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2388 jpm 1 
<?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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	 *	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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		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(ArgumentTypeException));
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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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		return $this->isspd;
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	}	//	function isSPD()
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	/**
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	 *	getL
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	 *
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	 *	Return triangular factor.
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	 *	@return Matrix Lower triangular matrix
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	 */
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	public function getL() {
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		return new Matrix($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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		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(MatrixDimensionException));
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			}
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		} else {
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			throw new PHPExcel_Calculation_Exception(JAMAError(ArgumentTypeException));
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		}
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	}	//	function solve()
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}	//	class CholeskyDecomposition