1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 2011, 2012 Free Software Foundation, Inc.
4 This program is free software: you can redistribute it and/or modify
5 it under the terms of the GNU General Public License as published by
6 the Free Software Foundation, either version 3 of the License, or
7 (at your option) any later version.
9 This program is distributed in the hope that it will be useful,
10 but WITHOUT ANY WARRANTY; without even the implied warranty of
11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12 GNU General Public License for more details.
14 You should have received a copy of the GNU General Public License
15 along with this program. If not, see <http://www.gnu.org/licenses/>. */
19 #include "data/case.h"
20 #include "data/casegrouper.h"
21 #include "data/casereader.h"
22 #include "data/dataset.h"
23 #include "data/dictionary.h"
24 #include "data/format.h"
25 #include "data/variable.h"
27 #include "language/command.h"
28 #include "language/lexer/lexer.h"
29 #include "language/lexer/variable-parser.h"
31 #include "libpspp/misc.h"
32 #include "libpspp/pool.h"
34 #include "math/categoricals.h"
35 #include "math/interaction.h"
36 #include "math/moments.h"
38 #include "output/tab.h"
43 #define _(msgid) gettext (msgid)
44 #define N_(msgid) (msgid)
56 typedef void *stat_create (struct pool *pool);
57 typedef void stat_update (void *stat, double w, double x);
58 typedef double stat_get (const struct per_var_data *, void *aux);
62 /* Printable title for output */
65 /* Keyword for syntax */
80 harmonic_create (struct pool *pool)
82 struct harmonic_mean *hm = pool_alloc (pool, sizeof *hm);
92 harmonic_update (void *stat, double w, double x)
94 struct harmonic_mean *hm = stat;
101 harmonic_get (const struct per_var_data *pvd UNUSED, void *stat)
103 struct harmonic_mean *hm = stat;
105 return hm->n / hm->rsum;
110 struct geometric_mean
118 geometric_create (struct pool *pool)
120 struct geometric_mean *gm = pool_alloc (pool, sizeof *gm);
130 geometric_update (void *stat, double w, double x)
132 struct geometric_mean *gm = stat;
133 gm->prod *= pow (x, w);
139 geometric_get (const struct per_var_data *pvd UNUSED, void *stat)
141 struct geometric_mean *gm = stat;
143 return pow (gm->prod, 1.0 / gm->n);
149 sum_get (const struct per_var_data *pvd, void *stat UNUSED)
153 moments1_calculate (pvd->mom, &n, &mean, 0, 0, 0);
160 n_get (const struct per_var_data *pvd, void *stat UNUSED)
164 moments1_calculate (pvd->mom, &n, 0, 0, 0, 0);
170 arithmean_get (const struct per_var_data *pvd, void *stat UNUSED)
174 moments1_calculate (pvd->mom, &n, &mean, 0, 0, 0);
180 variance_get (const struct per_var_data *pvd, void *stat UNUSED)
182 double n, mean, variance;
184 moments1_calculate (pvd->mom, &n, &mean, &variance, 0, 0);
191 stddev_get (const struct per_var_data *pvd, void *stat)
193 return sqrt (variance_get (pvd, stat));
200 skew_get (const struct per_var_data *pvd, void *stat UNUSED)
204 moments1_calculate (pvd->mom, NULL, NULL, NULL, &skew, 0);
210 sekurt_get (const struct per_var_data *pvd, void *stat UNUSED)
214 moments1_calculate (pvd->mom, &n, NULL, NULL, NULL, NULL);
216 return calc_sekurt (n);
220 seskew_get (const struct per_var_data *pvd, void *stat UNUSED)
224 moments1_calculate (pvd->mom, &n, NULL, NULL, NULL, NULL);
226 return calc_seskew (n);
230 kurt_get (const struct per_var_data *pvd, void *stat UNUSED)
234 moments1_calculate (pvd->mom, NULL, NULL, NULL, NULL, &kurt);
240 semean_get (const struct per_var_data *pvd, void *stat UNUSED)
244 moments1_calculate (pvd->mom, &n, NULL, &var, NULL, NULL);
246 return sqrt (var / n);
252 min_create (struct pool *pool)
254 double *r = pool_alloc (pool, sizeof *r);
262 min_update (void *stat, double w UNUSED, double x)
271 min_get (const struct per_var_data *pvd UNUSED, void *stat)
279 max_create (struct pool *pool)
281 double *r = pool_alloc (pool, sizeof *r);
289 max_update (void *stat, double w UNUSED, double x)
298 max_get (const struct per_var_data *pvd UNUSED, void *stat)
314 range_create (struct pool *pool)
316 struct range *r = pool_alloc (pool, sizeof *r);
325 range_update (void *stat, double w UNUSED, double x)
327 struct range *r = stat;
337 range_get (const struct per_var_data *pvd UNUSED, void *stat)
339 struct range *r = stat;
341 return r->max - r->min;
347 last_create (struct pool *pool)
349 double *l = pool_alloc (pool, sizeof *l);
355 last_update (void *stat, double w UNUSED, double x)
363 last_get (const struct per_var_data *pvd UNUSED, void *stat)
372 first_create (struct pool *pool)
374 double *f = pool_alloc (pool, sizeof *f);
382 first_update (void *stat, double w UNUSED, double x)
391 first_get (const struct per_var_data *pvd UNUSED, void *stat)
405 /* Table of cell_specs */
406 static const struct cell_spec cell_spec[] = {
407 {N_("Mean"), "MEAN", NULL, NULL, arithmean_get},
408 {N_("N"), "COUNT", NULL, NULL, n_get},
409 {N_("Std. Deviation"), "STDDEV", NULL, NULL, stddev_get},
411 {N_("Median"), "MEDIAN", NULL, NULL, NULL},
412 {N_("Group Median"), "GMEDIAN", NULL, NULL, NULL},
414 {N_("S.E. Mean"), "SEMEAN", NULL, NULL, semean_get},
415 {N_("Sum"), "SUM", NULL, NULL, sum_get},
416 {N_("Min"), "MIN", min_create, min_update, min_get},
417 {N_("Max"), "MAX", max_create, max_update, max_get},
418 {N_("Range"), "RANGE", range_create, range_update, range_get},
419 {N_("Variance"), "VARIANCE", NULL, NULL, variance_get},
420 {N_("Kurtosis"), "KURT", NULL, NULL, kurt_get},
421 {N_("S.E. Kurt"), "SEKURT", NULL, NULL, sekurt_get},
422 {N_("Skewness"), "SKEW", NULL, NULL, skew_get},
423 {N_("S.E. Skew"), "SESKEW", NULL, NULL, seskew_get},
424 {N_("First"), "FIRST", first_create, first_update, first_get},
425 {N_("Last"), "LAST", last_create, last_update, last_get},
427 {N_("Percent N"), "NPCT", NULL, NULL, NULL},
428 {N_("Percent Sum"), "SPCT", NULL, NULL, NULL},
430 {N_("Harmonic Mean"), "HARMONIC", harmonic_create, harmonic_update, harmonic_get},
431 {N_("Geom. Mean"), "GEOMETRIC", geometric_create, geometric_update, geometric_get}
434 #define n_C (sizeof (cell_spec) / sizeof (struct cell_spec))
440 casenumber non_missing;
444 /* The thing parsed after TABLES= */
448 const struct variable **dep_vars;
450 size_t n_interactions;
451 struct interaction **interactions;
452 struct summary *summary;
454 size_t *n_factor_vars;
455 const struct variable ***factor_vars;
461 struct categoricals *cats;
466 const struct dictionary *dict;
468 struct mtable *table;
471 /* Missing value class for categorical variables */
472 enum mv_class exclude;
474 /* Missing value class for dependent variables */
475 enum mv_class dep_exclude;
477 /* an array indicating which statistics are to be calculated */
483 /* Pool on which cell functions may allocate data */
489 run_means (struct means *cmd, struct casereader *input,
490 const struct dataset *ds);
492 /* Append all the variables belonging to layer and all subsequent layers
493 to iact. And then append iact to the means->interaction.
494 This is a recursive function.
497 iact_append_factor (struct mtable *means, int layer,
498 const struct interaction *iact)
501 const struct variable **fv;
503 if (layer >= means->n_layers)
506 fv = means->factor_vars[layer];
508 for (v = 0; v < means->n_factor_vars[layer]; ++v)
510 struct interaction *nexti = interaction_clone (iact);
512 interaction_add_variable (nexti, fv[v]);
514 iact_append_factor (means, layer + 1, nexti);
516 if (layer == means->n_layers - 1)
518 means->interactions[means->ii++] = nexti;
524 parse_means_table_syntax (struct lexer *lexer, const struct means *cmd, struct mtable *table)
528 table->factor_vars = NULL;
529 table->n_factor_vars = NULL;
531 /* Dependent variable (s) */
532 if (!parse_variables_const (lexer, cmd->dict,
533 &table->dep_vars, &table->n_dep_vars,
534 PV_NO_DUPLICATE | PV_NUMERIC))
537 /* Factor variable (s) */
538 while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
540 if (lex_match (lexer, T_BY))
544 xrealloc (table->factor_vars,
545 sizeof (*table->factor_vars) * table->n_layers);
547 table->n_factor_vars =
548 xrealloc (table->n_factor_vars,
549 sizeof (*table->n_factor_vars) * table->n_layers);
551 if (!parse_variables_const (lexer, cmd->dict,
552 &table->factor_vars[table->n_layers - 1],
553 &table->n_factor_vars[table->n_layers -
565 If the match succeeds, the variable will be placed in VAR.
566 Returns true if successful */
568 lex_is_variable (struct lexer *lexer, const struct dictionary *dict,
572 if (lex_next_token (lexer, n) != T_ID)
575 tstr = lex_next_tokcstr (lexer, n);
577 if (NULL == dict_lookup_var (dict, tstr) )
585 cmd_means (struct lexer *lexer, struct dataset *ds)
591 bool more_tables = true;
593 means.exclude = MV_ANY;
594 means.dep_exclude = MV_ANY;
598 means.dict = dataset_dict (ds);
601 means.cells = xcalloc (means.n_cells, sizeof (*means.cells));
604 /* The first three items (MEAN, COUNT, STDDEV) are the default */
605 for (i = 0; i < 3; ++i)
609 /* Optional TABLES = */
610 if (lex_match_id (lexer, "TABLES"))
612 lex_force_match (lexer, T_EQUALS);
617 /* Parse the "tables" */
621 means.table = xrealloc (means.table, means.n_tables * sizeof (*means.table));
623 if (! parse_means_table_syntax (lexer, &means,
624 &means.table[means.n_tables - 1]))
629 /* Look ahead to see if there are more tables to be parsed */
631 if ( T_SLASH == lex_next_token (lexer, 0) )
633 if (lex_is_variable (lexer, means.dict, 1) )
636 lex_force_match (lexer, T_SLASH);
641 /* /MISSING subcommand */
642 while (lex_token (lexer) != T_ENDCMD)
644 lex_match (lexer, T_SLASH);
646 if (lex_match_id (lexer, "MISSING"))
649 If no MISSING subcommand is specified, each combination of
650 a dependent variable and categorical variables is handled
653 lex_match (lexer, T_EQUALS);
654 if (lex_match_id (lexer, "INCLUDE"))
657 Use the subcommand "/MISSING=INCLUDE" to include user-missing
658 values in the analysis.
661 means.exclude = MV_SYSTEM;
662 means.dep_exclude = MV_SYSTEM;
664 else if (lex_match_id (lexer, "TABLE"))
666 This is the default. (I think).
667 Every case containing a complete set of variables for a given
668 table. If any variable, categorical or dependent for in a table
669 is missing (as defined by what?), then that variable will
670 be dropped FOR THAT TABLE ONLY.
673 means.exclude = MV_ANY;
674 means.dep_exclude = MV_ANY;
676 else if (lex_match_id (lexer, "DEPENDENT"))
678 Use the command "/MISSING=DEPENDENT" to
679 include user-missing values for the categorical variables,
680 while excluding them for the dependent variables.
682 Cases are dropped only when user-missing values
683 appear in dependent variables. User-missing
684 values for categorical variables are treated according to
687 Cases are ALWAYS dropped when System Missing values appear
688 in the categorical variables.
691 means.dep_exclude = MV_ANY;
692 means.exclude = MV_SYSTEM;
696 lex_error (lexer, NULL);
700 else if (lex_match_id (lexer, "CELLS"))
702 lex_match (lexer, T_EQUALS);
704 /* The default values become overwritten */
706 while (lex_token (lexer) != T_ENDCMD
707 && lex_token (lexer) != T_SLASH)
710 if (lex_match (lexer, T_ALL))
714 xrealloc (means.cells,
715 (means.n_cells += n_C) * sizeof (*means.cells));
717 for (x = 0; x < n_C; ++x)
718 means.cells[means.n_cells - (n_C - 1 - x) - 1] = x;
720 else if (lex_match_id (lexer, "NONE"))
724 else if (lex_match_id (lexer, "DEFAULT"))
727 xrealloc (means.cells,
728 (means.n_cells += 3) * sizeof (*means.cells));
730 means.cells[means.n_cells - 2 - 1] = MEANS_MEAN;
731 means.cells[means.n_cells - 1 - 1] = MEANS_N;
732 means.cells[means.n_cells - 0 - 1] = MEANS_STDDEV;
738 if (lex_match_id (lexer, cell_spec[k].keyword))
741 xrealloc (means.cells,
742 ++means.n_cells * sizeof (*means.cells));
744 means.cells[means.n_cells - 1] = k;
751 lex_error (lexer, NULL);
758 lex_error (lexer, NULL);
763 means.pool = pool_create ();
766 for (t = 0; t < means.n_tables; ++t)
768 struct mtable *table = &means.table[t];
769 table->n_interactions = 1;
770 for (l = 0; l < table->n_layers; ++l)
772 const int n_vars = table->n_factor_vars[l];
773 table->n_interactions *= n_vars;
776 table->interactions =
777 xcalloc (table->n_interactions, sizeof (*table->interactions));
780 xcalloc (table->n_dep_vars * table->n_interactions, sizeof (*table->summary));
783 if (table->n_layers > 0)
784 iact_append_factor (table, 0, interaction_create (NULL));
786 table->interactions[0] = interaction_create (NULL);
792 struct casegrouper *grouper;
793 struct casereader *group;
796 grouper = casegrouper_create_splits (proc_open (ds), means.dict);
797 while (casegrouper_get_next_group (grouper, &group))
799 run_means (&means, group, ds);
801 ok = casegrouper_destroy (grouper);
802 ok = proc_commit (ds) && ok;
815 is_missing (const struct means *cmd,
816 const struct variable *dvar,
817 const struct interaction *iact,
818 const struct ccase *c)
820 if ( interaction_case_is_missing (iact, c, cmd->exclude) )
824 if (var_is_value_missing (dvar,
832 static void output_case_processing_summary (const struct mtable *);
834 static void output_report (const struct means *, int, const struct mtable *);
839 struct per_var_data *pvd;
845 create_n (const void *aux1, void *aux2)
848 const struct means *means = aux1;
849 struct mtable *table = aux2;
850 struct per_cat_data *per_cat_data = xmalloc (sizeof *per_cat_data);
852 struct per_var_data *pvd = xcalloc (table->n_dep_vars, sizeof *pvd);
854 for (v = 0; v < table->n_dep_vars; ++v)
856 enum moment maxmom = MOMENT_KURTOSIS;
857 struct per_var_data *pp = &pvd[v];
859 pp->cell_stats = xcalloc (means->n_cells, sizeof *pp->cell_stats);
862 for (i = 0; i < means->n_cells; ++i)
864 int csi = means->cells[i];
865 const struct cell_spec *cs = &cell_spec[csi];
868 pp->cell_stats[i] = cs->sc (means->pool);
871 pp->mom = moments1_create (maxmom);
875 per_cat_data->pvd = pvd;
876 per_cat_data->warn = true;
881 update_n (const void *aux1, void *aux2, void *user_data, const struct ccase *c, double weight)
885 const struct means *means = aux1;
886 struct mtable *table = aux2;
887 struct per_cat_data *per_cat_data = user_data;
889 for (v = 0; v < table->n_dep_vars; ++v)
891 struct per_var_data *pvd = &per_cat_data->pvd[v];
893 const double x = case_data (c, table->dep_vars[v])->f;
895 for (i = 0; i < table->n_interactions; ++i)
897 if ( is_missing (means, table->dep_vars[v], table->interactions[i], c))
901 for (i = 0; i < means->n_cells; ++i)
903 const int csi = means->cells[i];
904 const struct cell_spec *cs = &cell_spec[csi];
908 cs->su (pvd->cell_stats[i],
912 moments1_add (pvd->mom, x, weight);
920 calculate_n (const void *aux1, void *aux2, void *user_data)
924 struct per_cat_data *per_cat_data = user_data;
925 const struct means *means = aux1;
926 struct mtable *table = aux2;
928 for (v = 0; v < table->n_dep_vars; ++v)
930 struct per_var_data *pvd = &per_cat_data->pvd[v];
931 for (i = 0; i < means->n_cells; ++i)
933 int csi = means->cells[i];
934 const struct cell_spec *cs = &cell_spec[csi];
937 cs->sd (pvd, pvd->cell_stats[i]);
944 run_means (struct means *cmd, struct casereader *input,
945 const struct dataset *ds UNUSED)
948 const struct variable *wv = dict_get_weight (cmd->dict);
950 struct casereader *reader;
952 struct payload payload;
953 payload.create = create_n;
954 payload.update = update_n;
955 payload.destroy = calculate_n;
957 for (t = 0; t < cmd->n_tables; ++t)
959 struct mtable *table = &cmd->table[t];
961 = categoricals_create (table->interactions,
962 table->n_interactions, wv, cmd->exclude);
964 categoricals_set_payload (table->cats, &payload, cmd, table);
967 for (reader = casereader_clone (input);
968 (c = casereader_read (reader)) != NULL; case_unref (c))
970 for (t = 0; t < cmd->n_tables; ++t)
973 struct mtable *table = &cmd->table[t];
975 for (v = 0; v < table->n_dep_vars; ++v)
978 for (i = 0; i < table->n_interactions; ++i)
981 is_missing (cmd, table->dep_vars[v],
982 table->interactions[i], c);
984 table->summary[v * table->n_interactions + i].missing++;
986 table->summary[v * table->n_interactions + i].non_missing++;
989 categoricals_update (table->cats, c);
992 casereader_destroy (reader);
994 for (t = 0; t < cmd->n_tables; ++t)
996 struct mtable *table = &cmd->table[t];
998 categoricals_done (table->cats);
1002 for (t = 0; t < cmd->n_tables; ++t)
1004 const struct mtable *table = &cmd->table[t];
1006 output_case_processing_summary (table);
1008 for (i = 0; i < table->n_interactions; ++i)
1010 output_report (cmd, i, table);
1013 categoricals_destroy (table->cats);
1019 output_case_processing_summary (const struct mtable *table)
1022 const int heading_columns = 1;
1023 const int heading_rows = 3;
1024 struct tab_table *t;
1026 const int nr = heading_rows + table->n_interactions * table->n_dep_vars;
1029 t = tab_create (nc, nr);
1030 tab_title (t, _("Case Processing Summary"));
1032 tab_headers (t, heading_columns, 0, heading_rows, 0);
1034 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, nc - 1, nr - 1);
1036 tab_hline (t, TAL_2, 0, nc - 1, heading_rows);
1037 tab_vline (t, TAL_2, heading_columns, 0, nr - 1);
1040 tab_joint_text (t, heading_columns, 0,
1041 nc - 1, 0, TAB_CENTER | TAT_TITLE, _("Cases"));
1043 tab_joint_text (t, 1, 1, 2, 1, TAB_CENTER | TAT_TITLE, _("Included"));
1044 tab_joint_text (t, 3, 1, 4, 1, TAB_CENTER | TAT_TITLE, _("Excluded"));
1045 tab_joint_text (t, 5, 1, 6, 1, TAB_CENTER | TAT_TITLE, _("Total"));
1047 tab_hline (t, TAL_1, heading_columns, nc - 1, 1);
1048 tab_hline (t, TAL_1, heading_columns, nc - 1, 2);
1051 for (i = 0; i < 3; ++i)
1053 tab_text (t, heading_columns + i * 2, 2, TAB_CENTER | TAT_TITLE,
1055 tab_text (t, heading_columns + i * 2 + 1, 2, TAB_CENTER | TAT_TITLE,
1059 for (v = 0; v < table->n_dep_vars; ++v)
1061 const struct variable *var = table->dep_vars[v];
1062 const char *dv_name = var_to_string (var);
1063 for (i = 0; i < table->n_interactions; ++i)
1065 const int row = v * table->n_interactions + i;
1066 const struct interaction *iact = table->interactions[i];
1070 ds_init_cstr (&str, dv_name);
1071 ds_put_cstr (&str, ": ");
1073 interaction_to_string (iact, &str);
1075 tab_text (t, 0, row + heading_rows,
1076 TAB_LEFT | TAT_TITLE, ds_cstr (&str));
1079 n_total = table->summary[row].missing +
1080 table->summary[row].non_missing;
1082 tab_double (t, 1, row + heading_rows,
1083 0, table->summary[row].non_missing, &F_8_0);
1085 tab_text_format (t, 2, row + heading_rows,
1087 table->summary[row].non_missing / (double) n_total * 100.0);
1090 tab_double (t, 3, row + heading_rows,
1091 0, table->summary[row].missing, &F_8_0);
1094 tab_text_format (t, 4, row + heading_rows,
1096 table->summary[row].missing / (double) n_total * 100.0);
1099 tab_double (t, 5, row + heading_rows,
1100 0, table->summary[row].missing +
1101 table->summary[row].non_missing, &F_8_0);
1103 tab_text_format (t, 6, row + heading_rows,
1105 n_total / (double) n_total * 100.0);
1118 output_report (const struct means *cmd, int iact_idx,
1119 const struct mtable *table)
1124 const struct interaction *iact = table->interactions[iact_idx];
1126 const int heading_columns = 1 + iact->n_vars;
1127 const int heading_rows = 1;
1128 struct tab_table *t;
1130 const int n_cats = categoricals_n_count (table->cats, iact_idx);
1132 const int nr = n_cats * table->n_dep_vars + heading_rows;
1134 const int nc = heading_columns + cmd->n_cells;
1136 t = tab_create (nc, nr);
1137 tab_title (t, _("Report"));
1139 tab_headers (t, heading_columns, 0, heading_rows, 0);
1141 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, nc - 1, nr - 1);
1143 tab_hline (t, TAL_2, 0, nc - 1, heading_rows);
1144 tab_vline (t, TAL_2, iact->n_vars, 0, nr - 1);
1146 for (i = 0; i < iact->n_vars; ++i)
1148 tab_text (t, 1 + i, 0, TAB_CENTER | TAT_TITLE,
1149 var_to_string (iact->vars[i]));
1152 for (i = 0; i < cmd->n_cells; ++i)
1154 tab_text (t, heading_columns + i, 0,
1155 TAB_CENTER | TAT_TITLE,
1156 gettext (cell_spec[cmd->cells[i]].title));
1160 for (i = 0; i < n_cats; ++i)
1163 const struct ccase *c =
1164 categoricals_get_case_by_category_real (table->cats, iact_idx, i);
1166 for (dv = 0; dv < table->n_dep_vars; ++dv)
1169 heading_rows + dv * n_cats,
1170 TAB_RIGHT | TAT_TITLE,
1171 var_get_name (table->dep_vars[dv])
1175 tab_hline (t, TAL_1, 0, nc - 1, heading_rows + dv * n_cats);
1177 for (v = 0; v < iact->n_vars; ++v)
1179 const struct variable *var = iact->vars[v];
1180 const union value *val = case_data (c, var);
1182 ds_init_empty (&str);
1183 var_append_value_name (var, val, &str);
1185 tab_text (t, 1 + v, heading_rows + dv * n_cats + i,
1186 TAB_RIGHT | TAT_TITLE, ds_cstr (&str));
1193 for (grp = 0; grp < n_cats; ++grp)
1196 struct per_cat_data *per_cat_data =
1197 categoricals_get_user_data_by_category_real (table->cats, iact_idx, grp);
1199 for (dv = 0; dv < table->n_dep_vars; ++dv)
1201 const struct per_var_data *pvd = &per_cat_data->pvd[dv];
1202 for (i = 0; i < cmd->n_cells; ++i)
1204 const int csi = cmd->cells[i];
1205 const struct cell_spec *cs = &cell_spec[csi];
1207 double result = cs->sd (pvd, pvd->cell_stats[i]);
1209 tab_double (t, heading_columns + i,
1210 heading_rows + grp + dv * n_cats,