static VALUE rb_gsl_linalg_complex_householder_mh(VALUE obj, VALUE t, VALUE vv, VALUE aa)
{
gsl_vector_complex *v = NULL;
gsl_complex *tau;
gsl_matrix_complex *A = NULL;
CHECK_COMPLEX(t);
CHECK_VECTOR_COMPLEX(vv);
CHECK_MATRIX_COMPLEX(aa);
Data_Get_Struct(t, gsl_complex, tau);
Data_Get_Struct(vv, gsl_vector_complex, v);
Data_Get_Struct(aa, gsl_matrix_complex, A);
gsl_linalg_complex_householder_hm(*tau, v, A);
return aa;
}
void
create_random_complex_posdef_matrix(gsl_matrix_complex *m, gsl_rng *r,
gsl_vector_complex *work)
{
const size_t N = m->size1;
size_t i, j;
double x, y;
gsl_complex z;
gsl_complex tau;
GSL_SET_IMAG(&z, 0.0);
/* make a positive diagonal matrix */
gsl_matrix_complex_set_zero(m);
for (i = 0; i < N; ++i)
{
x = gsl_rng_uniform(r);
GSL_SET_REAL(&z, x);
gsl_matrix_complex_set(m, i, i, z);
}
/* now generate random householder reflections and form P D P^H */
for (i = 0; i < N; ++i)
{
/* form complex vector */
for (j = 0; j < N; ++j)
{
x = 2.0 * gsl_rng_uniform(r) - 1.0;
y = 2.0 * gsl_rng_uniform(r) - 1.0;
GSL_SET_COMPLEX(&z, x, y);
gsl_vector_complex_set(work, j, z);
}
tau = gsl_linalg_complex_householder_transform(work);
gsl_linalg_complex_householder_hm(tau, work, m);
gsl_linalg_complex_householder_mh(gsl_complex_conjugate(tau), work, m);
}
} /* create_random_complex_posdef_matrix() */
/**
* C++ version of gsl_linalg_complex_householder_hm().
* @param tau A scalar
* @param v A vector
* @param A A matrix
* @return Error code on failure
*/
inline int complex_householder_hm( complex& tau, vector_complex const& v, matrix_complex& A ){
return gsl_linalg_complex_householder_hm( tau.get(), v.get(), A.get() ); }
int
gsl_linalg_hermtd_unpack (const gsl_matrix_complex * A,
const gsl_vector_complex * tau,
gsl_matrix_complex * U,
gsl_vector * diag,
gsl_vector * sdiag)
{
if (A->size1 != A->size2)
{
GSL_ERROR ("matrix A must be sqaure", GSL_ENOTSQR);
}
else if (tau->size + 1 != A->size1)
{
GSL_ERROR ("size of tau must be (matrix size - 1)", GSL_EBADLEN);
}
else if (U->size1 != A->size1 || U->size2 != A->size1)
{
GSL_ERROR ("size of U must match size of A", GSL_EBADLEN);
}
else if (diag->size != A->size1)
{
GSL_ERROR ("size of diagonal must match size of A", GSL_EBADLEN);
}
else if (sdiag->size + 1 != A->size1)
{
GSL_ERROR ("size of subdiagonal must be (matrix size - 1)", GSL_EBADLEN);
}
else
{
const size_t N = A->size1;
size_t i;
/* Initialize U to the identity */
gsl_matrix_complex_set_identity (U);
for (i = N - 1; i-- > 0;)
{
gsl_complex ti = gsl_vector_complex_get (tau, i);
gsl_vector_complex_const_view c = gsl_matrix_complex_const_column (A, i);
gsl_vector_complex_const_view h =
gsl_vector_complex_const_subvector (&c.vector, i + 1, N - (i+1));
gsl_matrix_complex_view m =
gsl_matrix_complex_submatrix (U, i + 1, i + 1, N-(i+1), N-(i+1));
gsl_linalg_complex_householder_hm (ti, &h.vector, &m.matrix);
}
/* Copy diagonal into diag */
for (i = 0; i < N; i++)
{
gsl_complex Aii = gsl_matrix_complex_get (A, i, i);
gsl_vector_set (diag, i, GSL_REAL(Aii));
}
/* Copy subdiagonal into sdiag */
for (i = 0; i < N - 1; i++)
{
gsl_complex Aji = gsl_matrix_complex_get (A, i+1, i);
gsl_vector_set (sdiag, i, GSL_REAL(Aji));
}
return GSL_SUCCESS;
}
}
