/**
* Compute inverse using determinants method
* We are expecting a non singular, square matrix (complete, n=m, n>1)
*
* @param \Chippyash\Matrix\Matrix $mA
* @return Matrix
*/
public function invert(NumericMatrix $mA)
{
$rows = $mA->rows();
$cols = $mA->columns();
$work = array();
$fDet = new Det();
$fCof = new Cofactor();
for ($row = 0; $row < $rows; $row++) {
for ($col = 0; $col < $cols; $col++) {
$t = $fDet($fCof($mA, [$row + 1, $col + 1]));
if (fmod($row + $col, 2) == 0) {
$work[$row][$col] = $t;
} else {
$work[$row][$col] = $t->negate();
}
$r = $row + 1;
$c = $col + 1;
}
}
$fTr = new Transpose();
$fDiv = new Scalar();
return $fTr($fDiv($this->createCorrectMatrixType($mA, $work), $fDet($mA)));
}
/**
*
* @param \Chippyash\Math\Matrix\NumericMatrix $mA
* @param \Chippyash\Math\Matrix\NumericMatrix $mB
* @throws ComputationException
*/
protected function checkRectangleMatrixCompatibility(NumericMatrix $mA, NumericMatrix $mB)
{
if ($mB->is('rectangle') && $mA->columns() != $mB->rows()) {
throw new ComputationException('Two matrices cannot be multiplied: mA->columns != mB->rows');
}
}
/**
* Set lower triangular factor.
*/
protected function setLowerProduct(NumericMatrix $mA)
{
$m = $this->LU->rows();
$n = $this->LU->columns();
$LU = $this->LU->toArray();
$rcFactor = $this->rows - $this->cols;
//set Lower
$this->set('L', function () use($m, $n, $LU, $rcFactor, $mA) {
$L = [];
for ($i = 0; $i < $m; $i++) {
for ($j = 0; $j < $n; $j++) {
if ($i > $j) {
$L[$i][$j] = $LU[$i][$j];
} elseif ($i == $j) {
$L[$i][$j] = $this->createCorrectScalarType($mA, 1);
} else {
$L[$i][$j] = $this->createCorrectScalarType($mA, 0);
}
}
}
//remove extra cols for non square matrices
if ($rcFactor < 0) {
$mLL = new NumericMatrix($L);
return $this->createCorrectMatrixType($mA, $mLL('Colslice', array(1, $mLL->columns() + $rcFactor))->toArray());
} else {
return $this->createCorrectMatrixType($mA, $L);
}
});
}