static int multifit_wlinear_svd (const gsl_matrix * X, const gsl_vector * w, const gsl_vector * y, double tol, int balance, size_t * rank, gsl_vector * c, gsl_matrix * cov, double *chisq, gsl_multifit_linear_workspace * work) { if (X->size1 != y->size) { GSL_ERROR ("number of observations in y does not match rows of matrix X", GSL_EBADLEN); } else if (X->size2 != c->size) { GSL_ERROR ("number of parameters c does not match columns of matrix X", GSL_EBADLEN); } else if (w->size != y->size) { GSL_ERROR ("number of weights does not match number of observations", GSL_EBADLEN); } else if (cov->size1 != cov->size2) { GSL_ERROR ("covariance matrix is not square", GSL_ENOTSQR); } else if (c->size != cov->size1) { GSL_ERROR ("number of parameters does not match size of covariance matrix", GSL_EBADLEN); } else if (X->size1 != work->n || X->size2 != work->p) { GSL_ERROR ("size of workspace does not match size of observation matrix", GSL_EBADLEN); } else { const size_t n = X->size1; const size_t p = X->size2; size_t i, j, p_eff; gsl_matrix *A = work->A; gsl_matrix *Q = work->Q; gsl_matrix *QSI = work->QSI; gsl_vector *S = work->S; gsl_vector *t = work->t; gsl_vector *xt = work->xt; gsl_vector *D = work->D; /* Scale X, A = sqrt(w) X */ gsl_matrix_memcpy (A, X); for (i = 0; i < n; i++) { double wi = gsl_vector_get (w, i); if (wi < 0) wi = 0; { gsl_vector_view row = gsl_matrix_row (A, i); gsl_vector_scale (&row.vector, sqrt (wi)); } } /* Balance the columns of the matrix A if requested */ if (balance) { gsl_linalg_balance_columns (A, D); } else { gsl_vector_set_all (D, 1.0); } /* Decompose A into U S Q^T */ gsl_linalg_SV_decomp_mod (A, QSI, Q, S, xt); /* Solve sqrt(w) y = A c for c, by first computing t = sqrt(w) y */ for (i = 0; i < n; i++) { double wi = gsl_vector_get (w, i); double yi = gsl_vector_get (y, i); if (wi < 0) wi = 0; gsl_vector_set (t, i, sqrt (wi) * yi); } gsl_blas_dgemv (CblasTrans, 1.0, A, t, 0.0, xt); /* Scale the matrix Q, Q' = Q S^-1 */ gsl_matrix_memcpy (QSI, Q); { double alpha0 = gsl_vector_get (S, 0); p_eff = 0; for (j = 0; j < p; j++) { gsl_vector_view column = gsl_matrix_column (QSI, j); double alpha = gsl_vector_get (S, j); if (alpha <= tol * alpha0) { alpha = 0.0; } else { alpha = 1.0 / alpha; p_eff++; } gsl_vector_scale (&column.vector, alpha); } *rank = p_eff; } gsl_vector_set_zero (c); /* Solution */ gsl_blas_dgemv (CblasNoTrans, 1.0, QSI, xt, 0.0, c); /* Unscale the balancing factors */ gsl_vector_div (c, D); /* Compute chisq, from residual r = y - X c */ { double r2 = 0; for (i = 0; i < n; i++) { double yi = gsl_vector_get (y, i); double wi = gsl_vector_get (w, i); gsl_vector_const_view row = gsl_matrix_const_row (X, i); double y_est, ri; gsl_blas_ddot (&row.vector, c, &y_est); ri = yi - y_est; r2 += wi * ri * ri; } *chisq = r2; /* Form covariance matrix cov = (X^T W X)^-1 = (Q S^-1) (Q S^-1)^T */ for (i = 0; i < p; i++) { gsl_vector_view row_i = gsl_matrix_row (QSI, i); double d_i = gsl_vector_get (D, i); for (j = i; j < p; j++) { gsl_vector_view row_j = gsl_matrix_row (QSI, j); double d_j = gsl_vector_get (D, j); double s; gsl_blas_ddot (&row_i.vector, &row_j.vector, &s); gsl_matrix_set (cov, i, j, s / (d_i * d_j)); gsl_matrix_set (cov, j, i, s / (d_i * d_j)); } } } return GSL_SUCCESS; } }
/** * C++ version of gsl_linalg_balance_columns(). * @param A A matrix * @param D A vector * @return Error code on failure */ inline int balance_columns( matrix& A, vector& D ){ return gsl_linalg_balance_columns( A.get(), D.get() ); }
int gsl_multifit_linear_svd (const gsl_matrix * X, const gsl_vector * y, double tol, size_t * rank, gsl_vector * c, gsl_matrix * cov, double *chisq, gsl_multifit_linear_workspace * work) { if (X->size1 != y->size) { GSL_ERROR ("number of observations in y does not match rows of matrix X", GSL_EBADLEN); } else if (X->size2 != c->size) { GSL_ERROR ("number of parameters c does not match columns of matrix X", GSL_EBADLEN); } else if (cov->size1 != cov->size2) { GSL_ERROR ("covariance matrix is not square", GSL_ENOTSQR); } else if (c->size != cov->size1) { GSL_ERROR ("number of parameters does not match size of covariance matrix", GSL_EBADLEN); } else if (X->size1 != work->n || X->size2 != work->p) { GSL_ERROR ("size of workspace does not match size of observation matrix", GSL_EBADLEN); } else if (tol <= 0) { GSL_ERROR ("tolerance must be positive", GSL_EINVAL); } else { const size_t n = X->size1; const size_t p = X->size2; size_t i, j, p_eff; gsl_matrix *A = work->A; gsl_matrix *Q = work->Q; gsl_matrix *QSI = work->QSI; gsl_vector *S = work->S; gsl_vector *xt = work->xt; gsl_vector *D = work->D; /* Copy X to workspace, A <= X */ gsl_matrix_memcpy (A, X); /* Balance the columns of the matrix A */ gsl_linalg_balance_columns (A, D); /* Decompose A into U S Q^T */ gsl_linalg_SV_decomp_mod (A, QSI, Q, S, xt); /* Solve y = A c for c */ gsl_blas_dgemv (CblasTrans, 1.0, A, y, 0.0, xt); /* Scale the matrix Q, Q' = Q S^-1 */ gsl_matrix_memcpy (QSI, Q); { double alpha0 = gsl_vector_get (S, 0); p_eff = 0; for (j = 0; j < p; j++) { gsl_vector_view column = gsl_matrix_column (QSI, j); double alpha = gsl_vector_get (S, j); if (alpha <= tol * alpha0) { alpha = 0.0; } else { alpha = 1.0 / alpha; p_eff++; } gsl_vector_scale (&column.vector, alpha); } *rank = p_eff; } gsl_vector_set_zero (c); gsl_blas_dgemv (CblasNoTrans, 1.0, QSI, xt, 0.0, c); /* Unscale the balancing factors */ gsl_vector_div (c, D); /* Compute chisq, from residual r = y - X c */ { double s2 = 0, r2 = 0; for (i = 0; i < n; i++) { double yi = gsl_vector_get (y, i); gsl_vector_const_view row = gsl_matrix_const_row (X, i); double y_est, ri; gsl_blas_ddot (&row.vector, c, &y_est); ri = yi - y_est; r2 += ri * ri; } s2 = r2 / (n - p_eff); /* p_eff == rank */ *chisq = r2; /* Form variance-covariance matrix cov = s2 * (Q S^-1) (Q S^-1)^T */ for (i = 0; i < p; i++) { gsl_vector_view row_i = gsl_matrix_row (QSI, i); double d_i = gsl_vector_get (D, i); for (j = i; j < p; j++) { gsl_vector_view row_j = gsl_matrix_row (QSI, j); double d_j = gsl_vector_get (D, j); double s; gsl_blas_ddot (&row_i.vector, &row_j.vector, &s); gsl_matrix_set (cov, i, j, s * s2 / (d_i * d_j)); gsl_matrix_set (cov, j, i, s * s2 / (d_i * d_j)); } } } return GSL_SUCCESS; } }