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Diffstat (limited to 'admin/survey/excel/PHPExcel/Shared/JAMA/LUDecomposition.php')
| -rw-r--r-- | admin/survey/excel/PHPExcel/Shared/JAMA/LUDecomposition.php | 258 |
1 files changed, 258 insertions, 0 deletions
diff --git a/admin/survey/excel/PHPExcel/Shared/JAMA/LUDecomposition.php b/admin/survey/excel/PHPExcel/Shared/JAMA/LUDecomposition.php new file mode 100644 index 0000000..98e918c --- /dev/null +++ b/admin/survey/excel/PHPExcel/Shared/JAMA/LUDecomposition.php @@ -0,0 +1,258 @@ +<?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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