/**
* Perform Guass Jordan Elimination on the two supplied matrices
*
* @param NumericMatrix $mA First matrix to act on - required
* @param NumericMatrix $extra Second matrix to act upon - required
*
* @return \Chippyash\Math\Matrix\DecompositionAbstractDecomposition Fluent Interface
*
* @throws \Chippyash\Math\Matrix\Exceptions\SingularMatrixException
*/
public function decompose(NumericMatrix $mA, $extra = null)
{
$this->assertParameterIsMatrix($extra, 'Parameter extra is not a matrix')->assertMatrixIsNumeric($extra, 'Parameter extra is not a numeric matrix')->assertMatrixIsSquare($mA, 'Parameter mA is not a square matrix')->assertMatrixRowsAreEqual($mA, $extra, 'mA->rows != extra->rows');
$rows = $mA->rows();
$dA = $mA->toArray();
$dB = $extra->toArray();
$zero = function () {
return RationalTypeFactory::create(0, 1);
};
$one = function () {
return RationalTypeFactory::create(1, 1);
};
$calc = new Calculator();
$comp = new Comparator();
$ipiv = array_fill(0, $rows, $zero());
$indxr = array_fill(0, $rows, 0);
$indxc = array_fill(0, $rows, 0);
// find the pivot element by searching the entire matrix for its largest value, but excluding columns already reduced.
$irow = $icol = 0;
for ($i = 0; $i < $rows; $i++) {
$big = $zero();
for ($j = 0; $j < $rows; $j++) {
if ($comp->neq($ipiv[$j], $one())) {
for ($k = 0; $k < $rows; $k++) {
if ($comp->eq($ipiv[$k], $zero())) {
$absVal = $dA[$j][$k]->abs();
if ($comp->gt($absVal, $big)) {
unset($big);
$big = clone $absVal;
$irow = $j;
$icol = $k;
}
} elseif ($comp->gt($ipiv[$k], $one())) {
throw new SingularMatrixException('GaussJordanElimination');
}
}
}
}
//Now interchange row to move the pivot element to a diagonal
$ipiv[$icol] = $calc->add($ipiv[$icol], $one());
if ($irow != $icol) {
$this->swapRows($dA, $irow, $icol);
$this->swapRows($dB, $irow, $icol);
}
// Remember permutations to later
$indxr[$i] = $irow;
$indxc[$i] = $icol;
if ($comp->eq($dA[$icol][$icol], $zero())) {
throw new SingularMatrixException('GaussJordanElimination');
}
// Now divide the found row to make the pivot element 1
// To maintain arithmetic integrity we use the reciprocal to multiply by
$pivinv = $calc->reciprocal($dA[$icol][$icol]);
$this->multRow($dA, $icol, $pivinv, $calc);
$this->multRow($dB, $icol, $pivinv, $calc);
// And reduce all other rows but the pivoted row with the value of the pivot row
for ($ll = 0; $ll < $rows; $ll++) {
if ($ll != $icol) {
$multiplier = clone $dA[$ll][$icol];
$multiplier->negate();
$this->addMultipleOfOtherRowToRow($dA, $multiplier, $icol, $ll, $calc);
$this->addMultipleOfOtherRowToRow($dB, $multiplier, $icol, $ll, $calc);
}
}
}
$this->set('left', $this->createCorrectMatrixType($mA, $dA));
$this->set('right', $this->createCorrectMatrixType($extra, $dB));
return clone $this;
}
/**
* LU Decomposition constructor.
*
* @param \Chippyash\Math\Matrix\NumericMatrix $mA
*/
protected function LUDecomposition(NumericMatrix $mA)
{
// Use a "left-looking", dot-product, Crout/Doolittle algorithm.
$LU = $mA->toArray();
$m = $this->rows = $mA->rows();
$n = $this->cols = $mA->columns();
for ($i = 0; $i < $m; $i++) {
$this->piv[$i] = $i;
}
$this->pivsign = 1;
$LUrowi = [];
$LUcolj = [];
$calc = new Calculator();
$comp = new Comparator();
$zeroInt = $this->createCorrectScalarType($mA, 0);
// Outer loop.
for ($j = 0; $j < $n; $j++) {
// Make a copy of the j-th column to localize references.
for ($i = 0; $i < $m; $i++) {
$LUcolj[$i] =& $LU[$i][$j];
}
// Apply previous transformations.
for ($i = 0; $i < $m; $i++) {
$LUrowi = $LU[$i];
// Most of the time is spent in the following dot product.
$kmax = min($i, $j);
$s = clone $zeroInt;
for ($k = 0; $k < $kmax; $k++) {
$s = $calc->add($s, $calc->mul($LUrowi[$k], $LUcolj[$k]));
}
$LUcolj[$i] = $calc->sub($LUcolj[$i], $s);
$LUrowi[$j] = $LUcolj[$i];
}
// Find pivot and exchange if necessary.
$p = $j;
for ($i = $j + 1; $i < $m; $i++) {
if ($comp->gt($LUcolj[$i]->abs(), $LUcolj[$p]->abs())) {
$p = $i;
}
}
if ($p != $j) {
for ($k = 0; $k < $n; $k++) {
//swap
$t = $LU[$p][$k];
$LU[$p][$k] = $LU[$j][$k];
$LU[$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 < $m && $comp->neq($LU[$j][$j], $zeroInt)) {
for ($i = $j + 1; $i < $m; $i++) {
$LU[$i][$j] = $calc->div($LU[$i][$j], $LU[$j][$j]);
}
}
}
$this->set('LU', $this->createCorrectMatrixType($mA, $LU));
}