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; } }