CAMLprim value ml_gsl_linalg_symmtd_unpack(value A, value TAU, value Q,
value DIAG, value SUBDIAG)
{
_DECLARE_MATRIX2(A, Q);
_DECLARE_VECTOR3(TAU, DIAG, SUBDIAG);
_CONVERT_MATRIX2(A, Q);
_CONVERT_VECTOR3(TAU, DIAG, SUBDIAG);
gsl_linalg_symmtd_unpack(&m_A, &v_TAU, &m_Q, &v_DIAG, &v_SUBDIAG);
return Val_unit;
}
/**
* C++ version of gsl_linalg_symmtd_unpack().
* @param A A matrix
* @param tau A vector
* @param Q A matrix
* @param diag A vector of diagonal elements
* @param subdiag The vector of subdiagonal elements
* @return Error code on failure
*/
inline int symmtd_unpack( matrix const& A, vector const& tau, matrix& Q,
vector& diag, vector& subdiag ){
return gsl_linalg_symmtd_unpack( A.get(), tau.get(), Q.get(), diag.get(), subdiag.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;
}
}
