/**
* 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)));
}
/**
* Compute determinant using a strategy
*
* @param \Chippyash\Math\Matrix\NumericMatrix $mA
* @return numeric
* @throws UndefinedComputationException
*
* @todo put back in LU determinant strategy once figured out what is wrong with it
*/
protected function getDeterminant(NumericMatrix $mA)
{
switch ($this->method) {
case self::METHOD_AUTO:
if ($mA->rows() <= self::$luLimit) {
$strategy = new Lu();
} else {
throw new UndefinedComputationException('No available strategy found to determine the determinant');
}
break;
case self::METHOD_LAPLACE:
$strategy = new Laplace();
break;
case self::METHOD_LU:
$strategy = new Lu();
break;
default:
throw new UndefinedComputationException('Unknown determinant computation method');
}
return $strategy->determinant($mA);
}
/**
* Massage where mA is rectangle
* @param \Chippyash\Math\Matrix\NumericMatrix $mA
* @param \Chippyash\Math\Matrix\NumericMatrix $mB
* @param array $product
* @return \Chippyash\Math\Matrix\NumericMatrix
*/
protected function massageRectangle(NumericMatrix $mA, NumericMatrix $mB, array $product)
{
if ($mB->is('rectangle') && $mA->rows() < $mB->rows()) {
return $this->createCorrectMatrixType($mA, [[$product[0][0], $product[0][1]], [$product[1][0], $product[1][1]]]);
}
return $this->createCorrectMatrixType($mA, $product);
}
/**
* Recursive determinant function
*
* @param \Chippyash\Math\Matrix\NumericMatrix $mA
* @return \Chippyash\Type\Interfaces\NumericTypeInterface
*/
protected function det(NumericMatrix $mA)
{
$rowCount = $mA->rows();
if ($rowCount == 0) {
return $this->createCorrectScalarType($mA, 1);
}
if ($rowCount == 1) {
return $mA->get(1, 1);
}
$possAnswer = $this->checkInCache($mA);
if ($possAnswer !== false) {
return $possAnswer;
}
if ($rowCount == 2) {
//2X2 matrix
$det = $this->det2($mA);
} else {
//nXn matrix
$det = $this->detN($mA);
}
$this->storeInCache($mA, $det);
return $det;
}
/**
* Set upper triangular factor.
*/
protected function setUpperProduct(NumericMatrix $mA)
{
$n = $this->LU->columns();
$LU = $this->LU->toArray();
$rcFactor = $this->cols - $this->rows;
$this->set('U', function () use($n, $LU, $rcFactor, $mA) {
$U = [];
for ($i = 0; $i < $n; $i++) {
for ($j = 0; $j < $n; $j++) {
if ($i <= $j) {
$U[$i][$j] = isset($LU[$i][$j]) ? $LU[$i][$j] : $this->createCorrectScalarType($mA, 0);
} else {
$U[$i][$j] = $this->createCorrectScalarType($mA, 0);
}
}
}
//remove extra rows for non square matrices
if ($rcFactor > 0) {
$mUU = new NumericMatrix($U);
return $this->createCorrectMatrixType($mA, $mUU('Rowslice', array(1, $mUU->rows() - $rcFactor))->toArray());
} else {
return $this->createCorrectMatrixType($mA, $U);
}
});
}
