/**
* Solves a linear system
*
* @param NumArray $squareMatrix matrix of size n*n
* @param NumArray $numArray vector of size n or matrix of size n*m
*
* @throws \NumPHP\LinAlg\Exception\SingularMatrixException will be thrown, if
* `$squareMatrix` is singular
* @throws \NumPHP\LinAlg\Exception\InvalidArgumentException will be thrown, if
* linear system of `$squareMatrix` and `$numArray` can not be solved
*
* @return NumArray
*
* @since 1.0.0
*/
public static function solve(NumArray $squareMatrix, NumArray $numArray)
{
if (!Helper::isNotSingularMatrix($squareMatrix)) {
throw new SingularMatrixException(sprintf("First Argument has to be a not singular square matrix"));
}
if (!Helper::isVector($numArray) && !Helper::isMatrix($numArray)) {
throw new InvalidArgumentException(sprintf("Second argument has to be a vector or a matrix, NumArray with dimension %d given", $numArray->getNDim()));
}
$shape1 = $squareMatrix->getShape();
$shape2 = $numArray->getShape();
if ($shape1[0] !== $shape2[0]) {
throw new InvalidArgumentException(sprintf("Can not solve a linear system with matrix (%s) and matrix (%s)", implode(', ', $shape1), implode(', ', $shape2)));
}
/**
* The result of LinAlg::lud is a array with three NumArrays
*
* @var NumArray $pMatrix
* @var NumArray $lMatrix
* @var NumArray $uMatrix
*/
list($pMatrix, $lMatrix, $uMatrix) = LinAlg::lud($squareMatrix);
$yNumArray = self::forwardSubstitution($lMatrix, $pMatrix->getTranspose()->dot($numArray));
$zNumArray = self::backSubstitution($uMatrix, $yNumArray);
return $zNumArray;
}
/**
* Tests if Helper::isNotSingularMatrix works with invalid not singular matrix
*/
public function testCheckNotSingularMatrixInvalid()
{
$numArray = NumPHP::identity(4);
$numArray->set(2, 2, 0);
$this->assertFalse(Helper::isNotSingularMatrix($numArray));
}
/**
* Calculates the inverse of a not singular square matrix
*
* @param mixed $squareMatrix not singular matrix
*
* @throws SingularMatrixException will be thrown, when `$squareMatrix` is singular
*
* @api
* @since 1.0.0
*
* @return NumArray
*/
public static function inv($squareMatrix)
{
if (!$squareMatrix instanceof NumArray) {
$squareMatrix = new NumArray($squareMatrix);
} elseif ($squareMatrix->inCache(self::CACHE_KEY_INVERSE)) {
return $squareMatrix->getCache(self::CACHE_KEY_INVERSE);
}
if (!Helper::isNotSingularMatrix($squareMatrix)) {
throw new SingularMatrixException("Matrix is singular");
}
$shape = $squareMatrix->getShape();
$inv = self::solve($squareMatrix, NumPHP::identity($shape[0]));
$squareMatrix->setCache(self::CACHE_KEY_INVERSE, $inv);
return self::inv($squareMatrix);
}
