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<?php
namespace PhpOffice\PhpSpreadsheet\Shared\JAMA;
use PhpOffice\PhpSpreadsheet\Calculation\Exception as CalculationException;
/**
* 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
*/
private $L = [];
/**
* Matrix row and column dimension.
*
* @var int
*/
private $m;
/**
* Symmetric positive definite flag.
*
* @var bool
*/
private $isspd = true;
/**
* CholeskyDecomposition.
*
* Class constructor - decomposes symmetric positive definite matrix
*
* @param Matrix $A Matrix square symmetric positive definite matrix
*/
public function __construct(Matrix $A)
{
$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;
}
}
}
/**
* Is the matrix symmetric and positive definite?
*
* @return bool
*/
public function isSPD()
{
return $this->isspd;
}
/**
* getL.
*
* Return triangular factor.
*
* @return Matrix Lower triangular matrix
*/
public function getL()
{
return new Matrix($this->L);
}
/**
* Solve A*X = B.
*
* @param $B Row-equal matrix
*
* @return Matrix L * L' * X = B
*/
public function solve(Matrix $B)
{
if ($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);
}
throw new CalculationException(Matrix::MATRIX_SPD_EXCEPTION);
}
throw new CalculationException(Matrix::MATRIX_DIMENSION_EXCEPTION);
}
}
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