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