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<?php
/**
* @package JAMA
*
* Cholesky decomposition class
*
* For a symmetric, positive definite matrix A, the Cholesky decomposition
* is an lower triangular matrix L so that A = L*L'.
*
* If the matrix is not symmetric or positive definite, the constructor
* returns a partial decomposition and sets an internal flag that may
* be queried by the isSPD() method.
*
* @author Paul Meagher
* @author Michael Bommarito
* @version 1.2
*/
class CholeskyDecomposition {
/**
* Decomposition storage
* @var array
* @access private
*/
private $L = array();
/**
* Matrix row and column dimension
* @var int
* @access private
*/
private $m;
/**
* Symmetric positive definite flag
* @var boolean
* @access private
*/
private $isspd = true;
/**
* CholeskyDecomposition
*
* Class constructor - decomposes symmetric positive definite matrix
* @param mixed Matrix square symmetric positive definite matrix
*/
public function __construct($A = null) {
if ($A instanceof Matrix) {
$this->L = $A->getArray();
$this->m = $A->getRowDimension();
for($i = 0; $i < $this->m; ++$i) {
for($j = $i; $j < $this->m; ++$j) {
for($sum = $this->L[$i][$j], $k = $i - 1; $k >= 0; --$k) {
$sum -= $this->L[$i][$k] * $this->L[$j][$k];
}
if ($i == $j) {
if ($sum >= 0) {
$this->L[$i][$i] = sqrt($sum);
} else {
$this->isspd = false;
}
} else {
if ($this->L[$i][$i] != 0) {
$this->L[$j][$i] = $sum / $this->L[$i][$i];
}
}
}
for ($k = $i+1; $k < $this->m; ++$k) {
$this->L[$i][$k] = 0.0;
}
}
} else {
throw new Exception(JAMAError(ArgumentTypeException));
}
} // function __construct()
/**
* Is the matrix symmetric and positive definite?
*
* @return boolean
*/
public function isSPD() {
return $this->isspd;
} // function isSPD()
/**
* getL
*
* Return triangular factor.
* @return Matrix Lower triangular matrix
*/
public function getL() {
return new Matrix($this->L);
} // function getL()
/**
* Solve A*X = B
*
* @param $B Row-equal matrix
* @return Matrix L * L' * X = B
*/
public function solve($B = null) {
if ($B instanceof Matrix) {
if ($B->getRowDimension() == $this->m) {
if ($this->isspd) {
$X = $B->getArrayCopy();
$nx = $B->getColumnDimension();
for ($k = 0; $k < $this->m; ++$k) {
for ($i = $k + 1; $i < $this->m; ++$i) {
for ($j = 0; $j < $nx; ++$j) {
$X[$i][$j] -= $X[$k][$j] * $this->L[$i][$k];
}
}
for ($j = 0; $j < $nx; ++$j) {
$X[$k][$j] /= $this->L[$k][$k];
}
}
for ($k = $this->m - 1; $k >= 0; --$k) {
for ($j = 0; $j < $nx; ++$j) {
$X[$k][$j] /= $this->L[$k][$k];
}
for ($i = 0; $i < $k; ++$i) {
for ($j = 0; $j < $nx; ++$j) {
$X[$i][$j] -= $X[$k][$j] * $this->L[$k][$i];
}
}
}
return new Matrix($X, $this->m, $nx);
} else {
throw new Exception(JAMAError(MatrixSPDException));
}
} else {
throw new Exception(JAMAError(MatrixDimensionException));
}
} else {
throw new Exception(JAMAError(ArgumentTypeException));
}
} // function solve()
} // class CholeskyDecomposition