The unit MATRIX offers some of the most important operations to manage and process two-dimensional real-valued and integer matrices. The object oriented approach of the unix MATRIX hides all the stuff dealing with array addressing and memory management. Thus the user may fully concentrate on his/her work. The unit MATRIX offers solutions for the following tasks:

• creation and management of matrices
• filling of matrices
• copying matrices
• matrix arithmetics
• determination of statistical parameters about the matrix elements
• inversion of a square matrix
• sorting of matrix elements
• LU decomposition and determinant

The unit MATRIX is part of the SDL Component Suite. More details can be found in the online help pages.

Tips, Tricks and Applications

Delphi Bits	Covariance of Samples and Populations	Why does the covariance matrix calculated by CalcCovar differ from the results obtained by Microsofts Excel(tm).
SDL TechNotes	Access Violation When Creating Matrix Objects	How to create a TMatrix instance in your program (without glueing a TMatrix component on your form).

 

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What's new:

• Release 10.7   [Aug-24, 2020]
   
  • TMat4D.LoadBinary now checks whether the file is too big for the 32-bit version
  • implemented TMat4D.CopyVectorToPixel and TMat4D.CopyPixelToVector
  • the LoadBinaryNoFmtCheck has been implemented to be able to load the old binary data format (which did not contain information on the numeric format)
  • the methods LoadBinary and SaveBinary have been extended to all four kinds of matrices (TMatrix, TIntMatrix, TMat3D and TMat4D)
  • the new methods RemoveRow and RemoveColumn delete specific columns or rows
  • the method Read4DLayer reads layer data from a binary TMat4D file
  • the method Read4DLayerAndAccumulate accumulates layer data obtained from binary TMat4D files
  • the new method TMat4DAccumulateLayer supports the accumulation of layers
  • the following methods of TMat4D have been converted to functions: AppendToBinaryFile, LoadBinary, ReadBinary, ReadLayer and SaveBinary
  • the new overloaded method TMat4D.FillLayer allows to fill a particular layer with differently distributed values
  • the method TMat4D.CopyPixelTo1DArray allows to copy a pixel of the 4D datacube
  • the methods TMatrix.Fill, TMatrix.FillRandomGauss and TMatrix.FillRandomUniform are now available in a second overloaded version
  • the method CalcHatMatrix calculates the hat matrix
  • implemented ExportAsASC and ImportASC
  • the classes TMatrix, TIntMatrix, TMat3D and TMat4D now provide public access to their internal data array if SDLPUBLICMAT is defined
  • added new overloaded versions of CopyFromArray and CopyToArray
  • added the method TMat3D.MeanVar
  
  
• Release 10.6   [Mar-09, 2018]
   
  • the following methods now support multi-processing to speed up calculations: TMatrix.Square, TMatrix.MeanOfLayersToMatrix, TMat4D.MinimumOfLayersToMatrix, TMat4D.MaximumOfLayersToMatrix, TMat4D.StdDevOfLayersToMatrix
  • the function TMat4D.CRCofData is now provided as a second overloaded version
  • the new procedure CopyArr3DLayerToArr2D copies a layer of a 3D array to a 2D array
  • the procedure CopyMatrixToArray copies a TMatrix to a 2D array
  • the procedure CopyArr3DLayerToMatrix copies a layer of a 3D array to a TMatrix
  • the methods TMatrix.CopyFromArray and TMatrix.CopyToArray copy matrix data from and to dynamic arrays
  • the methods TMat4D.CopyArrayToLayer, TMat4D.CopyLayerToArray, TMat4D.CopyTimeSlotToArray and TMat4D.CopyArrayToTimeSlot copy matrix data to and from dynamic arrays
  • the function Dichotomize compares the values of a matrix to a threshold
  • bug fix: TMatrix.Histogram created one bin less than required
  • bug fix: TIntMatrix.ExchangeRows addressed the wrong rows (offset by 1)
  • bug fix: TMat4D.CopyMat3DToTimeSlot used the default values of TMat4D instead of the source matrix if the indices were all zero
  • bug fix: TMat4D.Percentile returned a (wrong) zero quantile under certain circumstances
  
  
• Release 10.5   [Oct-10, 2016]
   
  • TMat4D.ReadBinary allows to read binary data without using memory
  • the new event OnReadElement provides elementwise feedback during reading a binary file
  • TMat4D.Transpose implemented
  • the methods TMat4D.CountValues and TMatrix.CountValues count values falling into an interval
  • the methods TMat4D.Resample and TMat4D.CRCofData now trigger the event OnPercentDone
  • the methods TMat3D.Fill and TMat4D.Fill now treat the special case of zeroing the data matrix
  • the speed of the method TMat4D.MeanOfLayersToMatrix has been improved considerably
  • TIntMatrix.SaveBinary, TIntMatrix.LoadBinary and TIntMatrix.OnPercentDone implemented
  • the new method TMat4D.SquaredSum calculates the sum of squares
  • the method TMat4D.ReadLayer allows to read a specific layer of a Mat4D matrix
  • the method CountMaskedZeros counts cells after applying a logical AND with a bitmask
  • the method TMat4D.Copy1DArrayToPixel copies a one-dimensional array into a pixel column
  • the method CholeskyDecomp decomposes a positive definite matrix into its Cholesky factor
  • bug fix: TMat4D.SaveBinary created an integer overflow for very large matrices (more than 2³¹ cells)
  
  
• Release 10.4   [Jun-02, 2015]
   
  • the methods QNormalizeColumns and QNormalizeRows normalize all columns/rows of a matrix to zero median and paticular quantile of 1.0
  • the method MultiplyTransposed performs a matrix multiplication using the transpose of the second matrix
  • the method CopyFrom is now available for TMat3D, as well
  • the method LoadFromFile now offers an auto-detection option
  • the new method DistanceOfObjects calculates the multivariate distance of rows
  • the methods MakeValidColRange, MakeValidRowRange, MakeValidLayerRange and MakeValidTSlotRange provide a means to check and correct array indices
  • the methods TMat4D.ConvertLinTo3DAddr and TMat4D.Lin3DAddr linearize 3D array indices
  • the method EdgeVector calculates various parameters along the edge of a matrix
  • the type declaration TEdgeOp specifies edge operations
  • the method EMult provides elementwise multiplication of matrices
  • the method CopyFromVec now provides an overloaded version to copy either row or column vectors
  • the new method Square calculates A'A (the square) of the matrix A
  • TMat4D has been optimized to reduce memory requirements for arrays with a low number of time slots
  • TMatrix.Percentile and TMat4D.Percentile offer now an overloaded version which is much faster for big data sets
  • TMat3D.MinMax implemented
  • TMatrix.MeanCenterColumns and TMatrix.MeanCenterRows now automatically adjust the size of the vector parameter "means"
  • the method MeanVec calculates the column or row means of a matrix
  • the method Multiply is now available in a second overloaded version working on vectors
  • the new methods TMat3D.CopyLayerToMatrix and TMat3D.CopyMatrixToLayer copy data between a layer and a two-dimensional matrix
  • TMatrix.Invert can now be aborted by setting AbortMathProc to TRUE
  
  
• Release 10.3   [Oct-06, 2014]
   
  • the new methods TMatrix.ResizeAndClear and TMat4D.ResizeAndClear both resize and clear the matrix in one step
  • TMat4D.Assign implemented
  • TMat4D.MinimumOfLayersToMatrix and TMat4D.MaximumOfLayersToMatrix retrieves the minimum and maximum of a range of layers of a 4D matrix, respectively
  • TMat4D.CopyFrom copies parts of another matrix into its own data area
  • TMat4D.CopyTimeSlotToMat3D copies part of a time slot into a 3D matrix
  • TMat4D.CopyMat3DToTimeSlot copies a 3D matrix into a particular time slot
  • TMat3D.Clone and TMat4D.Clone implemented
  • the method TMat4D.Resample allows to resample the data of the matrix
  • bug fix: ReadFromXMLStream did not adjust matrix size under certain conditions
  • bug fix: TMatrix.SkewKurtSample and TIntMatrix.SkewKurtSample caused an integer overflow for large matrices
  
  
• Release 10.2   [May-30, 2013]
   
  • the new method TMat4D.Percentile calculates percentiles of a 4-dimensional matrix
  • the new methods FillDiag (Matrix) and FillDiag (Mat4D) allow to set the diagonal of a matrix
  • the missing method Assign has been implemented
  • bug fix: TMat4D caused a memory leak
  
  
• Release 10.1   [Oct-29, 2012]
   
  • the new method TMatrix.Norm returns various matrix norms
  • new method TMat4D.FillLayer and TMat4D.Sum implemented
  • new methods TMatrix.LoadBinary, TMatrix.ReadBinaryHeader and TMatrix.SaveBinary support loading and saving matrices in binary format
  • the new method TMatrix.Correlate calculates the correlation coeffient of two matrices
  • the methods TMat4D.StdDevOfLayersToMatrix and TMat4D.MeanOfLayersToMatrix now provide a call to the MathFeedback
  • the new method MeanVar calculates mean and variance of a particular range of the matrix
  • the new method SAdd adds a scalar to the matrix
  • the new method CopyMatrixToLayer allows to copy the contents of a 2D matrix into a 4D layer
  • bug fix: missing overloaded version of TIntMatrix.LoadFromStream implemented
  
  
• Release 10.0   [Oct-4, 2011]
   
  • new class TMat4D allows to manage 4-dimensional hypercube matrices
  • matrix classes can now be set to zero dimensions
  • TMatrix.CopyFrom offers now an additional overloaded version to copy data from integer matrices (TIntMatrix).
  • the methods SaveToStream and LoadFromStream now support file streams, as well
  • new method TransposeAndMultiply allows to transpose and multiply in one step
  • the new methods FillRandomGauss and FillRandomUniform fill the matrix of type TMatrix, TIntMatrix and TMat3D with uniformly or normally distributed random numbers
  
  
• Release 9.7   [May-31, 2010]
   
  • new method CRCofData calculates the CRC over all matrix cells
  • new methods MirrorColumns and MirrorRows allow to mirror the matrix
  • new methods ExchangeRows and ExchangeColumns allow to exchange to rows or columns of a matrix
  • new function FindInSortedColumn searches a sorted column by a binary search
  • bug fix: depending on the data the calculation of the determinant resulted in a wrong sign (but correct absolute values) for matrices of even dimension (bug was introduced with release 9.51)
  • bug fix: sorting the matrix (both rows and columns) does no longer reduce the numeric precision to 12 significant digits
  
  
• Release 9.51   [Dec-01, 2008]
   
  • bug fix: methods Determinant and LUDecomposition now work correctly if first diagonal element is zero
  
  
• Release 9.5   [Oct-31, 2008]
   
  • new method Find searches for particular element in matrix
  • MeanCenterColumns and MeanCenterRows implemented
  • bug fix: methods Quartiles and Percentile calculate now more appropriate values for very small samples
  
  
• Release 9.0   [May-28, 2007]
   
  • the matrix inversion routine now works for matrices with very small values, too.
  
  
• Release 8.5   [Feb-18, 2006]
   
  • bug fix: method Percentile now calculates correct values (bug emerged only for less than 100 selected elements)
  
  
• Release 8.2   [Nov-03, 2004]
   
  • bug fix: method Transpose works now correctly
  
  
• Release 8.1   [Aug-29, 2004]
   
  • available for Delphi™ 8 for .NET
  
  
• Release 8.0   [Apr-15, 2004]
   
  • CalcDistMat now provides event OnCalcDistance if distance measure is user defined
  • new distance measure Dice coefficient
  
  
• Release 7.2   [Mar-23, 2003]
   
  • MATRIX is now part of MathPack
  • TMatrix, TIntMatrix and TMat3D are now components (no longer inherited from TObject)
  • properties NrOfRows, NrOfCols, NrOfLayers are no longer read-only and published
  • property DataID is now published
  • bug fix: Resize of TMat3D works now properly
  
  
• Release 7.0   [Sep-15, 2002]
   
  • available for Delphi™ 7.0
  • the unit is now CLX compatible
  • Percentile function implemented
  
  
• Release 6.5   [May-28, 2002]
   
  • available for C++Builder™ 6.0
  • new methods to export/import matrix data to/from XML files or streams: LoadFromXMLFile, ReadFromOpenXMLFile, ReadFromXMLStream, SaveAsXMLFile, WriteToOpenXMLFile, WriteToXMLStream
  • property DataID implemented
  • bug fix: sorting routine can now handle matrices with more than 65535 rows/columns
  
  
• Release 6.0  [Aug-06, 2001]
   
  • available for Delphi™ 6.0
  • new method SkewKurtSample of TMatrix and TIntMatrix implemented
  • methods GeometricMean and HarmonicMean implemented
  • bug fix: SkewKurt now calculates the skewness correctly
     
• Release 5.5   [Jun-09, 2000]
   
  • available for C++Builder™ 5.0
  • LoadFromStream and SaveToStream for TMatrix and TIntMatrix implemented
  • sparse Matrix implemented
     
• Release 5.0   [Oct-07, 1999]
   
  • MATRIX is now available for Delphi™ 5.0 (as part of the SDL Component Suite 5.0)
  • LoadFromFile of TMatrix and TIntMatrix extended
     
• Release 1.8   [Mar-28, 1999]
   
  • TMatrix & TIntMatrix have now OnSortExchange events
  • method Clone implemented
  • method Resize now does not execute if the new dimensions are equal to the old ones
  • method Trace implemented
  • property Elem is now default property
  • LU decomposition implemented
  • function Determinant implementedRelease 1.1 (Feb-12, 1997) :
  • new class TIntMatrix implemented
  • bug in method Destroy fixed, which resulted in occasional memory allocation problems
  • new methods: Add, Subtract, and SMult
     
• Release 1.7    [Aug-12, 1998]
   
  • MATRIX is now available for Delphi™ 4.0
  • Mat3D has now Resize method
  • bug fix: resize methods of TMatrix and TIntMatrix now function properly also in 16-bit mode
  • CalcDistMat (TMatrix) implemented
  • method Histogram implemented
     
• Release 1.6 (Feb-14, 1998):
   
  • new method Quartiles
  • bug fix: TMatrix and TIntMatrix are now classes of TObject
  • new event: OnChange (both TMatrix and TIntMatrix)
  • new method Change implemented
  • ESDLMatrixError replaces ELocompError
  • MATRIX is now available for all versions of Delphi™ (1.0, 2.0, 3.0), and for C++Builder™ (1.0 and 3.0)
  • TMat3D implemented
  • CopyRowToVec, CopyColToVec implemented
  • StandardizeColumns, and StandardizeRows implemented
  • bug in resize fixed: access violation for large matrices
  • create now initializes all elements to zero values
  • method Sum implemented
  • bug fixed which caused strange behavior for zero or negative array dimensions on create
     
• Release 1.5 (May-28, 1997)
   
  • bug in Resize fixed, which restricted 32-bit matrices to 64k
  • method Transpose implemented
  • MATRIX is now available for all three versions of Delphi™ and for C++Builder™