/** Solves A*x = B using SVD
* @param A :: [input] The matrix A
* @param B :: [input] The vector B
* @return :: The solution x
*/
std::vector<double> MaxEnt::solveSVD(const DblMatrix &A, const DblMatrix &B) {
size_t dim = A.size().first;
gsl_matrix *a = gsl_matrix_alloc(dim, dim);
gsl_matrix *v = gsl_matrix_alloc(dim, dim);
gsl_vector *s = gsl_vector_alloc(dim);
gsl_vector *w = gsl_vector_alloc(dim);
gsl_vector *x = gsl_vector_alloc(dim);
gsl_vector *b = gsl_vector_alloc(dim);
// Need to copy from DblMatrix to gsl matrix
for (size_t k = 0; k < dim; k++)
for (size_t l = 0; l < dim; l++)
gsl_matrix_set(a, k, l, A[k][l]);
for (size_t k = 0; k < dim; k++)
gsl_vector_set(b, k, B[k][0]);
// Singular value decomposition
gsl_linalg_SV_decomp(a, v, s, w);
// A could be singular or ill-conditioned. We can use SVD to obtain a least
// squares
// solution by setting the small (compared to the maximum) singular values to
// zero
// Find largest sing value
double max = gsl_vector_get(s, 0);
for (size_t i = 0; i < dim; i++) {
if (max < gsl_vector_get(s, i))
max = gsl_vector_get(s, i);
}
// Apply a threshold to small singular values
const double THRESHOLD = 1E-6;
double threshold = THRESHOLD * max;
for (size_t i = 0; i < dim; i++)
if (gsl_vector_get(s, i) > threshold)
gsl_vector_set(s, i, gsl_vector_get(s, i));
else
gsl_vector_set(s, i, 0);
// Solve A*x = B
gsl_linalg_SV_solve(a, v, s, b, x);
// From gsl_vector to vector
std::vector<double> delta(dim);
for (size_t k = 0; k < dim; k++)
delta[k] = gsl_vector_get(x, k);
gsl_matrix_free(a);
gsl_matrix_free(v);
gsl_vector_free(s);
gsl_vector_free(w);
gsl_vector_free(x);
gsl_vector_free(b);
return delta;
}
