diff docs/modules/txt/Matrix.txt @ 0:4816e4a8ae95 draft default tip

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+NAME
+    Matrix
+
+SYNOPSIS
+    use Matrix;
+
+    use Matrix qw(:all);
+
+DESCRIPTION
+    Matrix class provides the following methods:
+
+    new, AddColumnValues, AddRowValues, Copy, GetColumnValues,
+    GetColumnValuesAsColumnMatrix, GetColumnValuesAsRowMatrix,
+    GetColumnValuesAsString, GetColumnValuesAsVector, GetDiagonalValues,
+    GetDiagonalValuesAsColumnMatrix, GetDiagonalValuesAsRowMatrix,
+    GetDiagonalValuesAsString, GetDiagonalValuesAsVector, GetDimension,
+    GetMatrixValuesReference, GetNumOfColumns, GetNumOfRows, GetRowValues,
+    GetRowValuesAsColumnMatrix, GetRowValuesAsRowMatrix,
+    GetRowValuesAsString, GetRowValuesAsVector, GetSize, GetValue,
+    IdentityMatrix, IsAntiSymmetric, IsBiDiagonal, IsDiagonal, IsIdentity,
+    IsLeftTriangular, IsLowerBiDiagonal, IsLowerTriangular,
+    IsLowerUniTriangular, IsMatrix, IsNegative, IsPositive,
+    IsRightTriangular, IsSkewSymmetric, IsSquare, IsStrictlyLowerTriangular,
+    IsStrictlyUpperTriangular, IsSymmetric, IsTriDiagonal, IsUnit,
+    IsUnitLowerTriangular, IsUnitUpperTriangular, IsUpperBiDiagonal,
+    IsUpperTriangular, IsUpperUniTriangular, NewFromColumns,
+    NewFromDiagonal, NewFromRows, One, SetAllValues, SetColumnValues,
+    SetDiagonalValues, SetMatrixPrintStyle, SetRowValues, SetValue,
+    SetValuePrintFormat, StringifyMatrix, Transpose, UnitMatrix, Zero,
+    ZeroMatrix
+
+    The following functions are available:
+
+    IsMatrix, IdentityMatrix, NewFromRows, NewFromColumns, NewFromDiagonal,
+    UnitMatrix, ZeroMatrix
+
+    The following operators are overloaded:
+
+        "" bool !
+        @{}
+        + - * / ** %
+        == != < <= > >=
+        neg
+        abs exp log sqrt cos sin
+
+    The matrix row and column indicies start from zero.
+
+  FUNCTIONS
+    new
+            $NewMatrix = $Matrix->new($NumOfRows, $NumOfCols);
+
+        Creates a new Matrix of size *NumOfRows x NumOfCol* and returns
+        NewMatrix object.
+
+    AddColumnValues
+            $Matrix->AddColumnValues(@Values);
+            $Matrix->AddColumnValues(\@Values);
+            $Matrix->AddColumnValues($VectorObject);
+            $Matrix->AddColumnValues("Value1 Value2 Value3 ...");
+
+        Adds column values to *Matrix* using an array, reference to an
+        array, another vector, or space delimited value string and returns
+        *Matrix*.
+
+    AddRowValues
+            $Matrix->AddRowValues(@Values);
+            $Matrix->AddRowValues(\@Values);
+            $Matrix->AddRowValues($VectorObject);
+            $Matrix->AddRowValues("Value1 Value2 Value3 ...");
+
+        Adds row values to *Matrix* using an array, reference to an array,
+        another vector, or space delimited value string and returns Matrix.
+
+    Copy
+            $NewMatrix = $Matrix->Copy();
+
+        Creates a copy of *Matrix* and returns NewMatrix.
+
+    GetColumnValues
+            @Values = $Matrix->GetColumnValues($ColIndex);
+            $ValueCount = $Matrix->GetColumnValues($ColIndex);
+
+        Returns an array containing column value specified using *ColIndex*
+        with column index starting at 0. In scalar context, number of column
+        values is returned.
+
+    GetColumnValuesAsColumnMatrix
+            $ColumnMatrix = $Matrix->GetColumnValuesAsColumnMatrix($ColIndex);
+
+        Returns a new ColumnMatrix containing column values specified using
+        *ColIndex* with column index starting at 0.
+
+    GetColumnValuesAsRowMatrix
+            $RowMatrix = $Matrix->GetColumnValuesAsRowMatrix($ColIndex);
+
+        Returns a new RowMatrix containing column values specified using
+        *ColIndex* with column index starting at 0.
+
+    GetColumnValuesAsString
+            $ColumnValuesString = $Matrix->GetColumnValuesAsString($ColIndex);
+
+        Returns a space delimited ColumnValuesString column values specified
+        using *ColIndex* with column index starting at 0.
+
+    GetColumnValuesAsVector
+            $ColumnVector = $Matrix->GetColumnValuesAsVector($ColIndex);
+
+        Returns a new ColumnVector column values specified using *RowIndex*
+        with column index starting at 0.
+
+    GetDiagonalValues
+            @Values = $Matrix->GetDiagonalValues();
+            $ValueCount = $Matrix->GetDiagonalValues();
+
+        Returns an array containing diagonal values. In scalar context,
+        number of diagonal values is returned.
+
+    GetDiagonalValuesAsColumnMatrix
+            $ColumnMatrix = $Matrix->GetDiagonalValuesAsColumnMatrix();
+
+        Returns a new ColumnMatrix containing diagonal values corresponding
+        to *Matrix*.
+
+    GetDiagonalValuesAsRowMatrix
+            $RowMatrix = $Matrix->GetDiagonalValuesAsRowMatrix();
+
+        Returns a new RowMatrix containing diagonal values corresponding to
+        *Matrix*.
+
+    GetDiagonalValuesAsString
+            $DiagonalValuesString = $Matrix->GetDiagonalValuesAsString();
+
+        Returns a space delimited DiagonalValuesString containing diagonal
+        values corresponding to *Matrix*.
+
+    GetDiagonalValuesAsVector
+            $DiagonalVector = $Matrix->GetDiagonalValuesAsVector();
+
+        Returns a new DiagonalVector containing diagonal values
+        corresponding to *Matrix*.
+
+    GetDimension
+            ($NumOfRows, $NumOfCols) = $Matrix->GetDimension();
+
+        Returns size of *Matrix*.
+
+    GetMatrixValuesReference
+            $ValuesRef = $Matrix->GetMatrixValuesReference();
+
+        Returns a reference to array containing rows and column values
+        corresponding to *Matrix*.
+
+    GetNumOfColumns
+            $NumOfCols = $Matrix->GetNumOfColumns();
+
+        Returns NumOfCols in *Matrix*.
+
+    GetNumOfRows
+            $NumOfRows = $Matrix->GetNumOfRows();
+
+        Returns NumOfRows in *Matrix*.
+
+    GetRowValues
+            @Values = $Matrix->GetRowValues($RowIndex);
+            $ValueCount = $Matrix->GetRowValues($RowIndex);
+
+        Returns an array containing row value specified using *RowIndex*
+        with row index starting at 0. In scalar context, number of row
+        values is returned.
+
+    GetRowValuesAsColumnMatrix
+            $ColumnMatrix = $Matrix->GetRowValuesAsColumnMatrix($RowIndex);
+
+        Returns a new ColumnMatrix containing row values specified using
+        *RowIndex* with column index starting at 0.
+
+    GetRowValuesAsRowMatrix
+            $RowMatrix = $Matrix->GetRowValuesAsRowMatrix($RowIndex);
+
+        Returns a new RowMatrix containing row values specified using
+        *RowIndex* with row index starting at 0.
+
+    GetRowValuesAsString
+            $RowValuesString = $Matrix->GetRowValuesAsString($RowIndex);
+
+        Returns a space delimited RowValuesString row values specified using
+        *RowIndex* with row index starting at 0.
+
+    GetRowValuesAsVector
+            $RowVector = $Matrix->GetColumnValuesAsVector($RowIndex);
+
+        Returns a new RowVector row values specified using *RowIndex* with
+        row index starting at 0.
+
+    GetSize
+            ($NumOfRows, $NumOfCols) = $Matrix->GetSize();
+
+        Returns size of *Matrix*.
+
+    GetValue
+            $Value = $Matrix->GetValue($RowIndex, $ColIndex, [$SkipIndexCheck]);
+
+        Returns Value of *Matrix* element specified using *RowIndex* and
+        *ColIndex* with indicies starting at 0 with optional validation of
+        specified index values.
+
+    IdentityMatrix
+            $NewIdentityMatrix = $Matrix->IdentityMatrix($NumOfRows, $NumOfCols);
+            $NewIdentityMatrix = Matrix::IdentityMatrix($NumOfRows, $NumOfCols);
+            $NewIdentityMatrix = Matrix::IdentityMatrix();
+
+        Creates a new IdentityMatrix of specified size *NumOfRows x
+        NumOfCol* or of size 3 x 3 and returns NewIdentityMatrix object.
+
+    IsAntiSymmetric
+            $Status = $Matrix->IsAntiSymmetric();
+
+        Returns 1 or 0 based on whether *Matrix* is an anti symmetric
+        matrix.
+
+        A matrix is an anti symmetric matrix:
+
+            . It's a square matrix
+            . Its elements are asymmetric with respect to main diagonal. In other words,
+              elements below the main diagonal are equal to the negative of elements above
+              the main diagonal.
+
+        Transpose of an anti symmetric matrix equals the negative of the
+        matrix.
+
+    IsBiDiagonal
+            $Status = $Matrix->IsBiDiagonal();
+
+        Returns 1 or 0 based on whether *Matrix* is upper or lower
+        bidiagonal matrix.
+
+    IsDiagonal
+            $Status = $Matrix->IsDiagonal();
+
+        Returns 1 or 0 based on whether *Matrix* is a diagonal matrix.
+
+        A matrix is a diagonal matrix:
+
+            . It's a square matrix
+            . All its off-diagonal elements are zeros and its diagonal elements may or may not
+              be zeros
+
+    IsIdentity
+            $Status = $Matrix->IsIdentity();
+
+        Returns 1 or 0 based on whether *Matrix* is an identity matrix.
+
+    IsLeftTriangular
+            $Status = $Matrix->IsLeftTriangular();
+
+        Returns 1 or 0 based on whether *Matrix* is a left or lower matrix.
+
+        A matrix is a left triangular matrix:
+
+            . It's a square matrix
+            . All its entries above the main diagonal are zero
+
+    IsLowerBiDiagonal
+            $Status = $Matrix->IsLowerBiDiagonal();
+
+        Returns 1 or 0 based on whether *Matrix* is a lower bidiagonal
+        matrix.
+
+        A matrix is a lower bidiagonal matrix:
+
+            . It's a square matrix
+            . All its main diagonal and lower diagonal elements are non-zeros and all its
+              other elements are zeros
+
+    IsLowerTriangular
+            $Status = $Matrix->IsLowerTriangular();
+
+        Returns 1 or 0 based on whether *Matrix* is a left or lower
+        triangular matrix.
+
+        A matrix is a lower triangular matrix:
+
+            . It's a square matrix
+            . All its entries above the main diagonal are zero
+
+    IsLowerUniTriangular
+            $Status = $Matrix->IsLowerUniTriangular();
+
+        Returns 1 or 0 based on whether *Matrix* is a lower triangular
+        matrix.
+
+    IsMatrix
+            $Status = Matrix::IsMatrix($Object);
+
+        Returns 1 or 0 based on whether *Object* is a Matrix object.
+
+    IsNegative
+            $Status = $Matrix->IsNegative();
+
+        Returns 1 or 0 based on whether *Matrix* is a negative matrix
+        containing only values less than or equal to zero.
+
+    IsPositive
+            $Status = $Matrix->IsPositive();
+
+        Returns 1 or 0 based on whether *Matrix* is a negative matrix
+        containing only values greater than or equal to zero.
+
+    IsRightTriangular
+            $Status = $Matrix->IsRightTriangular();
+
+        Returns 1 or 0 based on whether *Matrix* is a right or upper
+        triangular matrix.
+
+    IsSkewSymmetric
+            $Status = $Matrix->IsSkewSymmetric();
+
+        Returns 1 or 0 based on whether *Matrix* is a skew or anti symmetric
+        matrix.
+
+    IsSquare
+            $Status = $Matrix->IsSquare();
+
+        Returns 1 or 0 based on whether *Matrix* is a square matrix
+        containing equal number of rows and columns.
+
+    IsStrictlyLowerTriangular
+            $Status = $Matrix->IsStrictlyLowerTriangular();
+
+        Returns 1 or 0 based on whether *Matrix* is a strictly lower
+        triangular matrix.
+
+        A matrix is a strictly lower triangular matrix:
+
+            . It's a square matrix
+            . All its entries on and above the main diagonal are zero
+
+    IsStrictlyUpperTriangular
+            $Status = $Matrix->IsStrictlyUpperTriangular();
+
+        Returns 1 or 0 based on whether *Matrix* is a strictly upper
+        triangular matrix.
+
+        A matrix is a strictly upper triangular matrix:
+
+            . It's a square matrix
+            . All its entries on and below the main diagonal are zero
+
+    IsSymmetric
+            $Status = $Matrix->IsSymmetric();
+
+        Returns 1 or 0 based on whether *Matrix* is a symmetric matrix.
+
+        A matrix is a symmetric matrix:
+
+            . It's a square matrix
+            . Its elements are symmetric with respect to main diagonal. In other words,
+              elements below the main diagonal are equal to the elements above the main
+              diagonal.
+
+        Transpose of a symmetric matrix equals the matrix itself.
+
+    IsTriDiagonal
+            $Status = $Matrix->IsTriDiagonal();
+
+        Returns 1 or 0 based on whether *Matrix* is a tridiagonal matrix.
+
+        A matrix is a tribidiagonal matrix:
+
+            . It's a square matrix
+            . All its main diagonal, upper diagonal, and lower diagonal elements are non-zeros and all its
+              other elements are zeros
+
+    IsUnit
+            $Status = $Matrix->IsUnit();
+
+        Returns 1 or 0 based on whether *Matrix* is a unit matrix.
+
+        A matrix is a unit matrix:
+
+            . It's a square matrix
+            . All its diagonal elements are ones and its off-diagonal elements are zeros
+
+    IsUnitLowerTriangular
+            $Status = $Matrix->IsUnitLowerTriangular();
+
+        Returns 1 or 0 based on whether *Matrix* is an unit lower triangular
+        matrix.
+
+        A matrix is an unit lower triangular matrix:
+
+            . It's a square matrix
+            . All its entries main diagonal are one
+            . All its entries above the main diagonal are zero
+
+    IsUnitUpperTriangular
+            $Status = $Matrix->IsUnitUpperTriangular();
+
+        Returns 1 or 0 based on whether *Matrix* is an unit upper triangular
+        matrix.
+
+        A matrix is an unit upper triangular matrix:
+
+            . It's a square matrix
+            . All its entries main diagonal are one
+            . All its entries below the main diagonal are zero
+
+    IsUpperBiDiagonal
+            $Status = $Matrix->IsUpperBiDiagonal();
+
+        Returns 1 or 0 based on whether *Matrix* is an upper bidiagonal
+        matrix.
+
+        A matrix is an upper bidiagonal matrix:
+
+            . It's a square matrix
+            . All its main diagonal and upper diagonal elements are non-zeros and all its
+              other elements are zeros
+
+    IsUpperTriangular
+            $Status = $Matrix->IsUpperTriangular();
+
+        Returns 1 or 0 based on whether *Matrix* is a right or upper
+        triangular matrix.
+
+        A matrix is an upper triangular matrix:
+
+            . It's a square matrix
+            . All its entries below the main diagonal are zero
+
+    IsUpperUniTriangular
+            $Status = $Matrix->IsUpperUniTriangular();
+
+        Returns 1 or 0 based on whether *Matrix* is a right or upper
+        triangular matrix.
+
+    NewFromColumns
+            $NewMatrix = Matrix::NewFromColumns($Col1Vector, $Col2Vector, ...);
+            $NewMatrix = Matrix::NewFromColumns($Col1ValuesRef, $Col2ValuesRef, ...);
+            $NewMatrix = Matrix::NewFromColumns("Val1 Val2 ...", "Val1 Val2", ...);
+
+            $NewMatrix = $Matrix->NewFromColumns($Col1Vector, $Col2Vector, ...);
+            $NewMatrix = $Matrix->NewFromColumns($Col1ValuesRef, $Col2ValuesRef, ...);
+            $NewMatrix = $Matrix->NewFromColumns("Val1 Val2 ...", "Val1 Val2", ...);
+
+        Creates a new Matrix using specified column values and returns
+        NewMatrix object.
+
+        The column values can be specified in one of the following formats:
+
+            . List of vector objects
+            . References to list of values
+            . List of strings containing columns values delimited by space
+
+        Each column must contain the same number of values.
+
+    NewFromDiagonal
+            $NewMatrix = Matrix::NewFromDiagonal($DiagonalVector);
+            $NewMatrix = Matrix::NewFromDiagonal($DiagonalValuesRef);
+            $NewMatrix = Matrix::NewFromDiagonal("Val1 Val2 ...");
+
+            $NewMatrix = Matrix->NewFromDiagonal($DiagonalVector);
+            $NewMatrix = Matrix->NewFromDiagonal($DiagonalValuesRef);
+            $NewMatrix = Matrix->NewFromDiagonal("Val1 Val2 ...");
+
+        Creates a new Matrix using specified diagonal values and returns
+        NewMatrix object.
+
+        The column values can be specified in one of the following formats:
+
+            . A vector object
+            . Reference to list of values
+            . Strings containing diagonal values delimited by space
+
+    NewFromRows
+            $NewMatrix = Matrix::NewFromRows($Row1Vector, $RowVector, ...);
+            $NewMatrix = Matrix::NewFromRows($Row1ValuesRef, $Row2ValuesRef, ...);
+            $NewMatrix = Matrix::NewFromRows("Val1 Val2 ...", "Val1 Val2", ...);
+
+            $NewMatrix = $Matrix->NewFromRows($Row1Vector, $Row2Vector, ...);
+            $NewMatrix = $Matrix->NewFromRows($Row1ValuesRef, $Row2ValuesRef, ...);
+            $NewMatrix = $Matrix->NewFromRows("Val1 Val2 ...", "Val1 Val2", ...);
+
+        Creates a new Matrix using specified row values and returns
+        NewMatrix object.
+
+        The row values can be specified in one of the following formats:
+
+            . List of vector objects
+            . References to list of values
+            . List of strings containing columns values delimited by space
+
+        Each row must contain the same number of values.
+
+    One
+            $Matrix->One();
+
+        Sets values of all *Matrix* elements to 1 and returns *Matrix*.
+
+    SetAllValues
+            $Matrix->SetAllValues($Value);
+
+        Sets values of all *Matrix* elements to specified *Value* and
+        returns *Matrix*.
+
+    SetColumnValues
+            $Matrix->SetColumnValues($ColIndex, @Values);
+            $Matrix->SetColumnValues($ColIndex, \@Values);
+            $Matrix->SetColumnValues($ColIndex, $VectorObject);
+            $Matrix->SetColumnValues($ColIndex, "Value1 Value2 Value3 ...");
+
+        Sets column values of a specified *ColIndex* of *Matrix* using an
+        array, reference to an array, another vector, or space delimited
+        value string and returns *Matrix*.
+
+    SetDiagonalValues
+            $Matrix->SetDiagonalValues(@Values);
+            $Matrix->SetDiagonalValues(\@Values);
+            $Matrix->SetDiagonalValues($VectorObject);
+            $Matrix->SetDiagonalValues("Value1 Value2 Value3 ...");
+
+        Sets values of the diagonal in square *Matrix* and returns *Matrix*.
+
+    SetMatrixPrintStyle
+            $Matrix->SetMatrixPrintStyle($MatrixStyle);
+            $Matrix::SetMatrixPrintStyle($MatrixStyle);
+
+        Sets print style for matrix rows for an individual object or the
+        whole class during StringifyMatrix operation. Possible *MatrixStyle*
+        values: *AllRowsInOneLine, OneRowPerLine*. Default:
+        *AllRowsInOneLine*.
+
+    SetRowValues
+            $Matrix->SetRowValues($ColIndex, @Values);
+            $Matrix->SetRowValues($ColIndex, \@Values);
+            $Matrix->SetRowValues($ColIndex, $VectorObjext);
+            $Matrix->SetRowValues($ColIndex, "Value1 Value2 Value3 ...");
+
+        Sets row values of a specified *RowIndex* of *Matrix* using an
+        array, reference to an array, another vector, or space delimited
+        value string and returns *Matrix*.
+
+    SetValue
+            $Matrix->SetValue($RowIndex, $ColIndex, $Value, [$SkipIndexCheck]);
+
+        Sets Value of *Matrix* element specified using *RowIndex* and
+        *ColIndex* with indicies starting at 0 with optional validation of
+        specified index values and return *Matrix*.
+
+    SetValuePrintFormat
+            $Matrix->SetValuePrintFormat($ValueFormat);
+            $Matrix::SetValuePrintFormat($ValueFormat);
+
+        Sets value print format for an individual object or the whole class
+        during StringifyMatrix operation and returns *Matrix*.
+
+    StringifyMatrix
+            $String = $Matrix->StringifyMatrix();
+
+        Returns a string containing information about *Matrix* object.
+
+    Transpose
+            $Matrix->Transpose();
+
+        Transposes *Matrix* by swaping rows with columns and returns
+        *Matrix*.
+
+    UnitMatrix
+            $NewUnitMatrix = $Matrix::UnitMatrix($NumOfRows, $NumOfCols);
+            $NewUnitMatrix = $Matrix::UnitMatrix();
+            $NewUnitMatrix = $Matrix->UnitMatrix($NumOfRows, $NumOfCols);
+
+        Creates a new UnitMatrix of specified size *NumOfRows x NumOfCol* or
+        of size 3 x 3 and returns NewUnitMatrix object.
+
+    Zero
+            $Matrix->Zero();
+
+        Sets values of all *Matrix* elements to 0 and returns *Matrix*.
+
+    ZeroMatrix
+            $NewZeroMatrix = $Matrix::ZeroMatrix($NumOfRows, $NumOfCols);
+            $NewZeroMatrix = $Matrix::ZeroMatrix();
+            $NewZeroMatrix = $Matrix->ZeroMatrix($NumOfRows, $NumOfCols);
+
+        Creates a new ZeroMatrix of specified size *NumOfRows x NumOfCol* or
+        of size 3 x 3 and returns NewZeroMatrix object.
+
+AUTHOR
+    Manish Sud <[e-mail]>
+
+SEE ALSO
+    Vector.pm
+
+COPYRIGHT
+    Copyright (C) 2015 Manish Sud. All rights reserved.
+
+    This file is part of MayaChemTools.
+
+    MayaChemTools is free software; you can redistribute it and/or modify it
+    under the terms of the GNU Lesser General Public License as published by
+    the Free Software Foundation; either version 3 of the License, or (at
+    your option) any later version.
+