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v3.0.1
General improvements
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‎README.md‎

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@@ -11,6 +11,7 @@ Although the main development goal of the class was the integration with [CSV In
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* __Basic math operators__: `+` `-` `*` `/` `\` `^` `!`
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* __Logical expressions__: `&` (AND), `|` (OR), `||` (XOR)
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* __Binary relations__: `<`, `<=`, `<>`, `>=`, `=`, `>`, `$` (LIKE)
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* __Outstanding matrix and statistical functions__: `CHOLESKY`, `MLR` (Multivariate Linear Regression), `FIT` (Curve fitting), `INVERSE`, and a lot more!
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* __More than 90 built-in functions__: `Max`, `Sin`, `IRR`, `GAUSS`, `LSQRSOLVE`, `Switch`, `Iff`, `DateDiff`, `Solve`, `fZero`, `Format`...
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* __Very flexible and powerful__: variables, constants and user-defined functions (UDFs) support.
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* __Implied multiplication for variables, constants and functions__: `5avg(2;abs(-3-7tan(5));9)`, `5(x)` and `x(2)(3)` are valid expressions.
@@ -194,23 +195,64 @@ End Sub
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'@------------------------------------------------------
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' Here a list of the new functions and its results
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'***********************************ADVANCED MATH FUNCTIONS***************************************************************
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''' FZERO('2x^2+x-12';-2;3) : x = 2.21221445045296 (find a zero for the given function in the interval -2<=x<=3)
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'''
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''' a = {1;0;4}; b = {1;1;6}; c = {-3;0;-10}; d = {2;3;4}
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''' LUDECOMP(ARRAY(a;b;c)) : {{-3;0;-10};{-0.333333333333333;1;2.66666666666667};{-0.333333333333333;0;0.666666666666667}}
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''' LUSOLVE(ARRAY(a;b;c);{{'x';'y';'z'}};{{2;3;4}};True) : x = -18; y = -9; z = 5
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''' MMULT(INVERSE(ARRAY(a;b;c));ARRAY(d)) : {{-18};{-9};{5}}
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''' MMULT(ARRAY(a;b;c);INVERSE(ARRAY(a;b;c))) : {{1;0;0};{0;1;0};{0;0;1}}
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'''
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''' A={{-2;40};{-1;50};{0;62};{1;58};{2;60}}
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''' FIT(A;1;4) : {{62 + 3.6667*x -9.6667*x^2 + 0.3333*x^3 + 1.6667*x^4};{1}} 4th degree polynomial fitting
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''' B={{0;0.1};{0.5;0.45};{1;2.15};{1.5;9.15};{2;40.35};{2.5;180.75}}
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''' FIT(B;2) : {{0.102*e^(2.9963*x)};{0.9998}} Exponential Fitting
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''' 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}}
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''' FIT(C;5) : {{0.9521*ln(x)+0.1049};{0.9752}} Logarithmic fitting
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''' ----------------------------------------------------------------------------
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''' | Fitting data model with a 4th degree polynomial |
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''' | FIT(A;1;4) : {{62 + 3.6667*x -9.6667*x^2 + 0.3333*x^3 + 1.6667*x^4};{1}} |
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''' | |
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''' | Exponential Fitting |
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''' | FIT(B;2) : {{0.102*e^(2.9963*x)};{0.9998}} |
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''' | |
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''' | Logarithmic Fitting |
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''' | FIT(C;5) : {{0.9521*ln(x)+0.1049};{0.9752}} |
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''' ----------------------------------------------------------------------------
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'''
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''' X={{1;1};{2;2};{3;3};{4;4};{5;1};{6;2};{7;3};{8;4}}
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''' Y={{2;4.1;5.8;7.8;5.5;5.2;8.2;11.1}}
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''' ------------------------------------------------------------------------------------------
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''' | Multivariate Linear Regression with regressors/predictors interaction. |
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''' | |
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''' | MLR(X;Y;True;'X1:X2') : {{0.8542 + 0.4458*X1 + 0.945*X2 + 0.0792*X1*X2};{0.947;0.9072}} |
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''' ------------------------------------------------------------------------------------------
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'''
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''' ----------------------------------------------------------------
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''' | Finding a zero for the given function in the interval -2<=x<=3 |
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''' | |
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''' | FZERO('2x^2+x-12';-2;3) : x = 2.21221445045296 |
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''' ----------------------------------------------------------------
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'''
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''' a = {1;0;4}; b = {1;1;6}; c = {-3;0;-10}; d = {2;3;4}
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''' ------------------------------------------------------------------------------------------------
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''' | Using LU decomposition for a given matrix |
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''' | |
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''' | LUDECOMP(ARRAY(a;b;c)) : |
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''' | |
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''' | {{-3;0;-10};{-0.333333333333333;1;2.66666666666667};{-0.333333333333333;0;0.666666666666667}} |
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''' ------------------------------------------------------------------------------------------------
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'''
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''' ----------------------------------------------------------------------------------
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''' | Using LU decomposition for solve linear equations system |
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''' | |
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''' | LUSOLVE(ARRAY(a;b;c);{{'x';'y';'z'}};{{2;3;4}};True) : x = -18; y = -9; z = 5 |
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''' ----------------------------------------------------------------------------------
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'''
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''' ---------------------------------------------------------------------------
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''' | Using matrix multiplication for solve a linear equations system |
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''' | |
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''' | MMULT(INVERSE(ARRAY(a;b;c));ARRAY(d)) : {{-18};{-9};{5}} |
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''' | MMULT(ARRAY(a;b;c);INVERSE(ARRAY(a;b;c))) : {{1;0;0};{0;1;0};{0;0;1}} |
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''' ---------------------------------------------------------------------------
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'''
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''' A={{2;4};{-5;1},{3;-8}};b={{10;-9.5;12}}
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''' MROUND(LSQRSOLVE(A;b);4) : {{2.6576};{-0.1196}} solve overdetermined system of equations using least squares and QRdec
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''' --------------------------------------------------------------------
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''' | Solving overdetermined system of equations using least squares and |
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''' | the QR decomposition |
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''' | |
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''' | MROUND(LSQRSOLVE(A;b);4) : {{2.6576;-0.1196}} |
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''' --------------------------------------------------------------------
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'''
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'***********************************STATISTICAL FUNCTIONS*******************************************************************************
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''' ROUND(NORM(0.05);8) = 0.96012239
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''' ROUND(CHISQ(4;15);8) = 0.99773734
@@ -249,13 +291,13 @@ End Sub
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''' YEAR(NOW()) = 2022
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''' WEEKDAYNAME(1;true;2) = 'lun.'
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''' WEEKDAY(NOW()) = 2
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''' TIMEVALUE(NOW()) = '7:53:00 a. m.'
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''' TIMESERIAL(x;y;z) = '6:45:50 a. m.' for x = 7; y = -15; z = 50
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''' TIMEVALUE(NOW()) = '7:53:00 a. m.'
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''' TIMESERIAL(x;y;z) = '6:45:50 a. m.' for x = 7; y = -15; z = 50
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''' MONTH(NOW()) = 10
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''' MONTHNAME(x;y) = 'marzo' for x = 3; y = false
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''' MONTH(x) = 10 for x = '10/10/2022 7:53:10 a. m.'
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''' MINUTE(x) = 53 for x = '10/10/2022 7:53:12 a. m.'
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''' HOUR(x) = 7 for x = '10/10/2022 7:53:15 a. m.'
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''' MONTH(x) = 10 for x = '10/10/2022 7:53:10 a. m.'
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''' MINUTE(x) = 53 for x = '10/10/2022 7:53:12 a. m.'
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''' HOUR(x) = 7 for x = '10/10/2022 7:53:15 a. m.'
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''' DAY(DATE()) = 10
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''' DATEVALUE(DATE()) = '10/10/2022'
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''' DATESERIAL(2022;x+2;3y) = '21/12/2022' for x = 10; y = 7

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