int gsl_linalg_symmtd_decomp (gsl_matrix * A, gsl_vector * tau) { if (A->size1 != A->size2) { GSL_ERROR ("symmetric 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; for (i = 0 ; i < N - 2; i++) { gsl_vector_view c = gsl_matrix_column (A, i); gsl_vector_view v = gsl_vector_subvector (&c.vector, i + 1, N - (i + 1)); double tau_i = gsl_linalg_householder_transform (&v.vector); /* Apply the transformation H^T A H to the remaining columns */ if (tau_i != 0.0) { gsl_matrix_view m = gsl_matrix_submatrix (A, i + 1, i + 1, N - (i+1), N - (i+1)); double ei = gsl_vector_get(&v.vector, 0); gsl_vector_view x = gsl_vector_subvector (tau, i, N-(i+1)); gsl_vector_set (&v.vector, 0, 1.0); /* x = tau * A * v */ gsl_blas_dsymv (CblasLower, tau_i, &m.matrix, &v.vector, 0.0, &x.vector); /* w = x - (1/2) tau * (x' * v) * v */ { double xv, alpha; gsl_blas_ddot(&x.vector, &v.vector, &xv); alpha = - (tau_i / 2.0) * xv; gsl_blas_daxpy(alpha, &v.vector, &x.vector); } /* apply the transformation A = A - v w' - w v' */ gsl_blas_dsyr2(CblasLower, -1.0, &v.vector, &x.vector, &m.matrix); gsl_vector_set (&v.vector, 0, ei); } gsl_vector_set (tau, i, tau_i); } return GSL_SUCCESS; } }
int gsl_eigen_gensymm_standardize(gsl_matrix *A, const gsl_matrix *B) { const size_t N = A->size1; size_t i; double a, b, c; for (i = 0; i < N; ++i) { /* update lower triangle of A(i:n, i:n) */ a = gsl_matrix_get(A, i, i); b = gsl_matrix_get(B, i, i); a /= b * b; gsl_matrix_set(A, i, i, a); if (i < N - 1) { gsl_vector_view ai = gsl_matrix_subcolumn(A, i, i + 1, N - i - 1); gsl_matrix_view ma = gsl_matrix_submatrix(A, i + 1, i + 1, N - i - 1, N - i - 1); gsl_vector_const_view bi = gsl_matrix_const_subcolumn(B, i, i + 1, N - i - 1); gsl_matrix_const_view mb = gsl_matrix_const_submatrix(B, i + 1, i + 1, N - i - 1, N - i - 1); gsl_blas_dscal(1.0 / b, &ai.vector); c = -0.5 * a; gsl_blas_daxpy(c, &bi.vector, &ai.vector); gsl_blas_dsyr2(CblasLower, -1.0, &ai.vector, &bi.vector, &ma.matrix); gsl_blas_daxpy(c, &bi.vector, &ai.vector); gsl_blas_dtrsv(CblasLower, CblasNoTrans, CblasNonUnit, &mb.matrix, &ai.vector); } } return GSL_SUCCESS; } /* gsl_eigen_gensymm_standardize() */
/** * C++ version of gsl_blas_dsyr2(). * @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 dsyr2( CBLAS_UPLO_t Uplo, double alpha, vector const& X, vector const& Y, matrix& A ){ return gsl_blas_dsyr2( Uplo, alpha, X.get(), Y.get(), A.get() ); }