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148 lines
4.4 KiB
148 lines
4.4 KiB
<?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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/** |
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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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{ |
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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(ARGUMENT_TYPE_EXCEPTION)); |
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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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{ |
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return $this->isspd; |
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} // function isSPD() |
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/** |
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* getL |
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* |
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* Return triangular factor. |
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* @return Matrix Lower triangular matrix |
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*/ |
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public function getL() |
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{ |
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return new Matrix($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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{ |
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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(MATRIX_DIMENSION_EXCEPTION)); |
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} |
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} else { |
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throw new PHPExcel_Calculation_Exception(JAMAError(ARGUMENT_TYPE_EXCEPTION)); |
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} |
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} // function solve() |
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}
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