static VALUE rb_gsl_linalg_complex_householder_transform(int argc, VALUE *argv, VALUE obj)
{
gsl_vector_complex *v = NULL;
gsl_complex *z;
switch (TYPE(obj)) {
case T_MODULE: case T_CLASS: case T_OBJECT:
if (argc < 1) rb_raise(rb_eArgError, "too few arguments.");
CHECK_VECTOR_COMPLEX(argv[0]);
Data_Get_Struct(argv[0], gsl_vector_complex, v);
break;
default:
Data_Get_Struct(obj, gsl_vector_complex, v);
break;
}
z = (gsl_complex*) malloc(sizeof(gsl_complex));
*z = gsl_linalg_complex_householder_transform(v);
return Data_Wrap_Struct(cgsl_complex, 0, free, z);
}
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_transform().
* @param v A vector
* @return The Householder transform
*/
inline complex complex_householder_transform( vector_complex& v ){
return gsl_linalg_complex_householder_transform( v.get() ); }
int
gsl_linalg_hermtd_decomp (gsl_matrix_complex * A, gsl_vector_complex * tau)
{
if (A->size1 != A->size2)
{
GSL_ERROR ("hermitian tridiagonal decomposition requires square matrix",
GSL_ENOTSQR);
}
else if (tau->size + 1 != A->size1)
{
GSL_ERROR ("size of tau must be (matrix size - 1)", GSL_EBADLEN);
}
else
{
const size_t N = A->size1;
size_t i;
const gsl_complex zero = gsl_complex_rect (0.0, 0.0);
const gsl_complex one = gsl_complex_rect (1.0, 0.0);
const gsl_complex neg_one = gsl_complex_rect (-1.0, 0.0);
for (i = 0 ; i < N - 1; i++)
{
gsl_vector_complex_view c = gsl_matrix_complex_column (A, i);
gsl_vector_complex_view v = gsl_vector_complex_subvector (&c.vector, i + 1, N - (i + 1));
gsl_complex tau_i = gsl_linalg_complex_householder_transform (&v.vector);
/* Apply the transformation H^T A H to the remaining columns */
if ((i + 1) < (N - 1)
&& !(GSL_REAL(tau_i) == 0.0 && GSL_IMAG(tau_i) == 0.0))
{
gsl_matrix_complex_view m =
gsl_matrix_complex_submatrix (A, i + 1, i + 1,
N - (i+1), N - (i+1));
gsl_complex ei = gsl_vector_complex_get(&v.vector, 0);
gsl_vector_complex_view x = gsl_vector_complex_subvector (tau, i, N-(i+1));
gsl_vector_complex_set (&v.vector, 0, one);
/* x = tau * A * v */
gsl_blas_zhemv (CblasLower, tau_i, &m.matrix, &v.vector, zero, &x.vector);
/* w = x - (1/2) tau * (x' * v) * v */
{
gsl_complex xv, txv, alpha;
gsl_blas_zdotc(&x.vector, &v.vector, &xv);
txv = gsl_complex_mul(tau_i, xv);
alpha = gsl_complex_mul_real(txv, -0.5);
gsl_blas_zaxpy(alpha, &v.vector, &x.vector);
}
/* apply the transformation A = A - v w' - w v' */
gsl_blas_zher2(CblasLower, neg_one, &v.vector, &x.vector, &m.matrix);
gsl_vector_complex_set (&v.vector, 0, ei);
}
gsl_vector_complex_set (tau, i, tau_i);
}
return GSL_SUCCESS;
}
}
