source: sourcecode/application/libraries/PHPExcel/Shared/JAMA/CholeskyDecomposition.php @ 1

<?php
/**
 *      @package JAMA
 *
 *      Cholesky decomposition class
 *
 *      For a symmetric, positive definite matrix A, the Cholesky decomposition
 *      is an lower triangular matrix L so that A = L*L'.
 *
 *      If the matrix is not symmetric or positive definite, the constructor
 *      returns a partial decomposition and sets an internal flag that may
 *      be queried by the isSPD() method.
 *
 *      @author Paul Meagher
 *      @author Michael Bommarito
 *      @version 1.2
 */
class CholeskyDecomposition {

        /**
         *      Decomposition storage
         *      @var array
         *      @access private
         */
        private $L = array();

        /**
         *      Matrix row and column dimension
         *      @var int
         *      @access private
         */
        private $m;

        /**
         *      Symmetric positive definite flag
         *      @var boolean
         *      @access private
         */
        private $isspd = true;


        /**
         *      CholeskyDecomposition
         *
         *      Class constructor - decomposes symmetric positive definite matrix
         *      @param mixed Matrix square symmetric positive definite matrix
         */
        public function __construct($A = null) {
                if ($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 PHPExcel_Calculation_Exception(JAMAError(ArgumentTypeException));
                }
        }       //      function __construct()


        /**
         *      Is the matrix symmetric and positive definite?
         *
         *      @return boolean
         */
        public function isSPD() {
                return $this->isspd;
        }       //      function isSPD()


        /**
         *      getL
         *
         *      Return triangular factor.
         *      @return Matrix Lower triangular matrix
         */
        public function getL() {
                return new Matrix($this->L);
        }       //      function getL()


        /**
         *      Solve A*X = B
         *
         *      @param $B Row-equal matrix
         *      @return Matrix L * L' * X = B
         */
        public function solve($B = null) {
                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 PHPExcel_Calculation_Exception(JAMAError(MatrixSPDException));
                                }
                        } else {
                                throw new PHPExcel_Calculation_Exception(JAMAError(MatrixDimensionException));
                        }
                } else {
                        throw new PHPExcel_Calculation_Exception(JAMAError(ArgumentTypeException));
                }
        }       //      function solve()

}       //      class CholeskyDecomposition