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<?php
/**
* @package JAMA
*
* For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n
* unit lower triangular matrix L, an n-by-n upper triangular matrix U,
* and a permutation vector piv of length m so that A(piv,:) = L*U.
* If m < n, then L is m-by-m and U is m-by-n.
*
* The LU decompostion with pivoting always exists, even if the matrix is
* singular, so the constructor will never fail. The primary use of the
* LU decomposition is in the solution of square systems of simultaneous
* linear equations. This will fail if isNonsingular() returns false.
*
* @author Paul Meagher
* @author Bartosz Matosiuk
* @author Michael Bommarito
* @version 1.1
* @license PHP v3.0
*/
class PHPExcel_Shared_JAMA_LUDecomposition {
const MatrixSingularException = "Can only perform operation on singular matrix.";
const MatrixSquareException = "Mismatched Row dimension";
/**
* Decomposition storage
* @var array
*/
private $LU = array();
/**
* Row dimension.
* @var int
*/
private $m;
/**
* Column dimension.
* @var int
*/
private $n;
/**
* Pivot sign.
* @var int
*/
private $pivsign;
/**
* Internal storage of pivot vector.
* @var array
*/
private $piv = array();
/**
* LU Decomposition constructor.
*
* @param $A Rectangular matrix
* @return Structure to access L, U and piv.
*/
public function __construct($A) {
if ($A instanceof PHPExcel_Shared_JAMA_Matrix) {
// Use a "left-looking", dot-product, Crout/Doolittle algorithm.
$this->LU = $A->getArray();
$this->m = $A->getRowDimension();
$this->n = $A->getColumnDimension();
for ($i = 0; $i < $this->m; ++$i) {
$this->piv[$i] = $i;
}
$this->pivsign = 1;
$LUrowi = $LUcolj = array();
// Outer loop.
for ($j = 0; $j < $this->n; ++$j) {
// Make a copy of the j-th column to localize references.
for ($i = 0; $i < $this->m; ++$i) {
$LUcolj[$i] = &$this->LU[$i][$j];
}
// Apply previous transformations.
for ($i = 0; $i < $this->m; ++$i) {
$LUrowi = $this->LU[$i];
// Most of the time is spent in the following dot product.
$kmax = min($i,$j);
$s = 0.0;
for ($k = 0; $k < $kmax; ++$k) {
$s += $LUrowi[$k] * $LUcolj[$k];
}
$LUrowi[$j] = $LUcolj[$i] -= $s;
}
// Find pivot and exchange if necessary.
$p = $j;
for ($i = $j+1; $i < $this->m; ++$i) {
if (abs($LUcolj[$i]) > abs($LUcolj[$p])) {
$p = $i;
}
}
if ($p != $j) {
for ($k = 0; $k < $this->n; ++$k) {
$t = $this->LU[$p][$k];
$this->LU[$p][$k] = $this->LU[$j][$k];
$this->LU[$j][$k] = $t;
}
$k = $this->piv[$p];
$this->piv[$p] = $this->piv[$j];
$this->piv[$j] = $k;
$this->pivsign = $this->pivsign * -1;
}
// Compute multipliers.
if (($j < $this->m) && ($this->LU[$j][$j] != 0.0)) {
for ($i = $j+1; $i < $this->m; ++$i) {
$this->LU[$i][$j] /= $this->LU[$j][$j];
}
}
}
} else {
throw new PHPExcel_Calculation_Exception(PHPExcel_Shared_JAMA_Matrix::ArgumentTypeException);
}
} // function __construct()
/**
* Get lower triangular factor.
*
* @return array Lower triangular factor
*/
public function getL() {
for ($i = 0; $i < $this->m; ++$i) {
for ($j = 0; $j < $this->n; ++$j) {
if ($i > $j) {
$L[$i][$j] = $this->LU[$i][$j];
} elseif ($i == $j) {
$L[$i][$j] = 1.0;
} else {
$L[$i][$j] = 0.0;
}
}
}
return new PHPExcel_Shared_JAMA_Matrix($L);
} // function getL()
/**
* Get upper triangular factor.
*
* @return array Upper triangular factor
*/
public function getU() {
for ($i = 0; $i < $this->n; ++$i) {
for ($j = 0; $j < $this->n; ++$j) {
if ($i <= $j) {
$U[$i][$j] = $this->LU[$i][$j];
} else {
$U[$i][$j] = 0.0;
}
}
}
return new PHPExcel_Shared_JAMA_Matrix($U);
} // function getU()
/**
* Return pivot permutation vector.
*
* @return array Pivot vector
*/
public function getPivot() {
return $this->piv;
} // function getPivot()
/**
* Alias for getPivot
*
* @see getPivot
*/
public function getDoublePivot() {
return $this->getPivot();
} // function getDoublePivot()
/**
* Is the matrix nonsingular?
*
* @return true if U, and hence A, is nonsingular.
*/
public function isNonsingular() {
for ($j = 0; $j < $this->n; ++$j) {
if ($this->LU[$j][$j] == 0) {
return false;
}
}
return true;
} // function isNonsingular()
/**
* Count determinants
*
* @return array d matrix deterninat
*/
public function det() {
if ($this->m == $this->n) {
$d = $this->pivsign;
for ($j = 0; $j < $this->n; ++$j) {
$d *= $this->LU[$j][$j];
}
return $d;
} else {
throw new PHPExcel_Calculation_Exception(PHPExcel_Shared_JAMA_Matrix::MatrixDimensionException);
}
} // function det()
/**
* Solve A*X = B
*
* @param $B A Matrix with as many rows as A and any number of columns.
* @return X so that L*U*X = B(piv,:)
* @PHPExcel_Calculation_Exception IllegalArgumentException Matrix row dimensions must agree.
* @PHPExcel_Calculation_Exception RuntimeException Matrix is singular.
*/
public function solve($B) {
if ($B->getRowDimension() == $this->m) {
if ($this->isNonsingular()) {
// Copy right hand side with pivoting
$nx = $B->getColumnDimension();
$X = $B->getMatrix($this->piv, 0, $nx-1);
// Solve L*Y = B(piv,:)
for ($k = 0; $k < $this->n; ++$k) {
for ($i = $k+1; $i < $this->n; ++$i) {
for ($j = 0; $j < $nx; ++$j) {
$X->A[$i][$j] -= $X->A[$k][$j] * $this->LU[$i][$k];
}
}
}
// Solve U*X = Y;
for ($k = $this->n-1; $k >= 0; --$k) {
for ($j = 0; $j < $nx; ++$j) {
$X->A[$k][$j] /= $this->LU[$k][$k];
}
for ($i = 0; $i < $k; ++$i) {
for ($j = 0; $j < $nx; ++$j) {
$X->A[$i][$j] -= $X->A[$k][$j] * $this->LU[$i][$k];
}
}
}
return $X;
} else {
throw new PHPExcel_Calculation_Exception(self::MatrixSingularException);
}
} else {
throw new PHPExcel_Calculation_Exception(self::MatrixSquareException);
}
} // function solve()
} // class PHPExcel_Shared_JAMA_LUDecomposition