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-<?php
-/**
- * @package JAMA
- *
- * For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n
- * unit lower triangular matrix L, an n-by-n upper triangular matrix U,
- * and a permutation vector piv of length m so that A(piv,:) = L*U.
- * If m < n, then L is m-by-m and U is m-by-n.
- *
- * The LU decompostion with pivoting always exists, even if the matrix is
- * singular, so the constructor will never fail. The primary use of the
- * LU decomposition is in the solution of square systems of simultaneous
- * linear equations. This will fail if isNonsingular() returns false.
- *
- * @author Paul Meagher
- * @author Bartosz Matosiuk
- * @author Michael Bommarito
- * @version 1.1
- * @license PHP v3.0
- */
-class PHPExcel_Shared_JAMA_LUDecomposition {
-
- const MatrixSingularException = "Can only perform operation on singular matrix.";
- const MatrixSquareException = "Mismatched Row dimension";
-
- /**
- * Decomposition storage
- * @var array
- */
- private $LU = array();
-
- /**
- * Row dimension.
- * @var int
- */
- private $m;
-
- /**
- * Column dimension.
- * @var int
- */
- private $n;
-
- /**
- * Pivot sign.
- * @var int
- */
- private $pivsign;
-
- /**
- * Internal storage of pivot vector.
- * @var array
- */
- private $piv = array();
-
-
- /**
- * LU Decomposition constructor.
- *
- * @param $A Rectangular matrix
- * @return Structure to access L, U and piv.
- */
- public function __construct($A) {
- if ($A instanceof PHPExcel_Shared_JAMA_Matrix) {
- // Use a "left-looking", dot-product, Crout/Doolittle algorithm.
- $this->LU = $A->getArray();
- $this->m = $A->getRowDimension();
- $this->n = $A->getColumnDimension();
- for ($i = 0; $i < $this->m; ++$i) {
- $this->piv[$i] = $i;
- }
- $this->pivsign = 1;
- $LUrowi = $LUcolj = array();
-
- // Outer loop.
- for ($j = 0; $j < $this->n; ++$j) {
- // Make a copy of the j-th column to localize references.
- for ($i = 0; $i < $this->m; ++$i) {
- $LUcolj[$i] = &$this->LU[$i][$j];
- }
- // Apply previous transformations.
- for ($i = 0; $i < $this->m; ++$i) {
- $LUrowi = $this->LU[$i];
- // Most of the time is spent in the following dot product.
- $kmax = min($i,$j);
- $s = 0.0;
- for ($k = 0; $k < $kmax; ++$k) {
- $s += $LUrowi[$k] * $LUcolj[$k];
- }
- $LUrowi[$j] = $LUcolj[$i] -= $s;
- }
- // Find pivot and exchange if necessary.
- $p = $j;
- for ($i = $j+1; $i < $this->m; ++$i) {
- if (abs($LUcolj[$i]) > abs($LUcolj[$p])) {
- $p = $i;
- }
- }
- if ($p != $j) {
- for ($k = 0; $k < $this->n; ++$k) {
- $t = $this->LU[$p][$k];
- $this->LU[$p][$k] = $this->LU[$j][$k];
- $this->LU[$j][$k] = $t;
- }
- $k = $this->piv[$p];
- $this->piv[$p] = $this->piv[$j];
- $this->piv[$j] = $k;
- $this->pivsign = $this->pivsign * -1;
- }
- // Compute multipliers.
- if (($j < $this->m) && ($this->LU[$j][$j] != 0.0)) {
- for ($i = $j+1; $i < $this->m; ++$i) {
- $this->LU[$i][$j] /= $this->LU[$j][$j];
- }
- }
- }
- } else {
- throw new Exception(PHPExcel_Shared_JAMA_Matrix::ArgumentTypeException);
- }
- } // function __construct()
-
-
- /**
- * Get lower triangular factor.
- *
- * @return array Lower triangular factor
- */
- public function getL() {
- for ($i = 0; $i < $this->m; ++$i) {
- for ($j = 0; $j < $this->n; ++$j) {
- if ($i > $j) {
- $L[$i][$j] = $this->LU[$i][$j];
- } elseif ($i == $j) {
- $L[$i][$j] = 1.0;
- } else {
- $L[$i][$j] = 0.0;
- }
- }
- }
- return new PHPExcel_Shared_JAMA_Matrix($L);
- } // function getL()
-
-
- /**
- * Get upper triangular factor.
- *
- * @return array Upper triangular factor
- */
- public function getU() {
- for ($i = 0; $i < $this->n; ++$i) {
- for ($j = 0; $j < $this->n; ++$j) {
- if ($i <= $j) {
- $U[$i][$j] = $this->LU[$i][$j];
- } else {
- $U[$i][$j] = 0.0;
- }
- }
- }
- return new PHPExcel_Shared_JAMA_Matrix($U);
- } // function getU()
-
-
- /**
- * Return pivot permutation vector.
- *
- * @return array Pivot vector
- */
- public function getPivot() {
- return $this->piv;
- } // function getPivot()
-
-
- /**
- * Alias for getPivot
- *
- * @see getPivot
- */
- public function getDoublePivot() {
- return $this->getPivot();
- } // function getDoublePivot()
-
-
- /**
- * Is the matrix nonsingular?
- *
- * @return true if U, and hence A, is nonsingular.
- */
- public function isNonsingular() {
- for ($j = 0; $j < $this->n; ++$j) {
- if ($this->LU[$j][$j] == 0) {
- return false;
- }
- }
- return true;
- } // function isNonsingular()
-
-
- /**
- * Count determinants
- *
- * @return array d matrix deterninat
- */
- public function det() {
- if ($this->m == $this->n) {
- $d = $this->pivsign;
- for ($j = 0; $j < $this->n; ++$j) {
- $d *= $this->LU[$j][$j];
- }
- return $d;
- } else {
- throw new Exception(PHPExcel_Shared_JAMA_Matrix::MatrixDimensionException);
- }
- } // function det()
-
-
- /**
- * Solve A*X = B
- *
- * @param $B A Matrix with as many rows as A and any number of columns.
- * @return X so that L*U*X = B(piv,:)
- * @exception IllegalArgumentException Matrix row dimensions must agree.
- * @exception RuntimeException Matrix is singular.
- */
- public function solve($B) {
- if ($B->getRowDimension() == $this->m) {
- if ($this->isNonsingular()) {
- // Copy right hand side with pivoting
- $nx = $B->getColumnDimension();
- $X = $B->getMatrix($this->piv, 0, $nx-1);
- // Solve L*Y = B(piv,:)
- for ($k = 0; $k < $this->n; ++$k) {
- for ($i = $k+1; $i < $this->n; ++$i) {
- for ($j = 0; $j < $nx; ++$j) {
- $X->A[$i][$j] -= $X->A[$k][$j] * $this->LU[$i][$k];
- }
- }
- }
- // Solve U*X = Y;
- for ($k = $this->n-1; $k >= 0; --$k) {
- for ($j = 0; $j < $nx; ++$j) {
- $X->A[$k][$j] /= $this->LU[$k][$k];
- }
- for ($i = 0; $i < $k; ++$i) {
- for ($j = 0; $j < $nx; ++$j) {
- $X->A[$i][$j] -= $X->A[$k][$j] * $this->LU[$i][$k];
- }
- }
- }
- return $X;
- } else {
- throw new Exception(self::MatrixSingularException);
- }
- } else {
- throw new Exception(self::MatrixSquareException);
- }
- } // function solve()
-
-} // class PHPExcel_Shared_JAMA_LUDecomposition
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