The unit MATH2 offers some of the most fundamental procedures of univariate statistics (such as mean values, standard deviations, or the correlation coefficient for a series of data pairs). In addition, several more advanced mathematical methods (such as the calculation of eigenvectors and principal components, a simple clustering algorithm, and the smoothing of data) are contained in this unit. The unit MATH2 also contains a simple, yet powerful class (TCurveFit) which supports curve fitting of univariate data. More details can be found in the online help pages.

The unit MATH2 is part of the SDL Component Suite.
 
 

What's new:

• Release 12.0   [Dec-12, 2023]
   
  • the class TMathExpression now supports the calculation of the minimum and maximum of a list of variables
  • the new function ClassScatterMatrices calculates the within-class and between-class scatter matrices
  • the new method TCurveFit.RMSDiff calculates the root mean square of the x-y differences
  • the class TCurveFit has been extended to provide a more convenient model fitting: CalcRegModel, Predict, Evaluate, ModelPar, PolyOrder, Residual, FitQual, StdDevResid and CPXShift
  • SDL_math2.FindCenters does not longer store auxiliary data in a file on the disk (it now stores it in a dynamic array)
  • the class TMathExpression now allows to block arithmetic exceptions (properties BlockExceptions and ErrorValue)
  • implemented a second overloaded version of MultiLinReg
  • the new function VarInflatFactor calculates the variance inflation factors of a dataset
  • bug fix: PolygonLength calculated wrong length for closed polygons
  
  
• Release 10.7   [Aug-24, 2020]
   
  • the function CalcRanks calculates the ranks of data in a vector
  • the function ReducePolygon allows to remove superfluous vertices from a polygon
  • the function CreateSigmoidArray fills an array with values of the sigmoid function
  • the function CreateGaussianPeaks generates a signal based on Gaussian peaks
  • the function Gauss2D fill an array with value from a Gaussian radial basis function
  • the functions ApplyCompassKernel and ApplyKirschKernel filter a 2D matrix by the compass and the Kirsch kernel, respectively
  • the new function KernelConvolve is a general 2D kernel convolving function
  • TMathExpression.HelperObject implemented
  • the function ExtractVarNames scans a mathematical expression for variable names
  • the functions ConvertFromDiffPolygon and ConvertToDiffPolygon allow to convert polygons between absolute and relative coordinates
  
  
• Release 10.6   [Mar-09, 2018]
   
  • TCurveFit.CalcLinFit raises now an exception if the slope becomes infinite
  • the function PolygonArea provides now a second overloaded version which counts the intersections
  • the function DistanceToPolygon calculates the closest distance from a point to a polygon
  • the function PolygonLength calculates the length of a polygon
  • the functions TCurveFit.CalcPolyFit and TCurveFit.CalcCenteredPolyFit have been extended by alpha (the p-values of the parameters)
  
  
• Release 10.5   [Oct-10, 2016]
   
  • the function CheckParanthInExp checks the correctness of parantheses in mathematical expressions
  • the OnVarRequest event of TMathExpression has been extended to include the position of the variable name
  • the procedure MovingKernelFilter implements a moving kernel filter
  • the following sinc filter kernels are now supported: CalcSincLPKernel, CalcSincHPKernel, CalcSincBPKernel, CalcSincBSKernel
  • Chebychev filter implemented: ChebychevFilter, CalcChebFilterCoeffs
  
  
• Release 10.4   [Jun-02, 2015]
   
  • the new function VertexCompAnalysis implements the vertex component analysis
  • EnterStatValue is now a function returning the number of stored data points
  • TMathExpression includes now a help context id on exceptions of the type ESDLMathExp.
  • the function kMeansEstimatedSteps returns the estimated number of required processing steps of kMeans clustering
  • the new procedure OuterRectOfPolygon returns the circumscribing rectangle of a polygon
  • bug fix: PointIsInsidePolygon returned wrong result in degenerate cases
  
  
• Release 10.3   [Oct-06, 2014]
   
  • speed of AgglomClustering increased substantially (factor five to ten)
  • kMeansClustering now provides an overloaded version to control the selection of the initial centers
  • kMeansClustering returns now the sum of squares of the intra-class distances
  • the procedure TCurveFit.FlipXY exchanges the x and y variables
  • TMathExpression now supports the predefined reference variable symbol ° (degree)
  • bug fix: TCurveFit.SpearmanRankCorr now works with large data sets as expected (was round-off and overflow error)
  
  
• Release 10.2   [May-30, 2013]
   
  • the new function MahalanobisDistance calculates the Mahalanobis distance between two points in n-dimensional space
  • the new function MovingMedianSmooth smoothes data by a moving median
  • the function EstimateByKNN now supports two new weighting modes (kwmLinear and kwmBiQuad)
  • bug fix: TCurveFit.SpearmanRankCorr, TCurveFit.KendallsTau, and TCurveFit.KruskalGamma crashed if all data were constant
  • bug fix: AgglomClustering returned slightly shifted distance values for Ward's method
  
  
• Release 10.1   [Oct-29, 2012]
   
  • the new function PseudoInverse calculates the Moore-Penrose inverse
  • the new function PointIsInsidePolygon tests whether a point is located within a closed polygon
  • the new procedures MovingAverageSmooth and WeightedAverageSmooth implement the "moving average" and the "weighted average" smoothing algorithms
  • the property TMathExpression.Expression supports now the calculation of the sum, the mean and the variance of a list of variables
  • the function AgglomClustering may now be aborted by setting the global variable AbortMathProc to TRUE
  • the property TCurveFit.KendallsTau has been changed to become a function which returns the level of signficance as a variable parameter
  • the property TExtractor.ExtractionCommands has been extended to accept the command "assign"
  • SimPLS now calls the global procedure MathFeedBackProc
  • bug fix and improvement: TCurveFit.SpearmanRankCorr now uses adjusted formula if ties occur in the data
  • bug fix and improvement: TCurveFit.CubicSpline now checks for equal x-values and raises an exception
  • bug fix: TCurveFit.KendallsTau does not create an integer overflow any more for large samples
  
  
• Release 10.0   [Oct-4, 2011]
   
  • the procedure SimPLS implements the SIMPLS algorithm for partial least squares regression
  • the new methods RidgeReg and RidgeRegStd provide the ridge regression algorithm
  • TMathExpression: variable names may now contain German umlauts
  • new class TStringSearch implemented
  • the class TCurveFit uses now extended precision internally to avoid floating point overflow in special cases
  • bug fix: TCurveFit.MeanX, TCurveFit.MeanY, TCurveFit.MeanDiff do no longer crash if no data has been entered
  
  
• Release 9.7   [May-31, 2010]
   
  • new methods TCurveFit.QuartilesX and TCurveFit.QuartilesY calculate the quartiles of data in the TCurveFit container
  • class TMathExpression supports now three new functions: nddens, ndint, and ndquant calculate the density, the integral, and the quantile of a standard normal distribution, respectively.
  • ExportAsASC is now a function (instead of a procedure) returning an error message if the file cannot be created or overwritten
  • the new method TCurveFit.CalcAnovaReg performs the analysis of variances
  • bug fix: CalcCovar crashed if the target matrix was too small
  • bug fix: TCurveFit.SpearmanRankCorr does not crash any more if more than approx. 1250 values are used for the calculation
  • bug fix: TCurveFit.SmoothedSpline calculates the smoothed spline at position TCurveFit.MaxX as well
  
  
• Release 9.51   [Dec-01, 2008]
   
  • new function PointIsInsideConvexHull checks whether a point is inside or outside of a convex hull
  • bug fix: procedure Convex2DHull produced wrong results if the x-coordinates of two neighboring points were exactly equal
  
  
• Release 9.5   [Oct-31, 2008]
   
  • properties TCurveFit.SkewnessX and TCurveFit.SkewnessY implemented
  • properties TCurveFit.KurtosisX and TCurveFit.KurtosisY implemented
  • methods TCurveFit.CalcPowerFit, TCurveFit.CalcHoerlFit, and TCurveFit.CalcExponentialFit now rise an exception if the function cannot be fitted
  • method TCurveFit.CalcCenteredPolyFit implemented
  • method TCurveFit.CalcPolyFit now provides feedback on numerical instabilities (parameter NearSingular)
  • TMathExpression now offers new function "sign" to calculate the sign of a variable
  • methods TCurveFit.CalcLinFit, TCurveFit.CalcParabolFit, TCurveFit.CalcGaussFit, ... improved to create better fit with data shifted far away from the origin
  • bug fix: TCurveFit.CalcCircleFit does not crash anymore, if radius becomes infinite
  • bug fix: TMathExpression now calculates the correct result if argument of an odd power is negative
  • bug fix: unary minus and signs are now interpreted correctly by TMathExpression
  • bug fix: TCurveFit.CalcLinFit does not crash anymore if all data points are zero
  • bug fix: TMathExpression.Evaluate: function Gauss does no longer create a range check error
  
  
• Release 9.0   [May-28, 2007]
   
  • The algorithm used for TCurveFit.CalcPolyFit has been replaced by an SVD based version which is much more stable for higher orders (up to MaxPolyFitOrder).
  • second order derivative of Savitzky-Golay smoothed filter implemented
  
  
• Release 8.5   [Feb-18, 2006]
   
  • the routine CalcPrincComp is now available in a second overloaded version which allows to select whether to normalize the eigenvalues or not.
  • CalcCovar now calculates the squared correlation coefficients and the sum of squared differences as additional options (mode=3, or 4)
  • kMeansClustering implemented
  • the coefficients of the Savitzky-Golay-Polynomials are now publicly available (see GolayPoly)
  • TCurveFit.MeanAngleX, TCurveFit.MeanAngleY for the calculation of mean angles implemented
  
  
• Release 8.2   [Nov-03, 2004]
   
  • TCurveFit now checks for any error conditions when calculating a fit
  • new curve fitting methods: CalcExponentialFit
  • function to calculate the correlation of images implemented: CalcImgCorrelation
  • bug fix: result of ScanDateTime is now stored as double (TDateTime instead of string)
  
  
• Release 8.1   [Aug-29, 2004]
   
  • available for Delphi™ 8 for .NET
  • command "scandatetime" added to TExtractor class
  • TExtractor: type of variable can now be determined by extraction script (as a syntax extension to the emit command)
  • TCurveFit offers now more regression functions: CalcCircleFit, CalcReciLogFit, CalcReciHyperbolFit, CalcPowerFit, and CalcHoerlFit
  • bug fix: PenalizedCubicSpline does no longer generate range check errors
  • bug fix: TExtractor.Source does not strip off leading or trailing blanks anymore
  
  
• Release 8.0   [Apr-15, 2004]
   
  • new function PolygonArea implemented
  • new function Convex2DHull calculates convex hull of a two-dimensional data set
  • new class TMathExpression supports the interpretation of mathematical formulas
  • new class TExtractor supports command driven extraction of values from strings
  • new procedure to calculate penalized splines implemented (PenalizedCubicSpline)
  • additional clustering method: Unweighted Pair Group with Arithmetic Mean (UPGMA)
  • AgglomClustering has now different feedback mode
  • TCurveFit: new properties MinX, MinY, MaxX, MaxY
  • TCurveFit: ExportAsASC, ImportASC
  • smoothed splines as additional curve fitting method (SplineSmoothingFactor, SmoothedSpline)
  
  
• Release 7.2   [Mar-23, 2003]
   
  • MATH2 is now part of MathPack
  • accuracy of SVD improved (had numerical problems when applying it to data covering a range of 8 decades or more)
  
  
• Release 7.0   [Sep-15, 2002]
   
  • available for Delphi™ 7.0
  • the unit is now CLX compatible
  • bug fix: memory leak in CubicSpline fixed
  
  
• Release 6.5   [May-28, 2002]
   
  • available for C++Builder™ 6.0
  • SphereGreatCircleDist implemented
  
  
• Release 6.0   [Aug-06, 2001]
   
• available for Delphi™ 6.0
• CalcEigVec now increments the ProcStat variable with better granularity
• CalcCovar and CalcEigVec can be aborted by setting AbortMathProc
• EstimateByKNN implemented
• FindNearestNeighbors improved: distance calculation can now be performed by a user defined function
   
• Release 5.5  [May-21, 2000]
   
• available for C++Builder™ 5.0
   
• Release 5.0  [Oct-09, 1999]
   
• MATH2 is now available for Delphi™ 5.0 (as part of the SDL Component Suite 5.0)
• cubic spline interpolation implemented (methods and properties CubicSpline, SplineNatural1, SplineNaturalN, SplineDerivY1, SplineDerivYN)
• multiple linear regression implemented (MultiLinreg)
• singular value decomposition implemented (SingValDecomp, SingValEquSolve)
• bug fixed in MeanDistanceKNN and FindNearestNeighbors which caused
• wrong results with Delphi™ 1 to 3 (but not Delphi™ 4)
   
• Release 1.8  [Mar-27, 1999]
   
• MATH2 now available for C++Builder™ 4.0
• TCurveFit now additionally stores the data entered to it
• properties DataX and DataY implemented
• method RemoveStatValue implemented
   
• Release 1.7   [Jul-23, 1998]
   
• MATH2 now available for Delphi™ 4.0
• statistical function moved to unit STATIS (Kolmogorov-Smirnov, WeibullDensity, LnGamma, LnBeta, LnBinomCoeff, BinomCoeff, nDistri, tDistri)
• agglomerative clustering implemented
   
• Release 1.6 (Apr-08, 1998)
   
• MATH2 is now available for all versions of Delphi™ (1.0, 2.0, 3.0), and for C++Builder™ (1.0 and 3.0)
• DCommon no longer needed
• Kolmogorov-Smirnov one-sample test statistic
• GetEigenSize implemented
• WeibullDensity implemented
• PolyFit implemented (basic code supplied by Kerry L. Davison - thanks Kerry !)
• calculation of Gamma function
• calculation of Beta function
• calculation of binomial coefficient
• exception ESDLMath2Error introduced
• Polynomial smoothing of data series (alg. Savitzky/Golay)
• Smoothed first derivative of a series of data points
   
• Release 1.5 (May-28, 1997)
  
 
• MATH2 is now available for all three versions of Delphi™ and for C++Builder™