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Diffstat (limited to 'admin/survey/excel/PHPExcel/Shared/JAMA/QRDecomposition.php')
| -rw-r--r-- | admin/survey/excel/PHPExcel/Shared/JAMA/QRDecomposition.php | 234 |
1 files changed, 0 insertions, 234 deletions
diff --git a/admin/survey/excel/PHPExcel/Shared/JAMA/QRDecomposition.php b/admin/survey/excel/PHPExcel/Shared/JAMA/QRDecomposition.php deleted file mode 100644 index 4492fa5..0000000 --- a/admin/survey/excel/PHPExcel/Shared/JAMA/QRDecomposition.php +++ /dev/null @@ -1,234 +0,0 @@ -<?php
-/**
- * @package JAMA
- *
- * For an m-by-n matrix A with m >= n, the QR decomposition is an m-by-n
- * orthogonal matrix Q and an n-by-n upper triangular matrix R so that
- * A = Q*R.
- *
- * The QR decompostion always exists, even if the matrix does not have
- * full rank, so the constructor will never fail. The primary use of the
- * QR decomposition is in the least squares solution of nonsquare systems
- * of simultaneous linear equations. This will fail if isFullRank()
- * returns false.
- *
- * @author Paul Meagher
- * @license PHP v3.0
- * @version 1.1
- */
-class PHPExcel_Shared_JAMA_QRDecomposition {
-
- const MatrixRankException = "Can only perform operation on full-rank matrix.";
-
- /**
- * Array for internal storage of decomposition.
- * @var array
- */
- private $QR = array();
-
- /**
- * Row dimension.
- * @var integer
- */
- private $m;
-
- /**
- * Column dimension.
- * @var integer
- */
- private $n;
-
- /**
- * Array for internal storage of diagonal of R.
- * @var array
- */
- private $Rdiag = array();
-
-
- /**
- * QR Decomposition computed by Householder reflections.
- *
- * @param matrix $A Rectangular matrix
- * @return Structure to access R and the Householder vectors and compute Q.
- */
- public function __construct($A) {
- if($A instanceof PHPExcel_Shared_JAMA_Matrix) {
- // Initialize.
- $this->QR = $A->getArrayCopy();
- $this->m = $A->getRowDimension();
- $this->n = $A->getColumnDimension();
- // Main loop.
- for ($k = 0; $k < $this->n; ++$k) {
- // Compute 2-norm of k-th column without under/overflow.
- $nrm = 0.0;
- for ($i = $k; $i < $this->m; ++$i) {
- $nrm = hypo($nrm, $this->QR[$i][$k]);
- }
- if ($nrm != 0.0) {
- // Form k-th Householder vector.
- if ($this->QR[$k][$k] < 0) {
- $nrm = -$nrm;
- }
- for ($i = $k; $i < $this->m; ++$i) {
- $this->QR[$i][$k] /= $nrm;
- }
- $this->QR[$k][$k] += 1.0;
- // Apply transformation to remaining columns.
- for ($j = $k+1; $j < $this->n; ++$j) {
- $s = 0.0;
- for ($i = $k; $i < $this->m; ++$i) {
- $s += $this->QR[$i][$k] * $this->QR[$i][$j];
- }
- $s = -$s/$this->QR[$k][$k];
- for ($i = $k; $i < $this->m; ++$i) {
- $this->QR[$i][$j] += $s * $this->QR[$i][$k];
- }
- }
- }
- $this->Rdiag[$k] = -$nrm;
- }
- } else {
- throw new Exception(PHPExcel_Shared_JAMA_Matrix::ArgumentTypeException);
- }
- } // function __construct()
-
-
- /**
- * Is the matrix full rank?
- *
- * @return boolean true if R, and hence A, has full rank, else false.
- */
- public function isFullRank() {
- for ($j = 0; $j < $this->n; ++$j) {
- if ($this->Rdiag[$j] == 0) {
- return false;
- }
- }
- return true;
- } // function isFullRank()
-
-
- /**
- * Return the Householder vectors
- *
- * @return Matrix Lower trapezoidal matrix whose columns define the reflections
- */
- public function getH() {
- for ($i = 0; $i < $this->m; ++$i) {
- for ($j = 0; $j < $this->n; ++$j) {
- if ($i >= $j) {
- $H[$i][$j] = $this->QR[$i][$j];
- } else {
- $H[$i][$j] = 0.0;
- }
- }
- }
- return new PHPExcel_Shared_JAMA_Matrix($H);
- } // function getH()
-
-
- /**
- * Return the upper triangular factor
- *
- * @return Matrix upper triangular factor
- */
- public function getR() {
- for ($i = 0; $i < $this->n; ++$i) {
- for ($j = 0; $j < $this->n; ++$j) {
- if ($i < $j) {
- $R[$i][$j] = $this->QR[$i][$j];
- } elseif ($i == $j) {
- $R[$i][$j] = $this->Rdiag[$i];
- } else {
- $R[$i][$j] = 0.0;
- }
- }
- }
- return new PHPExcel_Shared_JAMA_Matrix($R);
- } // function getR()
-
-
- /**
- * Generate and return the (economy-sized) orthogonal factor
- *
- * @return Matrix orthogonal factor
- */
- public function getQ() {
- for ($k = $this->n-1; $k >= 0; --$k) {
- for ($i = 0; $i < $this->m; ++$i) {
- $Q[$i][$k] = 0.0;
- }
- $Q[$k][$k] = 1.0;
- for ($j = $k; $j < $this->n; ++$j) {
- if ($this->QR[$k][$k] != 0) {
- $s = 0.0;
- for ($i = $k; $i < $this->m; ++$i) {
- $s += $this->QR[$i][$k] * $Q[$i][$j];
- }
- $s = -$s/$this->QR[$k][$k];
- for ($i = $k; $i < $this->m; ++$i) {
- $Q[$i][$j] += $s * $this->QR[$i][$k];
- }
- }
- }
- }
- /*
- for($i = 0; $i < count($Q); ++$i) {
- for($j = 0; $j < count($Q); ++$j) {
- if(! isset($Q[$i][$j]) ) {
- $Q[$i][$j] = 0;
- }
- }
- }
- */
- return new PHPExcel_Shared_JAMA_Matrix($Q);
- } // function getQ()
-
-
- /**
- * Least squares solution of A*X = B
- *
- * @param Matrix $B A Matrix with as many rows as A and any number of columns.
- * @return Matrix Matrix that minimizes the two norm of Q*R*X-B.
- */
- public function solve($B) {
- if ($B->getRowDimension() == $this->m) {
- if ($this->isFullRank()) {
- // Copy right hand side
- $nx = $B->getColumnDimension();
- $X = $B->getArrayCopy();
- // Compute Y = transpose(Q)*B
- for ($k = 0; $k < $this->n; ++$k) {
- for ($j = 0; $j < $nx; ++$j) {
- $s = 0.0;
- for ($i = $k; $i < $this->m; ++$i) {
- $s += $this->QR[$i][$k] * $X[$i][$j];
- }
- $s = -$s/$this->QR[$k][$k];
- for ($i = $k; $i < $this->m; ++$i) {
- $X[$i][$j] += $s * $this->QR[$i][$k];
- }
- }
- }
- // Solve R*X = Y;
- for ($k = $this->n-1; $k >= 0; --$k) {
- for ($j = 0; $j < $nx; ++$j) {
- $X[$k][$j] /= $this->Rdiag[$k];
- }
- for ($i = 0; $i < $k; ++$i) {
- for ($j = 0; $j < $nx; ++$j) {
- $X[$i][$j] -= $X[$k][$j]* $this->QR[$i][$k];
- }
- }
- }
- $X = new PHPExcel_Shared_JAMA_Matrix($X);
- return ($X->getMatrix(0, $this->n-1, 0, $nx));
- } else {
- throw new Exception(self::MatrixRankException);
- }
- } else {
- throw new Exception(PHPExcel_Shared_JAMA_Matrix::MatrixDimensionException);
- }
- } // function solve()
-
-} // PHPExcel_Shared_JAMA_class QRDecomposition
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