CAMLprim value ml_gsl_linalg_symmtd_unpack(value A, value TAU, value Q, value DIAG, value SUBDIAG) { _DECLARE_MATRIX2(A, Q); _DECLARE_VECTOR3(TAU, DIAG, SUBDIAG); _CONVERT_MATRIX2(A, Q); _CONVERT_VECTOR3(TAU, DIAG, SUBDIAG); gsl_linalg_symmtd_unpack(&m_A, &v_TAU, &m_Q, &v_DIAG, &v_SUBDIAG); return Val_unit; }
/** * C++ version of gsl_linalg_symmtd_unpack(). * @param A A matrix * @param tau A vector * @param Q A matrix * @param diag A vector of diagonal elements * @param subdiag The vector of subdiagonal elements * @return Error code on failure */ inline int symmtd_unpack( matrix const& A, vector const& tau, matrix& Q, vector& diag, vector& subdiag ){ return gsl_linalg_symmtd_unpack( A.get(), tau.get(), Q.get(), diag.get(), subdiag.get() ); }
int gsl_eigen_symmv (gsl_matrix * A, gsl_vector * eval, gsl_matrix * evec, gsl_eigen_symmv_workspace * w) { if (A->size1 != A->size2) { GSL_ERROR ("matrix must be square to compute eigenvalues", GSL_ENOTSQR); } else if (eval->size != A->size1) { GSL_ERROR ("eigenvalue vector must match matrix size", GSL_EBADLEN); } else if (evec->size1 != A->size1 || evec->size2 != A->size1) { GSL_ERROR ("eigenvector matrix must match matrix size", GSL_EBADLEN); } else { double *const d = w->d; double *const sd = w->sd; const size_t N = A->size1; size_t a, b; /* handle special case */ if (N == 1) { double A00 = gsl_matrix_get (A, 0, 0); gsl_vector_set (eval, 0, A00); gsl_matrix_set (evec, 0, 0, 1.0); return GSL_SUCCESS; } /* use sd as the temporary workspace for the decomposition when computing eigenvectors */ { gsl_vector_view d_vec = gsl_vector_view_array (d, N); gsl_vector_view sd_vec = gsl_vector_view_array (sd, N - 1); gsl_vector_view tau = gsl_vector_view_array (sd, N - 1); gsl_linalg_symmtd_decomp (A, &tau.vector); gsl_linalg_symmtd_unpack (A, &tau.vector, evec, &d_vec.vector, &sd_vec.vector); } /* Make an initial pass through the tridiagonal decomposition to remove off-diagonal elements which are effectively zero */ chop_small_elements (N, d, sd); /* Progressively reduce the matrix until it is diagonal */ b = N - 1; while (b > 0) { if (sd[b - 1] == 0.0 || isnan(sd[b - 1])) { b--; continue; } /* Find the largest unreduced block (a,b) starting from b and working backwards */ a = b - 1; while (a > 0) { if (sd[a - 1] == 0.0) { break; } a--; } { size_t i; const size_t n_block = b - a + 1; double *d_block = d + a; double *sd_block = sd + a; double * const gc = w->gc; double * const gs = w->gs; /* apply QR reduction with implicit deflation to the unreduced block */ qrstep (n_block, d_block, sd_block, gc, gs); /* Apply Givens rotation Gij(c,s) to matrix Q, Q <- Q G */ for (i = 0; i < n_block - 1; i++) { const double c = gc[i], s = gs[i]; size_t k; for (k = 0; k < N; k++) { double qki = gsl_matrix_get (evec, k, a + i); double qkj = gsl_matrix_get (evec, k, a + i + 1); gsl_matrix_set (evec, k, a + i, qki * c - qkj * s); gsl_matrix_set (evec, k, a + i + 1, qki * s + qkj * c); } } /* remove any small off-diagonal elements */ chop_small_elements (N, d, sd); } } { gsl_vector_view d_vec = gsl_vector_view_array (d, N); gsl_vector_memcpy (eval, &d_vec.vector); } return GSL_SUCCESS; } }