/* PSPP - a program for statistical analysis. Copyright (C) 2005, 2009 Free Software Foundation, Inc. This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . */ #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include "xalloc.h" #include "gettext.h" #define _(msgid) gettext (msgid) #define REG_LARGE_DATA 1000 /* (headers) */ /* (specification) "REGRESSION" (regression_): *variables=custom; +statistics[st_]=r, coeff, anova, outs, zpp, label, sha, ci, bcov, ses, xtx, collin, tol, selection, f, defaults, all; ^dependent=varlist; +save[sv_]=resid,pred; +method=enter. */ /* (declarations) */ /* (functions) */ static struct cmd_regression cmd; /* Moments for each of the variables used. */ struct moments_var { struct moments1 *m; const struct variable *v; }; /* Transformations for saving predicted values and residuals, etc. */ struct reg_trns { int n_trns; /* Number of transformations. */ int trns_id; /* Which trns is this one? */ linreg *c; /* Linear model for this trns. */ }; /* Variables used (both explanatory and response). */ static const struct variable **v_variables; /* Number of variables. */ static size_t n_variables; static bool run_regression (struct casereader *, struct cmd_regression *, struct dataset *, linreg **); /* STATISTICS subcommand output functions. */ static void reg_stats_r (linreg *); static void reg_stats_coeff (linreg *); static void reg_stats_anova (linreg *); static void reg_stats_outs (linreg *); static void reg_stats_zpp (linreg *); static void reg_stats_label (linreg *); static void reg_stats_sha (linreg *); static void reg_stats_ci (linreg *); static void reg_stats_f (linreg *); static void reg_stats_bcov (linreg *); static void reg_stats_ses (linreg *); static void reg_stats_xtx (linreg *); static void reg_stats_collin (linreg *); static void reg_stats_tol (linreg *); static void reg_stats_selection (linreg *); static void statistics_keyword_output (void (*)(linreg *), int, linreg *); static void reg_stats_r (linreg * c) { struct tab_table *t; int n_rows = 2; int n_cols = 5; double rsq; double adjrsq; double std_error; assert (c != NULL); rsq = linreg_ssreg (c) / linreg_sst (c); adjrsq = 1.0 - (1.0 - rsq) * (linreg_n_obs (c) - 1.0) / (linreg_n_obs (c) - linreg_n_coeffs (c)); std_error = sqrt (linreg_mse (c)); t = tab_create (n_cols, n_rows, 0); tab_dim (t, tab_natural_dimensions, NULL); tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, n_cols - 1, n_rows - 1); tab_hline (t, TAL_2, 0, n_cols - 1, 1); tab_vline (t, TAL_2, 2, 0, n_rows - 1); tab_vline (t, TAL_0, 1, 0, 0); tab_text (t, 1, 0, TAB_CENTER | TAT_TITLE, _("R")); tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("R Square")); tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("Adjusted R Square")); tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Std. Error of the Estimate")); tab_double (t, 1, 1, TAB_RIGHT, sqrt (rsq), NULL); tab_double (t, 2, 1, TAB_RIGHT, rsq, NULL); tab_double (t, 3, 1, TAB_RIGHT, adjrsq, NULL); tab_double (t, 4, 1, TAB_RIGHT, std_error, NULL); tab_title (t, _("Model Summary")); tab_submit (t); } /* Table showing estimated regression coefficients. */ static void reg_stats_coeff (linreg * c) { size_t j; int n_cols = 7; int n_rows; int this_row; double t_stat; double pval; double std_err; double beta; const char *label; const struct variable *v; struct tab_table *t; assert (c != NULL); n_rows = linreg_n_coeffs (c) + 3; t = tab_create (n_cols, n_rows, 0); tab_headers (t, 2, 0, 1, 0); tab_dim (t, tab_natural_dimensions, NULL); tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, n_cols - 1, n_rows - 1); tab_hline (t, TAL_2, 0, n_cols - 1, 1); tab_vline (t, TAL_2, 2, 0, n_rows - 1); tab_vline (t, TAL_0, 1, 0, 0); tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("B")); tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("Std. Error")); tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Beta")); tab_text (t, 5, 0, TAB_CENTER | TAT_TITLE, _("t")); tab_text (t, 6, 0, TAB_CENTER | TAT_TITLE, _("Significance")); tab_text (t, 1, 1, TAB_LEFT | TAT_TITLE, _("(Constant)")); tab_double (t, 2, 1, 0, linreg_intercept (c), NULL); std_err = sqrt (gsl_matrix_get (linreg_cov (c), 0, 0)); tab_double (t, 3, 1, 0, std_err, NULL); tab_double (t, 4, 1, 0, 0.0, NULL); t_stat = linreg_intercept (c) / std_err; tab_double (t, 5, 1, 0, t_stat, NULL); pval = 2 * gsl_cdf_tdist_Q (fabs (t_stat), 1.0); tab_double (t, 6, 1, 0, pval, NULL); for (j = 0; j < linreg_n_coeffs (c); j++) { struct string tstr; ds_init_empty (&tstr); this_row = j + 2; v = linreg_indep_var (c, j); label = var_to_string (v); /* Do not overwrite the variable's name. */ ds_put_cstr (&tstr, label); tab_text (t, 1, this_row, TAB_CENTER, ds_cstr (&tstr)); /* Regression coefficients. */ tab_double (t, 2, this_row, 0, linreg_coeff (c, j), NULL); /* Standard error of the coefficients. */ std_err = sqrt (gsl_matrix_get (linreg_cov (c), j + 1, j + 1)); tab_double (t, 3, this_row, 0, std_err, NULL); /* Standardized coefficient, i.e., regression coefficient if all variables had unit variance. */ beta = sqrt (gsl_matrix_get (linreg_cov (c), j, j)); beta *= linreg_coeff (c, j) / c->depvar_std; tab_double (t, 4, this_row, 0, beta, NULL); /* Test statistic for H0: coefficient is 0. */ t_stat = linreg_coeff (c, j) / std_err; tab_double (t, 5, this_row, 0, t_stat, NULL); /* P values for the test statistic above. */ pval = 2 * gsl_cdf_tdist_Q (fabs (t_stat), (double) (linreg_n_obs (c) - linreg_n_coeffs (c))); tab_double (t, 6, this_row, 0, pval, NULL); ds_destroy (&tstr); } tab_title (t, _("Coefficients")); tab_submit (t); } /* Display the ANOVA table. */ static void reg_stats_anova (linreg * c) { int n_cols = 7; int n_rows = 4; const double msm = linreg_ssreg (c) / linreg_dfmodel (c); const double mse = linreg_mse (c); const double F = msm / mse; const double pval = gsl_cdf_fdist_Q (F, c->dfm, c->dfe); struct tab_table *t; assert (c != NULL); t = tab_create (n_cols, n_rows, 0); tab_headers (t, 2, 0, 1, 0); tab_dim (t, tab_natural_dimensions, NULL); tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, n_cols - 1, n_rows - 1); tab_hline (t, TAL_2, 0, n_cols - 1, 1); tab_vline (t, TAL_2, 2, 0, n_rows - 1); tab_vline (t, TAL_0, 1, 0, 0); tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("Sum of Squares")); tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("df")); tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Mean Square")); tab_text (t, 5, 0, TAB_CENTER | TAT_TITLE, _("F")); tab_text (t, 6, 0, TAB_CENTER | TAT_TITLE, _("Significance")); tab_text (t, 1, 1, TAB_LEFT | TAT_TITLE, _("Regression")); tab_text (t, 1, 2, TAB_LEFT | TAT_TITLE, _("Residual")); tab_text (t, 1, 3, TAB_LEFT | TAT_TITLE, _("Total")); /* Sums of Squares */ tab_double (t, 2, 1, 0, linreg_ssreg (c), NULL); tab_double (t, 2, 3, 0, linreg_sst (c), NULL); tab_double (t, 2, 2, 0, linreg_sse (c), NULL); /* Degrees of freedom */ tab_text_format (t, 3, 1, TAB_RIGHT, "%g", c->dfm); tab_text_format (t, 3, 2, TAB_RIGHT, "%g", c->dfe); tab_text_format (t, 3, 3, TAB_RIGHT, "%g", c->dft); /* Mean Squares */ tab_double (t, 4, 1, TAB_RIGHT, msm, NULL); tab_double (t, 4, 2, TAB_RIGHT, mse, NULL); tab_double (t, 5, 1, 0, F, NULL); tab_double (t, 6, 1, 0, pval, NULL); tab_title (t, _("ANOVA")); tab_submit (t); } static void reg_stats_outs (linreg * c) { assert (c != NULL); } static void reg_stats_zpp (linreg * c) { assert (c != NULL); } static void reg_stats_label (linreg * c) { assert (c != NULL); } static void reg_stats_sha (linreg * c) { assert (c != NULL); } static void reg_stats_ci (linreg * c) { assert (c != NULL); } static void reg_stats_f (linreg * c) { assert (c != NULL); } static void reg_stats_bcov (linreg * c) { int n_cols; int n_rows; int i; int k; int row; int col; const char *label; struct tab_table *t; assert (c != NULL); n_cols = c->n_indeps + 1 + 2; n_rows = 2 * (c->n_indeps + 1); t = tab_create (n_cols, n_rows, 0); tab_headers (t, 2, 0, 1, 0); tab_dim (t, tab_natural_dimensions, NULL); tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, n_cols - 1, n_rows - 1); tab_hline (t, TAL_2, 0, n_cols - 1, 1); tab_vline (t, TAL_2, 2, 0, n_rows - 1); tab_vline (t, TAL_0, 1, 0, 0); tab_text (t, 0, 0, TAB_CENTER | TAT_TITLE, _("Model")); tab_text (t, 1, 1, TAB_CENTER | TAT_TITLE, _("Covariances")); for (i = 0; i < linreg_n_coeffs (c); i++) { const struct variable *v = linreg_indep_var (c, i); label = var_to_string (v); tab_text (t, 2, i, TAB_CENTER, label); tab_text (t, i + 2, 0, TAB_CENTER, label); for (k = 1; k < linreg_n_coeffs (c); k++) { col = (i <= k) ? k : i; row = (i <= k) ? i : k; tab_double (t, k + 2, i, TAB_CENTER, gsl_matrix_get (c->cov, row, col), NULL); } } tab_title (t, _("Coefficient Correlations")); tab_submit (t); } static void reg_stats_ses (linreg * c) { assert (c != NULL); } static void reg_stats_xtx (linreg * c) { assert (c != NULL); } static void reg_stats_collin (linreg * c) { assert (c != NULL); } static void reg_stats_tol (linreg * c) { assert (c != NULL); } static void reg_stats_selection (linreg * c) { assert (c != NULL); } static void statistics_keyword_output (void (*function) (linreg *), int keyword, linreg * c) { if (keyword) { (*function) (c); } } static void subcommand_statistics (int *keywords, linreg * c) { /* The order here must match the order in which the STATISTICS keywords appear in the specification section above. */ enum { r, coeff, anova, outs, zpp, label, sha, ci, bcov, ses, xtx, collin, tol, selection, f, defaults, all }; int i; int d = 1; if (keywords[all]) { /* Set everything but F. */ for (i = 0; i < f; i++) { keywords[i] = 1; } } else { for (i = 0; i < all; i++) { if (keywords[i]) { d = 0; } } /* Default output: ANOVA table, parameter estimates, and statistics for variables not entered into model, if appropriate. */ if (keywords[defaults] | d) { keywords[anova] = 1; keywords[outs] = 1; keywords[coeff] = 1; keywords[r] = 1; } } statistics_keyword_output (reg_stats_r, keywords[r], c); statistics_keyword_output (reg_stats_anova, keywords[anova], c); statistics_keyword_output (reg_stats_coeff, keywords[coeff], c); statistics_keyword_output (reg_stats_outs, keywords[outs], c); statistics_keyword_output (reg_stats_zpp, keywords[zpp], c); statistics_keyword_output (reg_stats_label, keywords[label], c); statistics_keyword_output (reg_stats_sha, keywords[sha], c); statistics_keyword_output (reg_stats_ci, keywords[ci], c); statistics_keyword_output (reg_stats_f, keywords[f], c); statistics_keyword_output (reg_stats_bcov, keywords[bcov], c); statistics_keyword_output (reg_stats_ses, keywords[ses], c); statistics_keyword_output (reg_stats_xtx, keywords[xtx], c); statistics_keyword_output (reg_stats_collin, keywords[collin], c); statistics_keyword_output (reg_stats_tol, keywords[tol], c); statistics_keyword_output (reg_stats_selection, keywords[selection], c); } /* Free the transformation. Free its linear model if this transformation is the last one. */ static bool regression_trns_free (void *t_) { bool result = true; struct reg_trns *t = t_; if (t->trns_id == t->n_trns) { result = linreg_free (t->c); } free (t); return result; } /* Gets the predicted values. */ static int regression_trns_pred_proc (void *t_, struct ccase **c, casenumber case_idx UNUSED) { size_t i; size_t n_vals; struct reg_trns *trns = t_; linreg *model; union value *output = NULL; const union value *tmp; double *vals; const struct variable **vars = NULL; assert (trns != NULL); model = trns->c; assert (model != NULL); assert (model->depvar != NULL); assert (model->pred != NULL); vars = linreg_get_vars (model); n_vals = linreg_n_coeffs (model); vals = xnmalloc (n_vals, sizeof (*vals)); *c = case_unshare (*c); output = case_data_rw (*c, model->pred); for (i = 0; i < n_vals; i++) { tmp = case_data (*c, vars[i]); vals[i] = tmp->f; } output->f = linreg_predict (model, vals, n_vals); free (vals); return TRNS_CONTINUE; } /* Gets the residuals. */ static int regression_trns_resid_proc (void *t_, struct ccase **c, casenumber case_idx UNUSED) { size_t i; size_t n_vals; struct reg_trns *trns = t_; linreg *model; union value *output = NULL; const union value *tmp; double *vals = NULL; double obs; const struct variable **vars = NULL; assert (trns != NULL); model = trns->c; assert (model != NULL); assert (model->depvar != NULL); assert (model->resid != NULL); vars = linreg_get_vars (model); n_vals = linreg_n_coeffs (model); vals = xnmalloc (n_vals, sizeof (*vals)); *c = case_unshare (*c); output = case_data_rw (*c, model->resid); assert (output != NULL); for (i = 0; i < n_vals; i++) { tmp = case_data (*c, vars[i]); vals[i] = tmp->f; } tmp = case_data (*c, model->depvar); obs = tmp->f; output->f = linreg_residual (model, obs, vals, n_vals); free (vals); return TRNS_CONTINUE; } /* Returns false if NAME is a duplicate of any existing variable name. */ static bool try_name (const struct dictionary *dict, const char *name) { if (dict_lookup_var (dict, name) != NULL) return false; return true; } static void reg_get_name (const struct dictionary *dict, char name[VAR_NAME_LEN], const char prefix[VAR_NAME_LEN]) { int i = 1; snprintf (name, VAR_NAME_LEN, "%s%d", prefix, i); while (!try_name (dict, name)) { i++; snprintf (name, VAR_NAME_LEN, "%s%d", prefix, i); } } static void reg_save_var (struct dataset *ds, const char *prefix, trns_proc_func * f, linreg * c, struct variable **v, int n_trns) { struct dictionary *dict = dataset_dict (ds); static int trns_index = 1; char name[VAR_NAME_LEN]; struct variable *new_var; struct reg_trns *t = NULL; t = xmalloc (sizeof (*t)); t->trns_id = trns_index; t->n_trns = n_trns; t->c = c; reg_get_name (dict, name, prefix); new_var = dict_create_var (dict, name, 0); assert (new_var != NULL); *v = new_var; add_transformation (ds, f, regression_trns_free, t); trns_index++; } static void subcommand_save (struct dataset *ds, int save, linreg ** models) { linreg **lc; int n_trns = 0; int i; if (save) { /* Count the number of transformations we will need. */ for (i = 0; i < REGRESSION_SV_count; i++) { if (cmd.a_save[i]) { n_trns++; } } n_trns *= cmd.n_dependent; for (lc = models; lc < models + cmd.n_dependent; lc++) { if (*lc != NULL) { if ((*lc)->depvar != NULL) { if (cmd.a_save[REGRESSION_SV_RESID]) { reg_save_var (ds, "RES", regression_trns_resid_proc, *lc, &(*lc)->resid, n_trns); } if (cmd.a_save[REGRESSION_SV_PRED]) { reg_save_var (ds, "PRED", regression_trns_pred_proc, *lc, &(*lc)->pred, n_trns); } } } } } else { for (lc = models; lc < models + cmd.n_dependent; lc++) { if (*lc != NULL) { linreg_free (*lc); } } } } int cmd_regression (struct lexer *lexer, struct dataset *ds) { struct casegrouper *grouper; struct casereader *group; linreg **models; bool ok; size_t i; if (!parse_regression (lexer, ds, &cmd, NULL)) { return CMD_FAILURE; } models = xnmalloc (cmd.n_dependent, sizeof *models); for (i = 0; i < cmd.n_dependent; i++) { models[i] = NULL; } /* Data pass. */ grouper = casegrouper_create_splits (proc_open (ds), dataset_dict (ds)); while (casegrouper_get_next_group (grouper, &group)) run_regression (group, &cmd, ds, models); ok = casegrouper_destroy (grouper); ok = proc_commit (ds) && ok; subcommand_save (ds, cmd.sbc_save, models); free (v_variables); free (models); free_regression (&cmd); return ok ? CMD_SUCCESS : CMD_FAILURE; } /* Is variable k the dependent variable? */ static bool is_depvar (size_t k, const struct variable *v) { return v == v_variables[k]; } /* Parser for the variables sub command */ static int regression_custom_variables (struct lexer *lexer, struct dataset *ds, struct cmd_regression *cmd UNUSED, void *aux UNUSED) { const struct dictionary *dict = dataset_dict (ds); lex_match (lexer, '='); if ((lex_token (lexer) != T_ID || dict_lookup_var (dict, lex_tokid (lexer)) == NULL) && lex_token (lexer) != T_ALL) return 2; if (!parse_variables_const (lexer, dict, &v_variables, &n_variables, PV_NONE)) { free (v_variables); return 0; } assert (n_variables); return 1; } /* Identify the explanatory variables in v_variables. Returns the number of independent variables. */ static int identify_indep_vars (const struct variable **indep_vars, const struct variable *depvar) { int n_indep_vars = 0; int i; for (i = 0; i < n_variables; i++) if (!is_depvar (i, depvar)) indep_vars[n_indep_vars++] = v_variables[i]; if ((n_indep_vars < 1) && is_depvar (0, depvar)) { /* There is only one independent variable, and it is the same as the dependent variable. Print a warning and continue. */ msg (SE, gettext ("The dependent variable is equal to the independent variable." "The least squares line is therefore Y=X." "Standard errors and related statistics may be meaningless.")); n_indep_vars = 1; indep_vars[0] = v_variables[0]; } return n_indep_vars; } static double fill_covariance (gsl_matrix *cov, struct covariance *all_cov, const struct variable **vars, size_t n_vars, const struct variable *dep_var, const struct variable **all_vars, size_t n_all_vars, double *means) { size_t i; size_t j; size_t dep_subscript; size_t *rows; const gsl_matrix *ssizes; const gsl_matrix *cm; const gsl_matrix *mean_matrix; double result = 0.0; cm = covariance_calculate (all_cov); rows = xnmalloc (cov->size1 - 1, sizeof (*rows)); for (i = 0; i < n_all_vars; i++) { for (j = 0; j < n_vars; j++) { if (vars[j] == all_vars[i]) { rows[j] = i; } } if (all_vars[i] == dep_var) { dep_subscript = i; } } mean_matrix = covariance_moments (all_cov, MOMENT_MEAN); for (i = 0; i < cov->size1 - 1; i++) { means[i] = gsl_matrix_get (mean_matrix, rows[i], 0); for (j = 0; j < cov->size2 - 1; j++) { gsl_matrix_set (cov, i, j, gsl_matrix_get (cm, rows[i], rows[j])); gsl_matrix_set (cov, j, i, gsl_matrix_get (cm, rows[j], rows[i])); } } means[cov->size1 - 1] = gsl_matrix_get (mean_matrix, dep_subscript, 0); ssizes = covariance_moments (all_cov, MOMENT_NONE); result = gsl_matrix_get (ssizes, dep_subscript, rows[0]); for (i = 0; i < cov->size1 - 1; i++) { gsl_matrix_set (cov, i, cov->size1 - 1, gsl_matrix_get (cm, rows[i], dep_subscript)); gsl_matrix_set (cov, cov->size1 - 1, i, gsl_matrix_get (cm, rows[i], dep_subscript)); if (result > gsl_matrix_get (ssizes, rows[i], dep_subscript)) { result = gsl_matrix_get (ssizes, rows[i], dep_subscript); } } gsl_matrix_set (cov, cov->size1 - 1, cov->size1 - 1, gsl_matrix_get (cm, dep_subscript, dep_subscript)); free (rows); return result; } static bool run_regression (struct casereader *input, struct cmd_regression *cmd, struct dataset *ds, linreg **models) { size_t i; int n_indep = 0; int k; double n_data; double *means; struct ccase *c; struct covariance *cov; const struct variable **vars; const struct variable *dep_var; struct casereader *reader; const struct dictionary *dict; gsl_matrix *this_cm; assert (models != NULL); for (i = 0; i < n_variables; i++) { if (!var_is_numeric (v_variables[i])) { msg (SE, _("REGRESSION requires numeric variables.")); return false; } } c = casereader_peek (input, 0); if (c == NULL) { casereader_destroy (input); return true; } output_split_file_values (ds, c); case_unref (c); dict = dataset_dict (ds); if (!v_variables) { dict_get_vars (dict, &v_variables, &n_variables, 0); } vars = xnmalloc (n_variables, sizeof (*vars)); means = xnmalloc (n_variables, sizeof (*means)); cov = covariance_1pass_create (n_variables, v_variables, dict_get_weight (dict), MV_ANY); reader = casereader_clone (input); reader = casereader_create_filter_missing (reader, v_variables, n_variables, MV_ANY, NULL, NULL); for (; (c = casereader_read (reader)) != NULL; case_unref (c)) { covariance_accumulate (cov, c); } for (k = 0; k < cmd->n_dependent; k++) { dep_var = cmd->v_dependent[k]; n_indep = identify_indep_vars (vars, dep_var); this_cm = gsl_matrix_alloc (n_indep + 1, n_indep + 1); n_data = fill_covariance (this_cm, cov, vars, n_indep, dep_var, v_variables, n_variables, means); models[k] = linreg_alloc (dep_var, (const struct variable **) vars, n_data, n_indep); models[k]->depvar = dep_var; for (i = 0; i < n_indep; i++) { linreg_set_indep_variable_mean (models[k], i, means[i]); } /* For large data sets, use QR decomposition. */ if (n_data > sqrt (n_indep) && n_data > REG_LARGE_DATA) { models[k]->method = LINREG_QR; } if (n_data > 0) { /* Find the least-squares estimates and other statistics. */ linreg_fit (this_cm, models[k]); if (!taint_has_tainted_successor (casereader_get_taint (input))) { subcommand_statistics (cmd->a_statistics, models[k]); } } else { msg (SE, gettext ("No valid data found. This command was skipped.")); linreg_free (models[k]); models[k] = NULL; } } casereader_destroy (reader); free (vars); free (means); casereader_destroy (input); covariance_destroy (cov); return true; } /* Local Variables: mode: c End: */