CholeskyDecomposition Class Reference

Collaboration diagram for CholeskyDecomposition:

Public Member Functions
	__construct ($A=null)
	CholeskyDecomposition.
	isSPD ()
	Is the matrix symmetric and positive definite?
	getL ()
	getL
	solve ($B=null)
	Solve A*X = B.

Private Attributes
	$L = array()
	$m
	$isspd = true

Detailed Description

Definition at line 18 of file CholeskyDecomposition.php.

Constructor & Destructor Documentation

CholeskyDecomposition::__construct

(

$A = null

)

CholeskyDecomposition.

Class constructor - decomposes symmetric positive definite matrix

Parameters

mixed

Matrix square symmetric positive definite matrix

Definition at line 48 of file CholeskyDecomposition.php.

References $m, ArgumentTypeException, and JAMAError().

                                               {
                if ($A instanceof Matrix) {
                        $this->L = $A->getArray();
                        $this->m = $A->getRowDimension();

                        for($i = 0; $i < $this->m; ++$i) {
                                for($j = $i; $j < $this->m; ++$j) {
                                        for($sum = $this->L[$i][$j], $k = $i - 1; $k >= 0; --$k) {
                                                $sum -= $this->L[$i][$k] * $this->L[$j][$k];
                                        }
                                        if ($i == $j) {
                                                if ($sum >= 0) {
                                                        $this->L[$i][$i] = sqrt($sum);
                                                } else {
                                                        $this->isspd = false;
                                                }
                                        } else {
                                                if ($this->L[$i][$i] != 0) {
                                                        $this->L[$j][$i] = $sum / $this->L[$i][$i];
                                                }
                                        }
                                }

                                for ($k = $i+1; $k < $this->m; ++$k) {
                                        $this->L[$i][$k] = 0.0;
                                }
                        }
                } else {
                        throw new Exception(JAMAError(ArgumentTypeException));
                }
        }       //      function __construct()

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Member Function Documentation

CholeskyDecomposition::getL

(

)

getL

Return triangular factor.

Returns

Matrix Lower triangular matrix

Definition at line 97 of file CholeskyDecomposition.php.

                               {
                return new Matrix($this->L);
        }       //      function getL()

CholeskyDecomposition::isSPD

(

)

Is the matrix symmetric and positive definite?

Returns

boolean

Definition at line 86 of file CholeskyDecomposition.php.

References $isspd.

                                {
                return $this->isspd;
        }       //      function isSPD()

CholeskyDecomposition::solve

(

$B = null

)

Solve A*X = B.

Parameters

$B	Row-equal matrix

Returns

Matrix L * L' * X = B

Definition at line 108 of file CholeskyDecomposition.php.

References $m, $X, ArgumentTypeException, JAMAError(), MatrixDimensionException, and MatrixSPDException.

                                         {
                if ($B instanceof Matrix) {
                        if ($B->getRowDimension() == $this->m) {
                                if ($this->isspd) {
                                        $X  = $B->getArrayCopy();
                                        $nx = $B->getColumnDimension();

                                        for ($k = 0; $k < $this->m; ++$k) {
                                                for ($i = $k + 1; $i < $this->m; ++$i) {
                                                        for ($j = 0; $j < $nx; ++$j) {
                                                                $X[$i][$j] -= $X[$k][$j] * $this->L[$i][$k];
                                                        }
                                                }
                                                for ($j = 0; $j < $nx; ++$j) {
                                                        $X[$k][$j] /= $this->L[$k][$k];
                                                }
                                        }

                                        for ($k = $this->m - 1; $k >= 0; --$k) {
                                                for ($j = 0; $j < $nx; ++$j) {
                                                        $X[$k][$j] /= $this->L[$k][$k];
                                                }
                                                for ($i = 0; $i < $k; ++$i) {
                                                        for ($j = 0; $j < $nx; ++$j) {
                                                                $X[$i][$j] -= $X[$k][$j] * $this->L[$k][$i];
                                                        }
                                                }
                                        }

                                        return new Matrix($X, $this->m, $nx);
                                } else {
                                        throw new Exception(JAMAError(MatrixSPDException));
                                }
                        } else {
                                throw new Exception(JAMAError(MatrixDimensionException));
                        }
                } else {
                        throw new Exception(JAMAError(ArgumentTypeException));
                }
        }       //      function solve()

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Field Documentation

CholeskyDecomposition::$isspd = true

private

Definition at line 39 of file CholeskyDecomposition.php.

Referenced by isSPD().

CholeskyDecomposition::$L = array()

private

Definition at line 25 of file CholeskyDecomposition.php.

CholeskyDecomposition::$m

private

Definition at line 32 of file CholeskyDecomposition.php.

Referenced by __construct(), and solve().

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The documentation for this class was generated from the following file:

• Services/Excel/classes/PHPExcel/Shared/JAMA/CholeskyDecomposition.php