150 lines
4.4 KiB
PHP
150 lines
4.4 KiB
PHP
<?php
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/**
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* @package JAMA
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*
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* Cholesky decomposition class
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*
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* For a symmetric, positive definite matrix A, the Cholesky decomposition
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* is an lower triangular matrix L so that A = L*L'.
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*
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* If the matrix is not symmetric or positive definite, the constructor
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* returns a partial decomposition and sets an internal flag that may
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* be queried by the isSPD() method.
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*
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* @author Paul Meagher
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* @author Michael Bommarito
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* @version 1.2
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*/
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class CholeskyDecomposition {
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/**
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* Decomposition storage
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* @var array
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* @access private
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*/
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private $L = array();
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/**
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* Matrix row and column dimension
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* @var int
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* @access private
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*/
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private $m;
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/**
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* Symmetric positive definite flag
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* @var boolean
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* @access private
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*/
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private $isspd = true;
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/**
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* CholeskyDecomposition
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*
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* Class constructor - decomposes symmetric positive definite matrix
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* @param mixed Matrix square symmetric positive definite matrix
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*/
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public function __construct($A = null) {
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if ($A instanceof Matrix) {
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$this->L = $A->getArray();
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$this->m = $A->getRowDimension();
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for($i = 0; $i < $this->m; ++$i) {
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for($j = $i; $j < $this->m; ++$j) {
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for($sum = $this->L[$i][$j], $k = $i - 1; $k >= 0; --$k) {
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$sum -= $this->L[$i][$k] * $this->L[$j][$k];
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}
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if ($i == $j) {
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if ($sum >= 0) {
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$this->L[$i][$i] = sqrt($sum);
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} else {
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$this->isspd = false;
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}
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} else {
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if ($this->L[$i][$i] != 0) {
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$this->L[$j][$i] = $sum / $this->L[$i][$i];
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}
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}
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}
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for ($k = $i+1; $k < $this->m; ++$k) {
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$this->L[$i][$k] = 0.0;
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}
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}
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} else {
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throw new PHPExcel_Calculation_Exception(JAMAError(ArgumentTypeException));
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}
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} // function __construct()
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/**
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* Is the matrix symmetric and positive definite?
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*
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* @return boolean
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*/
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public function isSPD() {
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return $this->isspd;
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} // function isSPD()
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/**
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* getL
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*
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* Return triangular factor.
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* @return Matrix Lower triangular matrix
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*/
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public function getL() {
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return new Matrix($this->L);
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} // function getL()
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/**
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* Solve A*X = B
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*
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* @param $B Row-equal matrix
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* @return Matrix L * L' * X = B
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*/
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public function solve($B = null) {
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if ($B instanceof Matrix) {
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if ($B->getRowDimension() == $this->m) {
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if ($this->isspd) {
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$X = $B->getArrayCopy();
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$nx = $B->getColumnDimension();
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for ($k = 0; $k < $this->m; ++$k) {
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for ($i = $k + 1; $i < $this->m; ++$i) {
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for ($j = 0; $j < $nx; ++$j) {
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$X[$i][$j] -= $X[$k][$j] * $this->L[$i][$k];
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}
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}
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for ($j = 0; $j < $nx; ++$j) {
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$X[$k][$j] /= $this->L[$k][$k];
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}
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}
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for ($k = $this->m - 1; $k >= 0; --$k) {
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for ($j = 0; $j < $nx; ++$j) {
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$X[$k][$j] /= $this->L[$k][$k];
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}
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for ($i = 0; $i < $k; ++$i) {
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for ($j = 0; $j < $nx; ++$j) {
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$X[$i][$j] -= $X[$k][$j] * $this->L[$k][$i];
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}
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}
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}
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return new Matrix($X, $this->m, $nx);
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} else {
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throw new PHPExcel_Calculation_Exception(JAMAError(MatrixSPDException));
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}
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} else {
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throw new PHPExcel_Calculation_Exception(JAMAError(MatrixDimensionException));
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}
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} else {
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throw new PHPExcel_Calculation_Exception(JAMAError(ArgumentTypeException));
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}
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} // function solve()
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} // class CholeskyDecomposition
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