VBA Expressions is a powerful string expression evaluator for VBA and LO Basic, which puts more than 100 mathematical, statistical, financial, date-time, logic and text manipulation functions at the user's fingertips. The VBAexpressions.cls class mediates almost all VBA functions as well as custom functions exposed through it.
Although the main development goal of the class was the integration with CSV Interface, VBA Expressions has evolved to become a support tool for students and teachers of science, accounting, statistics and engineering; this due to the added capability to solve systems of equations and non-linear equations in one variable.
- Easy to use and integrate.
- Basic math operators:
+-*/\^! - Logical expressions:
&(AND),|(OR),||(XOR) - Binary relations:
<,<=,<>,>=,=,>,$(LIKE) - Outstanding matrix and statistical functions:
CHOLESKY,MLR(Multivariate Linear Regression),FIT(Curve fitting),INVERSE, and a lot more! - More than 100 built-in functions:
Max,Sin,IRR,GAUSS,LSQRSOLVE,Switch,Iff,DateDiff,Solve,fZero,Format... - Very flexible and powerful: variables, constants and user-defined functions (UDFs) support.
- Implied multiplication for variables, constants and functions:
5avg(2;abs(-3-7tan(5));9),5(x)andx(2)(3)are valid expressions. - Evaluation of arrays of expressions given as text strings, as in Java: curly brackets must be used to define arrays
{{...};{...}} - Floating point notation input support:
-5E-5,(1.434E3+1000)*2/3.235E-5are valid inputs. - Free of external VBA dependencies: does not use dll.
The evaluation approach used is similar to the one we humans use: divide the function into sub-expressions, create a symbolic string to build an expression evaluation flow, split the sub-expressions into chunks of operations (tokens) by tokenization, evaluate all the tokens.
The module can evaluate mathematical expressions such as:
5*avg(2;abs(-3-7*tan(5));9)-12*pi-e+(7/sin(30)-4!)*min(cos(30);cos(150))min(cos(sin(30))+2^2;1)- *
GCD(1280;240;100;30*cos(0);10*DET({{sin(atn(1)*2); 0; 0}; {0; 2; 0}; {0; 0; 3}}))
*GCD is an user-defined function (UDF).
Allowed expressions must follow the following grammar:
Expression = ([{"("}] SubExpr [{Operator [{"("}] SubExpr [{")"}]}] [{")"}] | {["("] ["{"] List [{";" List}] ["}"] [")"]})
SubExpr = Token [{Operator Token}]
Token = [{Unary}] Argument [(Operator | Function) ["("] [{Unary}] [Argument] [")"]]
Argument = (List | Variable | Operand | Literal)
List = ["{"] ["{"] SubExpr [{";" SubExpr}] ["}"] ["}"]
Unary = "-" | "+" | ~
Literal = (Operand | "'"Alphabet"'")
Operand = ({Digit} [Decimal] [{Digit}] ["E"("-" | "+"){Digit}] | (True | False))
Variable = Alphabet [{Decimal}] [{(Digit | Alphabet)}]
Alphabet = "A-Z" | "a-z"
Decimal = "." | ","
Digit = "0-9"
Operator = "+" | "-" | "*" | "/" | "\" | "^" | "%" | "!" | "<" | "<=" | "<>" | ">" | ">=" | "=" | "$" | "&" | "|" | "||"
Function = "abs" | "sin" | "cos" | "min" |...|[UDF]
VBA expressions uses the following precedence rules to evaluate mathematical expressions:
()Grouping: evaluates functions arguments as well.! - +Unary operators: exponentiation is the only operation that violates this. Ex.:-2 ^ 2 = -4 | (-2) ^ 2 = 4.^Exponentiation: Although Excel and Matlab evaluate nested exponentiations from left to right, Google, mathematicians and several modern programming languages, such as Perl, Python and Ruby, evaluate this operation from right to left. VBA expressions also evals in Python way: a^b^c = a^(b^c).\* / %Multiplication, division, modulo: from left to right.+ -Addition and subtraction: from left to right.< <= <> >= = > $Binary relations.~Logical negation.&Logical AND.||Logical XOR.|Logical OR.
Users can enter variables and set/assign their values for the calculations. Variable names must meet the following requirements:
- Start with a letter.
- End in a letter or number.
"x.1","number1","value.a"are valid variable names. - A variable named
"A"is distinct from another variable named"a", since variables are case-sensitive. This rule is broken by the constantPI, sincePI=Pi=pi=pI. - The token
"E"cannot be used as variable due this token is reserved for floating point computation. For example, the expression"2.5pi+3.5e"will be evaluated to~17.3679680, but a expression like"2.5pi+3.5E"will return an error.
Users can register custom modules to expose and use their functions through the VBAcallBack.cls module. All UDFs must have a single Variant argument that will receive an one-dimensional array of strings (one element for each function argument).
Here is a working example of UDF function creation
Sub AddingNewFunctions()
Dim Evaluator As VBAexpressions
Dim UDFnames() As Variant
Dim Result As String
Set Evaluator = New VBAexpressions
UDFnames() = Array("GCD")
With Evaluator
.DeclareUDF UDFnames, "UserDefFunctions" 'Declare the Greatest Common Divisor function
'defined in the UDfunctions class module. This need
'an instance in the VBAcallBack class module.
' The determinant of a diagonal matrix. It is defined
' as the product of the elements in its diagonal.
' For our case: 1*2*3=6. (Note that sin(atn(1)*2)=sin(pi/2)=1)
.Create "GCD(1280;240;100;30*cos(0);10*DET({{sin(atn(1)*2); 0; 0}; {0; 2; 0}; {0; 0; 3}}))"
Result = .Eval
End With
End Sub
VBA expressions can evaluate matrix functions whose arguments are given as arrays/vectors, using a syntax like Java. The following expression will calculate, and format to percentage, the internal rate of return (IRR) of a cash flow described using a one dimensional array with 5 entries:
FORMAT(IRR({{-70000;12000;15000;18000;21000}});'Percent')
However, user-defined array functions need to take care of creating arrays from a string, the ArrayFromString method can be used for this purpose.
VBA Expressions is an easy-to-use library, this section shows some examples of how to use the most common properties and methods
The library only works on LibreOffice version 7.5 or higher and, since there is no 1-1 compatibility between VBA and LO Basic, users must be aware of certain changes required to recover some properties functionality. This applies mainly to those properties related to accessing variables, which were converted into functions to overcome the one-parameter limitation imposed by LO Basic when accessing them, as well as to other properties deprecated due to LO Basic's behaviour in handling class modules. An example of this is the
VarValueproperty which was split into two procedures:GetVarValueandLetVarValue. The rest of the syntax is shared between the two implementations.
Sub SimpleMathEval()
Dim Evaluator As VBAexpressions
Set Evaluator = New VBAexpressions
With Evaluator
.Create "(((((((((((-123.456-654.321)*1.1)*2.2)*3.3)+4.4)+5.5)+6.6)*7.7)*8.8)+9.9)+10.10)"
If .ReadyToEval Then 'Evaluates only if the expression was successfully parsed.
.Eval
End If
End With
End Sub
Sub LateVariableAssignment()
Dim Evaluator As VBAexpressions
Set Evaluator = New VBAexpressions
With Evaluator
.Create "Pi.e * 5.2Pie.1 + 3.1Pie"
If .ReadyToEval Then
Debug.Print "Variables: "; .CurrentVariables 'Print the list of parsed variables
.Eval ("Pi.e=1; Pie.1=2; Pie=3") 'Late variable assignment
Debug.Print .Expression; " = "; .Result; _
"; for: "; .CurrentVarValues 'Print stored result, expression and values used in evaluation
End If
End With
End Sub
Sub EarlyVariableAssignment()
Dim Evaluator As VBAexpressions
Set Evaluator = New VBAexpressions
With Evaluator
.Create "Pi.e * 5.2Pie.1 + 3.1Pie"
If .ReadyToEval Then
Debug.Print "Variables: "; .CurrentVariables
.VarValue("Pi.e") = 1
.ImplicitVarValue("Pie.1") = "2*Pi.e"
.ImplicitVarValue("Pie") = "Pie.1/3"
.Eval
Debug.Print .Expression; " = "; .Result; _
"; for: "; .CurrentVarValues
End If
End With
End Sub
Sub TrigFunctions()
Dim Evaluator As VBAexpressions
Set Evaluator = New VBAexpressions
With Evaluator
.Create "asin(sin(30))"
If .ReadyToEval Then
.Degrees = True 'Eval in degrees
.Eval
End If
End With
End Sub
Sub StringFunctions()
Dim Evaluator As VBAexpressions
Set Evaluator = New VBAexpressions
With Evaluator
.Create "CONCAT(CHOOSE(1;x;'2nd';'3th';'4th';'5th');'Element';'selected';'/')"
.Eval ("x='1st'")
End With
End Sub
Sub LogicalFunctions()
Dim Evaluator As VBAexpressions
Set Evaluator = New VBAexpressions
With Evaluator
.Create "IFF(x > y & x > 0; x; y)"
.Eval("x=70;y=15") 'This will be evaluated to 70
End With
End Sub
Sub SolveSystemOfLinearEquations()
Dim Evaluator As VBAexpressions
Set Evaluator = New VBAexpressions
With Evaluator
'Create an array of vectors a, b, c, d and e
.Create "SOLVE(ARRAY(a;b;c;d;e);{{'x1';'x2';'x3';'x4';'x5'}};{{100;100;100;100;100}};True)"
'Define coeficient vectors
.VarValue("a") = "{4;-1;0;1;0}"
.VarValue("b") = "{-1;4;-1;0;1}"
.VarValue("c") = "{0;-1;4;-1;0}"
.VarValue("d") = "{1;0;-1;4;-1}"
.VarValue("e") = "{0;1;0;-1;4}"
.Eval 'Evaluates to [x1 = 25; x2 = 35.7142857143; x3 = 42.8571428571; x4 = 35.7142857143; x5 = 25]
End With
End Sub
'@------------------------------------------------------
' Here a list of the new functions and its results
'***********************************ADVANCED MATH FUNCTIONS***************************************************************
''' A={{-2;40};{-1;50};{0;62};{1;58};{2;60}}
''' B={{0;0.1};{0.5;0.45};{1;2.15};{1.5;9.15};{2;40.35};{2.5;180.75}}
''' C={{1;0.01};{2;1};{3;1.15};{4;1.3};{5;1.52};{6;1.84};{7;2.01};{8;2.05};{9;2.3};{10;2.25}}
''' ----------------------------------------------------------------------------
''' | Fitting data model with a 4th degree polynomial |
''' | FIT(A;1;4) : {{62 + 3.6667*x -9.6667*x^2 + 0.3333*x^3 + 1.6667*x^4};{1}} |
''' | |
''' | Exponential Fitting |
''' | FIT(B;2) : {{0.102*e^(2.9963*x)};{0.9998}} |
''' | |
''' | Logarithmic Fitting |
''' | FIT(C;5) : {{0.9521*ln(x)+0.1049};{0.9752}} |
''' ----------------------------------------------------------------------------
'''
''' X={{1;1};{2;2};{3;3};{4;4};{5;1};{6;2};{7;3};{8;4}}
''' Y={{2;4.1;5.8;7.8;5.5;5.2;8.2;11.1}}
''' ------------------------------------------------------------------------------------------
''' | Multivariate Linear Regression with regressors/predictors interaction. |
''' | |
''' | MLR(X;Y;True;'X1:X2') : {{0.8542 + 0.4458*X1 + 0.945*X2 + 0.0792*X1*X2};{0.947;0.9072}} |
''' ------------------------------------------------------------------------------------------
'''
''' ----------------------------------------------------------------
''' | Finding a zero for the given function in the interval -2<=x<=3 |
''' | |
''' | FZERO('2x^2+x-12';-2;3) : x = 2.21221445045296 |
''' ----------------------------------------------------------------
'''
''' a = {1;0;4}; b = {1;1;6}; c = {-3;0;-10}; d = {2;3;4}
''' ------------------------------------------------------------------------------------------------
''' | Using LU decomposition for a given matrix |
''' | |
''' | LUDECOMP(ARRAY(a;b;c)) : |
''' | |
''' | {{-3;0;-10};{-0.333333333333333;1;2.66666666666667};{-0.333333333333333;0;0.666666666666667}} |
''' ------------------------------------------------------------------------------------------------
'''
''' ----------------------------------------------------------------------------------
''' | Using LU decomposition for solve linear equations system |
''' | |
''' | LUSOLVE(ARRAY(a;b;c);{{'x';'y';'z'}};{{2;3;4}};True) : x = -18; y = -9; z = 5 |
''' ----------------------------------------------------------------------------------
'''
''' ---------------------------------------------------------------------------
''' | Using matrix multiplication for solve a linear equations system |
''' | |
''' | MMULT(INVERSE(ARRAY(a;b;c));ARRAY(d)) : {{-18};{-9};{5}} |
''' | MMULT(ARRAY(a;b;c);INVERSE(ARRAY(a;b;c))) : {{1;0;0};{0;1;0};{0;0;1}} |
''' ---------------------------------------------------------------------------
'''
''' A={{2;4};{-5;1},{3;-8}};b={{10;-9.5;12}}
''' --------------------------------------------------------------------
''' | Solving overdetermined system of equations using least squares and |
''' | the QR decomposition |
''' | |
''' | MROUND(LSQRSOLVE(A;b);4) : {{2.6576;-0.1196}} |
''' --------------------------------------------------------------------
'''
'***********************************STATISTICAL FUNCTIONS*******************************************************************************
''' ROUND(NORM(0.05);8) = 0.96012239
''' ROUND(CHISQ(4;15);8) = 0.99773734
''' ROUND(GAUSS(0.05);8) = 0.01993881
''' ROUND(ERF(0.05);8) = 0.05637198
''' ROUND(STUDT(0.8;15);8) = 0.43619794
''' ROUND(ANORM(0.75);8) = 0.31863936
''' ROUND(AGAUSS(0.75);8) = 0.67448975
''' ROUND(AERF(0.95);8) = 1.38590382
''' ROUND(ACHISQ(0.75;15);8) = 11.03653766
''' ROUND(FISHF(5.5;1.5;3);8) = 0.21407698
''' ROUND(ASTUDT(0.05;15);8) = 2.13144955
''' ROUND(AFISHF(0.05;1.5;3);8) = 18.55325631
''' ROUND(iBETA(0.5;1;3);8) = 0.875
''' ROUND(BETAINV(0.5;1;3);8) = 0.20629947
'***********************************FINANTIAL FUNCTIONS*********************************************************************************
''' FORMAT(SYD(10000;5000;5;2);'Currency') = '$1,333.33'
''' FORMAT(SLN(10000;0;5);'Currency') = '$2,000.00'
''' FORMAT(RATE(2*12; -250; 5000; 0; 1);'Percent') = '1.66%'
''' FORMAT(PV(0.075/12; 2*12; 250; 0; 0);'Currency') = '($5,555.61)'
''' FORMAT(PPMT(0.06/52; 20; 4*52; 8000; 0; 0);'Currency') = '($34.81)'
''' FORMAT(PMT(0.075/12; 2*12; 5000; 0; 1);'Currency') = '($223.60)'
''' FORMAT(NPV(0.1;{{-10000;3000;4200;6800}});'Currency') = '$1,188.44'
''' FORMAT(NPER(0.0525/1; -200; 1500);'0.00') = '9.78'
''' FORMAT(MIRR({{-7500;3000;5000;1200;4000}};0.05;0.08);'Percent') = '18.74%'
'''
''' Microsoft example. VBA Expressions use a custom solver to compute IRR
''' FORMAT(IRR({{-70000;12000;15000;18000;21000}});'Percent') = '-2.12%'
''' FORMAT(IRR({{-70000;12000;15000;18000;21000;26000}});'Percent') = '8.66%'
''' FORMAT(IRR({{-70000;12000;15000}};true);'Percent') = '-44.35%' 'Find a solution with negative values for IRR
'''
''' FORMAT(IPMT(0.0525/1; 4; 10*1; 6500);'Currency') = '($256.50)'
''' FORMAT(FV(0.0525/1; 10*1; -100; -6500; 0);'Currency') = '$12,115.19'
''' FORMAT(DDB(10000; 5000; 5; 2);'Currency') = '$1,000.00'
'***********************************DATE AND TIME FUNCTIONS*****************************************************************************
''' YEAR(NOW()) = 2022
''' WEEKDAYNAME(1;true;2) = 'lun.'
''' WEEKDAY(NOW()) = 2
''' TIMEVALUE(NOW()) = '7:53:00 a. m.'
''' TIMESERIAL(x;y;z) = '6:45:50 a. m.' for x = 7; y = -15; z = 50
''' MONTH(NOW()) = 10
''' MONTHNAME(x;y) = 'marzo' for x = 3; y = false
''' MONTH(x) = 10 for x = '10/10/2022 7:53:10 a. m.'
''' MINUTE(x) = 53 for x = '10/10/2022 7:53:12 a. m.'
''' HOUR(x) = 7 for x = '10/10/2022 7:53:15 a. m.'
''' DAY(DATE()) = 10
''' DATEVALUE(DATE()) = '10/10/2022'
''' DATESERIAL(2022;x+2;3y) = '21/12/2022' for x = 10; y = 7
''' DATEPART(x;DATE()) = 2022 for x = 'yyyy'
''' DATEPART(x;DATE()) = 10 for x = 'm'
''' DATEPART(x;DATE()) = 10 for x = 'd'
''' DATEPART(x;DATE()) = 4 for x = 'q'
''' DATEDIFF(x;DATE();DATEADD(x;y;DATE())) = 3 for x = 'yyyy'; y = 3
''' DATEDIFF(x;DATE();DATEADD(x;y;DATE())) = 2 for x = 'q'; y = 2
''' DATEDIFF(x;DATE();DATEADD(x;y;DATE())) = 5 for x = 'm'; y = 5
''' DATEDIFF(x;DATE();DATEADD(x;y;DATE())) = 10 for x = 'd'; y = 10
''' DATEADD(x;y;DATE()) = 10/10/2025 for x = 'yyyy'; y = 3
''' DATEADD(x;y;DATE()) = 10/4/2023 for x = 'q'; y = 2
''' DATEADD(x;y;DATE()) = 10/3/2023 for x = 'm'; y = 5
''' DATEADD(x;y;DATE()) = 20/10/2022 for x = 'd'; y = 10
''' DATE() = '10/10/2022'
'***********************************STRING FUNCTIONS******************************************************************************
''' UCASE(x) = ' THIS STRING ' for x = ' This String '
''' TRIM(x) = 'Capi tal' for x = ' Capi tal '
''' RIGHT(2x+20-5+x;2) = '90' for x = 25
''' RIGHT(2x+20-5+x;2) = '09' for x = 98
''' REPLACE(x;'a';'A';1;2) = 'CApitAl' for x = 'Capital'
''' MID(x;4;3) = 'ion' for x = 'Region'
''' LEN(x) = 6 for x = 'Region'
''' LEFT(2x+20-5+x;2) = '90' for x = 25
''' LEFT(2x+20-5+x;2) = '30' for x = 98
''' LCASE(x) = 'this string' for x = 'This String'
''' LCASE(x) = '98' for x = 98
''' FORMAT(x;'Percent') = '98.10%' for x = 0.981
''' CHR(x) = ';' for x = 59
''' ASC(x) = 82 for x = 'Region'
''' SWITCH(x='Asia';1;x='Africa';2;x='Oceania';3) = 1 for x = 'Asia'
'@------------------------------------------------------
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