/**
* 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;
}
/**
* Factors a matrix into a pivot matrix, a lower and upper triangular matrix
*
* @param NumArray $array matrix
*
* @throws NoMatrixException will be thrown, if `array` is no matrix
*
* @return array
*
* @since 1.0.0
*/
public static function lud(NumArray $array)
{
if (!Helper::isMatrix($array)) {
throw new NoMatrixException(sprintf("NumArray with dimension %d given, NumArray should have 2 dimensions", $array->getNDim()));
}
$numArray = clone $array;
$shape = $numArray->getShape();
$mAxis = $shape[0];
$nAxis = $shape[1];
$size = min($mAxis, $nAxis);
$pArray = range(0, $mAxis - 1);
$lMatrix = NumPHP::zeros($mAxis, $size);
for ($i = 0; $i < $size; $i++) {
// pivoting
$maxIndex = self::getPivotIndex($numArray, $i);
if ($maxIndex !== $i) {
$temp = $numArray->get($i);
$numArray->set($i, $numArray->get($maxIndex));
$numArray->set($maxIndex, $temp);
$temp = $lMatrix->get($i);
$lMatrix->set($i, $lMatrix->get($maxIndex));
$lMatrix->set($maxIndex, $temp);
$temp = $pArray[$i];
$pArray[$i] = $pArray[$maxIndex];
$pArray[$maxIndex] = $temp;
}
// elimination
for ($j = $i + 1; $j < $mAxis; $j++) {
$fac = 0;
$facNumerator = $numArray->get($j, $i)->getData();
$facDenominator = $numArray->get($i, $i)->getData();
if ($facDenominator) {
$fac = $facNumerator / $facDenominator;
}
$lMatrix->set($j, $i, $fac);
$slice = sprintf("%d:", $i + 1);
$numArray->set($j, $slice, $numArray->get($j, $slice)->sub($numArray->get($i, $slice)->mult($fac)));
}
}
return [self::buildPivotMatrix($pArray), self::buildLMatrix($lMatrix), self::buildUMatrix($numArray)];
}
/**
* Tests if Helper::isMatrix works with invalid matrix
*/
public function testCheckMatrixInvalid()
{
$numArray = NumPHP::ones(3);
$this->assertFalse(Helper::isMatrix($numArray));
}
