MCordingley\LinearAlgebra\Decomposition\LUP::decompose PHP Method

    private function decompose(Matrix $source)
    {
        $sourceLiteral = $source->toArray();
        $decompositionLiteral = $sourceLiteral;
        if (!$source->isSquare()) {
            throw new MatrixException('Operation can only be called on square matrix: ' . print_r($decompositionLiteral, true));
        }
        $size = $source->getRowCount();
        $this->permutation = range(0, $size - 1);
        for ($k = 0; $k < $size; $k++) {
            $p = 0.0;
            $kPrime = $k;
            for ($i = $k; $i < $size; $i++) {
                $absolute = abs($decompositionLiteral[$i][$k]);
                if ($absolute > $p) {
                    $p = $absolute;
                    $kPrime = $i;
                }
            }
            if ($p === 0.0) {
                throw new MatrixException('Cannot take the LUP decomposition of a singular matrix: ' . print_r($sourceLiteral, true));
            }
            if ($k !== $kPrime) {
                list($this->permutation[$k], $this->permutation[$kPrime]) = [$this->permutation[$kPrime], $this->permutation[$k]];
                $this->parity++;
            }
            for ($i = 0; $i < $size; $i++) {
                list($decompositionLiteral[$k][$i], $decompositionLiteral[$kPrime][$i]) = [$decompositionLiteral[$kPrime][$i], $decompositionLiteral[$k][$i]];
            }
            for ($i = $k + 1; $i < $size; $i++) {
                $decompositionLiteral[$i][$k] = $decompositionLiteral[$i][$k] / $decompositionLiteral[$k][$k];
                for ($j = $k + 1; $j < $size; $j++) {
                    $decompositionLiteral[$i][$j] = $decompositionLiteral[$i][$j] - $decompositionLiteral[$i][$k] * $decompositionLiteral[$k][$j];
                }
            }
        }
        $this->decomposition = new Matrix($decompositionLiteral);
    }