/**
* 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;
}
/**
* @param InputInterface $input
* @param OutputInterface $output
*
* @SuppressWarnings(PHPMD.UnusedFormalParameter)
*/
protected function execute(InputInterface $input, OutputInterface $output)
{
$matrixA = new NumArray([[1, 6, 1], [2, 3, 2], [4, 2, 1]]);
$output->writeln('<comment>Matrix A:</comment>');
$output->writeln($matrixA->__toString());
$output->writeln('<info>LU decomposition</info>');
$time = microtime(true);
list($matrixP, $matrixL, $matrixU) = LinAlg::lud($matrixA);
$timeDiff = microtime(true) - $time;
$output->writeln('<comment>Matrix P:</comment>');
$output->writeln($matrixP->__toString());
$output->writeln('<comment>Matrix L:</comment>');
$output->writeln($matrixL->__toString());
$output->writeln('<comment>Matrix U:</comment>');
$output->writeln($matrixU->__toString());
$output->writeln('<info>Time for calculation: ' . $timeDiff . ' sec</info>');
}
/**
* Tests cache of LinAlg::lud
*/
public function testLUDecompositionCache()
{
$numArray = new NumArray(5);
$numArray->setCache(LUDecomposition::CACHE_KEY_LU_DECOMPOSITION, 8);
$this->assertSame(8, LinAlg::lud($numArray));
}