/**
* Solve A*X = B.
*
* @param
* b
* A Matrix with as many rows as A and any number of columns.
* @return X so that L*L'*X = b.
*/
public function solve(Matrix $b)
{
if ($b->getRows() != $this->n) {
throw new MatrixError("Matrix row dimensions must agree.");
}
if (!$this->isspd) {
throw new RuntimeException("Matrix is not symmetric positive definite.");
}
// Copy right hand side.
$x = $b->getArrayCopy();
$nx = $b->getCols();
// Solve L*Y = B;
for ($k = 0; $k < $this->n; ++$k) {
for ($j = 0; $j < $nx; ++$j) {
for ($i = 0; $i < $k; ++$i) {
$x[$k][$j] -= $x[$i][$j] * $this->l[$k][$i];
}
$x[$k][$j] /= $this->l[$k][$k];
}
}
// Solve L'*X = Y;
for ($k = $this->n - 1; $k >= 0; $k--) {
for ($j = 0; $j < $nx; ++$j) {
for ($i = $k + 1; $i < $this->n; ++$i) {
$x[$k][$j] -= $x[$i][$j] * $this->l[$i][$k];
}
$x[$k][$j] /= $this->l[$k][$k];
}
}
return Matrix::matrixFromDoubles($x);
}
