--- /dev/null
+/* PSPP - a program for statistical analysis.
+ Copyright (C) 1997-9, 2000, 2006, 2009, 2010, 2011, 2012, 2013, 2014, 2016 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 <http://www.gnu.org/licenses/>. */
+
+/* FIXME:
+
+ - How to calculate significance of some symmetric and directional measures?
+ - How to calculate ASE for symmetric Somers ' d?
+ - How to calculate ASE for Goodman and Kruskal's tau?
+ - How to calculate approx. T of symmetric uncertainty coefficient?
+
+*/
+
+#include <config.h>
+
+#include <ctype.h>
+#include <float.h>
+#include <gsl/gsl_cdf.h>
+#include <stdlib.h>
+#include <stdio.h>
+
+#include "data/case.h"
+#include "data/casegrouper.h"
+#include "data/casereader.h"
+#include "data/data-out.h"
+#include "data/dataset.h"
+#include "data/dictionary.h"
+#include "data/format.h"
+#include "data/value-labels.h"
+#include "data/variable.h"
+#include "language/command.h"
+#include "language/commands/freq.h"
+#include "language/commands/split-file.h"
+#include "language/lexer/lexer.h"
+#include "language/lexer/variable-parser.h"
+#include "libpspp/array.h"
+#include "libpspp/assertion.h"
+#include "libpspp/compiler.h"
+#include "libpspp/hash-functions.h"
+#include "libpspp/hmap.h"
+#include "libpspp/hmapx.h"
+#include "libpspp/message.h"
+#include "libpspp/misc.h"
+#include "libpspp/pool.h"
+#include "libpspp/str.h"
+#include "output/pivot-table.h"
+#include "output/charts/barchart.h"
+
+#include "gl/minmax.h"
+#include "gl/xalloc-oversized.h"
+#include "gl/xalloc.h"
+#include "gl/xsize.h"
+
+#include "gettext.h"
+#define _(msgid) gettext (msgid)
+#define N_(msgid) msgid
+
+/* Kinds of cells in the crosstabulation. */
+#define CRS_CELLS \
+ C(COUNT, N_("Count"), PIVOT_RC_COUNT) \
+ C(EXPECTED, N_("Expected"), PIVOT_RC_OTHER) \
+ C(ROW, N_("Row %"), PIVOT_RC_PERCENT) \
+ C(COLUMN, N_("Column %"), PIVOT_RC_PERCENT) \
+ C(TOTAL, N_("Total %"), PIVOT_RC_PERCENT) \
+ C(RESIDUAL, N_("Residual"), PIVOT_RC_RESIDUAL) \
+ C(SRESIDUAL, N_("Std. Residual"), PIVOT_RC_RESIDUAL) \
+ C(ASRESIDUAL, N_("Adjusted Residual"), PIVOT_RC_RESIDUAL)
+enum crs_cell
+ {
+#define C(KEYWORD, STRING, RC) CRS_CL_##KEYWORD,
+ CRS_CELLS
+#undef C
+ };
+enum {
+#define C(KEYWORD, STRING, RC) + 1
+ CRS_N_CELLS = CRS_CELLS
+#undef C
+};
+#define CRS_ALL_CELLS ((1u << CRS_N_CELLS) - 1)
+
+/* Kinds of statistics. */
+#define CRS_STATISTICS \
+ S(CHISQ) \
+ S(PHI) \
+ S(CC) \
+ S(LAMBDA) \
+ S(UC) \
+ S(BTAU) \
+ S(CTAU) \
+ S(RISK) \
+ S(GAMMA) \
+ S(D) \
+ S(KAPPA) \
+ S(ETA) \
+ S(CORR)
+enum crs_statistic_index {
+#define S(KEYWORD) CRS_ST_##KEYWORD##_INDEX,
+ CRS_STATISTICS
+#undef S
+};
+enum crs_statistic_bit {
+#define S(KEYWORD) CRS_ST_##KEYWORD = 1u << CRS_ST_##KEYWORD##_INDEX,
+ CRS_STATISTICS
+#undef S
+};
+enum {
+#define S(KEYWORD) + 1
+ CRS_N_STATISTICS = CRS_STATISTICS
+#undef S
+};
+#define CRS_ALL_STATISTICS ((1u << CRS_N_STATISTICS) - 1)
+
+/* Number of chi-square statistics. */
+#define N_CHISQ 5
+
+/* Number of symmetric statistics. */
+#define N_SYMMETRIC 9
+
+/* Number of directional statistics. */
+#define N_DIRECTIONAL 13
+
+/* Indexes into the 'vars' member of struct crosstabulation and
+ struct crosstab member. */
+enum
+ {
+ ROW_VAR = 0, /* Row variable. */
+ COL_VAR = 1 /* Column variable. */
+ /* Higher indexes cause multiple tables to be output. */
+ };
+
+struct xtab_var
+ {
+ const struct variable *var;
+ union value *values;
+ size_t n_values;
+ };
+
+/* A crosstabulation of 2 or more variables. */
+struct crosstabulation
+ {
+ struct crosstabs_proc *proc;
+ struct fmt_spec weight_format; /* Format for weight variable. */
+ double missing; /* Weight of missing cases. */
+
+ /* Variables (2 or more). */
+ size_t n_vars;
+ struct xtab_var *vars;
+
+ /* Constants (0 or more). */
+ size_t n_consts;
+ struct xtab_var *const_vars;
+ size_t *const_indexes;
+
+ /* Data. */
+ struct hmap data;
+ struct freq **entries;
+ size_t n_entries;
+
+ /* Number of statistically interesting columns/rows
+ (columns/rows with data in them). */
+ size_t ns_cols, ns_rows;
+
+ /* Matrix contents. */
+ double *mat; /* Matrix proper. */
+ double *row_tot; /* Row totals. */
+ double *col_tot; /* Column totals. */
+ double total; /* Grand total. */
+
+ /* Syntax. */
+ int start_ofs;
+ int end_ofs;
+ };
+
+/* Integer mode variable info. */
+struct var_range
+ {
+ struct hmap_node hmap_node; /* In struct crosstabs_proc var_ranges map. */
+ const struct variable *var; /* The variable. */
+ int min; /* Minimum value. */
+ int max; /* Maximum value + 1. */
+ int count; /* max - min. */
+ };
+
+struct crosstabs_proc
+ {
+ const struct dictionary *dict;
+ enum { INTEGER, GENERAL } mode;
+ enum mv_class exclude;
+ bool barchart;
+ bool bad_warn;
+ struct fmt_spec weight_format;
+
+ /* Variables specifies on VARIABLES. */
+ const struct variable **variables;
+ size_t n_variables;
+ struct hmap var_ranges;
+
+ /* TABLES. */
+ struct crosstabulation *pivots;
+ size_t n_pivots;
+
+ /* CELLS. */
+ size_t n_cells; /* Number of cells requested. */
+ unsigned int cells; /* Bit k is 1 if cell k is requested. */
+ int a_cells[CRS_N_CELLS]; /* 0...n_cells-1 are the requested cells. */
+
+ /* Rounding of cells. */
+ bool round_case_weights; /* Round case weights? */
+ bool round_cells; /* If !round_case_weights, round cells? */
+ bool round_down; /* Round down? (otherwise to nearest) */
+
+ /* STATISTICS. */
+ unsigned int statistics; /* Bit k is 1 if statistic k is requested. */
+
+ bool descending; /* True if descending sort order is requested. */
+ };
+
+static bool parse_crosstabs_tables (struct lexer *, struct dataset *,
+ struct crosstabs_proc *);
+static bool parse_crosstabs_variables (struct lexer *, struct dataset *,
+ struct crosstabs_proc *);
+
+static const struct var_range *get_var_range (const struct crosstabs_proc *,
+ const struct variable *);
+
+static bool should_tabulate_case (const struct crosstabulation *,
+ const struct ccase *, enum mv_class exclude);
+static void tabulate_general_case (struct crosstabulation *, const struct ccase *,
+ double weight);
+static void tabulate_integer_case (struct crosstabulation *, const struct ccase *,
+ double weight);
+static void postcalc (struct crosstabs_proc *, struct lexer *);
+
+static double
+round_weight (const struct crosstabs_proc *proc, double weight)
+{
+ return proc->round_down ? floor (weight) : floor (weight + 0.5);
+}
+
+#define FOR_EACH_POPULATED_COLUMN(C, XT) \
+ for (size_t C = next_populated_column (0, XT); \
+ C < (XT)->vars[COL_VAR].n_values; \
+ C = next_populated_column (C + 1, XT))
+static size_t
+next_populated_column (size_t c, const struct crosstabulation *xt)
+{
+ size_t n_columns = xt->vars[COL_VAR].n_values;
+ for (; c < n_columns; c++)
+ if (xt->col_tot[c])
+ break;
+ return c;
+}
+
+#define FOR_EACH_POPULATED_ROW(R, XT) \
+ for (size_t R = next_populated_row (0, XT); R < (XT)->vars[ROW_VAR].n_values; \
+ R = next_populated_row (R + 1, XT))
+static size_t
+next_populated_row (size_t r, const struct crosstabulation *xt)
+{
+ size_t n_rows = xt->vars[ROW_VAR].n_values;
+ for (; r < n_rows; r++)
+ if (xt->row_tot[r])
+ break;
+ return r;
+}
+
+/* Parses and executes the CROSSTABS procedure. */
+int
+cmd_crosstabs (struct lexer *lexer, struct dataset *ds)
+{
+ int result = CMD_FAILURE;
+
+ struct crosstabs_proc proc = {
+ .dict = dataset_dict (ds),
+ .mode = GENERAL,
+ .exclude = MV_ANY,
+ .barchart = false,
+ .bad_warn = true,
+ .weight_format = *dict_get_weight_format (dataset_dict (ds)),
+
+ .variables = NULL,
+ .n_variables = 0,
+ .var_ranges = HMAP_INITIALIZER (proc.var_ranges),
+
+ .pivots = NULL,
+ .n_pivots = 0,
+
+ .cells = 1u << CRS_CL_COUNT,
+ /* n_cells and a_cells will be filled in later. */
+
+ .round_case_weights = false,
+ .round_cells = false,
+ .round_down = false,
+
+ .statistics = 0,
+
+ .descending = false,
+ };
+ bool show_tables = true;
+ int exclude_ofs = 0;
+ lex_match (lexer, T_SLASH);
+ for (;;)
+ {
+ if (lex_match_id (lexer, "VARIABLES"))
+ {
+ if (!parse_crosstabs_variables (lexer, ds, &proc))
+ goto exit;
+ }
+ else if (lex_match_id (lexer, "MISSING"))
+ {
+ lex_match (lexer, T_EQUALS);
+ exclude_ofs = lex_ofs (lexer);
+ if (lex_match_id (lexer, "TABLE"))
+ proc.exclude = MV_ANY;
+ else if (lex_match_id (lexer, "INCLUDE"))
+ proc.exclude = MV_SYSTEM;
+ else if (lex_match_id (lexer, "REPORT"))
+ proc.exclude = 0;
+ else
+ {
+ lex_error_expecting (lexer, "TABLE", "INCLUDE", "REPORT");
+ goto exit;
+ }
+ }
+ else if (lex_match_id (lexer, "COUNT"))
+ {
+ lex_match (lexer, T_EQUALS);
+
+ /* Default is CELL. */
+ proc.round_case_weights = false;
+ proc.round_cells = true;
+
+ while (lex_token (lexer) != T_SLASH && lex_token (lexer) != T_ENDCMD)
+ {
+ if (lex_match_id (lexer, "ASIS"))
+ {
+ proc.round_case_weights = false;
+ proc.round_cells = false;
+ }
+ else if (lex_match_id (lexer, "CASE"))
+ {
+ proc.round_case_weights = true;
+ proc.round_cells = false;
+ }
+ else if (lex_match_id (lexer, "CELL"))
+ {
+ proc.round_case_weights = false;
+ proc.round_cells = true;
+ }
+ else if (lex_match_id (lexer, "ROUND"))
+ proc.round_down = false;
+ else if (lex_match_id (lexer, "TRUNCATE"))
+ proc.round_down = true;
+ else
+ {
+ lex_error_expecting (lexer, "ASIS", "CASE", "CELL",
+ "ROUND", "TRUNCATE");
+ goto exit;
+ }
+ lex_match (lexer, T_COMMA);
+ }
+ }
+ else if (lex_match_id (lexer, "FORMAT"))
+ {
+ lex_match (lexer, T_EQUALS);
+ while (lex_token (lexer) != T_SLASH && lex_token (lexer) != T_ENDCMD)
+ {
+ if (lex_match_id (lexer, "AVALUE"))
+ proc.descending = false;
+ else if (lex_match_id (lexer, "DVALUE"))
+ proc.descending = true;
+ else if (lex_match_id (lexer, "TABLES"))
+ show_tables = true;
+ else if (lex_match_id (lexer, "NOTABLES"))
+ show_tables = false;
+ else
+ {
+ lex_error_expecting (lexer, "AVALUE", "DVALUE",
+ "TABLES", "NOTABLES");
+ goto exit;
+ }
+ lex_match (lexer, T_COMMA);
+ }
+ }
+ else if (lex_match_id (lexer, "BARCHART"))
+ proc.barchart = true;
+ else if (lex_match_id (lexer, "CELLS"))
+ {
+ lex_match (lexer, T_EQUALS);
+
+ if (lex_match_id (lexer, "NONE"))
+ proc.cells = 0;
+ else if (lex_match (lexer, T_ALL))
+ proc.cells = CRS_ALL_CELLS;
+ else
+ {
+ proc.cells = 0;
+ while (lex_token (lexer) != T_SLASH && lex_token (lexer) != T_ENDCMD)
+ {
+#define C(KEYWORD, STRING, RC) \
+ if (lex_match_id (lexer, #KEYWORD)) \
+ { \
+ proc.cells |= 1u << CRS_CL_##KEYWORD; \
+ continue; \
+ }
+ CRS_CELLS
+#undef C
+
+ static const char *cells[] =
+ {
+#define C(KEYWORD, STRING, RC) #KEYWORD,
+ CRS_CELLS
+#undef C
+ };
+ lex_error_expecting_array (lexer, cells,
+ sizeof cells / sizeof *cells);
+ goto exit;
+ }
+ if (!proc.cells)
+ proc.cells = ((1u << CRS_CL_COUNT) | (1u << CRS_CL_ROW)
+ | (1u << CRS_CL_COLUMN) | (1u << CRS_CL_TOTAL));
+ }
+ }
+ else if (lex_match_id (lexer, "STATISTICS"))
+ {
+ lex_match (lexer, T_EQUALS);
+
+ if (lex_match_id (lexer, "NONE"))
+ proc.statistics = 0;
+ else if (lex_match (lexer, T_ALL))
+ proc.statistics = CRS_ALL_STATISTICS;
+ else
+ {
+ proc.statistics = 0;
+ while (lex_token (lexer) != T_SLASH && lex_token (lexer) != T_ENDCMD)
+ {
+#define S(KEYWORD) \
+ if (lex_match_id (lexer, #KEYWORD)) \
+ { \
+ proc.statistics |= CRS_ST_##KEYWORD; \
+ continue; \
+ }
+ CRS_STATISTICS
+#undef S
+ static const char *stats[] =
+ {
+#define S(KEYWORD) #KEYWORD,
+ CRS_STATISTICS
+#undef S
+ };
+ lex_error_expecting_array (lexer, stats,
+ sizeof stats / sizeof *stats);
+ goto exit;
+ }
+ if (!proc.statistics)
+ proc.statistics = CRS_ST_CHISQ;
+ }
+ }
+ else if (!parse_crosstabs_tables (lexer, ds, &proc))
+ goto exit;
+
+ if (!lex_match (lexer, T_SLASH))
+ break;
+ }
+ if (!lex_end_of_command (lexer))
+ goto exit;
+
+ if (!proc.n_pivots)
+ {
+ msg (SE, _("At least one crosstabulation must be requested (using "
+ "the TABLES subcommand)."));
+ goto exit;
+ }
+
+ /* Cells. */
+ if (!show_tables)
+ proc.cells = 0;
+ for (size_t i = 0; i < CRS_N_CELLS; i++)
+ if (proc.cells & (1u << i))
+ proc.a_cells[proc.n_cells++] = i;
+ assert (proc.n_cells < CRS_N_CELLS);
+
+ /* Missing values. */
+ if (proc.mode == GENERAL && !proc.exclude)
+ {
+ lex_ofs_msg (lexer, SW, exclude_ofs, exclude_ofs,
+ _("Missing mode %s not allowed in general mode. "
+ "Assuming %s."), "REPORT", "MISSING=TABLE");
+ proc.exclude = MV_ANY;
+ }
+
+ struct casereader *input = casereader_create_filter_weight (proc_open (ds),
+ dataset_dict (ds),
+ NULL, NULL);
+ struct casegrouper *grouper = casegrouper_create_splits (input, dataset_dict (ds));
+ struct casereader *group;
+ while (casegrouper_get_next_group (grouper, &group))
+ {
+ output_split_file_values_peek (ds, group);
+
+ /* Initialize hash tables. */
+ for (struct crosstabulation *xt = &proc.pivots[0];
+ xt < &proc.pivots[proc.n_pivots]; xt++)
+ hmap_init (&xt->data);
+
+ /* Tabulate. */
+ struct ccase *c;
+ for (; (c = casereader_read (group)) != NULL; case_unref (c))
+ for (struct crosstabulation *xt = &proc.pivots[0];
+ xt < &proc.pivots[proc.n_pivots]; xt++)
+ {
+ double weight = dict_get_case_weight (dataset_dict (ds), c,
+ &proc.bad_warn);
+ if (proc.round_case_weights)
+ {
+ weight = round_weight (&proc, weight);
+ if (weight == 0.)
+ continue;
+ }
+ if (should_tabulate_case (xt, c, proc.exclude))
+ {
+ if (proc.mode == GENERAL)
+ tabulate_general_case (xt, c, weight);
+ else
+ tabulate_integer_case (xt, c, weight);
+ }
+ else
+ xt->missing += weight;
+ }
+ casereader_destroy (group);
+
+ /* Output. */
+ postcalc (&proc, lexer);
+ }
+ bool ok = casegrouper_destroy (grouper);
+ ok = proc_commit (ds) && ok;
+
+ result = ok ? CMD_SUCCESS : CMD_FAILURE;
+
+exit:
+ free (proc.variables);
+
+ struct var_range *range, *next_range;
+ HMAP_FOR_EACH_SAFE (range, next_range, struct var_range, hmap_node,
+ &proc.var_ranges)
+ {
+ hmap_delete (&proc.var_ranges, &range->hmap_node);
+ free (range);
+ }
+ for (struct crosstabulation *xt = &proc.pivots[0];
+ xt < &proc.pivots[proc.n_pivots]; xt++)
+ {
+ free (xt->vars);
+ free (xt->const_vars);
+ free (xt->const_indexes);
+ }
+ free (proc.pivots);
+
+ return result;
+}
+
+/* Parses the TABLES subcommand. */
+static bool
+parse_crosstabs_tables (struct lexer *lexer, struct dataset *ds,
+ struct crosstabs_proc *proc)
+{
+ const struct variable ***by = NULL;
+ size_t *by_nvar = NULL;
+ bool ok = false;
+
+ /* Ensure that this is a TABLES subcommand. */
+ if (!lex_match_id (lexer, "TABLES")
+ && (lex_token (lexer) != T_ID ||
+ dict_lookup_var (dataset_dict (ds), lex_tokcstr (lexer)) == NULL)
+ && lex_token (lexer) != T_ALL)
+ {
+ lex_error (lexer, _("Syntax error expecting subcommand name or "
+ "variable name."));
+ return false;
+ }
+ lex_match (lexer, T_EQUALS);
+
+ struct const_var_set *var_set
+ = (proc->variables
+ ? const_var_set_create_from_array (proc->variables,
+ proc->n_variables)
+ : const_var_set_create_from_dict (dataset_dict (ds)));
+
+ size_t nx = 1;
+ size_t n_by = 0;
+ int vars_start = lex_ofs (lexer);
+ do
+ {
+ by = xnrealloc (by, n_by + 1, sizeof *by);
+ by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
+ if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
+ PV_NO_DUPLICATE | PV_NO_SCRATCH))
+ goto done;
+ size_t n = by_nvar[n_by++];
+ if (xalloc_oversized (nx, n))
+ {
+ lex_ofs_error (
+ lexer, vars_start, lex_ofs (lexer) - 1,
+ _("Too many cross-tabulation variables or dimensions."));
+ goto done;
+ }
+ nx *= n;
+ }
+ while (lex_match (lexer, T_BY));
+ if (n_by < 2)
+ {
+ bool unused UNUSED = lex_force_match (lexer, T_BY);
+ goto done;
+ }
+ int vars_end = lex_ofs (lexer) - 1;
+
+ size_t *by_iter = XCALLOC (n_by, size_t);
+ proc->pivots = xnrealloc (proc->pivots,
+ proc->n_pivots + nx, sizeof *proc->pivots);
+ for (size_t i = 0; i < nx; i++)
+ {
+ struct crosstabulation *xt = &proc->pivots[proc->n_pivots++];
+
+ *xt = (struct crosstabulation) {
+ .proc = proc,
+ .weight_format = proc->weight_format,
+ .missing = 0.,
+ .n_vars = n_by,
+ .vars = xcalloc (n_by, sizeof *xt->vars),
+ .n_consts = 0,
+ .const_vars = NULL,
+ .const_indexes = NULL,
+ .start_ofs = vars_start,
+ .end_ofs = vars_end,
+ };
+
+ for (size_t j = 0; j < n_by; j++)
+ xt->vars[j].var = by[j][by_iter[j]];
+
+ for (int j = n_by - 1; j >= 0; j--)
+ {
+ if (++by_iter[j] < by_nvar[j])
+ break;
+ by_iter[j] = 0;
+ }
+ }
+ free (by_iter);
+ ok = true;
+
+done:
+ /* All return paths lead here. */
+ for (size_t i = 0; i < n_by; i++)
+ free (by[i]);
+ free (by);
+ free (by_nvar);
+
+ const_var_set_destroy (var_set);
+
+ return ok;
+}
+
+/* Parses the VARIABLES subcommand. */
+static bool
+parse_crosstabs_variables (struct lexer *lexer, struct dataset *ds,
+ struct crosstabs_proc *proc)
+{
+ if (proc->n_pivots)
+ {
+ lex_next_error (lexer, -1, -1, _("%s must be specified before %s."),
+ "VARIABLES", "TABLES");
+ return false;
+ }
+
+ lex_match (lexer, T_EQUALS);
+
+ for (;;)
+ {
+ size_t orig_nv = proc->n_variables;
+
+ if (!parse_variables_const (lexer, dataset_dict (ds),
+ &proc->variables, &proc->n_variables,
+ (PV_APPEND | PV_NUMERIC
+ | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
+ return false;
+
+ if (!lex_force_match (lexer, T_LPAREN))
+ goto error;
+
+ if (!lex_force_int (lexer))
+ goto error;
+ long min = lex_integer (lexer);
+ lex_get (lexer);
+
+ lex_match (lexer, T_COMMA);
+
+ if (!lex_force_int_range (lexer, NULL, min, LONG_MAX))
+ goto error;
+ long max = lex_integer (lexer);
+ lex_get (lexer);
+
+ if (!lex_force_match (lexer, T_RPAREN))
+ goto error;
+
+ for (size_t i = orig_nv; i < proc->n_variables; i++)
+ {
+ const struct variable *var = proc->variables[i];
+ struct var_range *vr = xmalloc (sizeof *vr);
+ *vr = (struct var_range) {
+ .var = var,
+ .min = min,
+ .max = max,
+ .count = max - min + 1,
+ };
+ hmap_insert (&proc->var_ranges, &vr->hmap_node,
+ hash_pointer (var, 0));
+ }
+
+ if (lex_token (lexer) == T_SLASH)
+ break;
+ }
+
+ proc->mode = INTEGER;
+ return true;
+
+ error:
+ free (proc->variables);
+ proc->variables = NULL;
+ proc->n_variables = 0;
+ return false;
+}
+\f
+/* Data file processing. */
+
+static const struct var_range *
+get_var_range (const struct crosstabs_proc *proc, const struct variable *var)
+{
+ if (!hmap_is_empty (&proc->var_ranges))
+ {
+ const struct var_range *range;
+
+ HMAP_FOR_EACH_IN_BUCKET (range, struct var_range, hmap_node,
+ hash_pointer (var, 0), &proc->var_ranges)
+ if (range->var == var)
+ return range;
+ }
+
+ return NULL;
+}
+
+static bool
+should_tabulate_case (const struct crosstabulation *xt, const struct ccase *c,
+ enum mv_class exclude)
+{
+ for (size_t j = 0; j < xt->n_vars; j++)
+ {
+ const struct variable *var = xt->vars[j].var;
+ const struct var_range *range = get_var_range (xt->proc, var);
+
+ if (var_is_value_missing (var, case_data (c, var)) & exclude)
+ return false;
+
+ if (range != NULL)
+ {
+ double num = case_num (c, var);
+ if (num < range->min || num >= range->max + 1.)
+ return false;
+ }
+ }
+ return true;
+}
+
+static void
+tabulate_integer_case (struct crosstabulation *xt, const struct ccase *c,
+ double weight)
+{
+ size_t hash = 0;
+ for (size_t j = 0; j < xt->n_vars; j++)
+ {
+ /* Throw away fractional parts of values. */
+ hash = hash_int (case_num (c, xt->vars[j].var), hash);
+ }
+
+ struct freq *te;
+ HMAP_FOR_EACH_WITH_HASH (te, struct freq, node, hash, &xt->data)
+ {
+ for (size_t j = 0; j < xt->n_vars; j++)
+ if ((int) case_num (c, xt->vars[j].var) != (int) te->values[j].f)
+ goto no_match;
+
+ /* Found an existing entry. */
+ te->count += weight;
+ return;
+
+ no_match: ;
+ }
+
+ /* No existing entry. Create a new one. */
+ te = xmalloc (table_entry_size (xt->n_vars));
+ te->count = weight;
+ for (size_t j = 0; j < xt->n_vars; j++)
+ te->values[j].f = (int) case_num (c, xt->vars[j].var);
+ hmap_insert (&xt->data, &te->node, hash);
+}
+
+static void
+tabulate_general_case (struct crosstabulation *xt, const struct ccase *c,
+ double weight)
+{
+ size_t hash = 0;
+ for (size_t j = 0; j < xt->n_vars; j++)
+ {
+ const struct variable *var = xt->vars[j].var;
+ hash = value_hash (case_data (c, var), var_get_width (var), hash);
+ }
+
+ struct freq *te;
+ HMAP_FOR_EACH_WITH_HASH (te, struct freq, node, hash, &xt->data)
+ {
+ for (size_t j = 0; j < xt->n_vars; j++)
+ {
+ const struct variable *var = xt->vars[j].var;
+ if (!value_equal (case_data (c, var), &te->values[j],
+ var_get_width (var)))
+ goto no_match;
+ }
+
+ /* Found an existing entry. */
+ te->count += weight;
+ return;
+
+ no_match: ;
+ }
+
+ /* No existing entry. Create a new one. */
+ te = xmalloc (table_entry_size (xt->n_vars));
+ te->count = weight;
+ for (size_t j = 0; j < xt->n_vars; j++)
+ {
+ const struct variable *var = xt->vars[j].var;
+ value_clone (&te->values[j], case_data (c, var), var_get_width (var));
+ }
+ hmap_insert (&xt->data, &te->node, hash);
+}
+\f
+/* Post-data reading calculations. */
+
+static int compare_table_entry_vars_3way (const struct freq *a,
+ const struct freq *b,
+ const struct crosstabulation *xt,
+ int idx0, int idx1);
+static int compare_table_entry_3way (const void *ap_, const void *bp_,
+ const void *xt_);
+static int compare_table_entry_3way_inv (const void *ap_, const void *bp_,
+ const void *xt_);
+
+static void enum_var_values (const struct crosstabulation *, int var_idx,
+ bool descending);
+static void free_var_values (const struct crosstabulation *, int var_idx);
+static void output_crosstabulation (struct crosstabs_proc *,
+ struct crosstabulation *,
+ struct lexer *);
+static void make_crosstabulation_subset (struct crosstabulation *xt,
+ size_t row0, size_t row1,
+ struct crosstabulation *subset);
+static void make_summary_table (struct crosstabs_proc *);
+static bool find_crosstab (struct crosstabulation *, size_t *row0p,
+ size_t *row1p);
+
+static void
+postcalc (struct crosstabs_proc *proc, struct lexer *lexer)
+{
+ /* Round hash table entries, if requested
+
+ If this causes any of the cell counts to fall to zero, delete those
+ cells. */
+ if (proc->round_cells)
+ for (struct crosstabulation *xt = proc->pivots;
+ xt < &proc->pivots[proc->n_pivots]; xt++)
+ {
+ struct freq *e, *next;
+ HMAP_FOR_EACH_SAFE (e, next, struct freq, node, &xt->data)
+ {
+ e->count = round_weight (proc, e->count);
+ if (e->count == 0.0)
+ {
+ hmap_delete (&xt->data, &e->node);
+ free (e);
+ }
+ }
+ }
+
+ /* Convert hash tables into sorted arrays of entries. */
+ for (struct crosstabulation *xt = proc->pivots;
+ xt < &proc->pivots[proc->n_pivots]; xt++)
+ {
+ xt->n_entries = hmap_count (&xt->data);
+ xt->entries = xnmalloc (xt->n_entries, sizeof *xt->entries);
+
+ size_t i = 0;
+ struct freq *e;
+ HMAP_FOR_EACH (e, struct freq, node, &xt->data)
+ xt->entries[i++] = e;
+
+ hmap_destroy (&xt->data);
+
+ sort (xt->entries, xt->n_entries, sizeof *xt->entries,
+ proc->descending ? compare_table_entry_3way_inv : compare_table_entry_3way,
+ xt);
+ }
+
+ make_summary_table (proc);
+
+ /* Output each pivot table. */
+ for (struct crosstabulation *xt = proc->pivots;
+ xt < &proc->pivots[proc->n_pivots]; xt++)
+ {
+ output_crosstabulation (proc, xt, lexer);
+ if (proc->barchart)
+ {
+ int n_vars = (xt->n_vars > 2 ? 2 : xt->n_vars);
+ const struct variable **vars = XCALLOC (n_vars, const struct variable*);
+ for (size_t i = 0; i < n_vars; i++)
+ vars[i] = xt->vars[i].var;
+ chart_submit (barchart_create (vars, n_vars, _("Count"),
+ false,
+ xt->entries, xt->n_entries));
+ free (vars);
+ }
+ }
+
+ /* Free output and prepare for next split file. */
+ for (struct crosstabulation *xt = proc->pivots;
+ xt < &proc->pivots[proc->n_pivots]; xt++)
+ {
+ xt->missing = 0.0;
+
+ /* Free the members that were allocated in this function(and the values
+ owned by the entries.
+
+ The other pointer members are either both allocated and destroyed at a
+ lower level (in output_crosstabulation), or both allocated and
+ destroyed at a higher level (in crs_custom_tables and free_proc,
+ respectively). */
+ for (size_t i = 0; i < xt->n_vars; i++)
+ {
+ int width = var_get_width (xt->vars[i].var);
+ if (value_needs_init (width))
+ for (size_t j = 0; j < xt->n_entries; j++)
+ value_destroy (&xt->entries[j]->values[i], width);
+ }
+
+ for (size_t i = 0; i < xt->n_entries; i++)
+ free (xt->entries[i]);
+ free (xt->entries);
+ }
+}
+
+static void
+make_crosstabulation_subset (struct crosstabulation *xt, size_t row0,
+ size_t row1, struct crosstabulation *subset)
+{
+ *subset = *xt;
+ if (xt->n_vars > 2)
+ {
+ assert (xt->n_consts == 0);
+ subset->n_vars = 2;
+ subset->vars = xt->vars;
+
+ subset->n_consts = xt->n_vars - 2;
+ subset->const_vars = xt->vars + 2;
+ subset->const_indexes = xcalloc (subset->n_consts,
+ sizeof *subset->const_indexes);
+ for (size_t i = 0; i < subset->n_consts; i++)
+ {
+ const union value *value = &xt->entries[row0]->values[2 + i];
+
+ for (size_t j = 0; j < xt->vars[2 + i].n_values; j++)
+ if (value_equal (&xt->vars[2 + i].values[j], value,
+ var_get_width (xt->vars[2 + i].var)))
+ {
+ subset->const_indexes[i] = j;
+ goto found;
+ }
+ NOT_REACHED ();
+ found: ;
+ }
+ }
+ subset->entries = &xt->entries[row0];
+ subset->n_entries = row1 - row0;
+}
+
+static int
+compare_table_entry_var_3way (const struct freq *a,
+ const struct freq *b,
+ const struct crosstabulation *xt,
+ int idx)
+{
+ return value_compare_3way (&a->values[idx], &b->values[idx],
+ var_get_width (xt->vars[idx].var));
+}
+
+static int
+compare_table_entry_vars_3way (const struct freq *a,
+ const struct freq *b,
+ const struct crosstabulation *xt,
+ int idx0, int idx1)
+{
+ for (int i = idx1 - 1; i >= idx0; i--)
+ {
+ int cmp = compare_table_entry_var_3way (a, b, xt, i);
+ if (cmp != 0)
+ return cmp;
+ }
+ return 0;
+}
+
+/* Compare the struct freq at *AP to the one at *BP and
+ return a strcmp()-type result. */
+static int
+compare_table_entry_3way (const void *ap_, const void *bp_, const void *xt_)
+{
+ const struct freq *const *ap = ap_;
+ const struct freq *const *bp = bp_;
+ const struct freq *a = *ap;
+ const struct freq *b = *bp;
+ const struct crosstabulation *xt = xt_;
+
+ int cmp = compare_table_entry_vars_3way (a, b, xt, 2, xt->n_vars);
+ if (cmp != 0)
+ return cmp;
+
+ cmp = compare_table_entry_var_3way (a, b, xt, ROW_VAR);
+ if (cmp != 0)
+ return cmp;
+
+ return compare_table_entry_var_3way (a, b, xt, COL_VAR);
+}
+
+/* Inverted version of compare_table_entry_3way */
+static int
+compare_table_entry_3way_inv (const void *ap_, const void *bp_, const void *xt_)
+{
+ return -compare_table_entry_3way (ap_, bp_, xt_);
+}
+
+/* Output a table summarizing the cases processed. */
+static void
+make_summary_table (struct crosstabs_proc *proc)
+{
+ struct pivot_table *table = pivot_table_create (N_("Summary"));
+ pivot_table_set_weight_var (table, dict_get_weight (proc->dict));
+
+ pivot_dimension_create (table, PIVOT_AXIS_COLUMN, N_("Statistics"),
+ N_("N"), PIVOT_RC_COUNT,
+ N_("Percent"), PIVOT_RC_PERCENT);
+
+ struct pivot_dimension *cases = pivot_dimension_create (
+ table, PIVOT_AXIS_COLUMN, N_("Cases"),
+ N_("Valid"), N_("Missing"), N_("Total"));
+ cases->root->show_label = true;
+
+ struct pivot_dimension *tables = pivot_dimension_create (
+ table, PIVOT_AXIS_ROW, N_("Crosstabulation"));
+ for (struct crosstabulation *xt = &proc->pivots[0];
+ xt < &proc->pivots[proc->n_pivots]; xt++)
+ {
+ struct string name = DS_EMPTY_INITIALIZER;
+ for (size_t i = 0; i < xt->n_vars; i++)
+ {
+ if (i > 0)
+ ds_put_cstr (&name, " × ");
+ ds_put_cstr (&name, var_to_string (xt->vars[i].var));
+ }
+
+ int row = pivot_category_create_leaf (
+ tables->root,
+ pivot_value_new_user_text_nocopy (ds_steal_cstr (&name)));
+
+ double valid = 0.;
+ for (size_t i = 0; i < xt->n_entries; i++)
+ valid += xt->entries[i]->count;
+
+ double n[3];
+ n[0] = valid;
+ n[1] = xt->missing;
+ n[2] = n[0] + n[1];
+ for (int i = 0; i < 3; i++)
+ {
+ pivot_table_put3 (table, 0, i, row, pivot_value_new_number (n[i]));
+ pivot_table_put3 (table, 1, i, row,
+ pivot_value_new_number (n[i] / n[2] * 100.0));
+ }
+ }
+
+ pivot_table_submit (table);
+}
+\f
+/* Output. */
+
+static struct pivot_table *create_crosstab_table (
+ struct crosstabs_proc *, struct crosstabulation *,
+ size_t crs_leaves[CRS_N_CELLS]);
+static struct pivot_table *create_chisq_table (struct crosstabulation *);
+static struct pivot_table *create_sym_table (struct crosstabulation *);
+static struct pivot_table *create_risk_table (
+ struct crosstabulation *, struct pivot_dimension **risk_statistics);
+static struct pivot_table *create_direct_table (struct crosstabulation *);
+static void display_crosstabulation (struct crosstabs_proc *,
+ struct crosstabulation *,
+ struct pivot_table *,
+ size_t crs_leaves[CRS_N_CELLS]);
+static void display_chisq (struct crosstabulation *, struct pivot_table *);
+static void display_symmetric (struct crosstabs_proc *,
+ struct crosstabulation *, struct pivot_table *);
+static void display_risk (struct crosstabulation *, struct pivot_table *,
+ struct pivot_dimension *risk_statistics);
+static void display_directional (struct crosstabs_proc *,
+ struct crosstabulation *,
+ struct pivot_table *);
+static void delete_missing (struct crosstabulation *);
+static void build_matrix (struct crosstabulation *);
+
+/* Output pivot table XT in the context of PROC. */
+static void
+output_crosstabulation (struct crosstabs_proc *proc, struct crosstabulation *xt,
+ struct lexer *lexer)
+{
+ for (size_t i = 0; i < xt->n_vars; i++)
+ enum_var_values (xt, i, proc->descending);
+
+ if (xt->vars[COL_VAR].n_values == 0)
+ {
+ struct string vars;
+
+ ds_init_cstr (&vars, var_to_string (xt->vars[0].var));
+ for (size_t i = 1; i < xt->n_vars; i++)
+ ds_put_format (&vars, " × %s", var_to_string (xt->vars[i].var));
+
+ /* TRANSLATORS: The %s here describes a crosstabulation. It takes the
+ form "var1 * var2 * var3 * ...". */
+ lex_ofs_msg (lexer, SW, xt->start_ofs, xt->end_ofs,
+ _("Crosstabulation %s contained no non-missing cases."),
+ ds_cstr (&vars));
+
+ ds_destroy (&vars);
+ for (size_t i = 0; i < xt->n_vars; i++)
+ free_var_values (xt, i);
+ return;
+ }
+
+ size_t crs_leaves[CRS_N_CELLS];
+ struct pivot_table *table = (proc->cells
+ ? create_crosstab_table (proc, xt, crs_leaves)
+ : NULL);
+ struct pivot_table *chisq = (proc->statistics & CRS_ST_CHISQ
+ ? create_chisq_table (xt)
+ : NULL);
+ struct pivot_table *sym
+ = (proc->statistics & (CRS_ST_PHI | CRS_ST_CC | CRS_ST_BTAU | CRS_ST_CTAU
+ | CRS_ST_GAMMA | CRS_ST_CORR | CRS_ST_KAPPA)
+ ? create_sym_table (xt)
+ : NULL);
+ struct pivot_dimension *risk_statistics = NULL;
+ struct pivot_table *risk = (proc->statistics & CRS_ST_RISK
+ ? create_risk_table (xt, &risk_statistics)
+ : NULL);
+ struct pivot_table *direct
+ = (proc->statistics & (CRS_ST_LAMBDA | CRS_ST_UC | CRS_ST_D | CRS_ST_ETA)
+ ? create_direct_table (xt)
+ : NULL);
+
+ size_t row0 = 0;
+ size_t row1 = 0;
+ while (find_crosstab (xt, &row0, &row1))
+ {
+ struct crosstabulation x;
+
+ make_crosstabulation_subset (xt, row0, row1, &x);
+
+ size_t n_rows = x.vars[ROW_VAR].n_values;
+ size_t n_cols = x.vars[COL_VAR].n_values;
+ if (size_overflow_p (xtimes (xtimes (n_rows, n_cols), sizeof (double))))
+ xalloc_die ();
+ x.row_tot = xmalloc (n_rows * sizeof *x.row_tot);
+ x.col_tot = xmalloc (n_cols * sizeof *x.col_tot);
+ x.mat = xmalloc (n_rows * n_cols * sizeof *x.mat);
+
+ build_matrix (&x);
+
+ /* Find the first variable that differs from the last subtable. */
+ if (table)
+ display_crosstabulation (proc, &x, table, crs_leaves);
+
+ if (proc->exclude == 0)
+ delete_missing (&x);
+
+ if (chisq)
+ display_chisq (&x, chisq);
+
+ if (sym)
+ display_symmetric (proc, &x, sym);
+ if (risk)
+ display_risk (&x, risk, risk_statistics);
+ if (direct)
+ display_directional (proc, &x, direct);
+
+ free (x.mat);
+ free (x.row_tot);
+ free (x.col_tot);
+ free (x.const_indexes);
+ }
+
+ if (table)
+ pivot_table_submit (table);
+
+ if (chisq)
+ pivot_table_submit (chisq);
+
+ if (sym)
+ pivot_table_submit (sym);
+
+ if (risk)
+ {
+ if (!pivot_table_is_empty (risk))
+ pivot_table_submit (risk);
+ else
+ pivot_table_unref (risk);
+ }
+
+ if (direct)
+ pivot_table_submit (direct);
+
+ for (size_t i = 0; i < xt->n_vars; i++)
+ free_var_values (xt, i);
+}
+
+static void
+build_matrix (struct crosstabulation *x)
+{
+ const int col_var_width = var_get_width (x->vars[COL_VAR].var);
+ const int row_var_width = var_get_width (x->vars[ROW_VAR].var);
+ size_t n_rows = x->vars[ROW_VAR].n_values;
+ size_t n_cols = x->vars[COL_VAR].n_values;
+
+ double *mp = x->mat;
+ size_t col = 0;
+ size_t row = 0;
+ for (struct freq **p = x->entries; p < &x->entries[x->n_entries]; p++)
+ {
+ const struct freq *te = *p;
+
+ while (!value_equal (&x->vars[ROW_VAR].values[row],
+ &te->values[ROW_VAR], row_var_width))
+ {
+ for (; col < n_cols; col++)
+ *mp++ = 0.0;
+ col = 0;
+ row++;
+ }
+
+ while (!value_equal (&x->vars[COL_VAR].values[col],
+ &te->values[COL_VAR], col_var_width))
+ {
+ *mp++ = 0.0;
+ col++;
+ }
+
+ *mp++ = te->count;
+ if (++col >= n_cols)
+ {
+ col = 0;
+ row++;
+ }
+ }
+ while (mp < &x->mat[n_cols * n_rows])
+ *mp++ = 0.0;
+ assert (mp == &x->mat[n_cols * n_rows]);
+
+ /* Column totals, row totals, ns_rows. */
+ mp = x->mat;
+ for (col = 0; col < n_cols; col++)
+ x->col_tot[col] = 0.0;
+ for (row = 0; row < n_rows; row++)
+ x->row_tot[row] = 0.0;
+ x->ns_rows = 0;
+ for (row = 0; row < n_rows; row++)
+ {
+ bool row_is_empty = true;
+ for (col = 0; col < n_cols; col++)
+ {
+ if (*mp != 0.0)
+ {
+ row_is_empty = false;
+ x->col_tot[col] += *mp;
+ x->row_tot[row] += *mp;
+ }
+ mp++;
+ }
+ if (!row_is_empty)
+ x->ns_rows++;
+ }
+ assert (mp == &x->mat[n_cols * n_rows]);
+
+ /* ns_cols. */
+ x->ns_cols = 0;
+ for (col = 0; col < n_cols; col++)
+ for (row = 0; row < n_rows; row++)
+ if (x->mat[col + row * n_cols] != 0.0)
+ {
+ x->ns_cols++;
+ break;
+ }
+
+ /* Grand total. */
+ x->total = 0.0;
+ for (col = 0; col < n_cols; col++)
+ x->total += x->col_tot[col];
+}
+
+static void
+add_var_dimension (struct pivot_table *table, const struct xtab_var *var,
+ enum pivot_axis_type axis_type, bool total)
+{
+ struct pivot_dimension *d = pivot_dimension_create__ (
+ table, axis_type, pivot_value_new_variable (var->var));
+
+ struct pivot_footnote *missing_footnote = pivot_table_create_footnote (
+ table, pivot_value_new_text (N_("Missing value")));
+
+ struct pivot_category *group = pivot_category_create_group__ (
+ d->root, pivot_value_new_variable (var->var));
+ for (size_t j = 0; j < var->n_values; j++)
+ {
+ struct pivot_value *value = pivot_value_new_var_value (
+ var->var, &var->values[j]);
+ if (var_is_value_missing (var->var, &var->values[j]))
+ pivot_value_add_footnote (value, missing_footnote);
+ pivot_category_create_leaf (group, value);
+ }
+
+ if (total)
+ pivot_category_create_leaf (d->root, pivot_value_new_text (N_("Total")));
+}
+
+static struct pivot_table *
+create_crosstab_table (struct crosstabs_proc *proc, struct crosstabulation *xt,
+ size_t crs_leaves[CRS_N_CELLS])
+{
+ /* Title. */
+ struct string title = DS_EMPTY_INITIALIZER;
+ for (size_t i = 0; i < xt->n_vars; i++)
+ {
+ if (i)
+ ds_put_cstr (&title, " × ");
+ ds_put_cstr (&title, var_to_string (xt->vars[i].var));
+ }
+ for (size_t i = 0; i < xt->n_consts; i++)
+ {
+ const struct variable *var = xt->const_vars[i].var;
+ const union value *value = &xt->entries[0]->values[2 + i];
+ char *s;
+
+ ds_put_format (&title, ", %s=", var_to_string (var));
+
+ /* Insert the formatted value of VAR without any leading spaces. */
+ s = data_out (value, var_get_encoding (var), var_get_print_format (var),
+ settings_get_fmt_settings ());
+ ds_put_cstr (&title, s + strspn (s, " "));
+ free (s);
+ }
+ struct pivot_table *table = pivot_table_create__ (
+ pivot_value_new_user_text_nocopy (ds_steal_cstr (&title)),
+ "Crosstabulation");
+ pivot_table_set_weight_format (table, &proc->weight_format);
+
+ struct pivot_dimension *statistics = pivot_dimension_create (
+ table, PIVOT_AXIS_ROW, N_("Statistics"));
+
+ struct statistic
+ {
+ const char *label;
+ const char *rc;
+ };
+ static const struct statistic stats[CRS_N_CELLS] =
+ {
+#define C(KEYWORD, STRING, RC) { STRING, RC },
+ CRS_CELLS
+#undef C
+ };
+ for (size_t i = 0; i < CRS_N_CELLS; i++)
+ if (proc->cells & (1u << i) && stats[i].label)
+ crs_leaves[i] = pivot_category_create_leaf_rc (
+ statistics->root, pivot_value_new_text (stats[i].label),
+ stats[i].rc);
+
+ for (size_t i = 0; i < xt->n_vars; i++)
+ add_var_dimension (table, &xt->vars[i],
+ i == COL_VAR ? PIVOT_AXIS_COLUMN : PIVOT_AXIS_ROW,
+ true);
+
+ return table;
+}
+
+static struct pivot_table *
+create_chisq_table (struct crosstabulation *xt)
+{
+ struct pivot_table *chisq = pivot_table_create (N_("Chi-Square Tests"));
+ pivot_table_set_weight_format (chisq, &xt->weight_format);
+
+ pivot_dimension_create (
+ chisq, PIVOT_AXIS_ROW, N_("Statistics"),
+ N_("Pearson Chi-Square"),
+ N_("Likelihood Ratio"),
+ N_("Fisher's Exact Test"),
+ N_("Continuity Correction"),
+ N_("Linear-by-Linear Association"),
+ N_("N of Valid Cases"), PIVOT_RC_COUNT);
+
+ pivot_dimension_create (
+ chisq, PIVOT_AXIS_COLUMN, N_("Statistics"),
+ N_("Value"), PIVOT_RC_OTHER,
+ N_("df"), PIVOT_RC_COUNT,
+ N_("Asymptotic Sig. (2-tailed)"), PIVOT_RC_SIGNIFICANCE,
+ N_("Exact Sig. (2-tailed)"), PIVOT_RC_SIGNIFICANCE,
+ N_("Exact Sig. (1-tailed)"), PIVOT_RC_SIGNIFICANCE);
+
+ for (size_t i = 2; i < xt->n_vars; i++)
+ add_var_dimension (chisq, &xt->vars[i], PIVOT_AXIS_ROW, false);
+
+ return chisq;
+}
+
+/* Symmetric measures. */
+static struct pivot_table *
+create_sym_table (struct crosstabulation *xt)
+{
+ struct pivot_table *sym = pivot_table_create (N_("Symmetric Measures"));
+ pivot_table_set_weight_format (sym, &xt->weight_format);
+
+ pivot_dimension_create (
+ sym, PIVOT_AXIS_COLUMN, N_("Values"),
+ N_("Value"), PIVOT_RC_OTHER,
+ N_("Asymp. Std. Error"), PIVOT_RC_OTHER,
+ N_("Approx. T"), PIVOT_RC_OTHER,
+ N_("Approx. Sig."), PIVOT_RC_SIGNIFICANCE);
+
+ struct pivot_dimension *statistics = pivot_dimension_create (
+ sym, PIVOT_AXIS_ROW, N_("Statistics"));
+ pivot_category_create_group (
+ statistics->root, N_("Nominal by Nominal"),
+ N_("Phi"), N_("Cramer's V"), N_("Contingency Coefficient"));
+ pivot_category_create_group (
+ statistics->root, N_("Ordinal by Ordinal"),
+ N_("Kendall's tau-b"), N_("Kendall's tau-c"),
+ N_("Gamma"), N_("Spearman Correlation"));
+ pivot_category_create_group (
+ statistics->root, N_("Interval by Interval"),
+ N_("Pearson's R"));
+ pivot_category_create_group (
+ statistics->root, N_("Measure of Agreement"),
+ N_("Kappa"));
+ pivot_category_create_leaves (statistics->root, N_("N of Valid Cases"),
+ PIVOT_RC_COUNT);
+
+ for (size_t i = 2; i < xt->n_vars; i++)
+ add_var_dimension (sym, &xt->vars[i], PIVOT_AXIS_ROW, false);
+
+ return sym;
+}
+
+/* Risk estimate. */
+static struct pivot_table *
+create_risk_table (struct crosstabulation *xt,
+ struct pivot_dimension **risk_statistics)
+{
+ struct pivot_table *risk = pivot_table_create (N_("Risk Estimate"));
+ pivot_table_set_weight_format (risk, &xt->weight_format);
+
+ struct pivot_dimension *values = pivot_dimension_create (
+ risk, PIVOT_AXIS_COLUMN, N_("Values"),
+ N_("Value"), PIVOT_RC_OTHER);
+ pivot_category_create_group (
+ /* xgettext:no-c-format */
+ values->root, N_("95% Confidence Interval"),
+ N_("Lower"), PIVOT_RC_OTHER,
+ N_("Upper"), PIVOT_RC_OTHER);
+
+ *risk_statistics = pivot_dimension_create (
+ risk, PIVOT_AXIS_ROW, N_("Statistics"));
+
+ for (size_t i = 2; i < xt->n_vars; i++)
+ add_var_dimension (risk, &xt->vars[i], PIVOT_AXIS_ROW, false);
+
+ return risk;
+}
+
+static void
+create_direct_stat (struct pivot_category *parent,
+ const struct crosstabulation *xt,
+ const char *name, bool symmetric)
+{
+ struct pivot_category *group = pivot_category_create_group (
+ parent, name);
+ if (symmetric)
+ pivot_category_create_leaf (group, pivot_value_new_text (N_("Symmetric")));
+
+ char *row_label = xasprintf (_("%s Dependent"),
+ var_to_string (xt->vars[ROW_VAR].var));
+ pivot_category_create_leaf (group, pivot_value_new_user_text_nocopy (
+ row_label));
+
+ char *col_label = xasprintf (_("%s Dependent"),
+ var_to_string (xt->vars[COL_VAR].var));
+ pivot_category_create_leaf (group, pivot_value_new_user_text_nocopy (
+ col_label));
+}
+
+/* Directional measures. */
+static struct pivot_table *
+create_direct_table (struct crosstabulation *xt)
+{
+ struct pivot_table *direct = pivot_table_create (N_("Directional Measures"));
+ pivot_table_set_weight_format (direct, &xt->weight_format);
+
+ pivot_dimension_create (
+ direct, PIVOT_AXIS_COLUMN, N_("Values"),
+ N_("Value"), PIVOT_RC_OTHER,
+ N_("Asymp. Std. Error"), PIVOT_RC_OTHER,
+ N_("Approx. T"), PIVOT_RC_OTHER,
+ N_("Approx. Sig."), PIVOT_RC_SIGNIFICANCE);
+
+ struct pivot_dimension *statistics = pivot_dimension_create (
+ direct, PIVOT_AXIS_ROW, N_("Statistics"));
+ struct pivot_category *nn = pivot_category_create_group (
+ statistics->root, N_("Nominal by Nominal"));
+ create_direct_stat (nn, xt, N_("Lambda"), true);
+ create_direct_stat (nn, xt, N_("Goodman and Kruskal tau"), false);
+ create_direct_stat (nn, xt, N_("Uncertainty Coefficient"), true);
+ struct pivot_category *oo = pivot_category_create_group (
+ statistics->root, N_("Ordinal by Ordinal"));
+ create_direct_stat (oo, xt, N_("Somers' d"), true);
+ struct pivot_category *ni = pivot_category_create_group (
+ statistics->root, N_("Nominal by Interval"));
+ create_direct_stat (ni, xt, N_("Eta"), false);
+
+ for (size_t i = 2; i < xt->n_vars; i++)
+ add_var_dimension (direct, &xt->vars[i], PIVOT_AXIS_ROW, false);
+
+ return direct;
+}
+
+/* Delete missing rows and columns for statistical analysis when
+ /MISSING=REPORT. */
+static void
+delete_missing (struct crosstabulation *xt)
+{
+ size_t n_rows = xt->vars[ROW_VAR].n_values;
+ size_t n_cols = xt->vars[COL_VAR].n_values;
+
+ for (size_t r = 0; r < n_rows; r++)
+ if (var_is_num_missing (xt->vars[ROW_VAR].var,
+ xt->vars[ROW_VAR].values[r].f) == MV_USER)
+ {
+ for (size_t c = 0; c < n_cols; c++)
+ xt->mat[c + r * n_cols] = 0.;
+ xt->ns_rows--;
+ }
+
+
+ for (size_t c = 0; c < n_cols; c++)
+ if (var_is_num_missing (xt->vars[COL_VAR].var,
+ xt->vars[COL_VAR].values[c].f) == MV_USER)
+ {
+ for (size_t r = 0; r < n_rows; r++)
+ xt->mat[c + r * n_cols] = 0.;
+ xt->ns_cols--;
+ }
+}
+
+static bool
+find_crosstab (struct crosstabulation *xt, size_t *row0p, size_t *row1p)
+{
+ size_t row0 = *row1p;
+ if (row0 >= xt->n_entries)
+ return false;
+
+ size_t row1;
+ for (row1 = row0 + 1; row1 < xt->n_entries; row1++)
+ {
+ struct freq *a = xt->entries[row0];
+ struct freq *b = xt->entries[row1];
+ if (compare_table_entry_vars_3way (a, b, xt, 2, xt->n_vars) != 0)
+ break;
+ }
+ *row0p = row0;
+ *row1p = row1;
+ return true;
+}
+
+/* Compares `union value's A_ and B_ and returns a strcmp()-like
+ result. WIDTH_ points to an int which is either 0 for a
+ numeric value or a string width for a string value. */
+static int
+compare_value_3way (const void *a_, const void *b_, const void *width_)
+{
+ const union value *a = a_;
+ const union value *b = b_;
+ const int *width = width_;
+
+ return value_compare_3way (a, b, *width);
+}
+
+/* Inverted version of the above */
+static int
+compare_value_3way_inv (const void *a_, const void *b_, const void *width_)
+{
+ return -compare_value_3way (a_, b_, width_);
+}
+
+
+/* Given an array of ENTRY_CNT table_entry structures starting at
+ ENTRIES, creates a sorted list of the values that the variable
+ with index VAR_IDX takes on. Stores the array of the values in
+ XT->values and the number of values in XT->n_values. */
+static void
+enum_var_values (const struct crosstabulation *xt, int var_idx,
+ bool descending)
+{
+ struct xtab_var *xv = &xt->vars[var_idx];
+ const struct var_range *range = get_var_range (xt->proc, xv->var);
+
+ if (range)
+ {
+ xv->values = xnmalloc (range->count, sizeof *xv->values);
+ xv->n_values = range->count;
+ for (size_t i = 0; i < range->count; i++)
+ xv->values[i].f = range->min + i;
+ }
+ else
+ {
+ int width = var_get_width (xv->var);
+ struct hmapx set = HMAPX_INITIALIZER (set);
+
+ for (size_t i = 0; i < xt->n_entries; i++)
+ {
+ const struct freq *te = xt->entries[i];
+ const union value *value = &te->values[var_idx];
+ size_t hash = value_hash (value, width, 0);
+
+ const union value *iter;
+ struct hmapx_node *node;
+ HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
+ if (value_equal (iter, value, width))
+ goto next_entry;
+
+ hmapx_insert (&set, (union value *) value, hash);
+
+ next_entry: ;
+ }
+
+ xv->n_values = hmapx_count (&set);
+ xv->values = xnmalloc (xv->n_values, sizeof *xv->values);
+ size_t i = 0;
+ const union value *iter;
+ struct hmapx_node *node;
+ HMAPX_FOR_EACH (iter, node, &set)
+ xv->values[i++] = *iter;
+ hmapx_destroy (&set);
+
+ sort (xv->values, xv->n_values, sizeof *xv->values,
+ descending ? compare_value_3way_inv : compare_value_3way,
+ &width);
+ }
+}
+
+static void
+free_var_values (const struct crosstabulation *xt, int var_idx)
+{
+ struct xtab_var *xv = &xt->vars[var_idx];
+ free (xv->values);
+ xv->values = NULL;
+ xv->n_values = 0;
+}
+
+/* Displays the crosstabulation table. */
+static void
+display_crosstabulation (struct crosstabs_proc *proc,
+ struct crosstabulation *xt, struct pivot_table *table,
+ size_t crs_leaves[CRS_N_CELLS])
+{
+ size_t n_rows = xt->vars[ROW_VAR].n_values;
+ size_t n_cols = xt->vars[COL_VAR].n_values;
+
+ size_t *indexes = xnmalloc (table->n_dimensions, sizeof *indexes);
+ assert (xt->n_vars == 2);
+ for (size_t i = 0; i < xt->n_consts; i++)
+ indexes[i + 3] = xt->const_indexes[i];
+
+ /* Put in the actual cells. */
+ double *mp = xt->mat;
+ for (size_t r = 0; r < n_rows; r++)
+ {
+ if (!xt->row_tot[r] && proc->mode != INTEGER)
+ continue;
+
+ indexes[ROW_VAR + 1] = r;
+ for (size_t c = 0; c < n_cols; c++)
+ {
+ if (!xt->col_tot[c] && proc->mode != INTEGER)
+ continue;
+
+ indexes[COL_VAR + 1] = c;
+
+ double expected_value = xt->row_tot[r] * xt->col_tot[c] / xt->total;
+ double residual = *mp - expected_value;
+ double sresidual = residual / sqrt (expected_value);
+ double asresidual
+ = residual / sqrt (expected_value
+ * (1. - xt->row_tot[r] / xt->total)
+ * (1. - xt->col_tot[c] / xt->total));
+ double entries[CRS_N_CELLS] = {
+ [CRS_CL_COUNT] = *mp,
+ [CRS_CL_ROW] = *mp / xt->row_tot[r] * 100.,
+ [CRS_CL_COLUMN] = *mp / xt->col_tot[c] * 100.,
+ [CRS_CL_TOTAL] = *mp / xt->total * 100.,
+ [CRS_CL_EXPECTED] = expected_value,
+ [CRS_CL_RESIDUAL] = residual,
+ [CRS_CL_SRESIDUAL] = sresidual,
+ [CRS_CL_ASRESIDUAL] = asresidual,
+ };
+ for (size_t i = 0; i < proc->n_cells; i++)
+ {
+ int cell = proc->a_cells[i];
+ indexes[0] = crs_leaves[cell];
+ pivot_table_put (table, indexes, table->n_dimensions,
+ pivot_value_new_number (entries[cell]));
+ }
+
+ mp++;
+ }
+ }
+
+ /* Row totals. */
+ for (size_t r = 0; r < n_rows; r++)
+ {
+ if (!xt->row_tot[r] && proc->mode != INTEGER)
+ continue;
+
+ double expected_value = xt->row_tot[r] / xt->total;
+ double entries[CRS_N_CELLS] = {
+ [CRS_CL_COUNT] = xt->row_tot[r],
+ [CRS_CL_ROW] = 100.0,
+ [CRS_CL_COLUMN] = expected_value * 100.,
+ [CRS_CL_TOTAL] = expected_value * 100.,
+ [CRS_CL_EXPECTED] = expected_value,
+ [CRS_CL_RESIDUAL] = SYSMIS,
+ [CRS_CL_SRESIDUAL] = SYSMIS,
+ [CRS_CL_ASRESIDUAL] = SYSMIS,
+ };
+ for (size_t i = 0; i < proc->n_cells; i++)
+ {
+ int cell = proc->a_cells[i];
+ double entry = entries[cell];
+ if (entry != SYSMIS)
+ {
+ indexes[ROW_VAR + 1] = r;
+ indexes[COL_VAR + 1] = n_cols;
+ indexes[0] = crs_leaves[cell];
+ pivot_table_put (table, indexes, table->n_dimensions,
+ pivot_value_new_number (entry));
+ }
+ }
+ }
+
+ for (size_t c = 0; c <= n_cols; c++)
+ {
+ if (c < n_cols && !xt->col_tot[c] && proc->mode != INTEGER)
+ continue;
+
+ double ct = c < n_cols ? xt->col_tot[c] : xt->total;
+ double expected_value = ct / xt->total;
+ double entries[CRS_N_CELLS] = {
+ [CRS_CL_COUNT] = ct,
+ [CRS_CL_ROW] = expected_value * 100.0,
+ [CRS_CL_COLUMN] = 100.0,
+ [CRS_CL_TOTAL] = expected_value * 100.,
+ [CRS_CL_EXPECTED] = expected_value,
+ [CRS_CL_RESIDUAL] = SYSMIS,
+ [CRS_CL_SRESIDUAL] = SYSMIS,
+ [CRS_CL_ASRESIDUAL] = SYSMIS,
+ };
+ for (size_t i = 0; i < proc->n_cells; i++)
+ {
+ size_t cell = proc->a_cells[i];
+ double entry = entries[cell];
+ if (entry != SYSMIS)
+ {
+ indexes[ROW_VAR + 1] = n_rows;
+ indexes[COL_VAR + 1] = c;
+ indexes[0] = crs_leaves[cell];
+ pivot_table_put (table, indexes, table->n_dimensions,
+ pivot_value_new_number (entry));
+ }
+ }
+ }
+
+ free (indexes);
+}
+
+static void calc_r (struct crosstabulation *,
+ double *XT, double *Y, double *, double *, double *);
+static void calc_chisq (struct crosstabulation *,
+ double[N_CHISQ], int[N_CHISQ], double *, double *);
+
+/* Display chi-square statistics. */
+static void
+display_chisq (struct crosstabulation *xt, struct pivot_table *chisq)
+{
+ double chisq_v[N_CHISQ];
+ double fisher1, fisher2;
+ int df[N_CHISQ];
+ calc_chisq (xt, chisq_v, df, &fisher1, &fisher2);
+
+ size_t *indexes = xnmalloc (chisq->n_dimensions, sizeof *indexes);
+ assert (xt->n_vars == 2);
+ for (size_t i = 0; i < xt->n_consts; i++)
+ indexes[i + 2] = xt->const_indexes[i];
+ for (size_t i = 0; i < N_CHISQ; i++)
+ {
+ indexes[0] = i;
+
+ double entries[5] = { SYSMIS, SYSMIS, SYSMIS, SYSMIS, SYSMIS };
+ if (i == 2)
+ {
+ entries[3] = fisher2;
+ entries[4] = fisher1;
+ }
+ else if (chisq_v[i] != SYSMIS)
+ {
+ entries[0] = chisq_v[i];
+ entries[1] = df[i];
+ entries[2] = gsl_cdf_chisq_Q (chisq_v[i], df[i]);
+ }
+
+ for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
+ if (entries[j] != SYSMIS)
+ {
+ indexes[1] = j;
+ pivot_table_put (chisq, indexes, chisq->n_dimensions,
+ pivot_value_new_number (entries[j]));
+ }
+ }
+
+ indexes[0] = 5;
+ indexes[1] = 0;
+ pivot_table_put (chisq, indexes, chisq->n_dimensions,
+ pivot_value_new_number (xt->total));
+
+ free (indexes);
+}
+
+static bool calc_symmetric (struct crosstabs_proc *, struct crosstabulation *,
+ double[N_SYMMETRIC], double[N_SYMMETRIC],
+ double[N_SYMMETRIC],
+ double[3], double[3], double[3]);
+
+/* Display symmetric measures. */
+static void
+display_symmetric (struct crosstabs_proc *proc, struct crosstabulation *xt,
+ struct pivot_table *sym)
+{
+ double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
+ double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
+
+ if (!calc_symmetric (proc, xt, sym_v, sym_ase, sym_t,
+ somers_d_v, somers_d_ase, somers_d_t))
+ return;
+
+ size_t *indexes = xnmalloc (sym->n_dimensions, sizeof *indexes);
+ assert (xt->n_vars == 2);
+ for (size_t i = 0; i < xt->n_consts; i++)
+ indexes[i + 2] = xt->const_indexes[i];
+
+ for (size_t i = 0; i < N_SYMMETRIC; i++)
+ {
+ if (sym_v[i] == SYSMIS)
+ continue;
+
+ indexes[1] = i;
+
+ double entries[] = { sym_v[i], sym_ase[i], sym_t[i] };
+ for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
+ if (entries[j] != SYSMIS)
+ {
+ indexes[0] = j;
+ pivot_table_put (sym, indexes, sym->n_dimensions,
+ pivot_value_new_number (entries[j]));
+ }
+ }
+
+ indexes[1] = N_SYMMETRIC;
+ indexes[0] = 0;
+ struct pivot_value *total = pivot_value_new_number (xt->total);
+ pivot_value_set_rc (sym, total, PIVOT_RC_COUNT);
+ pivot_table_put (sym, indexes, sym->n_dimensions, total);
+
+ free (indexes);
+}
+
+static bool calc_risk (struct crosstabulation *,
+ double[], double[], double[], union value *,
+ double *);
+
+/* Display risk estimate. */
+static void
+display_risk (struct crosstabulation *xt, struct pivot_table *risk,
+ struct pivot_dimension *risk_statistics)
+{
+ double risk_v[3], lower[3], upper[3], n_valid;
+ union value c[2];
+ if (!calc_risk (xt, risk_v, upper, lower, c, &n_valid))
+ return;
+ assert (risk_statistics);
+
+ size_t *indexes = xnmalloc (risk->n_dimensions, sizeof *indexes);
+ assert (xt->n_vars == 2);
+ for (size_t i = 0; i < xt->n_consts; i++)
+ indexes[i + 2] = xt->const_indexes[i];
+
+ for (size_t i = 0; i < 3; i++)
+ {
+ const struct variable *cv = xt->vars[COL_VAR].var;
+ const struct variable *rv = xt->vars[ROW_VAR].var;
+
+ if (risk_v[i] == SYSMIS)
+ continue;
+
+ struct string label = DS_EMPTY_INITIALIZER;
+ switch (i)
+ {
+ case 0:
+ ds_put_format (&label, _("Odds Ratio for %s"), var_to_string (rv));
+ ds_put_cstr (&label, " (");
+ var_append_value_name (rv, &c[0], &label);
+ ds_put_cstr (&label, " / ");
+ var_append_value_name (rv, &c[1], &label);
+ ds_put_cstr (&label, ")");
+ break;
+ case 1:
+ case 2:
+ ds_put_format (&label, _("For cohort %s = "), var_to_string (cv));
+ var_append_value_name (cv, &xt->vars[ROW_VAR].values[i - 1], &label);
+ break;
+ }
+
+ indexes[1] = pivot_category_create_leaf (
+ risk_statistics->root,
+ pivot_value_new_user_text_nocopy (ds_steal_cstr (&label)));
+
+ double entries[] = { risk_v[i], lower[i], upper[i] };
+ for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
+ {
+ indexes[0] = j;
+ pivot_table_put (risk, indexes, risk->n_dimensions,
+ pivot_value_new_number (entries[i]));
+ }
+ }
+ indexes[1] = pivot_category_create_leaf (
+ risk_statistics->root,
+ pivot_value_new_text (N_("N of Valid Cases")));
+ indexes[0] = 0;
+ pivot_table_put (risk, indexes, risk->n_dimensions,
+ pivot_value_new_number (n_valid));
+ free (indexes);
+}
+
+static void calc_directional (struct crosstabs_proc *, struct crosstabulation *,
+ double[N_DIRECTIONAL], double[N_DIRECTIONAL],
+ double[N_DIRECTIONAL], double[N_DIRECTIONAL]);
+
+/* Display directional measures. */
+static void
+display_directional (struct crosstabs_proc *proc,
+ struct crosstabulation *xt, struct pivot_table *direct)
+{
+ double direct_v[N_DIRECTIONAL];
+ double direct_ase[N_DIRECTIONAL];
+ double direct_t[N_DIRECTIONAL];
+ double sig[N_DIRECTIONAL];
+ calc_directional (proc, xt, direct_v, direct_ase, direct_t, sig);
+
+ size_t *indexes = xnmalloc (direct->n_dimensions, sizeof *indexes);
+ assert (xt->n_vars == 2);
+ for (size_t i = 0; i < xt->n_consts; i++)
+ indexes[i + 2] = xt->const_indexes[i];
+
+ for (size_t i = 0; i < N_DIRECTIONAL; i++)
+ {
+ if (direct_v[i] == SYSMIS)
+ continue;
+
+ indexes[1] = i;
+
+ double entries[] = {
+ direct_v[i], direct_ase[i], direct_t[i], sig[i],
+ };
+ for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
+ if (entries[j] != SYSMIS)
+ {
+ indexes[0] = j;
+ pivot_table_put (direct, indexes, direct->n_dimensions,
+ pivot_value_new_number (entries[j]));
+ }
+ }
+
+ free (indexes);
+}
+\f
+/* Statistical calculations. */
+
+/* Returns the value of the logarithm of gamma (factorial) function for an integer
+ argument XT. */
+static double
+log_gamma_int (double xt)
+{
+ double r = 0;
+ for (int i = 2; i < xt; i++)
+ r += log(i);
+ return r;
+}
+
+/* Calculate P_r as specified in _SPSS Statistical Algorithms_,
+ Appendix 5. */
+static inline double
+Pr (int a, int b, int c, int d)
+{
+ return exp (log_gamma_int (a + b + 1.) - log_gamma_int (a + 1.)
+ + log_gamma_int (c + d + 1.) - log_gamma_int (b + 1.)
+ + log_gamma_int (a + c + 1.) - log_gamma_int (c + 1.)
+ + log_gamma_int (b + d + 1.) - log_gamma_int (d + 1.)
+ - log_gamma_int (a + b + c + d + 1.));
+}
+
+/* Swap the contents of A and B. */
+static inline void
+swap (int *a, int *b)
+{
+ int t = *a;
+ *a = *b;
+ *b = t;
+}
+
+/* Calculate significance for Fisher's exact test as specified in
+ _SPSS Statistical Algorithms_, Appendix 5. */
+static void
+calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
+{
+ if (MIN (c, d) < MIN (a, b))
+ swap (&a, &c), swap (&b, &d);
+ if (MIN (b, d) < MIN (a, c))
+ swap (&a, &b), swap (&c, &d);
+ if (b * c < a * d)
+ {
+ if (b < c)
+ swap (&a, &b), swap (&c, &d);
+ else
+ swap (&a, &c), swap (&b, &d);
+ }
+
+ double pn1 = Pr (a, b, c, d);
+ *fisher1 = pn1;
+ for (int xt = 1; xt <= a; xt++)
+ *fisher1 += Pr (a - xt, b + xt, c + xt, d - xt);
+
+ *fisher2 = *fisher1;
+ for (int xt = 1; xt <= b; xt++)
+ {
+ double p = Pr (a + xt, b - xt, c - xt, d + xt);
+ if (p < pn1)
+ *fisher2 += p;
+ }
+}
+
+/* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
+ columns with values COLS and N_ROWS rows with values ROWS. Values
+ in the matrix sum to xt->total. */
+static void
+calc_chisq (struct crosstabulation *xt,
+ double chisq[N_CHISQ], int df[N_CHISQ],
+ double *fisher1, double *fisher2)
+{
+ chisq[0] = chisq[1] = 0.;
+ chisq[2] = chisq[3] = chisq[4] = SYSMIS;
+ *fisher1 = *fisher2 = SYSMIS;
+
+ df[0] = df[1] = (xt->ns_cols - 1) * (xt->ns_rows - 1);
+
+ if (xt->ns_rows <= 1 || xt->ns_cols <= 1)
+ {
+ chisq[0] = chisq[1] = SYSMIS;
+ return;
+ }
+
+ size_t n_cols = xt->vars[COL_VAR].n_values;
+ FOR_EACH_POPULATED_ROW (r, xt)
+ FOR_EACH_POPULATED_COLUMN (c, xt)
+ {
+ const double expected = xt->row_tot[r] * xt->col_tot[c] / xt->total;
+ const double freq = xt->mat[n_cols * r + c];
+ const double residual = freq - expected;
+
+ chisq[0] += residual * residual / expected;
+ if (freq)
+ chisq[1] += freq * log (expected / freq);
+ }
+
+ if (chisq[0] == 0.)
+ chisq[0] = SYSMIS;
+
+ if (chisq[1] != 0.)
+ chisq[1] *= -2.;
+ else
+ chisq[1] = SYSMIS;
+
+ /* Calculate Yates and Fisher exact test. */
+ if (xt->ns_cols == 2 && xt->ns_rows == 2)
+ {
+ int nz_cols[2];
+
+ size_t j = 0;
+ FOR_EACH_POPULATED_COLUMN (c, xt)
+ {
+ nz_cols[j++] = c;
+ if (j == 2)
+ break;
+ }
+ assert (j == 2);
+
+ double f11 = xt->mat[nz_cols[0]];
+ double f12 = xt->mat[nz_cols[1]];
+ double f21 = xt->mat[nz_cols[0] + n_cols];
+ double f22 = xt->mat[nz_cols[1] + n_cols];
+
+ /* Yates. */
+ const double xt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * xt->total;
+
+ if (xt_ > 0.)
+ chisq[3] = (xt->total * pow2 (xt_)
+ / (f11 + f12) / (f21 + f22)
+ / (f11 + f21) / (f12 + f22));
+ else
+ chisq[3] = 0.;
+
+ df[3] = 1.;
+
+ /* Fisher. */
+ calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
+ }
+
+ /* Calculate Mantel-Haenszel. */
+ if (var_is_numeric (xt->vars[ROW_VAR].var)
+ && var_is_numeric (xt->vars[COL_VAR].var))
+ {
+ double r, ase_0, ase_1;
+ calc_r (xt, (double *) xt->vars[ROW_VAR].values,
+ (double *) xt->vars[COL_VAR].values,
+ &r, &ase_0, &ase_1);
+
+ chisq[4] = (xt->total - 1.) * r * r;
+ df[4] = 1;
+ }
+}
+
+/* Calculate the value of Pearson's r. r is stored into R, its T value into
+ T, and standard error into ERROR. The row and column values must be
+ passed in XT and Y. */
+static void
+calc_r (struct crosstabulation *xt,
+ double *XT, double *Y, double *r, double *t, double *error)
+{
+ size_t n_rows = xt->vars[ROW_VAR].n_values;
+ size_t n_cols = xt->vars[COL_VAR].n_values;
+
+ double sum_XYf = 0;
+ for (size_t i = 0; i < n_rows; i++)
+ for (size_t j = 0; j < n_cols; j++)
+ {
+ double fij = xt->mat[j + i * n_cols];
+ double product = XT[i] * Y[j];
+ double temp = fij * product;
+ sum_XYf += temp;
+ }
+
+ double sum_Xr = 0;
+ double sum_X2r = 0;
+ for (size_t i = 0; i < n_rows; i++)
+ {
+ sum_Xr += XT[i] * xt->row_tot[i];
+ sum_X2r += pow2 (XT[i]) * xt->row_tot[i];
+ }
+ double Xbar = sum_Xr / xt->total;
+
+ double sum_Yc = 0;
+ double sum_Y2c = 0;
+ for (size_t i = 0; i < n_cols; i++)
+ {
+ sum_Yc += Y[i] * xt->col_tot[i];
+ sum_Y2c += Y[i] * Y[i] * xt->col_tot[i];
+ }
+ double Ybar = sum_Yc / xt->total;
+
+ double S = sum_XYf - sum_Xr * sum_Yc / xt->total;
+ double SX = sum_X2r - pow2 (sum_Xr) / xt->total;
+ double SY = sum_Y2c - pow2 (sum_Yc) / xt->total;
+ double T = sqrt (SX * SY);
+ *r = S / T;
+ *t = *r / sqrt (1 - pow2 (*r)) * sqrt (xt->total - 2);
+
+ double s = 0;
+ double c = 0;
+ for (size_t i = 0; i < n_rows; i++)
+ for (size_t j = 0; j < n_cols; j++)
+ {
+ double Xresid = XT[i] - Xbar;
+ double Yresid = Y[j] - Ybar;
+ double temp = (T * Xresid * Yresid
+ - ((S / (2. * T))
+ * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
+ double y = xt->mat[j + i * n_cols] * temp * temp - c;
+ double t = s + y;
+ c = (t - s) - y;
+ s = t;
+ }
+ *error = sqrt (s) / (T * T);
+}
+
+/* Calculate symmetric statistics and their asymptotic standard
+ errors. Returns false if none could be calculated. */
+static bool
+calc_symmetric (struct crosstabs_proc *proc, struct crosstabulation *xt,
+ double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
+ double t[N_SYMMETRIC],
+ double somers_d_v[3], double somers_d_ase[3],
+ double somers_d_t[3])
+{
+ size_t n_rows = xt->vars[ROW_VAR].n_values;
+ size_t n_cols = xt->vars[COL_VAR].n_values;
+
+ size_t q = MIN (xt->ns_rows, xt->ns_cols);
+ if (q <= 1)
+ return false;
+
+ for (size_t i = 0; i < N_SYMMETRIC; i++)
+ v[i] = ase[i] = t[i] = SYSMIS;
+
+ /* Phi, Cramer's V, contingency coefficient. */
+ if (proc->statistics & (CRS_ST_PHI | CRS_ST_CC))
+ {
+ double Xp = 0.; /* Pearson chi-square. */
+
+ FOR_EACH_POPULATED_ROW (r, xt)
+ FOR_EACH_POPULATED_COLUMN (c, xt)
+ {
+ double expected = xt->row_tot[r] * xt->col_tot[c] / xt->total;
+ double freq = xt->mat[n_cols * r + c];
+ double residual = freq - expected;
+
+ Xp += residual * residual / expected;
+ }
+
+ if (proc->statistics & CRS_ST_PHI)
+ {
+ v[0] = sqrt (Xp / xt->total);
+ v[1] = sqrt (Xp / (xt->total * (q - 1)));
+ }
+ if (proc->statistics & CRS_ST_CC)
+ v[2] = sqrt (Xp / (Xp + xt->total));
+ }
+
+ if (proc->statistics & (CRS_ST_BTAU | CRS_ST_CTAU
+ | CRS_ST_GAMMA | CRS_ST_D))
+ {
+ double Dr = pow2 (xt->total);
+ for (size_t r = 0; r < n_rows; r++)
+ Dr -= pow2 (xt->row_tot[r]);
+
+ double Dc = pow2 (xt->total);
+ for (size_t c = 0; c < n_cols; c++)
+ Dc -= pow2 (xt->col_tot[c]);
+
+ double *cum = xnmalloc (n_cols * n_rows, sizeof *cum);
+ for (size_t c = 0; c < n_cols; c++)
+ {
+ double ct = 0.;
+
+ for (size_t r = 0; r < n_rows; r++)
+ cum[c + r * n_cols] = ct += xt->mat[c + r * n_cols];
+ }
+
+ /* P and Q. */
+ double P = 0;
+ double Q = 0;
+ for (size_t i = 0; i < n_rows; i++)
+ {
+ double Cij = 0;
+ for (size_t j = 1; j < n_cols; j++)
+ Cij += xt->col_tot[j] - cum[j + i * n_cols];
+
+ double Dij = 0;
+ if (i > 0)
+ for (size_t j = 1; j < n_cols; j++)
+ Dij += cum[j + (i - 1) * n_cols];
+
+ for (size_t j = 0;;)
+ {
+ double fij = xt->mat[j + i * n_cols];
+ P += fij * Cij;
+ Q += fij * Dij;
+
+ if (++j >= n_cols)
+ break;
+
+ Cij -= xt->col_tot[j] - cum[j + i * n_cols];
+ Dij += xt->col_tot[j - 1] - cum[j - 1 + i * n_cols];
+
+ if (i > 0)
+ {
+ Cij += cum[j - 1 + (i - 1) * n_cols];
+ Dij -= cum[j + (i - 1) * n_cols];
+ }
+ }
+ }
+
+ if (proc->statistics & CRS_ST_BTAU)
+ v[3] = (P - Q) / sqrt (Dr * Dc);
+ if (proc->statistics & CRS_ST_CTAU)
+ v[4] = (q * (P - Q)) / (pow2 (xt->total) * (q - 1));
+ if (proc->statistics & CRS_ST_GAMMA)
+ v[5] = (P - Q) / (P + Q);
+
+ /* ASE for tau-b, tau-c, gamma. Calculations could be
+ eliminated here, at expense of memory. */
+ double btau_cum = 0;
+ double ctau_cum = 0;
+ double gamma_cum = 0;
+ double d_yx_cum = 0;
+ double d_xy_cum = 0;
+ for (size_t i = 0; i < n_rows; i++)
+ {
+ double Cij = 0;
+ for (size_t j = 1; j < n_cols; j++)
+ Cij += xt->col_tot[j] - cum[j + i * n_cols];
+
+ double Dij = 0;
+ if (i > 0)
+ for (size_t j = 1; j < n_cols; j++)
+ Dij += cum[j + (i - 1) * n_cols];
+
+ for (size_t j = 0;;)
+ {
+ double fij = xt->mat[j + i * n_cols];
+
+ if (proc->statistics & CRS_ST_BTAU)
+ btau_cum += fij * pow2 (2. * sqrt (Dr * Dc) * (Cij - Dij)
+ + v[3] * (xt->row_tot[i] * Dc
+ + xt->col_tot[j] * Dr));
+ ctau_cum += fij * pow2 (Cij - Dij);
+
+ if (proc->statistics & CRS_ST_GAMMA)
+ gamma_cum += fij * pow2 (Q * Cij - P * Dij);
+
+ if (proc->statistics & CRS_ST_D)
+ {
+ d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
+ - (P - Q) * (xt->total - xt->row_tot[i]));
+ d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
+ - (Q - P) * (xt->total - xt->col_tot[j]));
+ }
+
+ if (++j >= n_cols)
+ break;
+
+ Cij -= xt->col_tot[j] - cum[j + i * n_cols];
+ Dij += xt->col_tot[j - 1] - cum[j - 1 + i * n_cols];
+
+ if (i > 0)
+ {
+ Cij += cum[j - 1 + (i - 1) * n_cols];
+ Dij -= cum[j + (i - 1) * n_cols];
+ }
+ }
+ }
+
+ if (proc->statistics & CRS_ST_BTAU)
+ {
+ double btau_var = ((btau_cum
+ - (xt->total * pow2 (xt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
+ / pow2 (Dr * Dc));
+ ase[3] = sqrt (btau_var);
+ t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / xt->total)
+ / (Dr * Dc)));
+ }
+ if (proc->statistics & CRS_ST_CTAU)
+ {
+ ase[4] = ((2 * q / ((q - 1) * pow2 (xt->total)))
+ * sqrt (ctau_cum - (P - Q) * (P - Q) / xt->total));
+ t[4] = v[4] / ase[4];
+ }
+ if (proc->statistics & CRS_ST_GAMMA)
+ {
+ ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
+ t[5] = v[5] / (2. / (P + Q)
+ * sqrt (ctau_cum - (P - Q) * (P - Q) / xt->total));
+ }
+ if (proc->statistics & CRS_ST_D)
+ {
+ somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
+ somers_d_ase[0] = SYSMIS;
+ somers_d_t[0] = (somers_d_v[0]
+ / (4 / (Dc + Dr)
+ * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
+ somers_d_v[1] = (P - Q) / Dc;
+ somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
+ somers_d_t[1] = (somers_d_v[1]
+ / (2. / Dc
+ * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
+ somers_d_v[2] = (P - Q) / Dr;
+ somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
+ somers_d_t[2] = (somers_d_v[2]
+ / (2. / Dr
+ * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
+ }
+
+ free (cum);
+ }
+
+ /* Spearman correlation, Pearson's r. */
+ if (proc->statistics & CRS_ST_CORR)
+ {
+ double *R = xmalloc (sizeof *R * n_rows);
+ double c = 0;
+ double s = 0;
+ for (size_t i = 0; i < n_rows; i++)
+ {
+ R[i] = s + (xt->row_tot[i] + 1.) / 2.;
+ double y = xt->row_tot[i] - c;
+ double t = s + y;
+ c = (t - s) - y;
+ s = t;
+ }
+
+ double *C = xmalloc (sizeof *C * n_cols);
+ c = s = 0;
+ for (size_t j = 0; j < n_cols; j++)
+ {
+ C[j] = s + (xt->col_tot[j] + 1.) / 2;
+ double y = xt->col_tot[j] - c;
+ double t = s + y;
+ c = (t - s) - y;
+ s = t;
+ }
+
+ calc_r (xt, R, C, &v[6], &t[6], &ase[6]);
+
+ free (R);
+ free (C);
+
+ calc_r (xt, (double *) xt->vars[ROW_VAR].values,
+ (double *) xt->vars[COL_VAR].values,
+ &v[7], &t[7], &ase[7]);
+ }
+
+ /* Cohen's kappa. */
+ if (proc->statistics & CRS_ST_KAPPA && xt->ns_rows == xt->ns_cols)
+ {
+ double sum_fii = 0;
+ double sum_rici = 0;
+ double sum_fiiri_ci = 0;
+ double sum_riciri_ci = 0;
+ for (size_t i = 0, j = 0; i < xt->ns_rows; i++, j++)
+ {
+ while (xt->col_tot[j] == 0.)
+ j++;
+
+ double prod = xt->row_tot[i] * xt->col_tot[j];
+ double sum = xt->row_tot[i] + xt->col_tot[j];
+
+ sum_fii += xt->mat[j + i * n_cols];
+ sum_rici += prod;
+ sum_fiiri_ci += xt->mat[j + i * n_cols] * sum;
+ sum_riciri_ci += prod * sum;
+ }
+
+ double sum_fijri_ci2 = 0;
+ for (size_t i = 0; i < xt->ns_rows; i++)
+ for (size_t j = 0; j < xt->ns_cols; j++)
+ {
+ double sum = xt->row_tot[i] + xt->col_tot[j];
+ sum_fijri_ci2 += xt->mat[j + i * n_cols] * sum * sum;
+ }
+
+ v[8] = (xt->total * sum_fii - sum_rici) / (pow2 (xt->total) - sum_rici);
+
+ double ase_under_h0 = sqrt ((pow2 (xt->total) * sum_rici
+ + sum_rici * sum_rici
+ - xt->total * sum_riciri_ci)
+ / (xt->total * (pow2 (xt->total) - sum_rici) * (pow2 (xt->total) - sum_rici)));
+
+ ase[8] = sqrt (xt->total * (((sum_fii * (xt->total - sum_fii))
+ / pow2 (pow2 (xt->total) - sum_rici))
+ + ((2. * (xt->total - sum_fii)
+ * (2. * sum_fii * sum_rici
+ - xt->total * sum_fiiri_ci))
+ / pow3 (pow2 (xt->total) - sum_rici))
+ + (pow2 (xt->total - sum_fii)
+ * (xt->total * sum_fijri_ci2 - 4.
+ * sum_rici * sum_rici)
+ / pow4 (pow2 (xt->total) - sum_rici))));
+
+ t[8] = v[8] / ase_under_h0;
+ }
+
+ return true;
+}
+
+/* Calculate risk estimate. */
+static bool
+calc_risk (struct crosstabulation *xt,
+ double *value, double *upper, double *lower, union value *c,
+ double *n_valid)
+{
+ size_t n_cols = xt->vars[COL_VAR].n_values;
+
+ for (size_t i = 0; i < 3; i++)
+ value[i] = upper[i] = lower[i] = SYSMIS;
+
+ if (xt->ns_rows != 2 || xt->ns_cols != 2)
+ return false;
+
+ /* Find populated columns. */
+ size_t nz_cols[2];
+ size_t n = 0;
+ FOR_EACH_POPULATED_COLUMN (c, xt)
+ nz_cols[n++] = c;
+ assert (n == 2);
+
+ /* Find populated rows. */
+ size_t nz_rows[2];
+ n = 0;
+ FOR_EACH_POPULATED_ROW (r, xt)
+ nz_rows[n++] = r;
+ assert (n == 2);
+
+ double f11 = xt->mat[nz_cols[0] + n_cols * nz_rows[0]];
+ double f12 = xt->mat[nz_cols[1] + n_cols * nz_rows[0]];
+ double f21 = xt->mat[nz_cols[0] + n_cols * nz_rows[1]];
+ double f22 = xt->mat[nz_cols[1] + n_cols * nz_rows[1]];
+ *n_valid = f11 + f12 + f21 + f22;
+
+ c[0] = xt->vars[COL_VAR].values[nz_cols[0]];
+ c[1] = xt->vars[COL_VAR].values[nz_cols[1]];
+
+ value[0] = (f11 * f22) / (f12 * f21);
+ double v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
+ lower[0] = value[0] * exp (-1.960 * v);
+ upper[0] = value[0] * exp (1.960 * v);
+
+ value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
+ v = sqrt ((f12 / (f11 * (f11 + f12)))
+ + (f22 / (f21 * (f21 + f22))));
+ lower[1] = value[1] * exp (-1.960 * v);
+ upper[1] = value[1] * exp (1.960 * v);
+
+ value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
+ v = sqrt ((f11 / (f12 * (f11 + f12)))
+ + (f21 / (f22 * (f21 + f22))));
+ lower[2] = value[2] * exp (-1.960 * v);
+ upper[2] = value[2] * exp (1.960 * v);
+
+ return true;
+}
+
+/* Calculate directional measures. */
+static void
+calc_directional (struct crosstabs_proc *proc, struct crosstabulation *xt,
+ double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
+ double t[N_DIRECTIONAL], double sig[N_DIRECTIONAL])
+{
+ size_t n_rows = xt->vars[ROW_VAR].n_values;
+ size_t n_cols = xt->vars[COL_VAR].n_values;
+ for (size_t i = 0; i < N_DIRECTIONAL; i++)
+ v[i] = ase[i] = t[i] = sig[i] = SYSMIS;
+
+ /* Lambda. */
+ if (proc->statistics & CRS_ST_LAMBDA)
+ {
+ /* Find maximum for each row and their sum. */
+ double *fim = xnmalloc (n_rows, sizeof *fim);
+ size_t *fim_index = xnmalloc (n_rows, sizeof *fim_index);
+ double sum_fim = 0.0;
+ for (size_t i = 0; i < n_rows; i++)
+ {
+ double max = xt->mat[i * n_cols];
+ size_t index = 0;
+
+ for (size_t j = 1; j < n_cols; j++)
+ if (xt->mat[j + i * n_cols] > max)
+ {
+ max = xt->mat[j + i * n_cols];
+ index = j;
+ }
+
+ fim[i] = max;
+ sum_fim += max;
+ fim_index[i] = index;
+ }
+
+ /* Find maximum for each column. */
+ double *fmj = xnmalloc (n_cols, sizeof *fmj);
+ size_t *fmj_index = xnmalloc (n_cols, sizeof *fmj_index);
+ double sum_fmj = 0.0;
+ for (size_t j = 0; j < n_cols; j++)
+ {
+ double max = xt->mat[j];
+ size_t index = 0;
+
+ for (size_t i = 1; i < n_rows; i++)
+ if (xt->mat[j + i * n_cols] > max)
+ {
+ max = xt->mat[j + i * n_cols];
+ index = i;
+ }
+
+ fmj[j] = max;
+ sum_fmj += max;
+ fmj_index[j] = index;
+ }
+
+ /* Find maximum row total. */
+ double rm = xt->row_tot[0];
+ size_t rm_index = 0;
+ for (size_t i = 1; i < n_rows; i++)
+ if (xt->row_tot[i] > rm)
+ {
+ rm = xt->row_tot[i];
+ rm_index = i;
+ }
+
+ /* Find maximum column total. */
+ double cm = xt->col_tot[0];
+ size_t cm_index = 0;
+ for (size_t j = 1; j < n_cols; j++)
+ if (xt->col_tot[j] > cm)
+ {
+ cm = xt->col_tot[j];
+ cm_index = j;
+ }
+
+ v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * xt->total - rm - cm);
+ v[1] = (sum_fmj - rm) / (xt->total - rm);
+ v[2] = (sum_fim - cm) / (xt->total - cm);
+
+ /* ASE1 for Y given XT. */
+ {
+ double accum = 0.0;
+ for (size_t i = 0; i < n_rows; i++)
+ if (cm_index == fim_index[i])
+ accum += fim[i];
+ ase[2] = sqrt ((xt->total - sum_fim) * (sum_fim + cm - 2. * accum)
+ / pow3 (xt->total - cm));
+ }
+
+ /* ASE0 for Y given XT. */
+ {
+ double accum = 0.0;
+ for (size_t i = 0; i < n_rows; i++)
+ if (cm_index != fim_index[i])
+ accum += (xt->mat[i * n_cols + fim_index[i]]
+ + xt->mat[i * n_cols + cm_index]);
+ t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / xt->total) / (xt->total - cm));
+ }
+
+ /* ASE1 for XT given Y. */
+ {
+ double accum = 0.0;
+ for (size_t j = 0; j < n_cols; j++)
+ if (rm_index == fmj_index[j])
+ accum += fmj[j];
+ ase[1] = sqrt ((xt->total - sum_fmj) * (sum_fmj + rm - 2. * accum)
+ / pow3 (xt->total - rm));
+ }
+
+ /* ASE0 for XT given Y. */
+ {
+ double accum = 0.0;
+ for (size_t j = 0; j < n_cols; j++)
+ if (rm_index != fmj_index[j])
+ accum += (xt->mat[j + n_cols * fmj_index[j]]
+ + xt->mat[j + n_cols * rm_index]);
+ t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / xt->total) / (xt->total - rm));
+ }
+
+ /* Symmetric ASE0 and ASE1. */
+ {
+ double accum0 = 0.0;
+ double accum1 = 0.0;
+ for (size_t i = 0; i < n_rows; i++)
+ for (size_t j = 0; j < n_cols; j++)
+ {
+ int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
+ int temp1 = (i == rm_index) + (j == cm_index);
+ accum0 += xt->mat[j + i * n_cols] * pow2 (temp0 - temp1);
+ accum1 += (xt->mat[j + i * n_cols]
+ * pow2 (temp0 + (v[0] - 1.) * temp1));
+ }
+ ase[0] = sqrt (accum1 - 4. * xt->total * v[0] * v[0]) / (2. * xt->total - rm - cm);
+ t[0] = v[0] / (sqrt (accum0 - pow2 (sum_fim + sum_fmj - cm - rm) / xt->total)
+ / (2. * xt->total - rm - cm));
+ }
+
+ for (size_t i = 0; i < 3; i++)
+ sig[i] = 2 * gsl_cdf_ugaussian_Q (t[i]);
+
+ free (fim);
+ free (fim_index);
+ free (fmj);
+ free (fmj_index);
+
+ /* Tau. */
+ double sum_fij2_ri = 0.0;
+ double sum_fij2_ci = 0.0;
+ FOR_EACH_POPULATED_ROW (i, xt)
+ FOR_EACH_POPULATED_COLUMN (j, xt)
+ {
+ double temp = pow2 (xt->mat[j + i * n_cols]);
+ sum_fij2_ri += temp / xt->row_tot[i];
+ sum_fij2_ci += temp / xt->col_tot[j];
+ }
+
+ double sum_ri2 = 0.0;
+ for (size_t i = 0; i < n_rows; i++)
+ sum_ri2 += pow2 (xt->row_tot[i]);
+
+ double sum_cj2 = 0.0;
+ for (size_t j = 0; j < n_cols; j++)
+ sum_cj2 += pow2 (xt->col_tot[j]);
+
+ v[3] = (xt->total * sum_fij2_ci - sum_ri2) / (pow2 (xt->total) - sum_ri2);
+ v[4] = (xt->total * sum_fij2_ri - sum_cj2) / (pow2 (xt->total) - sum_cj2);
+ }
+
+ if (proc->statistics & CRS_ST_UC)
+ {
+ double UX = 0.0;
+ FOR_EACH_POPULATED_ROW (i, xt)
+ UX -= xt->row_tot[i] / xt->total * log (xt->row_tot[i] / xt->total);
+
+ double UY = 0.0;
+ FOR_EACH_POPULATED_COLUMN (j, xt)
+ UY -= xt->col_tot[j] / xt->total * log (xt->col_tot[j] / xt->total);
+
+ double UXY = 0.0;
+ double P = 0.0;
+ for (size_t i = 0; i < n_rows; i++)
+ for (size_t j = 0; j < n_cols; j++)
+ {
+ double entry = xt->mat[j + i * n_cols];
+
+ if (entry <= 0.)
+ continue;
+
+ P += entry * pow2 (log (xt->col_tot[j] * xt->row_tot[i] / (xt->total * entry)));
+ UXY -= entry / xt->total * log (entry / xt->total);
+ }
+
+ double ase1_yx = 0.0;
+ double ase1_xy = 0.0;
+ double ase1_sym = 0.0;
+ for (size_t i = 0; i < n_rows; i++)
+ for (size_t j = 0; j < n_cols; j++)
+ {
+ double entry = xt->mat[j + i * n_cols];
+
+ if (entry <= 0.)
+ continue;
+
+ ase1_yx += entry * pow2 (UY * log (entry / xt->row_tot[i])
+ + (UX - UXY) * log (xt->col_tot[j] / xt->total));
+ ase1_xy += entry * pow2 (UX * log (entry / xt->col_tot[j])
+ + (UY - UXY) * log (xt->row_tot[i] / xt->total));
+ ase1_sym += entry * pow2 ((UXY
+ * log (xt->row_tot[i] * xt->col_tot[j] / pow2 (xt->total)))
+ - (UX + UY) * log (entry / xt->total));
+ }
+
+ v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
+ ase[5] = (2. / (xt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
+ t[5] = SYSMIS;
+
+ v[6] = (UX + UY - UXY) / UX;
+ ase[6] = sqrt (ase1_xy) / (xt->total * UX * UX);
+ t[6] = v[6] / (sqrt (P - xt->total * pow2 (UX + UY - UXY)) / (xt->total * UX));
+
+ v[7] = (UX + UY - UXY) / UY;
+ ase[7] = sqrt (ase1_yx) / (xt->total * UY * UY);
+ t[7] = v[7] / (sqrt (P - xt->total * pow2 (UX + UY - UXY)) / (xt->total * UY));
+ }
+
+ /* Somers' D. */
+ if (proc->statistics & CRS_ST_D)
+ {
+ double v_dummy[N_SYMMETRIC];
+ double ase_dummy[N_SYMMETRIC];
+ double t_dummy[N_SYMMETRIC];
+ double somers_d_v[3];
+ double somers_d_ase[3];
+ double somers_d_t[3];
+
+ if (calc_symmetric (proc, xt, v_dummy, ase_dummy, t_dummy,
+ somers_d_v, somers_d_ase, somers_d_t))
+ {
+ for (size_t i = 0; i < 3; i++)
+ {
+ v[8 + i] = somers_d_v[i];
+ ase[8 + i] = somers_d_ase[i];
+ t[8 + i] = somers_d_t[i];
+ sig[8 + i] = 2 * gsl_cdf_ugaussian_Q (fabs (somers_d_t[i]));
+ }
+ }
+ }
+
+ /* Eta. */
+ if (proc->statistics & CRS_ST_ETA)
+ {
+ /* X dependent. */
+ double sum_Xr = 0.0;
+ double sum_X2r = 0.0;
+ for (size_t i = 0; i < n_rows; i++)
+ {
+ sum_Xr += xt->vars[ROW_VAR].values[i].f * xt->row_tot[i];
+ sum_X2r += pow2 (xt->vars[ROW_VAR].values[i].f) * xt->row_tot[i];
+ }
+ double SX = sum_X2r - pow2 (sum_Xr) / xt->total;
+
+ double SXW = 0.0;
+ FOR_EACH_POPULATED_COLUMN (j, xt)
+ {
+ double cum = 0.0;
+
+ for (size_t i = 0; i < n_rows; i++)
+ {
+ SXW += (pow2 (xt->vars[ROW_VAR].values[i].f)
+ * xt->mat[j + i * n_cols]);
+ cum += (xt->vars[ROW_VAR].values[i].f
+ * xt->mat[j + i * n_cols]);
+ }
+
+ SXW -= cum * cum / xt->col_tot[j];
+ }
+ v[11] = sqrt (1. - SXW / SX);
+
+ /* Y dependent. */
+ double sum_Yc = 0.0;
+ double sum_Y2c = 0.0;
+ for (size_t i = 0; i < n_cols; i++)
+ {
+ sum_Yc += xt->vars[COL_VAR].values[i].f * xt->col_tot[i];
+ sum_Y2c += pow2 (xt->vars[COL_VAR].values[i].f) * xt->col_tot[i];
+ }
+ double SY = sum_Y2c - pow2 (sum_Yc) / xt->total;
+
+ double SYW = 0.0;
+ FOR_EACH_POPULATED_ROW (i, xt)
+ {
+ double cum = 0.0;
+ for (size_t j = 0; j < n_cols; j++)
+ {
+ SYW += (pow2 (xt->vars[COL_VAR].values[j].f)
+ * xt->mat[j + i * n_cols]);
+ cum += (xt->vars[COL_VAR].values[j].f
+ * xt->mat[j + i * n_cols]);
+ }
+
+ SYW -= cum * cum / xt->row_tot[i];
+ }
+ v[12] = sqrt (1. - SYW / SY);
+ }
+}
projects / pspp / blobdiff