/** * C++ version of gsl_blas_zher2(). * @param Uplo Upper or lower triangular * @param alpha A constant * @param X A vector * @param Y A vector * @param A A matrix * @return Error code on failure */ int zher2( CBLAS_UPLO_t Uplo, complex const alpha, vector_complex const& X, vector_complex const& Y, matrix_complex& A ){ return gsl_blas_zher2( Uplo, alpha.get(), X.get(), Y.get(), A.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; } }