/* Tridiagonal Decomposition of Real Symmetric Matrices */
CAMLprim value ml_gsl_linalg_symmtd_decomp(value A, value TAU)
{
_DECLARE_MATRIX(A);
_DECLARE_VECTOR(TAU);
_CONVERT_MATRIX(A);
_CONVERT_VECTOR(TAU);
gsl_linalg_symmtd_decomp(&m_A, &v_TAU);
return Val_unit;
}
/**
* C++ version of gsl_linalg_symmtd_decomp().
* @param A A matrix
* @param tau A vector
* @return Error code on failure
*/
inline int symmtd_decomp( matrix& A, vector& tau ){
return gsl_linalg_symmtd_decomp( A.get(), tau.get() ); }
int
gsl_eigen_symmv (gsl_matrix * A, gsl_vector * eval, gsl_matrix * evec,
gsl_eigen_symmv_workspace * w)
{
if (A->size1 != A->size2)
{
GSL_ERROR ("matrix must be square to compute eigenvalues", GSL_ENOTSQR);
}
else if (eval->size != A->size1)
{
GSL_ERROR ("eigenvalue vector must match matrix size", GSL_EBADLEN);
}
else if (evec->size1 != A->size1 || evec->size2 != A->size1)
{
GSL_ERROR ("eigenvector matrix must match matrix size", GSL_EBADLEN);
}
else
{
double *const d = w->d;
double *const sd = w->sd;
const size_t N = A->size1;
size_t a, b;
/* handle special case */
if (N == 1)
{
double A00 = gsl_matrix_get (A, 0, 0);
gsl_vector_set (eval, 0, A00);
gsl_matrix_set (evec, 0, 0, 1.0);
return GSL_SUCCESS;
}
/* use sd as the temporary workspace for the decomposition when
computing eigenvectors */
{
gsl_vector_view d_vec = gsl_vector_view_array (d, N);
gsl_vector_view sd_vec = gsl_vector_view_array (sd, N - 1);
gsl_vector_view tau = gsl_vector_view_array (sd, N - 1);
gsl_linalg_symmtd_decomp (A, &tau.vector);
gsl_linalg_symmtd_unpack (A, &tau.vector, evec, &d_vec.vector, &sd_vec.vector);
}
/* Make an initial pass through the tridiagonal decomposition
to remove off-diagonal elements which are effectively zero */
chop_small_elements (N, d, sd);
/* Progressively reduce the matrix until it is diagonal */
b = N - 1;
while (b > 0)
{
if (sd[b - 1] == 0.0 || isnan(sd[b - 1]))
{
b--;
continue;
}
/* Find the largest unreduced block (a,b) starting from b
and working backwards */
a = b - 1;
while (a > 0)
{
if (sd[a - 1] == 0.0)
{
break;
}
a--;
}
{
size_t i;
const size_t n_block = b - a + 1;
double *d_block = d + a;
double *sd_block = sd + a;
double * const gc = w->gc;
double * const gs = w->gs;
/* apply QR reduction with implicit deflation to the
unreduced block */
qrstep (n_block, d_block, sd_block, gc, gs);
/* Apply Givens rotation Gij(c,s) to matrix Q, Q <- Q G */
for (i = 0; i < n_block - 1; i++)
{
const double c = gc[i], s = gs[i];
size_t k;
for (k = 0; k < N; k++)
{
double qki = gsl_matrix_get (evec, k, a + i);
double qkj = gsl_matrix_get (evec, k, a + i + 1);
gsl_matrix_set (evec, k, a + i, qki * c - qkj * s);
gsl_matrix_set (evec, k, a + i + 1, qki * s + qkj * c);
}
}
/* remove any small off-diagonal elements */
chop_small_elements (N, d, sd);
}
}
{
gsl_vector_view d_vec = gsl_vector_view_array (d, N);
gsl_vector_memcpy (eval, &d_vec.vector);
}
return GSL_SUCCESS;
}
}
int
gsl_eigen_symm (gsl_matrix * A, gsl_vector * eval,
gsl_eigen_symm_workspace * w)
{
if (A->size1 != A->size2)
{
GSL_ERROR ("matrix must be square to compute eigenvalues", GSL_ENOTSQR);
}
else if (eval->size != A->size1)
{
GSL_ERROR ("eigenvalue vector must match matrix size", GSL_EBADLEN);
}
else
{
const size_t N = A->size1;
double *const d = w->d;
double *const sd = w->sd;
size_t a, b;
/* handle special case */
if (N == 1)
{
double A00 = gsl_matrix_get (A, 0, 0);
gsl_vector_set (eval, 0, A00);
return GSL_SUCCESS;
}
/* use sd as the temporary workspace for the decomposition,
since we can discard the tau result immediately if we are not
computing eigenvectors */
{
gsl_vector_view d_vec = gsl_vector_view_array (d, N);
gsl_vector_view sd_vec = gsl_vector_view_array (sd, N - 1);
gsl_vector_view tau = gsl_vector_view_array (sd, N - 1);
gsl_linalg_symmtd_decomp (A, &tau.vector);
gsl_linalg_symmtd_unpack_T (A, &d_vec.vector, &sd_vec.vector);
}
/* Make an initial pass through the tridiagonal decomposition
to remove off-diagonal elements which are effectively zero */
chop_small_elements (N, d, sd);
/* Progressively reduce the matrix until it is diagonal */
b = N - 1;
while (b > 0)
{
if (sd[b - 1] == 0.0 || isnan(sd[b - 1]))
{
b--;
continue;
}
/* Find the largest unreduced block (a,b) starting from b
and working backwards */
a = b - 1;
while (a > 0)
{
if (sd[a - 1] == 0.0)
{
break;
}
a--;
}
{
const size_t n_block = b - a + 1;
double *d_block = d + a;
double *sd_block = sd + a;
/* apply QR reduction with implicit deflation to the
unreduced block */
qrstep (n_block, d_block, sd_block, NULL, NULL);
/* remove any small off-diagonal elements */
chop_small_elements (n_block, d_block, sd_block);
}
}
{
gsl_vector_view d_vec = gsl_vector_view_array (d, N);
gsl_vector_memcpy (eval, &d_vec.vector);
}
return GSL_SUCCESS;
}
}
int main(int argc, char **argv) {
gsl_rng *rng;
gsl_rng_env_setup();
const gsl_rng_type *rngType = gsl_rng_default;
rng = gsl_rng_alloc(rngType);
const size_t M = SIZE1;
const size_t N = SIZE2;
gsl_matrix *A = gsl_matrix_alloc(M, N);
int i = 0;
int j = 0;
int sigNum = 0;
for (i = 0; i < M; i++) {
for (j = 0; j < N; j++) {
gsl_matrix_set(A, i, j, gsl_ran_ugaussian(rng));
}
}
gsl_matrix *B = gsl_matrix_alloc(M, N);
gsl_matrix_memcpy(B, A);
gsl_matrix *C = gsl_matrix_alloc(M, N);
gsl_blas_dgemm(CblasNoTrans, CblasTrans, 1.0, A, B, 0.0, C);
gsl_matrix *D = gsl_matrix_alloc(M, N);
gsl_matrix_memcpy(D, C); // will be used in QTQ' decompostion
gsl_linalg_cholesky_decomp(C);
printf("%e\n", gsl_matrix_get(C, M/2, N/2));
gsl_matrix_free(B);
gsl_matrix *A1 = gsl_matrix_alloc(M, N);
gsl_matrix_memcpy(A1, A);
gsl_permutation *P = gsl_permutation_alloc(M); // will be used in
// other cases
gsl_permutation_init(P);
gsl_ran_shuffle (rng, P->data, M, sizeof(size_t));
gsl_linalg_LU_decomp(A1, P, &sigNum);
printf("%e\n", gsl_matrix_get(A1, M/2, N/2));
gsl_matrix *A2 = gsl_matrix_alloc(M, N);
gsl_matrix_memcpy(A2, A);
gsl_vector *tau = gsl_vector_alloc(GSL_MIN(M, N));
gsl_linalg_QR_decomp(A2, tau);
printf("%e\n", gsl_matrix_get(A2, M/2, N/2));
gsl_vector_free(tau);
gsl_matrix *A3 = gsl_matrix_alloc(M, N);
gsl_matrix_memcpy(A3, A);
gsl_matrix *svdV = gsl_matrix_alloc(N, N);
gsl_vector *svdS = gsl_vector_alloc(N);
gsl_vector *svdWorkspace = gsl_vector_alloc(N);
gsl_linalg_SV_decomp(A3, svdV, svdS, svdWorkspace);
printf("%e\n", gsl_vector_get(svdS, N/2));
gsl_vector *tau2 = gsl_vector_alloc(N - 1);
gsl_linalg_symmtd_decomp(D, tau2);
printf("%e\n", gsl_matrix_get(D, N/2, N/2));
return 0;
}