/**
* Matrix multiplication
* https://en.wikipedia.org/wiki/Matrix_multiplication#Matrix_product_.28two_matrices.29
*
* @param Matrix/Vector $B Matrix or Vector to multiply
*
* @return Matrix
*
* @throws IncorrectTypeException if parameter B is not a Matrix or Vector
* @throws MatrixException if matrix dimensions do not match
*/
public function multiply($B) : Matrix
{
if (!$B instanceof Matrix && !$B instanceof Vector) {
throw new Exception\IncorrectTypeException('Can only do matrix multiplication with a Matrix or Vector');
}
if ($B instanceof Vector) {
$B = $B->asColumnMatrix();
}
if ($B->getM() !== $this->n) {
throw new Exception\MatrixException("Matrix dimensions do not match");
}
$n = $B->getN();
$m = $this->m;
$R = [];
for ($i = 0; $i < $m; $i++) {
for ($j = 0; $j < $n; $j++) {
$VA = new Vector($this->getRow($i));
$VB = new Vector($B->getColumn($j));
$R[$i][$j] = $VA->dotProduct($VB);
}
}
return MatrixFactory::create($R);
}
/**
* Perpendicular of A on B
* https://en.wikipedia.org/wiki/Vector_projection#Vector_projection
*
* A⋅B⊥
* perpᵇA = ---- B⊥
* |B|²
*
* @param Vector $B
*
* @return Vector
*/
public function perp(Vector $B) : Vector
{
$A⋅B⊥ = $B->perpDotProduct($this);
$│B│² = $B->l2norm() ** 2;
$B⊥ = $B->perpendicular();
return $B⊥->scalarMultiply($A⋅B⊥ / $│B│²);
}