Matrix* matrix_qr_decomposition(Matrix M)
{
assert(is_matrix(M));
int m = M->r;
int n = M->c;
Matrix Q = matrix_new_empty(m, n);
for(int i = 0; i < n; i++) {
double* u = matrix_column_vector(M, i);
double* a = matrix_column_vector(M, i);
for(int k = 0; k < i; k++) {
double* e = matrix_column_vector(Q, k);
double* p = vector_projection(e, a, m);
free(e);
for(int j = 0; j < m; j++)
u[j] -= p[j];
free(p);
}
free(a);
double* e = vector_normalize(u, m);
free(u);
for(int l = 0; l < m; l++)
Q->A[l][i] = e[l];
free(e);
}
Matrix Qt = matrix_transpose(Q);
Matrix R = matrix_multiply(Qt, M);
matrix_free(Qt);
Matrix* QR = calloc(2, sizeof(Matrix));
QR[0] = Q;
QR[1] = R;
return QR;
}
void Bullet::rebound(sf::Vector2f center)
{
sf::Vector2f diff = pos - center;
sf::Vector2f proj = vector_projection(vel, diff);
vel -= (float)2.0 * proj;
}