class PHPExcel_Shared_JAMA_LUDecomposition in Loft Data Grids 6.2
Same name and namespace in other branches
- 7.2 vendor/phpoffice/phpexcel/Classes/PHPExcel/Shared/JAMA/LUDecomposition.php \PHPExcel_Shared_JAMA_LUDecomposition
@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
Hierarchy
Expanded class hierarchy of PHPExcel_Shared_JAMA_LUDecomposition
File
- vendor/
phpoffice/ phpexcel/ Classes/ PHPExcel/ Shared/ JAMA/ LUDecomposition.php, line 21
View source
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);
}
}
}