ 0.42737''
|-
|TODAY
|
|Returns the serial number of the current date
|
|}

Formula Specification in Templates

2024-10-31T14:25:05Z

PetrDlask: /* Date and Time */

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|SUMIF
|
|Returns the sum of all the values that meet a given criteria
|
|-
|SUMIFS
|
|Returns the sum of all the values that meet the given criterias
|
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RADIANS
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|-
|TEXT
|
|Converts number to text
|
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|AVERAGEIF
|
|Returns the average (arithmetic mean) of all the values that meet a given criteria
|
|-
|AVERAGEIFS
|
|Returns the average (arithmetic mean) of all the values that meet the given criterias
|
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|TRIMMEAN
|
|Returns the mean of the interior of a data set
|
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FILTERTABLE
|''FILTERTABLE(Coordinates X;Coordinates Y)''
|Filters repeating values and keeps the last one of them
Returns matrix with 2 columns:

Column 1: X - Filtered X

Column 2: Y - Filtered Y
|''Inputs linked to data''
''FILTERTABLE({'''X-value⇕'''};{'''Y-value⇕'''})''

(<s>2.000</s> ... ignored value, '''2.000''' ... saved value)
{| class="wikitable"
|+
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|'''''1'''''
|'''0.000'''
|'''17.000'''
|-
|<s>2</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|<s>3</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|'''4'''
|'''2.000'''
|'''25.000'''
|-
|<s>5</s>
|<s>4.000</s>
|<s>32.000</s>
|-
|'''6'''
|'''4.000'''
|'''32.000'''
|-
|<s>7</s>
|<s>6.000</s>
|<s>24.000</s>
|-
|'''8'''
|'''6.000'''
|'''24.000'''
|}
|⇒⇒⇒⇒
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|0.000
|17.000
|-
|2
|2.000
|25.000
|-
|3
|4.000
|32.000
|-
|4
|6.000
|24.000
|}
|}
|[[File:Filtertable function.png|center|thumb|360x360px|Filtertable function]]
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

=== Informative ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|ISIMPERIAL
|''ISIMPERIAL()''
|Returns TRUE if project is calculated in imperial units
|''If the project is in imperial [ft, in, ...] units:''
''ISIMPERIAL() ⇒ TRUE; ⇒ 1''

''ISMETRIC() ⇒ FALSE; ⇒ 0''
|
|-
|ISMETRIC
|''ISMETRIC()''
|Returns TRUE if project is calculated in metric units
|''If the project is in metric [m, mm, ...] units:''
''ISMETRIC() ⇒ TRUE; ⇒ 1''

''ISIMPERIAL() ⇒ FALSE; ⇒ 0''
|
|-
|ISNUMBER
|
|Returns TRUE if argument is number
|
|
|-
|ISTEXT
|
|Returns TRUE if argument is text
|
|
|-
|LANG
|''LANG()''
|LANG([ Application = False ])
|''If the application is in English and output language is Spanish:''
''LANG(FALSE()) ⇒ EN; LANG(0) ⇒ EN''

''LANG(TRUE()) ⇒ ES; LANG(1) ⇒ ES''
|
|}

=== Geotechnic ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FINESOILCLASSIFICATION
|''FINESOILCLASSIFICATION(Plasticity Index [-];Moisture [-];''
''Method 0 = EN ISO 14688-2 (2018); 1 = EN ISO 14688-2 (2013);''

''2 = ČSN 73 6133)''

For classification we can use these standards for plasticity diagram:[[File:Standards for plasticity diagram.png|thumb|Possible standards for plasticity diagram]]
|Returns the classification of fine soil according to selected method
For inputs use number from interval (0;1)

''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''

or percetage

''FINESOILCLASSIFICATION(13.7/100;33.3/100;0) ⇒ ClL''

or inputs linked to data according to unit

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]}/100;{LiqLimit⇓ [-]}/100;0)''

or inputs linked to data with unit setup

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]};{LiqLimit⇓ [-]};0)''[[File:Unit setup for input.png|thumb|Unit setup for input]]
|''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''[[File:Fine Soil Classification ISO 14-688-2 (2018).png|thumb|Fine Soil Classification EN ISO 14-688-2 (2018)|center|302x302px]]''FINESOILCLASSIFICATION(0.137;0.333;1) ⇒ ClL''[[File:Fine Soil Classification EN ISO 14-688-2 (2013).png|center|thumb|Fine Soil Classification EN ISO 14-688-2 (2013)]]
|-
|SOILCLASSIFICATION
|''SOILCLASSIFICATION(Size [mm];Fall [-];Method 0 = EN ISO 14688-2 (2018))''
|Returns the classification of soil according to selected method
|
{| class="wikitable"
|Číslo
|Průměr zrn
|Propad
|-
|
|[mm]
|[%]
|-
|1
|32,000
|100,00
|-
|2
|16,000
|100,00
|-
|3
|8,000
|100,00
|-
|4
|4,000
|99,76
|-
|5
|2,000
|98,76
|-
|6
|1,000
|97,52
|-
|7
|0,500
|95,52
|-
|8
|0,200
|91,52
|-
|9
|0,100
|85,02
|-
|10
|0,063
|79,02
|-
|11
|0,057
|76,40
|-
|12
|0,042
|70,70
|-
|13
|0,030
|67,50
|-
|14
|0,019
|65,00
|-
|15
|0,011
|60,50
|-
|16
|0,008
|57,40
|-
|17
|0,006
|55,00
|-
|18
|0,003
|51,20
|-
|19
|0,001
|46,10
|}
|}
=== Date and Time ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|DATE
|''DATE(Year;Month;Day)''
|Returns the serial number of a particular date
|''DATE(1899;12;30) ⇒ 0''
''DATE(2024;10;31) ⇒ 45596''

''Inputs linked to data''

'''''{MyYear}'''=2024;'''{MyMonth}'''=10;'''{MyDay}'''=31''

''DATE('''{MyYear}''';'''{MyMonth}''';'''{MyDay}''') ⇒ 45596''

|-
|NOW
|
|Returns the serial number of the current date and time
|
|-
|TIME
|''TIME(Hour;Minute;Second)''
|Returns the serial number of a particular time
|''TIME(0;0;0) ⇒ 0''
''TIME(18;15;20) ⇒ 0.760648''

''Inputs linked to data''

'''''{MyHour}'''=10[hour];'''{MyMinute}'''=15[min.];'''{MySecond}'''=25[sec.]''

''TIME('''{MyHour}''';'''{MyMinute}''';'''{MySecond}''') ⇒ 0.42737''
|-
|TODAY
|
|Returns the serial number of the current date
|
|}

Formula Specification in Templates

2024-10-22T09:01:25Z

PetrDlask: /* Date and Time */

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|SUMIF
|
|Returns the sum of all the values that meet a given criteria
|
|-
|SUMIFS
|
|Returns the sum of all the values that meet the given criterias
|
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RADIANS
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|-
|TEXT
|
|Converts number to text
|
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|AVERAGEIF
|
|Returns the average (arithmetic mean) of all the values that meet a given criteria
|
|-
|AVERAGEIFS
|
|Returns the average (arithmetic mean) of all the values that meet the given criterias
|
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|TRIMMEAN
|
|Returns the mean of the interior of a data set
|
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FILTERTABLE
|''FILTERTABLE(Coordinates X;Coordinates Y)''
|Filters repeating values and keeps the last one of them
Returns matrix with 2 columns:

Column 1: X - Filtered X

Column 2: Y - Filtered Y
|''Inputs linked to data''
''FILTERTABLE({'''X-value⇕'''};{'''Y-value⇕'''})''

(<s>2.000</s> ... ignored value, '''2.000''' ... saved value)
{| class="wikitable"
|+
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|'''''1'''''
|'''0.000'''
|'''17.000'''
|-
|<s>2</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|<s>3</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|'''4'''
|'''2.000'''
|'''25.000'''
|-
|<s>5</s>
|<s>4.000</s>
|<s>32.000</s>
|-
|'''6'''
|'''4.000'''
|'''32.000'''
|-
|<s>7</s>
|<s>6.000</s>
|<s>24.000</s>
|-
|'''8'''
|'''6.000'''
|'''24.000'''
|}
|⇒⇒⇒⇒
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|0.000
|17.000
|-
|2
|2.000
|25.000
|-
|3
|4.000
|32.000
|-
|4
|6.000
|24.000
|}
|}
|[[File:Filtertable function.png|center|thumb|360x360px|Filtertable function]]
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

=== Informative ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|ISIMPERIAL
|''ISIMPERIAL()''
|Returns TRUE if project is calculated in imperial units
|''If the project is in imperial [ft, in, ...] units:''
''ISIMPERIAL() ⇒ TRUE; ⇒ 1''

''ISMETRIC() ⇒ FALSE; ⇒ 0''
|
|-
|ISMETRIC
|''ISMETRIC()''
|Returns TRUE if project is calculated in metric units
|''If the project is in metric [m, mm, ...] units:''
''ISMETRIC() ⇒ TRUE; ⇒ 1''

''ISIMPERIAL() ⇒ FALSE; ⇒ 0''
|
|-
|ISNUMBER
|
|Returns TRUE if argument is number
|
|
|-
|ISTEXT
|
|Returns TRUE if argument is text
|
|
|-
|LANG
|''LANG()''
|LANG([ Application = False ])
|''If the application is in English and output language is Spanish:''
''LANG(FALSE()) ⇒ EN; LANG(0) ⇒ EN''

''LANG(TRUE()) ⇒ ES; LANG(1) ⇒ ES''
|
|}

=== Geotechnic ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FINESOILCLASSIFICATION
|''FINESOILCLASSIFICATION(Plasticity Index [-];Moisture [-];''
''Method 0 = EN ISO 14688-2 (2018); 1 = EN ISO 14688-2 (2013);''

''2 = ČSN 73 6133)''

For classification we can use these standards for plasticity diagram:[[File:Standards for plasticity diagram.png|thumb|Possible standards for plasticity diagram]]
|Returns the classification of fine soil according to selected method
For inputs use number from interval (0;1)

''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''

or percetage

''FINESOILCLASSIFICATION(13.7/100;33.3/100;0) ⇒ ClL''

or inputs linked to data according to unit

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]}/100;{LiqLimit⇓ [-]}/100;0)''

or inputs linked to data with unit setup

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]};{LiqLimit⇓ [-]};0)''[[File:Unit setup for input.png|thumb|Unit setup for input]]
|''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''[[File:Fine Soil Classification ISO 14-688-2 (2018).png|thumb|Fine Soil Classification EN ISO 14-688-2 (2018)|center|302x302px]]''FINESOILCLASSIFICATION(0.137;0.333;1) ⇒ ClL''[[File:Fine Soil Classification EN ISO 14-688-2 (2013).png|center|thumb|Fine Soil Classification EN ISO 14-688-2 (2013)]]
|-
|SOILCLASSIFICATION
|''SOILCLASSIFICATION(Size [mm];Fall [-];Method 0 = EN ISO 14688-2 (2018))''
|Returns the classification of soil according to selected method
|
{| class="wikitable"
|Číslo
|Průměr zrn
|Propad
|-
|
|[mm]
|[%]
|-
|1
|32,000
|100,00
|-
|2
|16,000
|100,00
|-
|3
|8,000
|100,00
|-
|4
|4,000
|99,76
|-
|5
|2,000
|98,76
|-
|6
|1,000
|97,52
|-
|7
|0,500
|95,52
|-
|8
|0,200
|91,52
|-
|9
|0,100
|85,02
|-
|10
|0,063
|79,02
|-
|11
|0,057
|76,40
|-
|12
|0,042
|70,70
|-
|13
|0,030
|67,50
|-
|14
|0,019
|65,00
|-
|15
|0,011
|60,50
|-
|16
|0,008
|57,40
|-
|17
|0,006
|55,00
|-
|18
|0,003
|51,20
|-
|19
|0,001
|46,10
|}
|}
=== Date and Time ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|DATE
|
|Returns the serial number of a particular date
|
|-
|NOW
|
|Returns the serial number of the current date and time
|
|-
|TIME
|
|Returns the serial number of a particular time
|
|-
|TODAY
|
|Returns the serial number of the current date
|
|}

Formula Specification in Templates

2024-10-15T13:24:05Z

PetrDlask: /* Date and Time */

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|SUMIF
|
|Returns the sum of all the values that meet a given criteria
|
|-
|SUMIFS
|
|Returns the sum of all the values that meet the given criterias
|
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RADIANS
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|-
|TEXT
|
|Converts number to text
|
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|AVERAGEIF
|
|Returns the average (arithmetic mean) of all the values that meet a given criteria
|
|-
|AVERAGEIFS
|
|Returns the average (arithmetic mean) of all the values that meet the given criterias
|
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|TRIMMEAN
|
|Returns the mean of the interior of a data set
|
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FILTERTABLE
|''FILTERTABLE(Coordinates X;Coordinates Y)''
|Filters repeating values and keeps the last one of them
Returns matrix with 2 columns:

Column 1: X - Filtered X

Column 2: Y - Filtered Y
|''Inputs linked to data''
''FILTERTABLE({'''X-value⇕'''};{'''Y-value⇕'''})''

(<s>2.000</s> ... ignored value, '''2.000''' ... saved value)
{| class="wikitable"
|+
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|'''''1'''''
|'''0.000'''
|'''17.000'''
|-
|<s>2</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|<s>3</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|'''4'''
|'''2.000'''
|'''25.000'''
|-
|<s>5</s>
|<s>4.000</s>
|<s>32.000</s>
|-
|'''6'''
|'''4.000'''
|'''32.000'''
|-
|<s>7</s>
|<s>6.000</s>
|<s>24.000</s>
|-
|'''8'''
|'''6.000'''
|'''24.000'''
|}
|⇒⇒⇒⇒
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|0.000
|17.000
|-
|2
|2.000
|25.000
|-
|3
|4.000
|32.000
|-
|4
|6.000
|24.000
|}
|}
|[[File:Filtertable function.png|center|thumb|360x360px|Filtertable function]]
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

=== Informative ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|ISIMPERIAL
|''ISIMPERIAL()''
|Returns TRUE if project is calculated in imperial units
|''If the project is in imperial [ft, in, ...] units:''
''ISIMPERIAL() ⇒ TRUE; ⇒ 1''

''ISMETRIC() ⇒ FALSE; ⇒ 0''
|
|-
|ISMETRIC
|''ISMETRIC()''
|Returns TRUE if project is calculated in metric units
|''If the project is in metric [m, mm, ...] units:''
''ISMETRIC() ⇒ TRUE; ⇒ 1''

''ISIMPERIAL() ⇒ FALSE; ⇒ 0''
|
|-
|ISNUMBER
|
|Returns TRUE if argument is number
|
|
|-
|ISTEXT
|
|Returns TRUE if argument is text
|
|
|-
|LANG
|''LANG()''
|LANG([ Application = False ])
|''If the application is in English and output language is Spanish:''
''LANG(FALSE()) ⇒ EN; LANG(0) ⇒ EN''

''LANG(TRUE()) ⇒ ES; LANG(1) ⇒ ES''
|
|}

=== Geotechnic ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FINESOILCLASSIFICATION
|''FINESOILCLASSIFICATION(Plasticity Index [-];Moisture [-];''
''Method 0 = EN ISO 14688-2 (2018); 1 = EN ISO 14688-2 (2013);''

''2 = ČSN 73 6133)''

For classification we can use these standards for plasticity diagram:[[File:Standards for plasticity diagram.png|thumb|Possible standards for plasticity diagram]]
|Returns the classification of fine soil according to selected method
For inputs use number from interval (0;1)

''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''

or percetage

''FINESOILCLASSIFICATION(13.7/100;33.3/100;0) ⇒ ClL''

or inputs linked to data according to unit

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]}/100;{LiqLimit⇓ [-]}/100;0)''

or inputs linked to data with unit setup

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]};{LiqLimit⇓ [-]};0)''[[File:Unit setup for input.png|thumb|Unit setup for input]]
|''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''[[File:Fine Soil Classification ISO 14-688-2 (2018).png|thumb|Fine Soil Classification EN ISO 14-688-2 (2018)|center|302x302px]]''FINESOILCLASSIFICATION(0.137;0.333;1) ⇒ ClL''[[File:Fine Soil Classification EN ISO 14-688-2 (2013).png|center|thumb|Fine Soil Classification EN ISO 14-688-2 (2013)]]
|-
|SOILCLASSIFICATION
|''SOILCLASSIFICATION(Size [mm];Fall [-];Method 0 = EN ISO 14688-2 (2018))''
|Returns the classification of soil according to selected method
|
{| class="wikitable"
|Číslo
|Průměr zrn
|Propad
|-
|
|[mm]
|[%]
|-
|1
|32,000
|100,00
|-
|2
|16,000
|100,00
|-
|3
|8,000
|100,00
|-
|4
|4,000
|99,76
|-
|5
|2,000
|98,76
|-
|6
|1,000
|97,52
|-
|7
|0,500
|95,52
|-
|8
|0,200
|91,52
|-
|9
|0,100
|85,02
|-
|10
|0,063
|79,02
|-
|11
|0,057
|76,40
|-
|12
|0,042
|70,70
|-
|13
|0,030
|67,50
|-
|14
|0,019
|65,00
|-
|15
|0,011
|60,50
|-
|16
|0,008
|57,40
|-
|17
|0,006
|55,00
|-
|18
|0,003
|51,20
|-
|19
|0,001
|46,10
|}
|}
=== Date and Time ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|NOW
|
|Returns the serial number of the current date and time
|
|-
|TODAY
|
|Returns the serial number of the current date
|
|}

Formula Specification in Templates

2024-10-15T13:22:17Z

PetrDlask:

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|SUMIF
|
|Returns the sum of all the values that meet a given criteria
|
|-
|SUMIFS
|
|Returns the sum of all the values that meet the given criterias
|
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RADIANS
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|-
|TEXT
|
|Converts number to text
|
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|AVERAGEIF
|
|Returns the average (arithmetic mean) of all the values that meet a given criteria
|
|-
|AVERAGEIFS
|
|Returns the average (arithmetic mean) of all the values that meet the given criterias
|
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|TRIMMEAN
|
|Returns the mean of the interior of a data set
|
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FILTERTABLE
|''FILTERTABLE(Coordinates X;Coordinates Y)''
|Filters repeating values and keeps the last one of them
Returns matrix with 2 columns:

Column 1: X - Filtered X

Column 2: Y - Filtered Y
|''Inputs linked to data''
''FILTERTABLE({'''X-value⇕'''};{'''Y-value⇕'''})''

(<s>2.000</s> ... ignored value, '''2.000''' ... saved value)
{| class="wikitable"
|+
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|'''''1'''''
|'''0.000'''
|'''17.000'''
|-
|<s>2</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|<s>3</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|'''4'''
|'''2.000'''
|'''25.000'''
|-
|<s>5</s>
|<s>4.000</s>
|<s>32.000</s>
|-
|'''6'''
|'''4.000'''
|'''32.000'''
|-
|<s>7</s>
|<s>6.000</s>
|<s>24.000</s>
|-
|'''8'''
|'''6.000'''
|'''24.000'''
|}
|⇒⇒⇒⇒
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|0.000
|17.000
|-
|2
|2.000
|25.000
|-
|3
|4.000
|32.000
|-
|4
|6.000
|24.000
|}
|}
|[[File:Filtertable function.png|center|thumb|360x360px|Filtertable function]]
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

=== Informative ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|ISIMPERIAL
|''ISIMPERIAL()''
|Returns TRUE if project is calculated in imperial units
|''If the project is in imperial [ft, in, ...] units:''
''ISIMPERIAL() ⇒ TRUE; ⇒ 1''

''ISMETRIC() ⇒ FALSE; ⇒ 0''
|
|-
|ISMETRIC
|''ISMETRIC()''
|Returns TRUE if project is calculated in metric units
|''If the project is in metric [m, mm, ...] units:''
''ISMETRIC() ⇒ TRUE; ⇒ 1''

''ISIMPERIAL() ⇒ FALSE; ⇒ 0''
|
|-
|ISNUMBER
|
|Returns TRUE if argument is number
|
|
|-
|ISTEXT
|
|Returns TRUE if argument is text
|
|
|-
|LANG
|''LANG()''
|LANG([ Application = False ])
|''If the application is in English and output language is Spanish:''
''LANG(FALSE()) ⇒ EN; LANG(0) ⇒ EN''

''LANG(TRUE()) ⇒ ES; LANG(1) ⇒ ES''
|
|}

=== Geotechnic ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FINESOILCLASSIFICATION
|''FINESOILCLASSIFICATION(Plasticity Index [-];Moisture [-];''
''Method 0 = EN ISO 14688-2 (2018); 1 = EN ISO 14688-2 (2013);''

''2 = ČSN 73 6133)''

For classification we can use these standards for plasticity diagram:[[File:Standards for plasticity diagram.png|thumb|Possible standards for plasticity diagram]]
|Returns the classification of fine soil according to selected method
For inputs use number from interval (0;1)

''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''

or percetage

''FINESOILCLASSIFICATION(13.7/100;33.3/100;0) ⇒ ClL''

or inputs linked to data according to unit

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]}/100;{LiqLimit⇓ [-]}/100;0)''

or inputs linked to data with unit setup

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]};{LiqLimit⇓ [-]};0)''[[File:Unit setup for input.png|thumb|Unit setup for input]]
|''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''[[File:Fine Soil Classification ISO 14-688-2 (2018).png|thumb|Fine Soil Classification EN ISO 14-688-2 (2018)|center|302x302px]]''FINESOILCLASSIFICATION(0.137;0.333;1) ⇒ ClL''[[File:Fine Soil Classification EN ISO 14-688-2 (2013).png|center|thumb|Fine Soil Classification EN ISO 14-688-2 (2013)]]
|-
|SOILCLASSIFICATION
|''SOILCLASSIFICATION(Size [mm];Fall [-];Method 0 = EN ISO 14688-2 (2018))''
|Returns the classification of soil according to selected method
|
{| class="wikitable"
|Číslo
|Průměr zrn
|Propad
|-
|
|[mm]
|[%]
|-
|1
|32,000
|100,00
|-
|2
|16,000
|100,00
|-
|3
|8,000
|100,00
|-
|4
|4,000
|99,76
|-
|5
|2,000
|98,76
|-
|6
|1,000
|97,52
|-
|7
|0,500
|95,52
|-
|8
|0,200
|91,52
|-
|9
|0,100
|85,02
|-
|10
|0,063
|79,02
|-
|11
|0,057
|76,40
|-
|12
|0,042
|70,70
|-
|13
|0,030
|67,50
|-
|14
|0,019
|65,00
|-
|15
|0,011
|60,50
|-
|16
|0,008
|57,40
|-
|17
|0,006
|55,00
|-
|18
|0,003
|51,20
|-
|19
|0,001
|46,10
|}
|}
=== Date and Time ===

Formula Specification in Templates

2024-10-15T13:20:12Z

PetrDlask: /* Text */

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|SUMIF
|
|Returns the sum of all the values that meet a given criteria
|
|-
|SUMIFS
|
|Returns the sum of all the values that meet the given criterias
|
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RADIANS
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|-
|TEXT
|
|Converts number to text
|
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|AVERAGEIF
|
|Returns the average (arithmetic mean) of all the values that meet a given criteria
|
|-
|AVERAGEIFS
|
|Returns the average (arithmetic mean) of all the values that meet the given criterias
|
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|TRIMMEAN
|
|Returns the mean of the interior of a data set
|
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FILTERTABLE
|''FILTERTABLE(Coordinates X;Coordinates Y)''
|Filters repeating values and keeps the last one of them
Returns matrix with 2 columns:

Column 1: X - Filtered X

Column 2: Y - Filtered Y
|''Inputs linked to data''
''FILTERTABLE({'''X-value⇕'''};{'''Y-value⇕'''})''

(<s>2.000</s> ... ignored value, '''2.000''' ... saved value)
{| class="wikitable"
|+
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|'''''1'''''
|'''0.000'''
|'''17.000'''
|-
|<s>2</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|<s>3</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|'''4'''
|'''2.000'''
|'''25.000'''
|-
|<s>5</s>
|<s>4.000</s>
|<s>32.000</s>
|-
|'''6'''
|'''4.000'''
|'''32.000'''
|-
|<s>7</s>
|<s>6.000</s>
|<s>24.000</s>
|-
|'''8'''
|'''6.000'''
|'''24.000'''
|}
|⇒⇒⇒⇒
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|0.000
|17.000
|-
|2
|2.000
|25.000
|-
|3
|4.000
|32.000
|-
|4
|6.000
|24.000
|}
|}
|[[File:Filtertable function.png|center|thumb|360x360px|Filtertable function]]
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

=== Informative ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|ISIMPERIAL
|''ISIMPERIAL()''
|Returns TRUE if project is calculated in imperial units
|''If the project is in imperial [ft, in, ...] units:''
''ISIMPERIAL() ⇒ TRUE; ⇒ 1''

''ISMETRIC() ⇒ FALSE; ⇒ 0''
|
|-
|ISMETRIC
|''ISMETRIC()''
|Returns TRUE if project is calculated in metric units
|''If the project is in metric [m, mm, ...] units:''
''ISMETRIC() ⇒ TRUE; ⇒ 1''

''ISIMPERIAL() ⇒ FALSE; ⇒ 0''
|
|-
|ISNUMBER
|
|Returns TRUE if argument is number
|
|
|-
|ISTEXT
|
|Returns TRUE if argument is text
|
|
|-
|LANG
|''LANG()''
|LANG([ Application = False ])
|''If the application is in English and output language is Spanish:''
''LANG(FALSE()) ⇒ EN; LANG(0) ⇒ EN''

''LANG(TRUE()) ⇒ ES; LANG(1) ⇒ ES''
|
|}

=== Geotechnic ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FINESOILCLASSIFICATION
|''FINESOILCLASSIFICATION(Plasticity Index [-];Moisture [-];''
''Method 0 = EN ISO 14688-2 (2018); 1 = EN ISO 14688-2 (2013);''

''2 = ČSN 73 6133)''

For classification we can use these standards for plasticity diagram:[[File:Standards for plasticity diagram.png|thumb|Possible standards for plasticity diagram]]
|Returns the classification of fine soil according to selected method
For inputs use number from interval (0;1)

''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''

or percetage

''FINESOILCLASSIFICATION(13.7/100;33.3/100;0) ⇒ ClL''

or inputs linked to data according to unit

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]}/100;{LiqLimit⇓ [-]}/100;0)''

or inputs linked to data with unit setup

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]};{LiqLimit⇓ [-]};0)''[[File:Unit setup for input.png|thumb|Unit setup for input]]
|''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''[[File:Fine Soil Classification ISO 14-688-2 (2018).png|thumb|Fine Soil Classification EN ISO 14-688-2 (2018)|center|302x302px]]''FINESOILCLASSIFICATION(0.137;0.333;1) ⇒ ClL''[[File:Fine Soil Classification EN ISO 14-688-2 (2013).png|center|thumb|Fine Soil Classification EN ISO 14-688-2 (2013)]]
|-
|SOILCLASSIFICATION
|''SOILCLASSIFICATION(Size [mm];Fall [-];Method 0 = EN ISO 14688-2 (2018))''
|Returns the classification of soil according to selected method
|
{| class="wikitable"
|Číslo
|Průměr zrn
|Propad
|-
|
|[mm]
|[%]
|-
|1
|32,000
|100,00
|-
|2
|16,000
|100,00
|-
|3
|8,000
|100,00
|-
|4
|4,000
|99,76
|-
|5
|2,000
|98,76
|-
|6
|1,000
|97,52
|-
|7
|0,500
|95,52
|-
|8
|0,200
|91,52
|-
|9
|0,100
|85,02
|-
|10
|0,063
|79,02
|-
|11
|0,057
|76,40
|-
|12
|0,042
|70,70
|-
|13
|0,030
|67,50
|-
|14
|0,019
|65,00
|-
|15
|0,011
|60,50
|-
|16
|0,008
|57,40
|-
|17
|0,006
|55,00
|-
|18
|0,003
|51,20
|-
|19
|0,001
|46,10
|}
|}

Formula Specification in Templates

2024-10-15T13:16:48Z

PetrDlask: /* Statistical */

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|SUMIF
|
|Returns the sum of all the values that meet a given criteria
|
|-
|SUMIFS
|
|Returns the sum of all the values that meet the given criterias
|
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RADIANS
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|AVERAGEIF
|
|Returns the average (arithmetic mean) of all the values that meet a given criteria
|
|-
|AVERAGEIFS
|
|Returns the average (arithmetic mean) of all the values that meet the given criterias
|
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|TRIMMEAN
|
|Returns the mean of the interior of a data set
|
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FILTERTABLE
|''FILTERTABLE(Coordinates X;Coordinates Y)''
|Filters repeating values and keeps the last one of them
Returns matrix with 2 columns:

Column 1: X - Filtered X

Column 2: Y - Filtered Y
|''Inputs linked to data''
''FILTERTABLE({'''X-value⇕'''};{'''Y-value⇕'''})''

(<s>2.000</s> ... ignored value, '''2.000''' ... saved value)
{| class="wikitable"
|+
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|'''''1'''''
|'''0.000'''
|'''17.000'''
|-
|<s>2</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|<s>3</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|'''4'''
|'''2.000'''
|'''25.000'''
|-
|<s>5</s>
|<s>4.000</s>
|<s>32.000</s>
|-
|'''6'''
|'''4.000'''
|'''32.000'''
|-
|<s>7</s>
|<s>6.000</s>
|<s>24.000</s>
|-
|'''8'''
|'''6.000'''
|'''24.000'''
|}
|⇒⇒⇒⇒
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|0.000
|17.000
|-
|2
|2.000
|25.000
|-
|3
|4.000
|32.000
|-
|4
|6.000
|24.000
|}
|}
|[[File:Filtertable function.png|center|thumb|360x360px|Filtertable function]]
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

=== Informative ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|ISIMPERIAL
|''ISIMPERIAL()''
|Returns TRUE if project is calculated in imperial units
|''If the project is in imperial [ft, in, ...] units:''
''ISIMPERIAL() ⇒ TRUE; ⇒ 1''

''ISMETRIC() ⇒ FALSE; ⇒ 0''
|
|-
|ISMETRIC
|''ISMETRIC()''
|Returns TRUE if project is calculated in metric units
|''If the project is in metric [m, mm, ...] units:''
''ISMETRIC() ⇒ TRUE; ⇒ 1''

''ISIMPERIAL() ⇒ FALSE; ⇒ 0''
|
|-
|ISNUMBER
|
|Returns TRUE if argument is number
|
|
|-
|ISTEXT
|
|Returns TRUE if argument is text
|
|
|-
|LANG
|''LANG()''
|LANG([ Application = False ])
|''If the application is in English and output language is Spanish:''
''LANG(FALSE()) ⇒ EN; LANG(0) ⇒ EN''

''LANG(TRUE()) ⇒ ES; LANG(1) ⇒ ES''
|
|}

=== Geotechnic ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FINESOILCLASSIFICATION
|''FINESOILCLASSIFICATION(Plasticity Index [-];Moisture [-];''
''Method 0 = EN ISO 14688-2 (2018); 1 = EN ISO 14688-2 (2013);''

''2 = ČSN 73 6133)''

For classification we can use these standards for plasticity diagram:[[File:Standards for plasticity diagram.png|thumb|Possible standards for plasticity diagram]]
|Returns the classification of fine soil according to selected method
For inputs use number from interval (0;1)

''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''

or percetage

''FINESOILCLASSIFICATION(13.7/100;33.3/100;0) ⇒ ClL''

or inputs linked to data according to unit

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]}/100;{LiqLimit⇓ [-]}/100;0)''

or inputs linked to data with unit setup

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]};{LiqLimit⇓ [-]};0)''[[File:Unit setup for input.png|thumb|Unit setup for input]]
|''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''[[File:Fine Soil Classification ISO 14-688-2 (2018).png|thumb|Fine Soil Classification EN ISO 14-688-2 (2018)|center|302x302px]]''FINESOILCLASSIFICATION(0.137;0.333;1) ⇒ ClL''[[File:Fine Soil Classification EN ISO 14-688-2 (2013).png|center|thumb|Fine Soil Classification EN ISO 14-688-2 (2013)]]
|-
|SOILCLASSIFICATION
|''SOILCLASSIFICATION(Size [mm];Fall [-];Method 0 = EN ISO 14688-2 (2018))''
|Returns the classification of soil according to selected method
|
{| class="wikitable"
|Číslo
|Průměr zrn
|Propad
|-
|
|[mm]
|[%]
|-
|1
|32,000
|100,00
|-
|2
|16,000
|100,00
|-
|3
|8,000
|100,00
|-
|4
|4,000
|99,76
|-
|5
|2,000
|98,76
|-
|6
|1,000
|97,52
|-
|7
|0,500
|95,52
|-
|8
|0,200
|91,52
|-
|9
|0,100
|85,02
|-
|10
|0,063
|79,02
|-
|11
|0,057
|76,40
|-
|12
|0,042
|70,70
|-
|13
|0,030
|67,50
|-
|14
|0,019
|65,00
|-
|15
|0,011
|60,50
|-
|16
|0,008
|57,40
|-
|17
|0,006
|55,00
|-
|18
|0,003
|51,20
|-
|19
|0,001
|46,10
|}
|}

Formula Specification in Templates

2024-10-15T13:13:50Z

PetrDlask: /* Mathematical */

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|SUMIF
|
|Returns the sum of all the values that meet a given criteria
|
|-
|SUMIFS
|
|Returns the sum of all the values that meet the given criterias
|
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RADIANS
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FILTERTABLE
|''FILTERTABLE(Coordinates X;Coordinates Y)''
|Filters repeating values and keeps the last one of them
Returns matrix with 2 columns:

Column 1: X - Filtered X

Column 2: Y - Filtered Y
|''Inputs linked to data''
''FILTERTABLE({'''X-value⇕'''};{'''Y-value⇕'''})''

(<s>2.000</s> ... ignored value, '''2.000''' ... saved value)
{| class="wikitable"
|+
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|'''''1'''''
|'''0.000'''
|'''17.000'''
|-
|<s>2</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|<s>3</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|'''4'''
|'''2.000'''
|'''25.000'''
|-
|<s>5</s>
|<s>4.000</s>
|<s>32.000</s>
|-
|'''6'''
|'''4.000'''
|'''32.000'''
|-
|<s>7</s>
|<s>6.000</s>
|<s>24.000</s>
|-
|'''8'''
|'''6.000'''
|'''24.000'''
|}
|⇒⇒⇒⇒
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|0.000
|17.000
|-
|2
|2.000
|25.000
|-
|3
|4.000
|32.000
|-
|4
|6.000
|24.000
|}
|}
|[[File:Filtertable function.png|center|thumb|360x360px|Filtertable function]]
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

=== Informative ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|ISIMPERIAL
|''ISIMPERIAL()''
|Returns TRUE if project is calculated in imperial units
|''If the project is in imperial [ft, in, ...] units:''
''ISIMPERIAL() ⇒ TRUE; ⇒ 1''

''ISMETRIC() ⇒ FALSE; ⇒ 0''
|
|-
|ISMETRIC
|''ISMETRIC()''
|Returns TRUE if project is calculated in metric units
|''If the project is in metric [m, mm, ...] units:''
''ISMETRIC() ⇒ TRUE; ⇒ 1''

''ISIMPERIAL() ⇒ FALSE; ⇒ 0''
|
|-
|LANG
|''LANG()''
|LANG([ Application = False ])
|''If the application is in English and output language is Spanish:''
''LANG(FALSE()) ⇒ EN; LANG(0) ⇒ EN''

''LANG(TRUE()) ⇒ ES; LANG(1) ⇒ ES''
|
|}

=== Geotechnic ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FINESOILCLASSIFICATION
|''FINESOILCLASSIFICATION(Plasticity Index [-];Moisture [-];''
''Method 0 = EN ISO 14688-2 (2018); 1 = EN ISO 14688-2 (2013);''

''2 = ČSN 73 6133)''

For classification we can use these standards for plasticity diagram:[[File:Standards for plasticity diagram.png|thumb|Possible standards for plasticity diagram]]
|Returns the classification of fine soil according to selected method
For inputs use number from interval (0;1)

''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''

or percetage

''FINESOILCLASSIFICATION(13.7/100;33.3/100;0) ⇒ ClL''

or inputs linked to data according to unit

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]}/100;{LiqLimit⇓ [-]}/100;0)''

or inputs linked to data with unit setup

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]};{LiqLimit⇓ [-]};0)''[[File:Unit setup for input.png|thumb|Unit setup for input]]
|''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''[[File:Fine Soil Classification ISO 14-688-2 (2018).png|thumb|Fine Soil Classification EN ISO 14-688-2 (2018)|center|302x302px]]''FINESOILCLASSIFICATION(0.137;0.333;1) ⇒ ClL''[[File:Fine Soil Classification EN ISO 14-688-2 (2013).png|center|thumb|Fine Soil Classification EN ISO 14-688-2 (2013)]]
|-
|SOILCLASSIFICATION
|''SOILCLASSIFICATION(Size [mm];Fall [-];Method 0 = EN ISO 14688-2 (2018))''
|Returns the classification of soil according to selected method
|
{| class="wikitable"
|Číslo
|Průměr zrn
|Propad
|-
|
|[mm]
|[%]
|-
|1
|32,000
|100,00
|-
|2
|16,000
|100,00
|-
|3
|8,000
|100,00
|-
|4
|4,000
|99,76
|-
|5
|2,000
|98,76
|-
|6
|1,000
|97,52
|-
|7
|0,500
|95,52
|-
|8
|0,200
|91,52
|-
|9
|0,100
|85,02
|-
|10
|0,063
|79,02
|-
|11
|0,057
|76,40
|-
|12
|0,042
|70,70
|-
|13
|0,030
|67,50
|-
|14
|0,019
|65,00
|-
|15
|0,011
|60,50
|-
|16
|0,008
|57,40
|-
|17
|0,006
|55,00
|-
|18
|0,003
|51,20
|-
|19
|0,001
|46,10
|}
|}

Formula Specification in Templates

2024-01-10T08:26:01Z

PetrDlask: /* Geotechnic */

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RADIANS
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FILTERTABLE
|''FILTERTABLE(Coordinates X;Coordinates Y)''
|Filters repeating values and keeps the last one of them
Returns matrix with 2 columns:

Column 1: X - Filtered X

Column 2: Y - Filtered Y
|''Inputs linked to data''
''FILTERTABLE({'''X-value⇕'''};{'''Y-value⇕'''})''

(<s>2.000</s> ... ignored value, '''2.000''' ... saved value)
{| class="wikitable"
|+
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|'''''1'''''
|'''0.000'''
|'''17.000'''
|-
|<s>2</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|<s>3</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|'''4'''
|'''2.000'''
|'''25.000'''
|-
|<s>5</s>
|<s>4.000</s>
|<s>32.000</s>
|-
|'''6'''
|'''4.000'''
|'''32.000'''
|-
|<s>7</s>
|<s>6.000</s>
|<s>24.000</s>
|-
|'''8'''
|'''6.000'''
|'''24.000'''
|}
|⇒⇒⇒⇒
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|0.000
|17.000
|-
|2
|2.000
|25.000
|-
|3
|4.000
|32.000
|-
|4
|6.000
|24.000
|}
|}
|[[File:Filtertable function.png|center|thumb|360x360px|Filtertable function]]
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

=== Informative ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|ISIMPERIAL
|''ISIMPERIAL()''
|Returns TRUE if project is calculated in imperial units
|''If the project is in imperial [ft, in, ...] units:''
''ISIMPERIAL() ⇒ TRUE; ⇒ 1''

''ISMETRIC() ⇒ FALSE; ⇒ 0''
|
|-
|ISMETRIC
|''ISMETRIC()''
|Returns TRUE if project is calculated in metric units
|''If the project is in metric [m, mm, ...] units:''
''ISMETRIC() ⇒ TRUE; ⇒ 1''

''ISIMPERIAL() ⇒ FALSE; ⇒ 0''
|
|-
|LANG
|''LANG()''
|LANG([ Application = False ])
|''If the application is in English and output language is Spanish:''
''LANG(FALSE()) ⇒ EN; LANG(0) ⇒ EN''

''LANG(TRUE()) ⇒ ES; LANG(1) ⇒ ES''
|
|}

=== Geotechnic ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FINESOILCLASSIFICATION
|''FINESOILCLASSIFICATION(Plasticity Index [-];Moisture [-];''
''Method 0 = EN ISO 14688-2 (2018); 1 = EN ISO 14688-2 (2013);''

''2 = ČSN 73 6133)''

For classification we can use these standards for plasticity diagram:[[File:Standards for plasticity diagram.png|thumb|Possible standards for plasticity diagram]]
|Returns the classification of fine soil according to selected method
For inputs use number from interval (0;1)

''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''

or percetage

''FINESOILCLASSIFICATION(13.7/100;33.3/100;0) ⇒ ClL''

or inputs linked to data according to unit

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]}/100;{LiqLimit⇓ [-]}/100;0)''

or inputs linked to data with unit setup

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]};{LiqLimit⇓ [-]};0)''[[File:Unit setup for input.png|thumb|Unit setup for input]]
|''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''[[File:Fine Soil Classification ISO 14-688-2 (2018).png|thumb|Fine Soil Classification EN ISO 14-688-2 (2018)|center|302x302px]]''FINESOILCLASSIFICATION(0.137;0.333;1) ⇒ ClL''[[File:Fine Soil Classification EN ISO 14-688-2 (2013).png|center|thumb|Fine Soil Classification EN ISO 14-688-2 (2013)]]
|-
|SOILCLASSIFICATION
|''SOILCLASSIFICATION(Size [mm];Fall [-];Method 0 = EN ISO 14688-2 (2018))''
|Returns the classification of soil according to selected method
|
{| class="wikitable"
|Číslo
|Průměr zrn
|Propad
|-
|
|[mm]
|[%]
|-
|1
|32,000
|100,00
|-
|2
|16,000
|100,00
|-
|3
|8,000
|100,00
|-
|4
|4,000
|99,76
|-
|5
|2,000
|98,76
|-
|6
|1,000
|97,52
|-
|7
|0,500
|95,52
|-
|8
|0,200
|91,52
|-
|9
|0,100
|85,02
|-
|10
|0,063
|79,02
|-
|11
|0,057
|76,40
|-
|12
|0,042
|70,70
|-
|13
|0,030
|67,50
|-
|14
|0,019
|65,00
|-
|15
|0,011
|60,50
|-
|16
|0,008
|57,40
|-
|17
|0,006
|55,00
|-
|18
|0,003
|51,20
|-
|19
|0,001
|46,10
|}
|}

Formula Specification in Templates

2024-01-09T14:56:20Z

PetrDlask: /* Geotechnic */

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RADIANS
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FILTERTABLE
|''FILTERTABLE(Coordinates X;Coordinates Y)''
|Filters repeating values and keeps the last one of them
Returns matrix with 2 columns:

Column 1: X - Filtered X

Column 2: Y - Filtered Y
|''Inputs linked to data''
''FILTERTABLE({'''X-value⇕'''};{'''Y-value⇕'''})''

(<s>2.000</s> ... ignored value, '''2.000''' ... saved value)
{| class="wikitable"
|+
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|'''''1'''''
|'''0.000'''
|'''17.000'''
|-
|<s>2</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|<s>3</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|'''4'''
|'''2.000'''
|'''25.000'''
|-
|<s>5</s>
|<s>4.000</s>
|<s>32.000</s>
|-
|'''6'''
|'''4.000'''
|'''32.000'''
|-
|<s>7</s>
|<s>6.000</s>
|<s>24.000</s>
|-
|'''8'''
|'''6.000'''
|'''24.000'''
|}
|⇒⇒⇒⇒
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|0.000
|17.000
|-
|2
|2.000
|25.000
|-
|3
|4.000
|32.000
|-
|4
|6.000
|24.000
|}
|}
|[[File:Filtertable function.png|center|thumb|360x360px|Filtertable function]]
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

=== Informative ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|ISIMPERIAL
|''ISIMPERIAL()''
|Returns TRUE if project is calculated in imperial units
|''If the project is in imperial [ft, in, ...] units:''
''ISIMPERIAL() ⇒ TRUE; ⇒ 1''

''ISMETRIC() ⇒ FALSE; ⇒ 0''
|
|-
|ISMETRIC
|''ISMETRIC()''
|Returns TRUE if project is calculated in metric units
|''If the project is in metric [m, mm, ...] units:''
''ISMETRIC() ⇒ TRUE; ⇒ 1''

''ISIMPERIAL() ⇒ FALSE; ⇒ 0''
|
|-
|LANG
|''LANG()''
|LANG([ Application = False ])
|''If the application is in English and output language is Spanish:''
''LANG(FALSE()) ⇒ EN; LANG(0) ⇒ EN''

''LANG(TRUE()) ⇒ ES; LANG(1) ⇒ ES''
|
|}

=== Geotechnic ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FINESOILCLASSIFICATION
|''FINESOILCLASSIFICATION(Plasticity Index [-];Moisture [-];''
''Method 0 = EN ISO 14688-2 (2018); 1 = EN ISO 14688-2 (2013);''

''2 = ČSN 73 6133)''

For classification we can use these standards for plasticity diagram:[[File:Standards for plasticity diagram.png|thumb|Possible standards for plasticity diagram]]
|Returns the classification of fine soil according to selected method
For inputs use number from interval (0;1)

''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''

or percetage

''FINESOILCLASSIFICATION(13.7/100;33.3/100;0) ⇒ ClL''

or inputs linked to data according to unit

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]}/100;{LiqLimit⇓ [-]}/100;0)''

or inputs linked to data with unit setup

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]};{LiqLimit⇓ [-]};0)''[[File:Unit setup for input.png|thumb|Unit setup for input]]
|''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''[[File:Fine Soil Classification ISO 14-688-2 (2018).png|thumb|Fine Soil Classification EN ISO 14-688-2 (2018)|center|302x302px]]''FINESOILCLASSIFICATION(0.137;0.333;1) ⇒ ClL''[[File:Fine Soil Classification EN ISO 14-688-2 (2013).png|center|thumb|Fine Soil Classification EN ISO 14-688-2 (2013)]]
|-
|SOILCLASSIFICATION
|''SOILCLASSIFICATION(Size [mm];Fall [-];Method 0 = EN ISO 14688-2 (2018))''
|Returns the classification of soil according to selected method
|
|}

Formula Specification in Templates

2024-01-09T13:14:17Z

PetrDlask: /* Geotechnic */

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RADIANS
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FILTERTABLE
|''FILTERTABLE(Coordinates X;Coordinates Y)''
|Filters repeating values and keeps the last one of them
Returns matrix with 2 columns:

Column 1: X - Filtered X

Column 2: Y - Filtered Y
|''Inputs linked to data''
''FILTERTABLE({'''X-value⇕'''};{'''Y-value⇕'''})''

(<s>2.000</s> ... ignored value, '''2.000''' ... saved value)
{| class="wikitable"
|+
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|'''''1'''''
|'''0.000'''
|'''17.000'''
|-
|<s>2</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|<s>3</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|'''4'''
|'''2.000'''
|'''25.000'''
|-
|<s>5</s>
|<s>4.000</s>
|<s>32.000</s>
|-
|'''6'''
|'''4.000'''
|'''32.000'''
|-
|<s>7</s>
|<s>6.000</s>
|<s>24.000</s>
|-
|'''8'''
|'''6.000'''
|'''24.000'''
|}
|⇒⇒⇒⇒
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|0.000
|17.000
|-
|2
|2.000
|25.000
|-
|3
|4.000
|32.000
|-
|4
|6.000
|24.000
|}
|}
|[[File:Filtertable function.png|center|thumb|360x360px|Filtertable function]]
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

=== Informative ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|ISIMPERIAL
|''ISIMPERIAL()''
|Returns TRUE if project is calculated in imperial units
|''If the project is in imperial [ft, in, ...] units:''
''ISIMPERIAL() ⇒ TRUE; ⇒ 1''

''ISMETRIC() ⇒ FALSE; ⇒ 0''
|
|-
|ISMETRIC
|''ISMETRIC()''
|Returns TRUE if project is calculated in metric units
|''If the project is in metric [m, mm, ...] units:''
''ISMETRIC() ⇒ TRUE; ⇒ 1''

''ISIMPERIAL() ⇒ FALSE; ⇒ 0''
|
|-
|LANG
|''LANG()''
|LANG([ Application = False ])
|''If the application is in English and output language is Spanish:''
''LANG(FALSE()) ⇒ EN; LANG(0) ⇒ EN''

''LANG(TRUE()) ⇒ ES; LANG(1) ⇒ ES''
|
|}

=== Geotechnic ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FINESOILCLASSIFICATION
|FINESOILCLASSIFICATION(Plasticity Index [-];Moisture [-];Method 0 = EN ISO 14688-2 (2018); 1 = EN ISO 14688-2 (2013); 2 = ČSN 73 6133)

For classification we can use these standards for plasticity diagram:[[File:Standards for plasticity diagram.png|left|thumb|Possible standards for plasticity diagram]]
|Returns the classification of fine soil according to selected method
For inputs use number from interval (0;1)

''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''

or percetage

''FINESOILCLASSIFICATION(13.7/100;33.3/100;0) ⇒ ClL''

or inputs linked to data according to unit

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]}/100;{LiqLimit⇓ [-]}/100;0)''

or inputs linked to data

''FINESOILCLASSIFICATION({I\_p\-⇓ [-]};{LiqLimit⇓ [-]};0)''[[File:Unit setup for input.png|thumb|Unit setup for input]]
|''FINESOILCLASSIFICATION(0.137;0.333;0) ⇒ ClL''[[File:Fine Soil Classification ISO 14-688-2 (2018).png|thumb|Fine Soil Classification EN ISO 14-688-2 (2018)|center|302x302px]]''FINESOILCLASSIFICATION(0.137;0.333;1) ⇒ ClL''[[File:Fine Soil Classification EN ISO 14-688-2 (2013).png|center|thumb|Fine Soil Classification EN ISO 14-688-2 (2013)]]
|}
{| class="wikitable sortable mw-collapsible"
|-
|
|-
|SOILCLASSIFICATION
|SOILCLASSIFICATION(Size [mm];Fall [-];Method 0 = EN ISO 14688-2 (2018))
|Returns the classification of soil according to selected method
|
|
|}

File:Standards for plasticity diagram.png

2024-01-09T13:12:47Z

PetrDlask:

Standards for plasticity diagram

File:Unit setup for input.png

2024-01-09T13:08:10Z

PetrDlask:

Unit setup for input

File:Fine Soil Classification EN ISO 14-688-2 (2013).png

2024-01-09T12:15:48Z

PetrDlask:

Fine Soil Classification EN ISO 14-688-2 (2013)

Formula Specification in Templates

2024-01-09T11:05:09Z

PetrDlask: /* Geotechnic */

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RADIANS
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FILTERTABLE
|''FILTERTABLE(Coordinates X;Coordinates Y)''
|Filters repeating values and keeps the last one of them
Returns matrix with 2 columns:

Column 1: X - Filtered X

Column 2: Y - Filtered Y
|''Inputs linked to data''
''FILTERTABLE({'''X-value⇕'''};{'''Y-value⇕'''})''

(<s>2.000</s> ... ignored value, '''2.000''' ... saved value)
{| class="wikitable"
|+
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|'''''1'''''
|'''0.000'''
|'''17.000'''
|-
|<s>2</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|<s>3</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|'''4'''
|'''2.000'''
|'''25.000'''
|-
|<s>5</s>
|<s>4.000</s>
|<s>32.000</s>
|-
|'''6'''
|'''4.000'''
|'''32.000'''
|-
|<s>7</s>
|<s>6.000</s>
|<s>24.000</s>
|-
|'''8'''
|'''6.000'''
|'''24.000'''
|}
|⇒⇒⇒⇒
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|0.000
|17.000
|-
|2
|2.000
|25.000
|-
|3
|4.000
|32.000
|-
|4
|6.000
|24.000
|}
|}
|[[File:Filtertable function.png|center|thumb|360x360px|Filtertable function]]
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

=== Informative ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|ISIMPERIAL
|''ISIMPERIAL()''
|Returns TRUE if project is calculated in imperial units
|''If the project is in imperial [ft, in, ...] units:''
''ISIMPERIAL() ⇒ TRUE; ⇒ 1''

''ISMETRIC() ⇒ FALSE; ⇒ 0''
|
|-
|ISMETRIC
|''ISMETRIC()''
|Returns TRUE if project is calculated in metric units
|''If the project is in metric [m, mm, ...] units:''
''ISMETRIC() ⇒ TRUE; ⇒ 1''

''ISIMPERIAL() ⇒ FALSE; ⇒ 0''
|
|-
|LANG
|''LANG()''
|LANG([ Application = False ])
|''If the application is in English and output language is Spanish:''
''LANG(FALSE()) ⇒ EN; LANG(0) ⇒ EN''

''LANG(TRUE()) ⇒ ES; LANG(1) ⇒ ES''
|
|}

=== Geotechnic ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FINESOILCLASSIFICATION
|FINESOILCLASSIFICATION(Plasticity Index [-];Moisture [-];Method 0 = EN ISO 14688-2 (2018); 1 = EN ISO 14688-2 (2013); 2 = ČSN 73 6133)
|Returns the classification of fine soil according to selected method
|[[File:Fine Soil Classification ISO 14-688-2 (2018).png|thumb|Fine Soil Classification ISO 14-688-2 (2018)]]
|
|-
|SOILCLASSIFICATION
|SOILCLASSIFICATION(Size [mm];Fall [-];Method 0 = EN ISO 14688-2 (2018))
|Returns the classification of soil according to selected method
|
|
|}

File:Fine Soil Classification ISO 14-688-2 (2018).png

2024-01-09T11:04:46Z

PetrDlask:

Fine Soil Classification ISO 14-688-2 (2018)

Formula Specification in Templates

2023-11-15T10:16:49Z

PetrDlask: /* Informative */

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RADIANS
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FILTERTABLE
|''FILTERTABLE(Coordinates X;Coordinates Y)''
|Filters repeating values and keeps the last one of them
Returns matrix with 2 columns:

Column 1: X - Filtered X

Column 2: Y - Filtered Y
|''Inputs linked to data''
''FILTERTABLE({'''X-value⇕'''};{'''Y-value⇕'''})''

(<s>2.000</s> ... ignored value, '''2.000''' ... saved value)
{| class="wikitable"
|+
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|'''''1'''''
|'''0.000'''
|'''17.000'''
|-
|<s>2</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|<s>3</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|'''4'''
|'''2.000'''
|'''25.000'''
|-
|<s>5</s>
|<s>4.000</s>
|<s>32.000</s>
|-
|'''6'''
|'''4.000'''
|'''32.000'''
|-
|<s>7</s>
|<s>6.000</s>
|<s>24.000</s>
|-
|'''8'''
|'''6.000'''
|'''24.000'''
|}
|⇒⇒⇒⇒
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|0.000
|17.000
|-
|2
|2.000
|25.000
|-
|3
|4.000
|32.000
|-
|4
|6.000
|24.000
|}
|}
|[[File:Filtertable function.png|center|thumb|360x360px|Filtertable function]]
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

=== Informative ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|ISIMPERIAL
|''ISIMPERIAL()''
|Returns TRUE if project is calculated in imperial units
|''If the project is in imperial [ft, in, ...] units:''
''ISIMPERIAL() ⇒ TRUE; ⇒ 1''

''ISMETRIC() ⇒ FALSE; ⇒ 0''
|
|-
|ISMETRIC
|''ISMETRIC()''
|Returns TRUE if project is calculated in metric units
|''If the project is in metric [m, mm, ...] units:''
''ISMETRIC() ⇒ TRUE; ⇒ 1''

''ISIMPERIAL() ⇒ FALSE; ⇒ 0''
|
|-
|LANG
|''LANG()''
|LANG([ Application = False ])
|''If the application is in English and output language is Spanish:''
''LANG(FALSE()) ⇒ EN; LANG(0) ⇒ EN''

''LANG(TRUE()) ⇒ ES; LANG(1) ⇒ ES''
|
|}

=== Geotechnic ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FINESOILCLASSIFICATION
|FINESOILCLASSIFICATION(Plasticity Index [-];Moisture [-];Method 0 = EN ISO 14688-2 (2018); 1 = EN ISO 14688-2 (2013); 2 = ČSN 73 6133)
|Returns the classification of fine soil according to selected method
|
|
|-
|SOILCLASSIFICATION
|SOILCLASSIFICATION(Size [mm];Fall [-];Method 0 = EN ISO 14688-2 (2018))
|Returns the classification of soil according to selected method
|
|
|}

Formula Specification in Templates

2023-11-14T14:24:26Z

PetrDlask: /* Matrix */

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RADIANS
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FILTERTABLE
|''FILTERTABLE(Coordinates X;Coordinates Y)''
|Filters repeating values and keeps the last one of them
Returns matrix with 2 columns:

Column 1: X - Filtered X

Column 2: Y - Filtered Y
|''Inputs linked to data''
''FILTERTABLE({'''X-value⇕'''};{'''Y-value⇕'''})''

(<s>2.000</s> ... ignored value, '''2.000''' ... saved value)
{| class="wikitable"
|+
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|'''''1'''''
|'''0.000'''
|'''17.000'''
|-
|<s>2</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|<s>3</s>
|<s>2.000</s>
|<s>25.000</s>
|-
|'''4'''
|'''2.000'''
|'''25.000'''
|-
|<s>5</s>
|<s>4.000</s>
|<s>32.000</s>
|-
|'''6'''
|'''4.000'''
|'''32.000'''
|-
|<s>7</s>
|<s>6.000</s>
|<s>24.000</s>
|-
|'''8'''
|'''6.000'''
|'''24.000'''
|}
|⇒⇒⇒⇒
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|0.000
|17.000
|-
|2
|2.000
|25.000
|-
|3
|4.000
|32.000
|-
|4
|6.000
|24.000
|}
|}
|[[File:Filtertable function.png|center|thumb|360x360px|Filtertable function]]
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

=== Informative ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|ISIMPERIAL
|''ISIMPERIAL()''
|Returns TRUE if project is calculated in imperial units
|
|
|-
|ISMETRIC
|''ISMETRIC()''
|Returns TRUE if project is calculated in metric units
|
|
|-
|LANG
|''LANG()''
|LANG([ Application = False ])
|
|
|}

=== Geotechnic ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FINESOILCLASSIFICATION
|FINESOILCLASSIFICATION(Plasticity Index [-];Moisture [-];Method 0 = EN ISO 14688-2 (2018); 1 = EN ISO 14688-2 (2013); 2 = ČSN 73 6133)
|Returns the classification of fine soil according to selected method
|
|
|-
|SOILCLASSIFICATION
|SOILCLASSIFICATION(Size [mm];Fall [-];Method 0 = EN ISO 14688-2 (2018))
|Returns the classification of soil according to selected method
|
|
|}

Formula Specification in Templates

2023-11-14T14:18:31Z

PetrDlask: /* Matrix */

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RADIANS
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FILTERTABLE
|''FILTERTABLE(Coordinates X;Coordinates Y)''
|Filters repeating values and keeps the last one of them
Returns matrix with 2 columns:

Column 1: X - Filtered X

Column 2: Y - Filtered Y
|''Inputs linked to data''
''FILTERTABLE({'''X-value⇕'''};{'''Y-value⇕'''})''
{| class="wikitable"
|+
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|'''''1'''''
|'''0,000'''
|'''17,000'''
|-
|<s>2</s>
|<s>2,000</s>
|<s>25,000</s>
|-
|<s>3</s>
|<s>2,000</s>
|<s>25,000</s>
|-
|'''4'''
|'''2,000'''
|'''25,000'''
|-
|<s>5</s>
|<s>4,000</s>
|<s>32,000</s>
|-
|'''6'''
|'''4,000'''
|'''32,000'''
|-
|<s>7</s>
|<s>6,000</s>
|<s>24,000</s>
|-
|'''8'''
|'''6,000'''
|'''24,000'''
|}
|⇒⇒⇒⇒
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|0,000
|17,000
|-
|2
|2,000
|25,000
|-
|3
|4,000
|32,000
|-
|4
|6,000
|24,000
|}
|}
|[[File:Filtertable function.png|center|thumb|360x360px|Filtertable function]]
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

=== Informative ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|ISIMPERIAL
|''ISIMPERIAL()''
|Returns TRUE if project is calculated in imperial units
|
|
|-
|ISMETRIC
|''ISMETRIC()''
|Returns TRUE if project is calculated in metric units
|
|
|-
|LANG
|''LANG()''
|LANG([ Application = False ])
|
|
|}

=== Geotechnic ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FINESOILCLASSIFICATION
|FINESOILCLASSIFICATION(Plasticity Index [-];Moisture [-];Method 0 = EN ISO 14688-2 (2018); 1 = EN ISO 14688-2 (2013); 2 = ČSN 73 6133)
|Returns the classification of fine soil according to selected method
|
|
|-
|SOILCLASSIFICATION
|SOILCLASSIFICATION(Size [mm];Fall [-];Method 0 = EN ISO 14688-2 (2018))
|Returns the classification of soil according to selected method
|
|
|}

File:Filtertable function.png

2023-11-14T14:16:08Z

PetrDlask:

Filtertable function

Formula Specification in Templates

2023-11-14T14:14:58Z

PetrDlask: /* Matrix */

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RADIANS
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FILTERTABLE
|''FILTERTABLE(Coordinates X;Coordinates Y)''
|Filters repeating values and keeps the last one of them
Returns matrix with 2 columns:

Column 1: X - Filtered X

Column 2: Y - Filtered Y
|''Inputs linked to data''
''FILTERTABLE({'''X-value⇕'''};{'''Y-value⇕'''})''
{| class="wikitable"
|+
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|'''''1'''''
|'''0,000'''
|'''17,000'''
|-
|2
|2,000
|25,000
|-
|3
|2,000
|25,000
|-
|'''4'''
|'''2,000'''
|'''25,000'''
|-
|5
|4,000
|32,000
|-
|'''6'''
|'''4,000'''
|'''32,000'''
|-
|7
|6,000
|24,000
|-
|'''8'''
|'''6,000'''
|'''24,000'''
|}
|⇒⇒⇒⇒
|
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|0,000
|17,000
|-
|2
|2,000
|25,000
|-
|3
|4,000
|32,000
|-
|4
|6,000
|24,000
|}
|}
|
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

=== Informative ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|ISIMPERIAL
|''ISIMPERIAL()''
|Returns TRUE if project is calculated in imperial units
|
|
|-
|ISMETRIC
|''ISMETRIC()''
|Returns TRUE if project is calculated in metric units
|
|
|-
|LANG
|''LANG()''
|LANG([ Application = False ])
|
|
|}

=== Geotechnic ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FINESOILCLASSIFICATION
|FINESOILCLASSIFICATION(Plasticity Index [-];Moisture [-];Method 0 = EN ISO 14688-2 (2018); 1 = EN ISO 14688-2 (2013); 2 = ČSN 73 6133)
|Returns the classification of fine soil according to selected method
|
|
|-
|SOILCLASSIFICATION
|SOILCLASSIFICATION(Size [mm];Fall [-];Method 0 = EN ISO 14688-2 (2018))
|Returns the classification of soil according to selected method
|
|
|}

Formula Specification in Templates

2023-11-13T14:03:23Z

PetrDlask: /* Informative */

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RADIANS
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FILTERTABLE
|''FILTERTABLE(Coordinates X;Coordinates Y)''
|Filters repeating values and keeps the last one of them
Returns matrix with 2 columns:

Column 1: X - Filtered X

Column 2: Y - Filtered Y
|
|
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

=== Informative ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|ISIMPERIAL
|''ISIMPERIAL()''
|Returns TRUE if project is calculated in imperial units
|
|
|-
|ISMETRIC
|''ISMETRIC()''
|Returns TRUE if project is calculated in metric units
|
|
|-
|LANG
|''LANG()''
|LANG([ Application = False ])
|
|
|}

=== Geotechnic ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FINESOILCLASSIFICATION
|FINESOILCLASSIFICATION(Plasticity Index [-];Moisture [-];Method 0 = EN ISO 14688-2 (2018); 1 = EN ISO 14688-2 (2013); 2 = ČSN 73 6133)
|Returns the classification of fine soil according to selected method
|
|
|-
|SOILCLASSIFICATION
|SOILCLASSIFICATION(Size [mm];Fall [-];Method 0 = EN ISO 14688-2 (2018))
|Returns the classification of soil according to selected method
|
|
|}

Formula Specification in Templates

2023-11-13T13:16:44Z

PetrDlask: /* Matrix */

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RADIANS
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FILTERTABLE
|''FILTERTABLE(Coordinates X;Coordinates Y)''
|Filters repeating values and keeps the last one of them
Returns matrix with 2 columns:

Column 1: X - Filtered X

Column 2: Y - Filtered Y
|
|
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

=== Informative ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|
|
|
|
|
|}

=== Geotechnic ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|
|
|
|
|
|}

Formula Specification in Templates

2023-11-13T13:13:00Z

PetrDlask:

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RADIANS
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|FILTERTABLE
|''FILTERTABLE(Coordinates X;Coordinates Y)''
|Filters repeating values and keeps the last one of them
Returns matrix with 2 columns:

Column 1: X - Filtered X

Column 2: Y - Filtered Y
|
|
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

Formula Specification in Templates

2023-10-23T10:44:28Z

PetrDlask:

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RAD
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

Main Page

2023-10-23T10:43:31Z

PetrDlask:

[[Named Data]]

[[Units]]

[[Colors]]

[[Legend of XML elements|Legend]]

[[Exchange with mobile application]]

[[IFC|IFC specification]]

[[Formula Specification in Templates|Formula Specification in Templates]]

[[Original MediaWiki Help]]

Main Page

2023-10-23T10:43:03Z

PetrDlask:

[[Named Data]]

[[Units]]

[[Colors]]

[[Legend of XML elements|Legend]]

[[Exchange with mobile application]]

[[IFC|IFC specification]]

[[Formula Specification in Templates|Formulas templates specification]]

[[Original MediaWiki Help]]

Formula Specification in Templates

2023-10-23T10:41:27Z

PetrDlask: PetrDlask moved page Formulas templates specification to Formula Specification in Templates without leaving a redirect

PB: prejmenovat stranku na Formula Specification in Templates

The list of formula specifications used in Templates. (Notes: bold inputs for functions are linked to the data in program).

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RAD
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

Formula Specification in Templates

2023-10-04T09:13:25Z

PetrDlask: /* Matrix */

List of formula specification using in Templates. (Notes: bold inputs for functions are linked to the data in program).

Categories of functions:

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RAD
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation|350x350px]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function|350x350px]]
|}

Formula Specification in Templates

2023-10-04T09:09:59Z

PetrDlask: /* Matrix */

List of formula specification using in Templates. (Notes: bold inputs for functions are linked to the data in program).

Categories of functions:

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RAD
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''

Results:
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline running through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y

Coordinates X and Y are part of the Spline curve

Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''

''Results:''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function]]
|}

Formula Specification in Templates

2023-10-04T09:01:36Z

PetrDlask: /* Matrix */

List of formula specification using in Templates. (Notes: bold inputs for functions are linked to the data in program).

Categories of functions:

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RAD
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Input⇕];[Y-Input⇕];2;9)''

''Order = 2''

''Points count = 9''

''Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''
{| class="wikitable"
!''Row''
!''Col. 1''
''c''
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|''8.238''
| ''1''
|''20.121''
|-
|''2.''
|''13.203''
| ''2''
|''29.364''
|-
|''3.''
| ''-1.32''
| ''3''
|''35.965''
|-
|''4.''
|
| ''4''
|''39.926''
|-
|''5.''
|
| ''5''
|''41.247''
|-
|''6.''
|
|''6''
|''39.926''
|-
|''7.''
|
|''7''
|''35.965''
|-
|''8.''
|
|''8''
|''29.364''
|-
|''9.''
|
|''9''
|''20.121''
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline runnig through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y
|''SPLINE([X-Input⇕];[Y-Input⇕];[Num of Points])''
''Num of Points = 8''
''Inputs:''
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''5''
|''5''
|-
|''2.''
| ''10''
|''7''
|-
|''3.''
| ''15''
|''3''
|-
|''4.''
|''20''
|''6''
|}
''Results:''
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
|''5,000''
|''5,000''
|-
|''2.''
|''5,465''
|''5,313''
|-
|''3.''
|''6,016''
|''5,668''
|-
|''4.''
|''6,633''
|''6,035''
|-
|''5.''
|''7,296''
|''6,385''
|-
|''6.''
|''...''
|''...''
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function]]
|}

Formula Specification in Templates

2023-10-04T08:59:41Z

PetrDlask: /* Matrix */

List of formula specification using in Templates. (Notes: bold inputs for functions are linked to the data in program).

Categories of functions:

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RAD
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Inpout⇕];[Y-Inpout⇕];2;9)''

''Order = 2''

''Points count = 9''

Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''
{| class="wikitable"
!''Row''
!''Col. 1''
c
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|8.238
| 1
|20.121
|-
|''2.''
|13.203
| ''2''
|29.364
|-
|''3.''
| -1.32
| 3
|35.965
|-
|''4.''
|
| 4
|39.926
|-
|''5.''
|
| 5
|41.247
|-
|''6.''
|
|''6''
|39.926
|-
|''7.''
|
|7
|35.965
|-
|''8.''
|
|8
|29.364
|-
|''9.''
|
|9
|20.121
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline runnig through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y
|SPLINE([X-SplineInput⇕];[Y-SplineInput⇕];[Num of Points])
Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| 5
|5
|-
|''2.''
| 10
|7
|-
|''3.''
| 15
|3
|-
|4.
|20
|6
|}
Results:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|1.
|5,000
|5,000
|-
|2.
|5,465
|5,313
|-
|3.
|6,016
|5,668
|-
|4.
|6,633
|6,035
|-
|5.
|7,296
|6,385
|-
|6.
|...
|...
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function]]
|}

Formula Specification in Templates

2023-10-04T08:58:32Z

PetrDlask: /* Matrix */

List of formula specification using in Templates. (Notes: bold inputs for functions are linked to the data in program).

Categories of functions:

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RAD
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Inpout⇕];[Y-Inpout⇕];2;9)''

''Order = 2''

''Points count = 9''

Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''
{| class="wikitable"
!''Row''
!''Col. 1''
c
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|8.238
| 1
|20.121
|-
|''2.''
|13.203
| ''2''
|29.364
|-
|''3.''
| -1.32
| 3
|35.965
|-
|''4.''
|
| 4
|39.926
|-
|''5.''
|
| 5
|41.247
|-
|''6.''
|
|''6''
|39.926
|-
|''7.''
|
|7
|35.965
|-
|''8.''
|
|8
|29.364
|-
|''9.''
|
|9
|20.121
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline runnig through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y
|SPLINE([X-SplineInput⇕];[Y-SplineInput⇕];[Num of Points])
Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| 5
|5
|-
|''2.''
| 10
|7
|-
|''3.''
| 15
|3
|-
|4.
|20
|6
|}
Results:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|1.
|5,000
|5,000
|-
|2.
|5,465
|5,313
|-
|3.
|6,016
|5,668
|-
|4.
|6,633
|6,035
|-
|5.
|7,296
|6,385
|-
|6.
|...
|...
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function]]
|}

Formula Specification in Templates

2023-10-04T08:57:36Z

PetrDlask: /* Matrix */

List of formula specification using in Templates. (Notes: bold inputs for functions are linked to the data in program).

Categories of functions:

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RAD
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''Col. 1''
''X''
!''Col. 2''
''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Inpout⇕];[Y-Inpout⇕];2;9)''

''Order = 2''

''Points count = 9''

Coeff.: c0 = 8,238; c1 = 13.203; c2 = -1.32

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''
{| class="wikitable"
!''Row''
!''Col. 1''
c
!''Col. 2''
''X''
!''Col. 3''
''Y''
|-
|''1.''
|8.238
| 1
|20.121
|-
|''2.''
|13.203
| ''2''
|29.364
|-
|''3.''
| -1.32
| 3
|35.965
|-
|''4.''
|
| 4
|39.926
|-
|''5.''
|
| 5
|41.247
|-
|''6.''
|
|''6''
|39.926
|-
|''7.''
|
|7
|35.965
|-
|''8.''
|
|8
|29.364
|-
|''9.''
|
|9
|20.121
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1 coefficients:

c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y

Force origin: True ... if you want include point (0,0) in Coordinates X and Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline runnig through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y
|SPLINE([X-SplineInput⇕];[Y-SplineInput⇕];[Num of Points])
Inputs:
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| 5
|5
|-
|''2.''
| 10
|7
|-
|''3.''
| 15
|3
|-
|4.
|20
|6
|}
Results:
{| class="wikitable"
|1.
|5,000
|5,000
|-
|2.
|5,465
|5,313
|-
|3.
|6,016
|5,668
|-
|4.
|6,633
|6,035
|-
|5.
|7,296
|6,385
|-
|6.
|...
|...
|}
|[[File:Result of Spline function.png|center|thumb|Result of Spline function]]
|}

File:Result of Spline function.png

2023-10-04T08:51:34Z

PetrDlask:

Result of Spline function

Formula Specification in Templates

2023-10-04T08:05:45Z

PetrDlask: /* Matrix */

List of formula specification using in Templates. (Notes: bold inputs for functions are linked to the data in program).

Categories of functions:

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RAD
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1: c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Inpout⇕];[Y-Inpout⇕];2;9)''

''Order = 2''

''Points count = 9''

Const.: c0 = 8,238; c1 = 13.203; c2 = -1.32

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''
{| class="wikitable"
!''Row''
!c
!''X''
!''Y''
|-
|''1.''
|8.238
| 1
|20.121
|-
|''2.''
|13.203
| ''2''
|29.364
|-
|''3.''
| -1.32
| 3
|35.965
|-
|''4.''
|
| 4
|39.926
|-
|''5.''
|
| 5
|41.247
|-
|''6.''
|
|''6''
|39.926
|-
|''7.''
|
|7
|35.965
|-
|''8.''
|
|8
|29.364
|-
|''9.''
|
|9
|20.121
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1: c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline runnig through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y
|
|
|}

Formula Specification in Templates

2023-10-03T13:07:05Z

PetrDlask: /* Matrix */

List of formula specification using in Templates. (Notes: bold inputs for functions are linked to the data in program).

Categories of functions:

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RAD
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1: c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |''POLYNOMIALTRENDANDPOINTS([X-Inpout⇕];[Y-Inpout⇕];2;9)''

''Order = 2''

''Points count = 9''

''Approx. formula: y = -1,32x2 + 13,203x + 8,238''
{| class="wikitable"
!''Row''
!c
!''X''
!''Y''
|-
|''1.''
|8.238
| 1
|20.121
|-
|''2.''
|13.203
| ''2''
|29.364
|-
|''3.''
| -1.32
| 3
|35.965
|-
|''4.''
|
| 4
|39.926
|-
|''5.''
|
| 5
|41.247
|-
|''6.''
|
|''6''
|39.926
|-
|''7.''
|
|7
|35.965
|-
|''8.''
|
|8
|29.364
|-
|''9.''
|
|9
|20.121
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1: c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline runnig through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y
|
|
|}

Formula Specification in Templates

2023-10-03T13:02:03Z

PetrDlask: /* Matrix */

List of formula specification using in Templates. (Notes: bold inputs for functions are linked to the data in program).

Categories of functions:

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RAD
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1: c - Coefficients c0 + c1*x + c2*x2 + ...
| rowspan="2" |
{| class="wikitable"
!''Row''
!c
!''X''
!''Y''
|-
|''1.''
|8.238
| 1
|20.121
|-
|''2.''
|13.203
| ''2''
|29.364
|-
|''3.''
| -1.32
| 3
|35.965
|-
|''4.''
|
| 4
|39.926
|-
|''5.''
|
| 5
|41.247
|-
|''6.''
|
|''6''
|39.926
|-
|''7.''
|
|7
|35.965
|-
|''8.''
|
|8
|29.364
|-
|''9.''
|
|9
|20.121
|}
| rowspan="2" |[[File:Results of PolynomialPoints approximation.png|center|thumb|Results of PolynomialPoints approximation]]
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1: c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline runnig through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y
|
|
|}

File:Results of PolynomialPoints approximation.png

2023-10-03T12:57:01Z

PetrDlask:

Results of PolynomialPoints approximation

Formula Specification in Templates

2023-09-20T13:38:09Z

PetrDlask: /* Lookup */

List of formula specification using in Templates. (Notes: bold inputs for functions are linked to the data in program).

Categories of functions:

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RAD
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Result of Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1: c - Coefficients c0 + c1*x + c2*x2 + ...
|
|
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1: c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y
|
|
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline runnig through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y
|
|
|}

Formula Specification in Templates

2023-09-20T13:37:34Z

PetrDlask: /* Lookup */

List of formula specification using in Templates. (Notes: bold inputs for functions are linked to the data in program).

Categories of functions:

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RAD
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|[[File:GrafLinInterpolation.png|center|thumb|250x250px|Linear Interpolation]]
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1: c - Coefficients c0 + c1*x + c2*x2 + ...
|
|
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1: c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y
|
|
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline runnig through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y
|
|
|}

File:GrafLinInterpolation.png

2023-09-20T13:35:20Z

PetrDlask:

GrafLinInterpolation

Formula Specification in Templates

2023-09-19T09:58:38Z

PetrDlask: /* Mathematical */

List of formula specification using in Templates. (Notes: bold inputs for functions are linked to the data in program).

Categories of functions:

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
- rounds up, if the remainder after dividing the number by the multiple is ≥ to Multiple / 2.
|''MROUND(10.4;1) ⇒ 10''
''MROUND(10.4;2) ⇒ 10''

''MROUND(10;3) ⇒ 9 (Remainder = 1 < 1.5 (Multiple/2)''

''MROUND(11;3) ⇒ 12 (Remainder = 2 > 1.5 (Multiple/2)''
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RAD
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1: c - Coefficients c0 + c1*x + c2*x2 + ...
|
|
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1: c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y
|
|
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline runnig through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y
|
|
|}

Formula Specification in Templates

2023-09-19T09:42:24Z

PetrDlask: /* Mathematical */

List of formula specification using in Templates. (Notes: bold inputs for functions are linked to the data in program).

Categories of functions:

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded to zero''

- if Number<0 and Mode=0 ''⇒ result is rounded away from zero''
|''FLOOR(10.4;1;0) ⇒ 10''
''FLOOR(10.9;1;0) ⇒ 10''

''FLOOR(10.4;7;0) ⇒ 7''

''FLOOR(-10.4;1;0) ⇒ -11''

''FLOOR(-10.4;1;1) ⇒ -10''

''FLOOR(-10.4;7;0) ⇒ -14''

''FLOOR(-10.4;7;1) ⇒ -7''
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
|
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RAD
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1: c - Coefficients c0 + c1*x + c2*x2 + ...
|
|
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1: c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y
|
|
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline runnig through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y
|
|
|}

Formula Specification in Templates

2023-09-19T09:30:57Z

PetrDlask: /* Mathematical */

List of formula specification using in Templates. (Notes: bold inputs for functions are linked to the data in program).

Categories of functions:

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for Number=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for Number=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for Number=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
- if Number<0 and Mode<>0 ''⇒ result is rounded up''

- if Number<0 and Mode=0 ''⇒ result is rounded down''
|''CEILING(10.4) ⇒ 11''
''CEILING(10.4;1) ⇒ 11''

''CEILING(10.4;5) ⇒ 15''

''CEILING(10.8;5) ⇒ 15''

''CEILING(-10.4;5;0) ⇒ -10''

''CEILING(-10.4;5;1) ⇒ -15''

CEILING(-10.4;2;0) ''⇒'' -10

CEILING(-10.4;2;1) ''⇒'' -12
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer or to the nearest multiple of significance
|
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
|
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RAD
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1: c - Coefficients c0 + c1*x + c2*x2 + ...
|
|
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1: c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y
|
|
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline runnig through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y
|
|
|}

Formula Specification in Templates

2023-09-06T12:37:26Z

PetrDlask: /* Statistical */

List of formula specification using in Templates. (Notes: bold inputs for functions are linked to the data in program).

Categories of functions:

=== Logical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AND
|''AND(Boolean1;Boolean2; ... )''
|Returns TRUE if all of its arguments are TRUE
|''AND(3=3;2=2) ⇒ TRUE''
|-
|OR
|''OR(Boolean1;Boolean2; ... )''
|Returns TRUE if any of its arguments are TRUE
|''OR(3=4;2=3) ⇒ FALSE''
|-
|TRUE
|''TRUE()''
|Returns the logical value TRUE
|''IF(TRUE();1;2) ⇒ 1''
|-
|FALSE
|''FALSE()''
|Returns the logical value FALSE
|''IF(FALSE();1;2) ⇒ 2''
|-
|IF
|''IF(Test;Then;Else)''
|Specifies a logical test to perform
- inputs can be linked to data

- result can be number, text, logical value
|Result is number (bold inputs linked to data '''''X[0;1;2;3;4;5;6]'''''):
''IF(220>200;220-200;200-220) ⇒ 20''

''IF(120>MAX('''[X⇕]''');120;-1) ⇒ 120''

''IF(MAX('''[X⇓2:⇓3]''')>'''[X⇓7]''';MAX('''[X⇓2:⇓3]''');'''[X⇓7]''')) ⇒ 6''

''IF(MAX('''⟨1;2⟩''')>'''6''';MAX('''⟨1;2⟩''');'''6''') ⇒ 6''

Result is text:

''Input'' '''''[Coordinate Z]''''' ''= 210''';[GWT]''' = 180''

''IF('''[Coordinate Z]'''>0;"Above terrain";"Under terrain") ⇒ "Top above terrain"''

''IF('''[GWT]'''<'''[Coordinate Z]''';"GWT under top of the test.";"Measure error.") ⇒ "GWT under top of the test."''
|-
|IFS
|''IFS(Test1;Then1;Test2;Then2; ... ;Else)''
|Checks whether one or more conditions are met and returns a value that corresponds to the first TRUE condition
|''Input'' '''''[GWT]''''' ''= 15''
''IFS('''[GWT]'''>8;10;'''[GWT]'''>6;9;'''[GWT]'''>3;8;-1) ⇒ 10''
|-
|NOT
|''NOT(Boolean)''
|Reverses the logic of its argument
|''IF(NOT(5>6);175;155) ⇒ 175''
''IF(NOT(5>4);175;155) ⇒ 155''

''IF(NOT("A"="B");175;155)⇒ 175''
|-
|SWITCH
|''SWITCH(Switch;Case1;Result1;Case2;Result2; ... ;[ Else ])''
|Evaluates an expression against a list of values and returns the result corresponding to the first matching value. If there is no match, an optional default value may be returned
|''SWITCH(50>6;TRUE();44;FALSE();56;-111) ⇒ 44''
''SWITCH(30/6;3;120;4;220;5;320;420) ⇒ 320''
|}

=== Mathematical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|ABS
|''ABS(Number)''
|Returns the absolute value of a number
|''ABS(120) ⇒ 120;'' ''ABS(-120) ⇒ 120''
|-
|ACOS
|''ACOS(Number)''
|Returns the arccosine of a number ⟨-Pi/2; Pi/2⟩
|''for X=0.5 ... DEGREES(ACOS(0.5)) ⇒ 60°''
|-
|ACOT
|''ACOT(Number)''
|Returns the arccotangent of a number ⟨0; Pi⟩
|''for X=1 ... DEGREES(ACOT(1))'' ''⇒ 45°''
|-
|ASIN
|''ASIN(Number)''
|Returns the arcsine of a number ⟨-Pi/2; Pi/2⟩
|''for X=0.5 ... DEGREES(ASIN(0.5)) ⇒ 30°''
|-
|ATAN
|''ATAN(Number)''
|Returns the arctangent of a number ⟨-Pi/2; Pi/2⟩
|''for X=1 ... DEGREES(ATAN(1))'' ''⇒ 45°''
|-
|CEILING
|''CEILING(Number;[Multiple=1];[Mode=0])''
|Rounds a number to the nearest integer or to the nearest multiple of significance
|
|-
|COS
|''COS(Angle[rad])''
|Returns the cosine of the given angle in rad
|''for α=60° ... COS(RADIANS(60))'' ''⇒ 0.5''
|-
|SIN
|''SIN(Angle[rad])''
|Returns the sine of the given angle in rad
|''for α=30° ... SIN(RADIANS(30))'' ''⇒ 0.5''
|-
|COT
|''COT(Angle[rad])''
|Returns the cotangent of an angle in rad
|''for α=45° ... COT(RADIANS(45))'' ''⇒ 1''
|-
|TAN
|''TAN(Angle[rad])''
|Returns the tangent of an angle in rad
|''for α=45° ... TAN(RADIANS(45))'' ''⇒ 1''
|-
|EXP
|''EXP(Number)''
|Returns e raised to the power of a given number
|''EXP(1) ⇒ 2.71828''
|-
|FLOOR
|''FLOOR(Number;[Multiple=1];[Mode=0])''
|Rounds a number down, to the nearest integer or to the nearest multiple of significance
|
|-
|LN
|''LN(Number)''
|Returns the natural logarithm of a number
|''LN(1)) ⇒ 0; LN(EXP(1)) ⇒ 1''
|-
|LOG
|''LOG(Number;[Base=10])''
|Returns the logarithm of a number to a specified base (10 if missing)
|''LOG(1; 10) ⇒ 0; LOG(10; 10) ⇒ 1''
|-
|LOG10
|''LOG10(Number)''
|Returns the base-10 logarithm of a number
|''LOG10(1) ⇒ 0; LOG10(10) ⇒ 1''
|-
|MROUND
|''MROUND(Number;Multiple)''
|Returns a number rounded to the desired multiple
|
|-
|PI
|''PI()''
|Returns the value of pi
|''PI() ⇒ 3.141592653''
|-
|POWER
|''POWER(Base;Number)''
|Returns the result of a number raised to a power
|''POWER(2;4) ⇒ 16''
|-
|SQR
|''SQR(Number)''
|Returns the result of a squared number
|''SQR(5) ⇒ 25; SQR(-5) ⇒ 25''
|-
|SQRT
|''SQRT(Number)''
|Returns a positive square root of a positive Number
|''SQRT(36) ⇒ 6; SQRT(-36) ⇒ NAN''
|-
|SUM
|''SUM(Number1;Number2; ... )''
|Returns the sum of a series of numbers
|''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''SUM('''[X⇓2:⇓5]''') ... SUM('''⟨1; 2; 3; 4⟩''') ⇒ 10''

''SUM('''[X⇕]''') ⇒ 21''
|-
|DEG
|''DEGREES(Angle [rad])''
|Converts radians into degrees
|''DEGREES(PI()) ⇒ 180°; DEGREES(PI()/2) ⇒ 90°''
|-
|RAD
|''RADIANS(Number)''
|Converts degrees to radians
|''RADIANS(180) ⇒ π (3.141592653)''
|-
|ROUND
|''ROUND(Number;Places)''
|Rounds a number to a specified number of digits
- negative Places round to the left of the decimal point
|''ROUND(58.563;3) ⇒ 58.563''
''ROUND(58.563;2) ⇒ 58.56''

''ROUND(58.563;1) ⇒ 58.6''

''ROUND(58.563;0) ⇒ 59''

''ROUND(58.563;-1) ⇒ 60''

''ROUND(58.563;-2) ⇒ 100''
|-
|ROUNDUP
|''ROUNDUP(Number;Places)''
|Rounds a number up, toward zero
|''ROUNDUP(58.563;3) ⇒ 58.564''
''ROUNDUP(58.563;2) ⇒ 58.57''

''ROUNDUP(58.563;1) ⇒ 58.6''

''ROUNDUP(58.563;0) ⇒ 59''
|-
|ROUNDDOWN
|''ROUNDDOWN(Number;Places)''
|Rounds a number down, toward zero
|''ROUNDDOWN(58.563;3) ⇒ 58.563''
''ROUNDDOWN(58.563;2) ⇒ 58.56''

''ROUNDDOWN(58.563;1) ⇒ 58.5''

''ROUNDDOWN(58.563;0) ⇒ 58''

''ROUNDDOWN(58.563;-1) ⇒ 50''

''ROUNDDOWN(58.563;-2) ⇒ 0''
|}
=== Text ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|CONCAT
|''CONCAT(Value1;Value2; ... )''
|Combines the text from multiple ranges and/or strings, but it doesn't provide the delimiter or IgnoreEmpty arguments
- Value1, Value2, ... can be as Text or Number
|''CONCAT(12;34;56) ⇒ 123456.000''
''CONCAT("12";"34";"56") ⇒ 123456.000''

''CONCAT(12;"34";56) ⇒ 123456.000''

''Input '''[GWTb]''' = 15''

''CONCAT(['''GWTb'''];" m") ⇒ "15 m"''
|-
|LEFT
|''LEFT(Text;[Count=1])''
|Returns the leftmost characters from a text value
|''LEFT("qwert";3) ⇒ "qwe"''
''LEFT("qwert";1) ⇒ "q"''
|-
|RIGHT
|''RIGHT(Text;[Count=1])''
|Returns the rightmost characters from a text value
|''RIGHT("qwert";3) ⇒ "ert"''
''RIGHT("qwert";1) ⇒ "t"''
|-
|LEN
|''LEN(Text)''
|Returns the number of characters in a text string
|''LEN("qwert") ⇒ 5''
''LEN("") ⇒ 0''
|-
|SEARCH
|''SEARCH(Find text;Within text;[Start=1])''
|Finds one text value within another (not case-sensitive)
|''SEARCH("G";"Hello GEO!";1) ⇒ 7''
|}
=== Statistical ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|AVERAGE
|''AVERAGE(Number1;Number2; ... )''
|Returns the average of its arguments
|''AVERAGE(3;5;1) ⇒ 3''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''
''AVERAGE('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MAX
|''MAX(Number1;Number2; ... )''
|Returns the maximum value in a list of arguments
|''MAX(3;5;1) ⇒ 5''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MAX('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 3''
|-
|MIN
|MIN(Number1;Number2; ... )
|Returns the minimum value in a list of arguments
|''MIN(3;5;1) ⇒ 1''
''Inputs linked to data '''X[0;1;2;3;4;5;6]'''):''

''MIN('''[X⇓3:⇓5]''') ... AVERAGE('''⟨2; 3; 4⟩''') ⇒ 2''
|-
|PERCENTIL
|''PERCENTILE(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE(['''X⇕'''];0.5) ⇒ 3''
|-
|PERCENTILE.EXC
|''PERCENTILE.EXC(Array;k)''
|Returns the k-th percentile of values in a range, where k is in the range 0..1, exclusive
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ NAN''

''PERCENTILE.INC(['''X⇕'''];0.4) ⇒ 2.4''
|-
|PERCENTILE.INC
|''PERCENTILE.INC(Array;k)''
|Returns the k-th percentile of values in a range
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''PERCENTILE.INC(['''X⇕'''];1) ⇒ 5''
|-
|STDEV
|''STDEV(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV(['''X⇕''']) ⇒ 1.581''
|-
|STDEV.P
|''STDEV.P(Number1;Number2; ... )''
|Calculates standard deviation based on the entire population
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.P(['''X⇕''']) ⇒ 1.414''
|-
|STDEV.S
|''STDEV.S(Number1;Number2; ... )''
|Estimates standard deviation based on a sample
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''STDEV.S(['''X⇕''']) ⇒ 1.581''
|-
|MODE
|''MODE(Number1;Number2; ... )''
|Returns the most common value in a data set
|''Inputs linked to data '''X[1;2;3;4;5]'''):''
''MODE((['''X⇕''']) ⇒ NAN''

''MODE((['''X⇕'''];3) ⇒ 3''
|-
|MEDIAN
|''MEDIAN(Number1;Number2; ... )''
|Returns the median of the given numbers
|''MEDIAN(1;2;3;4;5;6;7) ⇒ 4''
|}

=== Lookup ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
|-
|INDEX
|''INDEX(Array;Index)''
|Uses an index to choose a value from a reference or array
|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
''INDEX('''[Y⇓]''';2) ⇒ 16''

''INDEX('''[Y⇓]''';4) ⇒ 27''

''INDEX('''[Y⇓]''';9) ⇒ NAN''
|-
|LINEARINTERPOLATION
|''LINEARINTERPOLATION(X;Coordinates X;Coordinates Y)''
|Calculates Y corresponding to X based upon linear interpolation of coordinates X, Y
|
|-
|MATCH
|''MATCH(Value;Array;[ Type = 1 ])''
|Looks up values in a reference or array
- ''Type = 1'' find max. value less or equal to ''Value''

''...values in Array'' must be sorted in ascending order

- ''Type = -1'' find min. value greater or equal to ''Value''

''...values in Array'' must be sorted in descending order

- ''Type = 0'' find first value equal to ''Value''

''...values in Array'' needn't to be sorted

|''Inputs linked to data '''Y[15;16;11;27;22]'''):''
MATCH(11;['''Y⇕''']) ''⇒ 3''

MATCH(27;['''Y⇕''']) ''⇒ 4''

MATCH(999;['''Y⇕''']) ''⇒ NAN''
|}
=== Matrix ===
{| class="wikitable sortable mw-collapsible"
!Name
!Syntax, parameters
!Description
!''Example''
!
|-
|LINEARTREND
|''LINEARTREND(Coordinates X;Coordinates Y)''
|Returns the linear trend line
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 1''
{| class="wikitable"
|+
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''2.5''
|''10.7''
|}
| rowspan="2" |[[File:LinTrendnew.jpg|center|thumb|400x400px|Results of linear trend]]
|-
|LINEARTRENDANDPOINTS
|''LINEARTRENDANDPOINTS(Coordinates X;Coordinates Y)''
|Returns the linear trend line and its point representation
Returns matrix with 2 rows and 4 columns:

{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[1;2;3;4;5]; Y[15;16;11;27;22]'''''

''LINEARTREND(['''X⇕'''];['''Y⇕'''])''

''NumRows = 2;''
{| class="wikitable"
|-
|+
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''2.5''
|''10.7''
|''0''
|''10.7''
|-
|''2.''
|''NAN''
|''NAN''
|''5''
|''23.2''
|}
|-
|LINEARTRENDSC
|''LINEARTRENDSC(Center X;Radius)''
|Returns the linear trend line for semi-circles
Returns matrix with 1 row and 2 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
|-
|1.
|k - Slope
|q - Offset
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSC([X⇕];[R⇕])''

''NumRows = 1''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1''
|''0.506''
|''1.42''
|}
| rowspan="2" |[[File:LinTrendSCnewA.jpg|center|thumb|450x450px|Results of linear trend and points]]
|-
|LINEARTRENDSCANDPOINTS
|''LINEARTRENDSCANDPOINTS(Center X;Radius)''
|Returns the linear trend line for semi-circles and its point representation
Returns matrix with 2 rows and 4 columns:
{| class="wikitable"
!Row
!Col. 1
!Col. 2
!Col. 3
!Col. 4
|-
|1.
|k - Slope
|q - Offset
|X1
|Y1
|-
|2.
|NAN
|NAN
|X2
|Y2
|}
|''Inputs linked to data''
'''''X[4;8;15]; R[3;5;8]'''''

''LINEARTRENDSCANDPOINTS([X⇕];[R⇕])''

''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
!''Col. 3''
!''Col. 4''
|-
|''1.''
|''0.506''
|''1.42''
|''0''
|''1.42''
|-
|''2.''
|''NAN''
|''NAN''
|''15''
|''9.01''
|}
|-
|LINEARTRENDTOPOINTS
|''LINEARTRENDTOPOINTS(Slope;Offset)''
|Returns points of the linear trend line
Returns matrix with 2 rows and 2 columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|}
|''LINEARTRENDTOPOINTS(0,5;3)''
''NumRows = 2''
{| class="wikitable"
!''Row''
!''Col. 1''
!''Col. 2''
|-
|''1.''
| ''-1000''
| ''-497''
|-
|''2.''
|''1000''
|''503''
|}
|[[File:LintrendToPoints.jpg|center|thumb|Results of linear trend]]
|-
|SEMICIRCLETOPOINTS
|''SEMICIRCLETOPOINTS(Center X;Radius;[Points count 10])''
|Returns points of the semi-circle
Returns matrix with 2 rows and ''[Points count]'' columns:
{| class="wikitable"
!Row
! Col. 1
! Col. 2
|-
|1.
|X1
|Y1
|-
|2.
|X2
|Y2
|-
|...
|...
|...
|-
|...
|...
|...
|-
|''[Points count]''
|Xn
|Yn
|}
|''SEMICIRCLETOPOINTS(0,5;3;10)''
''NumRows = 10''
{| class="wikitable"
!''Row''
!''X''
!''Y''
|-
|''1.''
| ''-2,5''
|''0''
|-
|''2.''
| ''-2,31908''
|''1,02606''
|-
|''3.''
| ''-1,79813''
|''1,928363''
|-
|''4.''
| ''-1''
|''2,598076''
|-
|''5.''
| ''-0,02094''
|''2,954423''
|-
|''6.''
|''1,020945''
|''2,954423''
|-
|''7.''
|''2''
|''2,598076''
|-
|''8.''
|''2,798133''
|''1,928363''
|-
|''9.''
|''3,319078''
|''1,02606''
|-
|''10.''
|''3,5''
|''3,67E-16''
|}
|[[File:SemicircleToPoints.jpg|center|thumb|Results of semi-circle to points]]
|-
|POLYNOMIALTREND
|POLYNOMIALTREND(Coordinates X;Coordinates Y;[Order=2];[Force origin=False])
|Returns the polynomial trend curve
Returns matrix with 1 columns:

Column 1: c - Coefficients c0 + c1*x + c2*x2 + ...
|
|
|-
|POLYNOMIALTRENDANDPOINTS
|POLYNOMIALTRENDANDPOINTS(Coordinates X;Coordinates Y;[Order=2 ];[Points count=10];[Force origin=False])
|Returns the polynomial trend curve and its point representation
Returns matrix with 3 columns:

Column 1: c - Coefficients c0 + c1*x + c2*x2 + ...

Column 2: X - Coordinates X

Column 3: Y - Coordinates Y
|
|
|-
|SPLINE
|SPLINE(Coordinates X;Coordinates Y;[Points count=20])
|Returns points of the spline runnig through given points
Returns matrix with 2 columns:

Column 1: X - Coordinates X

Column 2: Y - Coordinates Y
|
|
|}