<?php declare(strict_types=1);
/**
 *	@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
 *
 *  Slightly changed to adapt the original code to PHP-ML library
 *  @date 2017/04/24
 *  @author Mustafa Karabulut
 */

namespace Phpml\Math\LinearAlgebra;

use Phpml\Math\Matrix;
use Phpml\Exception\MatrixException;

class LUDecomposition
{
    /**
     *	Decomposition storage
     *	@var array
     */
    private $LU = [];

    /**
     *	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 = [];


    /**
     *	LU Decomposition constructor.
     *
     *	@param $A Rectangular matrix
     *	@return Structure to access L, U and piv.
     */
    public function __construct(Matrix $A)
    {
        if ($A->getRows() != $A->getColumns()) {
            throw MatrixException::notSquareMatrix();
        }

        // Use a "left-looking", dot-product, Crout/Doolittle algorithm.
        $this->LU = $A->toArray();
        $this->m  = $A->getRows();
        $this->n  = $A->getColumns();
        for ($i = 0; $i < $this->m; ++$i) {
            $this->piv[$i] = $i;
        }
        $this->pivsign = 1;
        $LUrowi = $LUcolj = [];

        // 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];
                }
            }
        }
    }    //	function __construct()


    /**
     *	Get lower triangular factor.
     *
     *	@return array Lower triangular factor
     */
    public function getL()
    {
        $L = [];
        for ($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][$j] = 0.0;
                }
            }
        }
        return new Matrix($L);
    }    //	function getL()


    /**
     *	Get upper triangular factor.
     *
     *	@return array Upper triangular factor
     */
    public function getU()
    {
        $U = [];
        for ($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][$j] = 0.0;
                }
            }
        }
        return new Matrix($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 MatrixException::notSquareMatrix();
        }
    }    //	function det()


    /**
     *	Solve A*X = B
     *
     * @param Matrix $B A Matrix with as many rows as A and any number of columns.
     *
     * @return array X so that L*U*X = B(piv,:)
     *
     * @throws MatrixException
     */
    public function solve(Matrix $B)
    {
        if ($B->getRows() != $this->m) {
            throw MatrixException::notSquareMatrix();
        }

        if (! $this->isNonsingular()) {
            throw MatrixException::singularMatrix();
        }

        // Copy right hand side with pivoting
        $nx = $B->getColumns();
        $X  = $this->getSubMatrix($B->toArray(), $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) {
                    $X[$i][$j] -= $X[$k][$j] * $this->LU[$i][$k];
                }
            }
        }
        // Solve U*X = Y;
        for ($k = $this->n-1; $k >= 0; --$k) {
            for ($j = 0; $j < $nx; ++$j) {
                $X[$k][$j] /= $this->LU[$k][$k];
            }
            for ($i = 0; $i < $k; ++$i) {
                for ($j = 0; $j < $nx; ++$j) {
                    $X[$i][$j] -= $X[$k][$j] * $this->LU[$i][$k];
                }
            }
        }
        return $X;
    }    //	function solve()

    /**
     * @param Matrix $matrix
     * @param int $j0
     * @param int $jF
     *
     * @return array
     */
    protected function getSubMatrix(array $matrix, array $RL, int $j0, int $jF)
    {
        $m = count($RL);
        $n = $jF - $j0;
        $R = array_fill(0, $m, array_fill(0, $n+1, 0.0));

        for ($i = 0; $i < $m; ++$i) {
            for ($j = $j0; $j <= $jF; ++$j) {
                $R[$i][$j - $j0]= $matrix[ $RL[$i] ][$j];
            }
        }

        return $R;
    }
}    //	class LUDecomposition