int
main(int argc, char *argv[])
{
int i, j;
int a[4][4] = { {1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}, {13, 14, 15, 16} };
int b[4][4] = { {1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}, {13, 14, 15, 16} };
int n;
int **c;
c = malloc(sizeof(int *) * 4);
for (i = 0; i < 4; i++)
c[i] = malloc(sizeof(int) * 4);
square_matrix_multiply((int *) a, (int *) b, 4, (int *) c);
debug_matrix((int *) c, 4);
return 0;
}
void separation(double * input_1, double * input_2, double * output_1, double * output_2, int nb, int time_delay) {
// Initialize vectors
Vector* v_s1 = malloc(sizeof(Vector));
Vector* v_s2 = malloc(sizeof(Vector));
v_s1->elems = input_1;
v_s2->elems = input_2;
v_s1->L = nb;
v_s2->L = nb;
// Center mixes
vector_substract_scalar_inplace(v_s1, vector_mean(v_s1));
vector_substract_scalar_inplace(v_s2, vector_mean(v_s2));
// Normalize
double normalisation = sqrt(2 / (vector_std(v_s1) * vector_std(v_s1) + vector_std(v_s2) * vector_std(v_s2)));
for (int i = 0; i < v_s1->L; i++) {
v_s1->elems[i] *= normalisation;
v_s2->elems[i] *= normalisation;
}
// Estimate covariance
int M = time_delay; // Number of time delays for correlation
int N = v_s1->L / M; // We assume s1 and s2 are the same length
/// Reshape 1xL to M*(L/M)
Matrix* m_x1 = reshape(v_s1, M, N);
Matrix* m_x2 = reshape(v_s2, M, N);
/// Covariance estimation
Matrix* m_x1t = transpose(m_x1);
Matrix* m_x2t = transpose(m_x2);
Matrix* m_r11 = multiply(m_x1, m_x1t);
matrix_multiply_scalar_inplace(m_r11, (1.0f / N));
Matrix* m_r12 = multiply(m_x1, m_x2t);
matrix_multiply_scalar_inplace(m_r12, (1.0f / N));
Matrix* m_r22 = multiply(m_x2, m_x2t);
matrix_multiply_scalar_inplace(m_r22, (1.0f / N));
///Compute coefficients
double s_f1 = off(m_r11);
double s_f2 = off(m_r22);
double s_f12 = off(m_r12);
double s_t1 = tr(m_r11);
double s_t2 = tr(m_r22);
double s_t12 = tr(m_r12);
double sigma2 = 0;
double alpha = (2 * s_f12 * s_t12) - (s_f1 * (s_t2 - sigma2) + s_f2 * (s_t1 - sigma2));
double beta = 2 * (pow(s_t12, 2) - (s_t1 - sigma2) * (s_t2 - sigma2));
double gamma2 = pow((s_f1*(s_t2 - sigma2) - s_f2*(s_t1 - sigma2)), 2)
+ 4 * (s_f12*(s_t2 - sigma2) - s_t12*s_f2) * (s_f12*(s_t1 - sigma2) - s_t12*s_f1);
double s_d1 = alpha - sqrt(gamma2);
double s_d2 = alpha + sqrt(gamma2);
// Generate matrix
Matrix* m_est = allocate_matrix(2, 2);
m_est->elems[0][0] = beta * s_f1 - s_t1 * s_d1;
m_est->elems[0][1] = beta * s_f12 - s_t12 * s_d2;
m_est->elems[1][0] = beta * s_f12 - s_t12 * s_d1;
m_est->elems[1][1] = beta * s_f2 - s_t2 * s_d2;
// Invert matrix
double det = (m_est->elems[0][0]* m_est->elems[1][1]) - (m_est->elems[0][1]* m_est->elems[1][0]);
Matrix* m_est_inv = allocate_matrix(2, 2);
m_est_inv->elems[0][0] = m_est->elems[1][1];
m_est_inv->elems[0][1] = -m_est->elems[0][1];
m_est_inv->elems[1][0] = -m_est->elems[1][0];
m_est_inv->elems[1][1] = m_est->elems[0][0];
matrix_multiply_scalar_inplace(m_est_inv, 1 / det);
printf("\nEstimated mixing matrix\n");
debug_matrix(m_est, 2, 2);
printf("\nEstimated invert mixing matrix\n");
debug_matrix(m_est_inv, 2, 2);
det = (m_est_inv->elems[0][0]* m_est_inv->elems[1][1]) - (m_est_inv->elems[0][1]* m_est_inv->elems[1][0]);
// Sources separation
for (int i = 0; i < v_s1->L; i++) {
output_1[i] = (m_est_inv->elems[0][0]*v_s1->elems[i] + m_est_inv->elems[0][1]*v_s2->elems[i]) / det;
output_2[i] = (m_est_inv->elems[1][0]*v_s1->elems[i] + m_est_inv->elems[1][1]*v_s2->elems[i]) / det;
}
}
