/* 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 . */
/* 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
#include
#include
#include
#include
#include
#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/stats/freq.h"
#include "language/dictionary/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/tab.h"
#include "output/chart-item.h"
#include "output/charts/barchart.h"
#include "gl/minmax.h"
#include "gl/xalloc.h"
#include "gl/xsize.h"
#include "gettext.h"
#define _(msgid) gettext (msgid)
#define N_(msgid) msgid
/* (headers) */
/* (specification)
crosstabs (crs_):
*^tables=custom;
+variables=custom;
missing=miss:!table/include/report;
count=roundwhat:asis/case/!cell,
roundhow:!round/truncate;
+write[wr_]=none,cells,all;
+format=val:!avalue/dvalue,
indx:!noindex/index,
tabl:!tables/notables,
box:!box/nobox,
pivot:!pivot/nopivot;
+barchart=;
+cells[cl_]=count,expected,row,column,total,residual,sresidual,
asresidual,all,none;
+statistics[st_]=chisq,phi,cc,lambda,uc,none,btau,ctau,risk,gamma,d,
kappa,eta,corr,all.
*/
/* (declarations) */
/* (functions) */
/* 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 pivot_table and
struct crosstab member. */
enum
{
ROW_VAR = 0, /* Row variable. */
COL_VAR = 1 /* Column variable. */
/* Higher indexes cause multiple tables to be output. */
};
/* A crosstabulation of 2 or more variables. */
struct pivot_table
{
struct crosstabs_proc *proc;
struct fmt_spec weight_format; /* Format for weight variable. */
double missing; /* Weight of missing cases. */
/* Variables (2 or more). */
int n_vars;
const struct variable **vars;
/* Constants (0 or more). */
int n_consts;
const struct variable **const_vars;
union value *const_values;
/* Data. */
struct hmap data;
struct freq **entries;
size_t n_entries;
/* Column values, number of columns. */
union value *cols;
int n_cols;
/* Row values, number of rows. */
union value *rows;
int n_rows;
/* Number of statistically interesting columns/rows
(columns/rows with data in them). */
int ns_cols, ns_rows;
/* Matrix contents. */
double *mat; /* Matrix proper. */
double *row_tot; /* Row totals. */
double *col_tot; /* Column totals. */
double total; /* Grand total. */
};
/* 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 pivot;
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 pivot_table *pivots;
int n_pivots;
/* CELLS. */
int n_cells; /* Number of cells requested. */
unsigned int cells; /* Bit k is 1 if cell k is requested. */
int a_cells[CRS_CL_count]; /* 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. */
};
const struct var_range *get_var_range (const struct crosstabs_proc *,
const struct variable *);
static bool should_tabulate_case (const struct pivot_table *,
const struct ccase *, enum mv_class exclude);
static void tabulate_general_case (struct pivot_table *, const struct ccase *,
double weight);
static void tabulate_integer_case (struct pivot_table *, const struct ccase *,
double weight);
static void postcalc (struct crosstabs_proc *);
static void submit (struct pivot_table *, struct tab_table *);
static double
round_weight (const struct crosstabs_proc *proc, double weight)
{
return proc->round_down ? floor (weight) : floor (weight + 0.5);
}
/* Parses and executes the CROSSTABS procedure. */
int
cmd_crosstabs (struct lexer *lexer, struct dataset *ds)
{
const struct variable *wv = dict_get_weight (dataset_dict (ds));
struct var_range *range, *next_range;
struct crosstabs_proc proc;
struct casegrouper *grouper;
struct casereader *input, *group;
struct cmd_crosstabs cmd;
struct pivot_table *pt;
int result;
bool ok;
int i;
proc.dict = dataset_dict (ds);
proc.bad_warn = true;
proc.variables = NULL;
proc.n_variables = 0;
hmap_init (&proc.var_ranges);
proc.pivots = NULL;
proc.n_pivots = 0;
proc.descending = false;
proc.weight_format = wv ? *var_get_print_format (wv) : F_8_0;
if (!parse_crosstabs (lexer, ds, &cmd, &proc))
{
result = CMD_FAILURE;
goto exit;
}
proc.mode = proc.n_variables ? INTEGER : GENERAL;
proc.barchart = cmd.sbc_barchart > 0;
proc.descending = cmd.val == CRS_DVALUE;
proc.round_case_weights = cmd.sbc_count && cmd.roundwhat == CRS_CASE;
proc.round_cells = cmd.sbc_count && cmd.roundwhat == CRS_CELL;
proc.round_down = cmd.roundhow == CRS_TRUNCATE;
/* CELLS. */
if (!cmd.sbc_cells)
proc.cells = 1u << CRS_CL_COUNT;
else if (cmd.a_cells[CRS_CL_ALL])
proc.cells = UINT_MAX;
else
{
proc.cells = 0;
for (i = 0; i < CRS_CL_count; i++)
if (cmd.a_cells[i])
proc.cells |= 1u << i;
if (proc.cells == 0)
proc.cells = ((1u << CRS_CL_COUNT)
| (1u << CRS_CL_ROW)
| (1u << CRS_CL_COLUMN)
| (1u << CRS_CL_TOTAL));
}
proc.cells &= ((1u << CRS_CL_count) - 1);
proc.cells &= ~((1u << CRS_CL_NONE) | (1u << CRS_CL_ALL));
proc.n_cells = 0;
for (i = 0; i < CRS_CL_count; i++)
if (proc.cells & (1u << i))
proc.a_cells[proc.n_cells++] = i;
/* STATISTICS. */
if (cmd.a_statistics[CRS_ST_ALL])
proc.statistics = UINT_MAX;
else if (cmd.sbc_statistics)
{
int i;
proc.statistics = 0;
for (i = 0; i < CRS_ST_count; i++)
if (cmd.a_statistics[i])
proc.statistics |= 1u << i;
if (proc.statistics == 0)
proc.statistics |= 1u << CRS_ST_CHISQ;
}
else
proc.statistics = 0;
/* MISSING. */
proc.exclude = (cmd.miss == CRS_TABLE ? MV_ANY
: cmd.miss == CRS_INCLUDE ? MV_SYSTEM
: MV_NEVER);
if (proc.mode == GENERAL && proc.exclude == MV_NEVER)
{
msg (SE, _("Missing mode %s not allowed in general mode. "
"Assuming %s."), "REPORT", "MISSING=TABLE");
proc.exclude = MV_ANY;
}
/* PIVOT. */
proc.pivot = cmd.pivot == CRS_PIVOT;
input = casereader_create_filter_weight (proc_open (ds), dataset_dict (ds),
NULL, NULL);
grouper = casegrouper_create_splits (input, dataset_dict (ds));
while (casegrouper_get_next_group (grouper, &group))
{
struct ccase *c;
/* Output SPLIT FILE variables. */
c = casereader_peek (group, 0);
if (c != NULL)
{
output_split_file_values (ds, c);
case_unref (c);
}
/* Initialize hash tables. */
for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
hmap_init (&pt->data);
/* Tabulate. */
for (; (c = casereader_read (group)) != NULL; case_unref (c))
for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
{
double weight = dict_get_case_weight (dataset_dict (ds), c,
&proc.bad_warn);
if (cmd.roundwhat == CRS_CASE)
{
weight = round_weight (&proc, weight);
if (weight == 0.)
continue;
}
if (should_tabulate_case (pt, c, proc.exclude))
{
if (proc.mode == GENERAL)
tabulate_general_case (pt, c, weight);
else
tabulate_integer_case (pt, c, weight);
}
else
pt->missing += weight;
}
casereader_destroy (group);
/* Output. */
postcalc (&proc);
}
ok = casegrouper_destroy (grouper);
ok = proc_commit (ds) && ok;
result = ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
exit:
free (proc.variables);
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 (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
{
free (pt->vars);
free (pt->const_vars);
/* We must not call value_destroy on const_values because
it is a wild pointer; it never pointed to anything owned
by the pivot_table.
The rest of the data was allocated and destroyed at a
lower level already. */
}
free (proc.pivots);
return result;
}
/* Parses the TABLES subcommand. */
static int
crs_custom_tables (struct lexer *lexer, struct dataset *ds,
struct cmd_crosstabs *cmd UNUSED, void *proc_)
{
struct crosstabs_proc *proc = proc_;
struct const_var_set *var_set;
int n_by;
const struct variable ***by = NULL;
int *by_iter;
size_t *by_nvar = NULL;
size_t nx = 1;
bool ok = false;
int i;
/* 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)
return 2;
lex_match (lexer, T_EQUALS);
if (proc->variables != NULL)
var_set = const_var_set_create_from_array (proc->variables,
proc->n_variables);
else
var_set = const_var_set_create_from_dict (dataset_dict (ds));
assert (var_set != NULL);
for (n_by = 0; ;)
{
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;
if (xalloc_oversized (nx, by_nvar[n_by]))
{
msg (SE, _("Too many cross-tabulation variables or dimensions."));
goto done;
}
nx *= by_nvar[n_by];
n_by++;
if (!lex_match (lexer, T_BY))
{
if (n_by < 2)
goto done;
else
break;
}
}
by_iter = xcalloc (n_by, sizeof *by_iter);
proc->pivots = xnrealloc (proc->pivots,
proc->n_pivots + nx, sizeof *proc->pivots);
for (i = 0; i < nx; i++)
{
struct pivot_table *pt = &proc->pivots[proc->n_pivots++];
int j;
pt->proc = proc;
pt->weight_format = proc->weight_format;
pt->missing = 0.;
pt->n_vars = n_by;
pt->vars = xmalloc (n_by * sizeof *pt->vars);
pt->n_consts = 0;
pt->const_vars = NULL;
pt->const_values = NULL;
for (j = 0; j < n_by; j++)
pt->vars[j] = by[j][by_iter[j]];
for (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 (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 int
crs_custom_variables (struct lexer *lexer, struct dataset *ds,
struct cmd_crosstabs *cmd UNUSED, void *proc_)
{
struct crosstabs_proc *proc = proc_;
if (proc->n_pivots)
{
msg (SE, _("%s must be specified before %s."), "VARIABLES", "TABLES");
return 0;
}
lex_match (lexer, T_EQUALS);
for (;;)
{
size_t orig_nv = proc->n_variables;
size_t i;
long min, max;
if (!parse_variables_const (lexer, dataset_dict (ds),
&proc->variables, &proc->n_variables,
(PV_APPEND | PV_NUMERIC
| PV_NO_DUPLICATE | PV_NO_SCRATCH)))
return 0;
if (!lex_force_match (lexer, T_LPAREN))
goto lossage;
if (!lex_force_int (lexer))
goto lossage;
min = lex_integer (lexer);
lex_get (lexer);
lex_match (lexer, T_COMMA);
if (!lex_force_int (lexer))
goto lossage;
max = lex_integer (lexer);
if (max < min)
{
msg (SE, _("Maximum value (%ld) less than minimum value (%ld)."),
max, min);
goto lossage;
}
lex_get (lexer);
if (!lex_force_match (lexer, T_RPAREN))
goto lossage;
for (i = orig_nv; i < proc->n_variables; i++)
{
const struct variable *var = proc->variables[i];
struct var_range *vr = xmalloc (sizeof *vr);
vr->var = var;
vr->min = min;
vr->max = max;
vr->count = max - min + 1;
hmap_insert (&proc->var_ranges, &vr->hmap_node,
hash_pointer (var, 0));
}
if (lex_token (lexer) == T_SLASH)
break;
}
return 1;
lossage:
free (proc->variables);
proc->variables = NULL;
proc->n_variables = 0;
return 0;
}
/* Data file processing. */
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 pivot_table *pt, const struct ccase *c,
enum mv_class exclude)
{
int j;
for (j = 0; j < pt->n_vars; j++)
{
const struct variable *var = pt->vars[j];
const struct var_range *range = get_var_range (pt->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 pivot_table *pt, const struct ccase *c,
double weight)
{
struct freq *te;
size_t hash;
int j;
hash = 0;
for (j = 0; j < pt->n_vars; j++)
{
/* Throw away fractional parts of values. */
hash = hash_int (case_num (c, pt->vars[j]), hash);
}
HMAP_FOR_EACH_WITH_HASH (te, struct freq, node, hash, &pt->data)
{
for (j = 0; j < pt->n_vars; j++)
if ((int) case_num (c, pt->vars[j]) != (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 (pt->n_vars));
te->count = weight;
for (j = 0; j < pt->n_vars; j++)
te->values[j].f = (int) case_num (c, pt->vars[j]);
hmap_insert (&pt->data, &te->node, hash);
}
static void
tabulate_general_case (struct pivot_table *pt, const struct ccase *c,
double weight)
{
struct freq *te;
size_t hash;
int j;
hash = 0;
for (j = 0; j < pt->n_vars; j++)
{
const struct variable *var = pt->vars[j];
hash = value_hash (case_data (c, var), var_get_width (var), hash);
}
HMAP_FOR_EACH_WITH_HASH (te, struct freq, node, hash, &pt->data)
{
for (j = 0; j < pt->n_vars; j++)
{
const struct variable *var = pt->vars[j];
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 (pt->n_vars));
te->count = weight;
for (j = 0; j < pt->n_vars; j++)
{
const struct variable *var = pt->vars[j];
value_clone (&te->values[j], case_data (c, var), var_get_width (var));
}
hmap_insert (&pt->data, &te->node, hash);
}
/* Post-data reading calculations. */
static int compare_table_entry_vars_3way (const struct freq *a,
const struct freq *b,
const struct pivot_table *pt,
int idx0, int idx1);
static int compare_table_entry_3way (const void *ap_, const void *bp_,
const void *pt_);
static int compare_table_entry_3way_inv (const void *ap_, const void *bp_,
const void *pt_);
static void enum_var_values (const struct pivot_table *, int var_idx,
union value **valuesp, int *n_values, bool descending);
static void output_pivot_table (struct crosstabs_proc *,
struct pivot_table *);
static void make_pivot_table_subset (struct pivot_table *pt,
size_t row0, size_t row1,
struct pivot_table *subset);
static void make_summary_table (struct crosstabs_proc *);
static bool find_crosstab (struct pivot_table *, size_t *row0p, size_t *row1p);
static void
postcalc (struct crosstabs_proc *proc)
{
/* 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 pivot_table *pt = proc->pivots;
pt < &proc->pivots[proc->n_pivots]; pt++)
{
struct freq *e, *next;
HMAP_FOR_EACH_SAFE (e, next, struct freq, node, &pt->data)
{
e->count = round_weight (proc, e->count);
if (e->count == 0.0)
{
hmap_delete (&pt->data, &e->node);
free (e);
}
}
}
/* Convert hash tables into sorted arrays of entries. */
for (struct pivot_table *pt = proc->pivots;
pt < &proc->pivots[proc->n_pivots]; pt++)
{
struct freq *e;
pt->n_entries = hmap_count (&pt->data);
pt->entries = xnmalloc (pt->n_entries, sizeof *pt->entries);
size_t i = 0;
HMAP_FOR_EACH (e, struct freq, node, &pt->data)
pt->entries[i++] = e;
hmap_destroy (&pt->data);
sort (pt->entries, pt->n_entries, sizeof *pt->entries,
proc->descending ? compare_table_entry_3way_inv : compare_table_entry_3way,
pt);
}
make_summary_table (proc);
/* Output each pivot table. */
for (struct pivot_table *pt = proc->pivots;
pt < &proc->pivots[proc->n_pivots]; pt++)
{
if (proc->pivot || pt->n_vars == 2)
output_pivot_table (proc, pt);
else
{
size_t row0 = 0, row1 = 0;
while (find_crosstab (pt, &row0, &row1))
{
struct pivot_table subset;
make_pivot_table_subset (pt, row0, row1, &subset);
output_pivot_table (proc, &subset);
}
}
if (proc->barchart)
chart_item_submit
(barchart_create (pt->vars, pt->n_vars, _("Count"), false, pt->entries, pt->n_entries));
}
/* Free output and prepare for next split file. */
for (struct pivot_table *pt = proc->pivots;
pt < &proc->pivots[proc->n_pivots]; pt++)
{
pt->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_pivot_table), or both allocated and destroyed
at a higher level (in crs_custom_tables and free_proc,
respectively). */
for (size_t i = 0; i < pt->n_vars; i++)
{
int width = var_get_width (pt->vars[i]);
if (value_needs_init (width))
{
size_t j;
for (j = 0; j < pt->n_entries; j++)
value_destroy (&pt->entries[j]->values[i], width);
}
}
for (size_t i = 0; i < pt->n_entries; i++)
free (pt->entries[i]);
free (pt->entries);
}
}
static void
make_pivot_table_subset (struct pivot_table *pt, size_t row0, size_t row1,
struct pivot_table *subset)
{
*subset = *pt;
if (pt->n_vars > 2)
{
assert (pt->n_consts == 0);
subset->missing = pt->missing;
subset->n_vars = 2;
subset->vars = pt->vars;
subset->n_consts = pt->n_vars - 2;
subset->const_vars = pt->vars + 2;
subset->const_values = &pt->entries[row0]->values[2];
}
subset->entries = &pt->entries[row0];
subset->n_entries = row1 - row0;
}
static int
compare_table_entry_var_3way (const struct freq *a,
const struct freq *b,
const struct pivot_table *pt,
int idx)
{
return value_compare_3way (&a->values[idx], &b->values[idx],
var_get_width (pt->vars[idx]));
}
static int
compare_table_entry_vars_3way (const struct freq *a,
const struct freq *b,
const struct pivot_table *pt,
int idx0, int idx1)
{
int i;
for (i = idx1 - 1; i >= idx0; i--)
{
int cmp = compare_table_entry_var_3way (a, b, pt, 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 *pt_)
{
const struct freq *const *ap = ap_;
const struct freq *const *bp = bp_;
const struct freq *a = *ap;
const struct freq *b = *bp;
const struct pivot_table *pt = pt_;
int cmp;
cmp = compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars);
if (cmp != 0)
return cmp;
cmp = compare_table_entry_var_3way (a, b, pt, ROW_VAR);
if (cmp != 0)
return cmp;
return compare_table_entry_var_3way (a, b, pt, COL_VAR);
}
/* Inverted version of compare_table_entry_3way */
static int
compare_table_entry_3way_inv (const void *ap_, const void *bp_, const void *pt_)
{
return -compare_table_entry_3way (ap_, bp_, pt_);
}
static int
find_first_difference (const struct pivot_table *pt, size_t row)
{
if (row == 0)
return pt->n_vars - 1;
else
{
const struct freq *a = pt->entries[row];
const struct freq *b = pt->entries[row - 1];
int col;
for (col = pt->n_vars - 1; col >= 0; col--)
if (compare_table_entry_var_3way (a, b, pt, col))
return col;
NOT_REACHED ();
}
}
/* Output a table summarizing the cases processed. */
static void
make_summary_table (struct crosstabs_proc *proc)
{
struct tab_table *summary;
struct pivot_table *pt;
struct string name;
int i;
summary = tab_create (7, 3 + proc->n_pivots);
tab_set_format (summary, RC_WEIGHT, &proc->weight_format);
tab_title (summary, _("Summary."));
tab_headers (summary, 1, 0, 3, 0);
tab_joint_text (summary, 1, 0, 6, 0, TAB_CENTER, _("Cases"));
tab_joint_text (summary, 1, 1, 2, 1, TAB_CENTER, _("Valid"));
tab_joint_text (summary, 3, 1, 4, 1, TAB_CENTER, _("Missing"));
tab_joint_text (summary, 5, 1, 6, 1, TAB_CENTER, _("Total"));
tab_hline (summary, TAL_1, 1, 6, 1);
tab_hline (summary, TAL_1, 1, 6, 2);
tab_vline (summary, TAL_1, 3, 1, 1);
tab_vline (summary, TAL_1, 5, 1, 1);
for (i = 0; i < 3; i++)
{
tab_text (summary, 1 + i * 2, 2, TAB_RIGHT, _("N"));
tab_text (summary, 2 + i * 2, 2, TAB_RIGHT, _("Percent"));
}
tab_offset (summary, 0, 3);
ds_init_empty (&name);
for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
{
double valid;
double n[3];
size_t i;
tab_hline (summary, TAL_1, 0, 6, 0);
ds_clear (&name);
for (i = 0; i < pt->n_vars; i++)
{
if (i > 0)
ds_put_cstr (&name, " * ");
ds_put_cstr (&name, var_to_string (pt->vars[i]));
}
tab_text (summary, 0, 0, TAB_LEFT, ds_cstr (&name));
valid = 0.;
for (i = 0; i < pt->n_entries; i++)
valid += pt->entries[i]->count;
n[0] = valid;
n[1] = pt->missing;
n[2] = n[0] + n[1];
for (i = 0; i < 3; i++)
{
tab_double (summary, i * 2 + 1, 0, TAB_RIGHT, n[i], NULL, RC_WEIGHT);
tab_text_format (summary, i * 2 + 2, 0, TAB_RIGHT, "%.1f%%",
n[i] / n[2] * 100.);
}
tab_next_row (summary);
}
ds_destroy (&name);
submit (NULL, summary);
}
/* Output. */
static struct tab_table *create_crosstab_table (struct crosstabs_proc *,
struct pivot_table *);
static struct tab_table *create_chisq_table (struct crosstabs_proc *proc, struct pivot_table *);
static struct tab_table *create_sym_table (struct crosstabs_proc *proc, struct pivot_table *);
static struct tab_table *create_risk_table (struct crosstabs_proc *proc, struct pivot_table *);
static struct tab_table *create_direct_table (struct crosstabs_proc *proc, struct pivot_table *);
static void display_dimensions (struct crosstabs_proc *, struct pivot_table *,
struct tab_table *, int first_difference);
static void display_crosstabulation (struct crosstabs_proc *,
struct pivot_table *,
struct tab_table *);
static void display_chisq (struct pivot_table *, struct tab_table *,
bool *showed_fisher);
static void display_symmetric (struct crosstabs_proc *, struct pivot_table *,
struct tab_table *);
static void display_risk (struct pivot_table *, struct tab_table *);
static void display_directional (struct crosstabs_proc *, struct pivot_table *,
struct tab_table *);
static void table_value_missing (struct crosstabs_proc *proc,
struct tab_table *table, int c, int r,
unsigned char opt, const union value *v,
const struct variable *var);
static void delete_missing (struct pivot_table *);
static void build_matrix (struct pivot_table *);
/* Output pivot table PT in the context of PROC. */
static void
output_pivot_table (struct crosstabs_proc *proc, struct pivot_table *pt)
{
struct tab_table *table = NULL; /* Crosstabulation table. */
struct tab_table *chisq = NULL; /* Chi-square table. */
bool showed_fisher = false;
struct tab_table *sym = NULL; /* Symmetric measures table. */
struct tab_table *risk = NULL; /* Risk estimate table. */
struct tab_table *direct = NULL; /* Directional measures table. */
size_t row0, row1;
enum_var_values (pt, COL_VAR, &pt->cols, &pt->n_cols, proc->descending);
if (pt->n_cols == 0)
{
struct string vars;
int i;
ds_init_cstr (&vars, var_to_string (pt->vars[0]));
for (i = 1; i < pt->n_vars; i++)
ds_put_format (&vars, " * %s", var_to_string (pt->vars[i]));
/* TRANSLATORS: The %s here describes a crosstabulation. It takes the
form "var1 * var2 * var3 * ...". */
msg (SW, _("Crosstabulation %s contained no non-missing cases."),
ds_cstr (&vars));
ds_destroy (&vars);
free (pt->cols);
return;
}
if (proc->cells)
table = create_crosstab_table (proc, pt);
if (proc->statistics & (1u << CRS_ST_CHISQ))
chisq = create_chisq_table (proc, pt);
if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)
| (1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
| (1u << CRS_ST_GAMMA) | (1u << CRS_ST_CORR)
| (1u << CRS_ST_KAPPA)))
sym = create_sym_table (proc, pt);
if (proc->statistics & (1u << CRS_ST_RISK))
risk = create_risk_table (proc, pt);
if (proc->statistics & ((1u << CRS_ST_LAMBDA) | (1u << CRS_ST_UC)
| (1u << CRS_ST_D) | (1u << CRS_ST_ETA)))
direct = create_direct_table (proc, pt);
row0 = row1 = 0;
while (find_crosstab (pt, &row0, &row1))
{
struct pivot_table x;
int first_difference;
make_pivot_table_subset (pt, row0, row1, &x);
/* Find all the row variable values. */
enum_var_values (&x, ROW_VAR, &x.rows, &x.n_rows, proc->descending);
if (size_overflow_p (xtimes (xtimes (x.n_rows, x.n_cols),
sizeof (double))))
xalloc_die ();
x.row_tot = xmalloc (x.n_rows * sizeof *x.row_tot);
x.col_tot = xmalloc (x.n_cols * sizeof *x.col_tot);
x.mat = xmalloc (x.n_rows * x.n_cols * sizeof *x.mat);
/* Allocate table space for the matrix. */
if (table
&& tab_row (table) + (x.n_rows + 1) * proc->n_cells > tab_nr (table))
tab_realloc (table, -1,
MAX (tab_nr (table) + (x.n_rows + 1) * proc->n_cells,
tab_nr (table) * pt->n_entries / x.n_entries));
build_matrix (&x);
/* Find the first variable that differs from the last subtable. */
first_difference = find_first_difference (pt, row0);
if (table)
{
display_dimensions (proc, &x, table, first_difference);
display_crosstabulation (proc, &x, table);
}
if (proc->exclude == MV_NEVER)
delete_missing (&x);
if (chisq)
{
display_dimensions (proc, &x, chisq, first_difference);
display_chisq (&x, chisq, &showed_fisher);
}
if (sym)
{
display_dimensions (proc, &x, sym, first_difference);
display_symmetric (proc, &x, sym);
}
if (risk)
{
display_dimensions (proc, &x, risk, first_difference);
display_risk (&x, risk);
}
if (direct)
{
display_dimensions (proc, &x, direct, first_difference);
display_directional (proc, &x, direct);
}
/* Free the parts of x that are not owned by pt. In
particular we must not free x.cols, which is the same as
pt->cols, which is freed at the end of this function. */
free (x.rows);
free (x.mat);
free (x.row_tot);
free (x.col_tot);
}
submit (NULL, table);
if (chisq)
{
if (!showed_fisher)
tab_resize (chisq, 4 + (pt->n_vars - 2), -1);
submit (pt, chisq);
}
submit (pt, sym);
submit (pt, risk);
submit (pt, direct);
free (pt->cols);
}
static void
build_matrix (struct pivot_table *x)
{
const int col_var_width = var_get_width (x->vars[COL_VAR]);
const int row_var_width = var_get_width (x->vars[ROW_VAR]);
int col, row;
double *mp;
struct freq **p;
mp = x->mat;
col = row = 0;
for (p = x->entries; p < &x->entries[x->n_entries]; p++)
{
const struct freq *te = *p;
while (!value_equal (&x->rows[row], &te->values[ROW_VAR], row_var_width))
{
for (; col < x->n_cols; col++)
*mp++ = 0.0;
col = 0;
row++;
}
while (!value_equal (&x->cols[col], &te->values[COL_VAR], col_var_width))
{
*mp++ = 0.0;
col++;
}
*mp++ = te->count;
if (++col >= x->n_cols)
{
col = 0;
row++;
}
}
while (mp < &x->mat[x->n_cols * x->n_rows])
*mp++ = 0.0;
assert (mp == &x->mat[x->n_cols * x->n_rows]);
/* Column totals, row totals, ns_rows. */
mp = x->mat;
for (col = 0; col < x->n_cols; col++)
x->col_tot[col] = 0.0;
for (row = 0; row < x->n_rows; row++)
x->row_tot[row] = 0.0;
x->ns_rows = 0;
for (row = 0; row < x->n_rows; row++)
{
bool row_is_empty = true;
for (col = 0; col < x->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[x->n_cols * x->n_rows]);
/* ns_cols. */
x->ns_cols = 0;
for (col = 0; col < x->n_cols; col++)
for (row = 0; row < x->n_rows; row++)
if (x->mat[col + row * x->n_cols] != 0.0)
{
x->ns_cols++;
break;
}
/* Grand total. */
x->total = 0.0;
for (col = 0; col < x->n_cols; col++)
x->total += x->col_tot[col];
}
static struct tab_table *
create_crosstab_table (struct crosstabs_proc *proc, struct pivot_table *pt)
{
struct tuple
{
int value;
const char *name;
};
static const struct tuple names[] =
{
{CRS_CL_COUNT, N_("count")},
{CRS_CL_ROW, N_("row %")},
{CRS_CL_COLUMN, N_("column %")},
{CRS_CL_TOTAL, N_("total %")},
{CRS_CL_EXPECTED, N_("expected")},
{CRS_CL_RESIDUAL, N_("residual")},
{CRS_CL_SRESIDUAL, N_("std. resid.")},
{CRS_CL_ASRESIDUAL, N_("adj. resid.")},
};
const int n_names = sizeof names / sizeof *names;
const struct tuple *t;
struct tab_table *table;
struct string title;
struct pivot_table x;
int i;
make_pivot_table_subset (pt, 0, 0, &x);
table = tab_create (x.n_consts + 1 + x.n_cols + 1,
(x.n_entries / x.n_cols) * 3 / 2 * proc->n_cells + 10);
tab_headers (table, x.n_consts + 1, 0, 2, 0);
tab_set_format (table, RC_WEIGHT, &proc->weight_format);
/* First header line. */
tab_joint_text (table, x.n_consts + 1, 0,
(x.n_consts + 1) + (x.n_cols - 1), 0,
TAB_CENTER | TAT_TITLE, var_to_string (x.vars[COL_VAR]));
tab_hline (table, TAL_1, x.n_consts + 1,
x.n_consts + 2 + x.n_cols - 2, 1);
/* Second header line. */
for (i = 2; i < x.n_consts + 2; i++)
tab_joint_text (table, x.n_consts + 2 - i - 1, 0,
x.n_consts + 2 - i - 1, 1,
TAB_RIGHT | TAT_TITLE, var_to_string (x.vars[i]));
tab_text (table, x.n_consts + 2 - 2, 1, TAB_RIGHT | TAT_TITLE,
var_to_string (x.vars[ROW_VAR]));
for (i = 0; i < x.n_cols; i++)
table_value_missing (proc, table, x.n_consts + 2 + i - 1, 1, TAB_RIGHT,
&x.cols[i], x.vars[COL_VAR]);
tab_text (table, x.n_consts + 2 + x.n_cols - 1, 1, TAB_CENTER, _("Total"));
tab_hline (table, TAL_1, 0, x.n_consts + 2 + x.n_cols - 1, 2);
tab_vline (table, TAL_1, x.n_consts + 2 + x.n_cols - 1, 0, 1);
/* Title. */
ds_init_empty (&title);
for (i = 0; i < x.n_consts + 2; i++)
{
if (i)
ds_put_cstr (&title, " * ");
ds_put_cstr (&title, var_to_string (x.vars[i]));
}
for (i = 0; i < pt->n_consts; i++)
{
const struct variable *var = pt->const_vars[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 (&pt->const_values[i], var_get_encoding (var),
var_get_print_format (var));
ds_put_cstr (&title, s + strspn (s, " "));
free (s);
}
ds_put_cstr (&title, " [");
i = 0;
for (t = names; t < &names[n_names]; t++)
if (proc->cells & (1u << t->value))
{
if (i++)
ds_put_cstr (&title, ", ");
ds_put_cstr (&title, gettext (t->name));
}
ds_put_cstr (&title, "].");
tab_title (table, "%s", ds_cstr (&title));
ds_destroy (&title);
tab_offset (table, 0, 2);
return table;
}
static struct tab_table *
create_chisq_table (struct crosstabs_proc *proc, struct pivot_table *pt)
{
struct tab_table *chisq;
chisq = tab_create (6 + (pt->n_vars - 2),
pt->n_entries / pt->n_cols * 3 / 2 * N_CHISQ + 10);
tab_headers (chisq, 1 + (pt->n_vars - 2), 0, 1, 0);
tab_set_format (chisq, RC_WEIGHT, &proc->weight_format);
tab_title (chisq, _("Chi-square tests."));
tab_offset (chisq, pt->n_vars - 2, 0);
tab_text (chisq, 0, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
tab_text (chisq, 1, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
tab_text (chisq, 2, 0, TAB_RIGHT | TAT_TITLE, _("df"));
tab_text (chisq, 3, 0, TAB_RIGHT | TAT_TITLE,
_("Asymp. Sig. (2-tailed)"));
tab_text_format (chisq, 4, 0, TAB_RIGHT | TAT_TITLE,
_("Exact Sig. (%d-tailed)"), 2);
tab_text_format (chisq, 5, 0, TAB_RIGHT | TAT_TITLE,
_("Exact Sig. (%d-tailed)"), 1);
tab_offset (chisq, 0, 1);
return chisq;
}
/* Symmetric measures. */
static struct tab_table *
create_sym_table (struct crosstabs_proc *proc, struct pivot_table *pt)
{
struct tab_table *sym;
sym = tab_create (6 + (pt->n_vars - 2),
pt->n_entries / pt->n_cols * 7 + 10);
tab_set_format (sym, RC_WEIGHT, &proc->weight_format);
tab_headers (sym, 2 + (pt->n_vars - 2), 0, 1, 0);
tab_title (sym, _("Symmetric measures."));
tab_offset (sym, pt->n_vars - 2, 0);
tab_text (sym, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
tab_text (sym, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
tab_text (sym, 2, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
tab_text (sym, 3, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
tab_text (sym, 4, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
tab_text (sym, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
tab_offset (sym, 0, 1);
return sym;
}
/* Risk estimate. */
static struct tab_table *
create_risk_table (struct crosstabs_proc *proc, struct pivot_table *pt)
{
struct tab_table *risk;
risk = tab_create (4 + (pt->n_vars - 2), pt->n_entries / pt->n_cols * 4 + 10);
tab_headers (risk, 1 + pt->n_vars - 2, 0, 2, 0);
tab_title (risk, _("Risk estimate."));
tab_set_format (risk, RC_WEIGHT, &proc->weight_format);
tab_offset (risk, pt->n_vars - 2, 0);
tab_joint_text_format (risk, 2, 0, 3, 0, TAB_CENTER | TAT_TITLE,
_("95%% Confidence Interval"));
tab_text (risk, 0, 1, TAB_LEFT | TAT_TITLE, _("Statistic"));
tab_text (risk, 1, 1, TAB_RIGHT | TAT_TITLE, _("Value"));
tab_text (risk, 2, 1, TAB_RIGHT | TAT_TITLE, _("Lower"));
tab_text (risk, 3, 1, TAB_RIGHT | TAT_TITLE, _("Upper"));
tab_hline (risk, TAL_1, 2, 3, 1);
tab_vline (risk, TAL_1, 2, 0, 1);
tab_offset (risk, 0, 2);
return risk;
}
/* Directional measures. */
static struct tab_table *
create_direct_table (struct crosstabs_proc *proc, struct pivot_table *pt)
{
struct tab_table *direct;
direct = tab_create (7 + (pt->n_vars - 2),
pt->n_entries / pt->n_cols * 7 + 10);
tab_headers (direct, 3 + (pt->n_vars - 2), 0, 1, 0);
tab_title (direct, _("Directional measures."));
tab_set_format (direct, RC_WEIGHT, &proc->weight_format);
tab_offset (direct, pt->n_vars - 2, 0);
tab_text (direct, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
tab_text (direct, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
tab_text (direct, 2, 0, TAB_LEFT | TAT_TITLE, _("Type"));
tab_text (direct, 3, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
tab_text (direct, 4, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
tab_text (direct, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
tab_text (direct, 6, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
tab_offset (direct, 0, 1);
return direct;
}
/* Delete missing rows and columns for statistical analysis when
/MISSING=REPORT. */
static void
delete_missing (struct pivot_table *pt)
{
int r, c;
for (r = 0; r < pt->n_rows; r++)
if (var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
{
for (c = 0; c < pt->n_cols; c++)
pt->mat[c + r * pt->n_cols] = 0.;
pt->ns_rows--;
}
for (c = 0; c < pt->n_cols; c++)
if (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
{
for (r = 0; r < pt->n_rows; r++)
pt->mat[c + r * pt->n_cols] = 0.;
pt->ns_cols--;
}
}
/* Prepare table T for submission, and submit it. */
static void
submit (struct pivot_table *pt, struct tab_table *t)
{
int i;
if (t == NULL)
return;
tab_resize (t, -1, 0);
if (tab_nr (t) == tab_t (t))
{
table_unref (&t->table);
return;
}
tab_offset (t, 0, 0);
if (pt != NULL)
for (i = 2; i < pt->n_vars; i++)
tab_text (t, pt->n_vars - i - 1, 0, TAB_RIGHT | TAT_TITLE,
var_to_string (pt->vars[i]));
tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, tab_nc (t) - 1, tab_nr (t) - 1);
tab_box (t, -1, -1, -1, TAL_1, tab_l (t), tab_t (t) - 1, tab_nc (t) - 1,
tab_nr (t) - 1);
tab_box (t, -1, -1, -1, TAL_GAP, 0, tab_t (t), tab_l (t) - 1,
tab_nr (t) - 1);
tab_vline (t, TAL_2, tab_l (t), 0, tab_nr (t) - 1);
tab_submit (t);
}
static bool
find_crosstab (struct pivot_table *pt, size_t *row0p, size_t *row1p)
{
size_t row0 = *row1p;
size_t row1;
if (row0 >= pt->n_entries)
return false;
for (row1 = row0 + 1; row1 < pt->n_entries; row1++)
{
struct freq *a = pt->entries[row0];
struct freq *b = pt->entries[row1];
if (compare_table_entry_vars_3way (a, b, pt, 2, pt->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. The values are returned as a
malloc()'d array stored in *VALUES, with the number of values
stored in *VALUE_CNT.
The caller must eventually free *VALUES, but each pointer in *VALUES points
to existing data not owned by *VALUES itself. */
static void
enum_var_values (const struct pivot_table *pt, int var_idx,
union value **valuesp, int *n_values, bool descending)
{
const struct variable *var = pt->vars[var_idx];
const struct var_range *range = get_var_range (pt->proc, var);
union value *values;
size_t i;
if (range)
{
values = *valuesp = xnmalloc (range->count, sizeof *values);
*n_values = range->count;
for (i = 0; i < range->count; i++)
values[i].f = range->min + i;
}
else
{
int width = var_get_width (var);
struct hmapx_node *node;
const union value *iter;
struct hmapx set;
hmapx_init (&set);
for (i = 0; i < pt->n_entries; i++)
{
const struct freq *te = pt->entries[i];
const union value *value = &te->values[var_idx];
size_t hash = value_hash (value, width, 0);
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: ;
}
*n_values = hmapx_count (&set);
values = *valuesp = xnmalloc (*n_values, sizeof *values);
i = 0;
HMAPX_FOR_EACH (iter, node, &set)
values[i++] = *iter;
hmapx_destroy (&set);
sort (values, *n_values, sizeof *values,
descending ? compare_value_3way_inv : compare_value_3way,
&width);
}
}
/* Sets cell (C,R) in TABLE, with options OPT, to have a value taken
from V, displayed with print format spec from variable VAR. When
in REPORT missing-value mode, missing values have an M appended. */
static void
table_value_missing (struct crosstabs_proc *proc,
struct tab_table *table, int c, int r, unsigned char opt,
const union value *v, const struct variable *var)
{
const char *label = var_lookup_value_label (var, v);
if (label != NULL)
tab_text (table, c, r, TAB_LEFT, label);
else
{
const struct fmt_spec *print = var_get_print_format (var);
if (proc->exclude == MV_NEVER && var_is_value_missing (var, v, MV_USER))
{
char *s = data_out (v, dict_get_encoding (proc->dict), print);
tab_text_format (table, c, r, opt, "%sM", s + strspn (s, " "));
free (s);
}
else
tab_value (table, c, r, opt, v, var, print);
}
}
/* Draws a line across TABLE at the current row to indicate the most
major dimension variable with index FIRST_DIFFERENCE out of N_VARS
that changed, and puts the values that changed into the table. TB
and PT must be the corresponding table_entry and crosstab,
respectively. */
static void
display_dimensions (struct crosstabs_proc *proc, struct pivot_table *pt,
struct tab_table *table, int first_difference)
{
tab_hline (table, TAL_1, pt->n_consts + pt->n_vars - first_difference - 1, tab_nc (table) - 1, 0);
for (; first_difference >= 2; first_difference--)
table_value_missing (proc, table, pt->n_consts + pt->n_vars - first_difference - 1, 0,
TAB_RIGHT, &pt->entries[0]->values[first_difference],
pt->vars[first_difference]);
}
/* Put VALUE into cell (C,R) of TABLE, suffixed with character
SUFFIX if nonzero. If MARK_MISSING is true the entry is
additionally suffixed with a letter `M'. */
static void
format_cell_entry (struct tab_table *table, int c, int r, double value,
char suffix, bool mark_missing, const struct dictionary *dict)
{
union value v;
char suffixes[3];
int suffix_len;
char *s;
v.f = value;
s = data_out (&v, dict_get_encoding (dict), settings_get_format ());
suffix_len = 0;
if (suffix != 0)
suffixes[suffix_len++] = suffix;
if (mark_missing)
suffixes[suffix_len++] = 'M';
suffixes[suffix_len] = '\0';
tab_text_format (table, c, r, TAB_RIGHT, "%s%s",
s + strspn (s, " "), suffixes);
free (s);
}
/* Displays the crosstabulation table. */
static void
display_crosstabulation (struct crosstabs_proc *proc, struct pivot_table *pt,
struct tab_table *table)
{
int last_row;
int r, c, i;
double *mp;
for (r = 0; r < pt->n_rows; r++)
table_value_missing (proc, table, pt->n_consts + pt->n_vars - 2,
r * proc->n_cells, TAB_RIGHT, &pt->rows[r],
pt->vars[ROW_VAR]);
tab_text (table, pt->n_vars - 2, pt->n_rows * proc->n_cells,
TAB_LEFT, _("Total"));
/* Put in the actual cells. */
mp = pt->mat;
tab_offset (table, pt->n_consts + pt->n_vars - 1, -1);
for (r = 0; r < pt->n_rows; r++)
{
if (proc->n_cells > 1)
tab_hline (table, TAL_1, -1, pt->n_cols, 0);
for (c = 0; c < pt->n_cols; c++)
{
bool mark_missing = false;
double expected_value = pt->row_tot[r] * pt->col_tot[c] / pt->total;
if (proc->exclude == MV_NEVER
&& (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER)
|| var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f,
MV_USER)))
mark_missing = true;
for (i = 0; i < proc->n_cells; i++)
{
double v;
int suffix = 0;
switch (proc->a_cells[i])
{
case CRS_CL_COUNT:
v = *mp;
break;
case CRS_CL_ROW:
v = *mp / pt->row_tot[r] * 100.;
suffix = '%';
break;
case CRS_CL_COLUMN:
v = *mp / pt->col_tot[c] * 100.;
suffix = '%';
break;
case CRS_CL_TOTAL:
v = *mp / pt->total * 100.;
suffix = '%';
break;
case CRS_CL_EXPECTED:
v = expected_value;
break;
case CRS_CL_RESIDUAL:
v = *mp - expected_value;
break;
case CRS_CL_SRESIDUAL:
v = (*mp - expected_value) / sqrt (expected_value);
break;
case CRS_CL_ASRESIDUAL:
v = ((*mp - expected_value)
/ sqrt (expected_value
* (1. - pt->row_tot[r] / pt->total)
* (1. - pt->col_tot[c] / pt->total)));
break;
default:
NOT_REACHED ();
}
format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
}
mp++;
}
tab_offset (table, -1, tab_row (table) + proc->n_cells);
}
/* Row totals. */
tab_offset (table, -1, tab_row (table) - proc->n_cells * pt->n_rows);
for (r = 0; r < pt->n_rows; r++)
{
bool mark_missing = false;
if (proc->exclude == MV_NEVER
&& var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
mark_missing = true;
for (i = 0; i < proc->n_cells; i++)
{
char suffix = 0;
double v;
switch (proc->a_cells[i])
{
case CRS_CL_COUNT:
v = pt->row_tot[r];
break;
case CRS_CL_ROW:
v = 100.0;
suffix = '%';
break;
case CRS_CL_COLUMN:
v = pt->row_tot[r] / pt->total * 100.;
suffix = '%';
break;
case CRS_CL_TOTAL:
v = pt->row_tot[r] / pt->total * 100.;
suffix = '%';
break;
case CRS_CL_EXPECTED:
case CRS_CL_RESIDUAL:
case CRS_CL_SRESIDUAL:
case CRS_CL_ASRESIDUAL:
v = 0.;
break;
default:
NOT_REACHED ();
}
format_cell_entry (table, pt->n_cols, 0, v, suffix, mark_missing, proc->dict);
tab_next_row (table);
}
}
/* Column totals, grand total. */
last_row = 0;
if (proc->n_cells > 1)
tab_hline (table, TAL_1, -1, pt->n_cols, 0);
for (c = 0; c <= pt->n_cols; c++)
{
double ct = c < pt->n_cols ? pt->col_tot[c] : pt->total;
bool mark_missing = false;
int i;
if (proc->exclude == MV_NEVER && c < pt->n_cols
&& var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
mark_missing = true;
for (i = 0; i < proc->n_cells; i++)
{
char suffix = 0;
double v;
switch (proc->a_cells[i])
{
case CRS_CL_COUNT:
v = ct;
break;
case CRS_CL_ROW:
v = ct / pt->total * 100.;
suffix = '%';
break;
case CRS_CL_COLUMN:
v = 100.;
suffix = '%';
break;
case CRS_CL_TOTAL:
v = ct / pt->total * 100.;
suffix = '%';
break;
case CRS_CL_EXPECTED:
case CRS_CL_RESIDUAL:
case CRS_CL_SRESIDUAL:
case CRS_CL_ASRESIDUAL:
continue;
default:
NOT_REACHED ();
}
format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
}
last_row = i;
}
tab_offset (table, -1, tab_row (table) + last_row);
tab_offset (table, 0, -1);
}
static void calc_r (struct pivot_table *,
double *PT, double *Y, double *, double *, double *);
static void calc_chisq (struct pivot_table *,
double[N_CHISQ], int[N_CHISQ], double *, double *);
/* Display chi-square statistics. */
static void
display_chisq (struct pivot_table *pt, struct tab_table *chisq,
bool *showed_fisher)
{
static const char *chisq_stats[N_CHISQ] =
{
N_("Pearson Chi-Square"),
N_("Likelihood Ratio"),
N_("Fisher's Exact Test"),
N_("Continuity Correction"),
N_("Linear-by-Linear Association"),
};
double chisq_v[N_CHISQ];
double fisher1, fisher2;
int df[N_CHISQ];
int i;
calc_chisq (pt, chisq_v, df, &fisher1, &fisher2);
tab_offset (chisq, pt->n_consts + pt->n_vars - 2, -1);
for (i = 0; i < N_CHISQ; i++)
{
if ((i != 2 && chisq_v[i] == SYSMIS)
|| (i == 2 && fisher1 == SYSMIS))
continue;
tab_text (chisq, 0, 0, TAB_LEFT, gettext (chisq_stats[i]));
if (i != 2)
{
tab_double (chisq, 1, 0, TAB_RIGHT, chisq_v[i], NULL, RC_OTHER);
tab_double (chisq, 2, 0, TAB_RIGHT, df[i], NULL, RC_WEIGHT);
tab_double (chisq, 3, 0, TAB_RIGHT,
gsl_cdf_chisq_Q (chisq_v[i], df[i]), NULL, RC_PVALUE);
}
else
{
*showed_fisher = true;
tab_double (chisq, 4, 0, TAB_RIGHT, fisher2, NULL, RC_PVALUE);
tab_double (chisq, 5, 0, TAB_RIGHT, fisher1, NULL, RC_PVALUE);
}
tab_next_row (chisq);
}
tab_text (chisq, 0, 0, TAB_LEFT, _("N of Valid Cases"));
tab_double (chisq, 1, 0, TAB_RIGHT, pt->total, NULL, RC_WEIGHT);
tab_next_row (chisq);
tab_offset (chisq, 0, -1);
}
static int calc_symmetric (struct crosstabs_proc *, struct pivot_table *,
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 pivot_table *pt,
struct tab_table *sym)
{
static const char *categories[] =
{
N_("Nominal by Nominal"),
N_("Ordinal by Ordinal"),
N_("Interval by Interval"),
N_("Measure of Agreement"),
};
static const char *stats[N_SYMMETRIC] =
{
N_("Phi"),
N_("Cramer's V"),
N_("Contingency Coefficient"),
N_("Kendall's tau-b"),
N_("Kendall's tau-c"),
N_("Gamma"),
N_("Spearman Correlation"),
N_("Pearson's R"),
N_("Kappa"),
};
static const int stats_categories[N_SYMMETRIC] =
{
0, 0, 0, 1, 1, 1, 1, 2, 3,
};
int last_cat = -1;
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];
int i;
if (!calc_symmetric (proc, pt, sym_v, sym_ase, sym_t,
somers_d_v, somers_d_ase, somers_d_t))
return;
tab_offset (sym, pt->n_consts + pt->n_vars - 2, -1);
for (i = 0; i < N_SYMMETRIC; i++)
{
if (sym_v[i] == SYSMIS)
continue;
if (stats_categories[i] != last_cat)
{
last_cat = stats_categories[i];
tab_text (sym, 0, 0, TAB_LEFT, gettext (categories[last_cat]));
}
tab_text (sym, 1, 0, TAB_LEFT, gettext (stats[i]));
tab_double (sym, 2, 0, TAB_RIGHT, sym_v[i], NULL, RC_OTHER);
if (sym_ase[i] != SYSMIS)
tab_double (sym, 3, 0, TAB_RIGHT, sym_ase[i], NULL, RC_OTHER);
if (sym_t[i] != SYSMIS)
tab_double (sym, 4, 0, TAB_RIGHT, sym_t[i], NULL, RC_OTHER);
/*tab_double (sym, 5, 0, TAB_RIGHT, normal_sig (sym_v[i]), NULL, RC_PVALUE);*/
tab_next_row (sym);
}
tab_text (sym, 0, 0, TAB_LEFT, _("N of Valid Cases"));
tab_double (sym, 2, 0, TAB_RIGHT, pt->total, NULL, RC_WEIGHT);
tab_next_row (sym);
tab_offset (sym, 0, -1);
}
static int calc_risk (struct pivot_table *,
double[], double[], double[], union value *);
/* Display risk estimate. */
static void
display_risk (struct pivot_table *pt, struct tab_table *risk)
{
char buf[256];
double risk_v[3], lower[3], upper[3];
union value c[2];
int i;
if (!calc_risk (pt, risk_v, upper, lower, c))
return;
tab_offset (risk, pt->n_consts + pt->n_vars - 2, -1);
for (i = 0; i < 3; i++)
{
const struct variable *cv = pt->vars[COL_VAR];
const struct variable *rv = pt->vars[ROW_VAR];
int cvw = var_get_width (cv);
int rvw = var_get_width (rv);
if (risk_v[i] == SYSMIS)
continue;
switch (i)
{
case 0:
if (var_is_numeric (cv))
sprintf (buf, _("Odds Ratio for %s (%g / %g)"),
var_to_string (cv), c[0].f, c[1].f);
else
sprintf (buf, _("Odds Ratio for %s (%.*s / %.*s)"),
var_to_string (cv),
cvw, value_str (&c[0], cvw),
cvw, value_str (&c[1], cvw));
break;
case 1:
case 2:
if (var_is_numeric (rv))
sprintf (buf, _("For cohort %s = %.*g"),
var_to_string (rv), DBL_DIG + 1, pt->rows[i - 1].f);
else
sprintf (buf, _("For cohort %s = %.*s"),
var_to_string (rv),
rvw, value_str (&pt->rows[i - 1], rvw));
break;
}
tab_text (risk, 0, 0, TAB_LEFT, buf);
tab_double (risk, 1, 0, TAB_RIGHT, risk_v[i], NULL, RC_OTHER);
tab_double (risk, 2, 0, TAB_RIGHT, lower[i], NULL, RC_OTHER);
tab_double (risk, 3, 0, TAB_RIGHT, upper[i], NULL, RC_OTHER);
tab_next_row (risk);
}
tab_text (risk, 0, 0, TAB_LEFT, _("N of Valid Cases"));
tab_double (risk, 1, 0, TAB_RIGHT, pt->total, NULL, RC_WEIGHT);
tab_next_row (risk);
tab_offset (risk, 0, -1);
}
static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
double[N_DIRECTIONAL], double[N_DIRECTIONAL],
double[N_DIRECTIONAL], double[N_DIRECTIONAL]);
/* Display directional measures. */
static void
display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
struct tab_table *direct)
{
static const char *categories[] =
{
N_("Nominal by Nominal"),
N_("Ordinal by Ordinal"),
N_("Nominal by Interval"),
};
static const char *stats[] =
{
N_("Lambda"),
N_("Goodman and Kruskal tau"),
N_("Uncertainty Coefficient"),
N_("Somers' d"),
N_("Eta"),
};
static const char *types[] =
{
N_("Symmetric"),
N_("%s Dependent"),
N_("%s Dependent"),
};
static const int stats_categories[N_DIRECTIONAL] =
{
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2,
};
static const int stats_stats[N_DIRECTIONAL] =
{
0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,
};
static const int stats_types[N_DIRECTIONAL] =
{
0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2,
};
static const int *stats_lookup[] =
{
stats_categories,
stats_stats,
stats_types,
};
static const char **stats_names[] =
{
categories,
stats,
types,
};
int last[3] =
{
-1, -1, -1,
};
double direct_v[N_DIRECTIONAL];
double direct_ase[N_DIRECTIONAL];
double direct_t[N_DIRECTIONAL];
double sig[N_DIRECTIONAL];
int i;
if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t, sig))
return;
tab_offset (direct, pt->n_consts + pt->n_vars - 2, -1);
for (i = 0; i < N_DIRECTIONAL; i++)
{
if (direct_v[i] == SYSMIS)
continue;
{
int j;
for (j = 0; j < 3; j++)
if (last[j] != stats_lookup[j][i])
{
if (j < 2)
tab_hline (direct, TAL_1, j, 6, 0);
for (; j < 3; j++)
{
const char *string;
int k = last[j] = stats_lookup[j][i];
if (k == 0)
string = NULL;
else if (k == 1)
string = var_to_string (pt->vars[0]);
else
string = var_to_string (pt->vars[1]);
tab_text_format (direct, j, 0, TAB_LEFT,
gettext (stats_names[j][k]), string);
}
}
}
tab_double (direct, 3, 0, TAB_RIGHT, direct_v[i], NULL, RC_OTHER);
if (direct_ase[i] != SYSMIS)
tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL, RC_OTHER);
if (direct_t[i] != SYSMIS)
tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL, RC_OTHER);
tab_double (direct, 6, 0, TAB_RIGHT, sig[i], NULL, RC_PVALUE);
tab_next_row (direct);
}
tab_offset (direct, 0, -1);
}
/* Statistical calculations. */
/* Returns the value of the logarithm of gamma (factorial) function for an integer
argument PT. */
static double
log_gamma_int (double pt)
{
double r = 0;
int i;
for (i = 2; i < pt; 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)
{
int pt;
double pn1;
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);
}
pn1 = Pr (a, b, c, d);
*fisher1 = pn1;
for (pt = 1; pt <= a; pt++)
{
*fisher1 += Pr (a - pt, b + pt, c + pt, d - pt);
}
*fisher2 = *fisher1;
for (pt = 1; pt <= b; pt++)
{
double p = Pr (a + pt, b - pt, c - pt, d + pt);
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 pt->total. */
static void
calc_chisq (struct pivot_table *pt,
double chisq[N_CHISQ], int df[N_CHISQ],
double *fisher1, double *fisher2)
{
int r, c;
chisq[0] = chisq[1] = 0.;
chisq[2] = chisq[3] = chisq[4] = SYSMIS;
*fisher1 = *fisher2 = SYSMIS;
df[0] = df[1] = (pt->ns_cols - 1) * (pt->ns_rows - 1);
if (pt->ns_rows <= 1 || pt->ns_cols <= 1)
{
chisq[0] = chisq[1] = SYSMIS;
return;
}
for (r = 0; r < pt->n_rows; r++)
for (c = 0; c < pt->n_cols; c++)
{
const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
const double freq = pt->mat[pt->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 (pt->ns_cols == 2 && pt->ns_rows == 2)
{
double f11, f12, f21, f22;
{
int nz_cols[2];
int i, j;
for (i = j = 0; i < pt->n_cols; i++)
if (pt->col_tot[i] != 0.)
{
nz_cols[j++] = i;
if (j == 2)
break;
}
assert (j == 2);
f11 = pt->mat[nz_cols[0]];
f12 = pt->mat[nz_cols[1]];
f21 = pt->mat[nz_cols[0] + pt->n_cols];
f22 = pt->mat[nz_cols[1] + pt->n_cols];
}
/* Yates. */
{
const double pt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * pt->total;
if (pt_ > 0.)
chisq[3] = (pt->total * pow2 (pt_)
/ (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 (pt->vars[ROW_VAR]) && var_is_numeric (pt->vars[COL_VAR]))
{
double r, ase_0, ase_1;
calc_r (pt, (double *) pt->rows, (double *) pt->cols, &r, &ase_0, &ase_1);
chisq[4] = (pt->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 PT and Y. */
static void
calc_r (struct pivot_table *pt,
double *PT, double *Y, double *r, double *t, double *error)
{
double SX, SY, S, T;
double Xbar, Ybar;
double sum_XYf, sum_X2Y2f;
double sum_Xr, sum_X2r;
double sum_Yc, sum_Y2c;
int i, j;
for (sum_X2Y2f = sum_XYf = 0., i = 0; i < pt->n_rows; i++)
for (j = 0; j < pt->n_cols; j++)
{
double fij = pt->mat[j + i * pt->n_cols];
double product = PT[i] * Y[j];
double temp = fij * product;
sum_XYf += temp;
sum_X2Y2f += temp * product;
}
for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
{
sum_Xr += PT[i] * pt->row_tot[i];
sum_X2r += pow2 (PT[i]) * pt->row_tot[i];
}
Xbar = sum_Xr / pt->total;
for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
{
sum_Yc += Y[i] * pt->col_tot[i];
sum_Y2c += Y[i] * Y[i] * pt->col_tot[i];
}
Ybar = sum_Yc / pt->total;
S = sum_XYf - sum_Xr * sum_Yc / pt->total;
SX = sum_X2r - pow2 (sum_Xr) / pt->total;
SY = sum_Y2c - pow2 (sum_Yc) / pt->total;
T = sqrt (SX * SY);
*r = S / T;
*t = *r / sqrt (1 - pow2 (*r)) * sqrt (pt->total - 2);
{
double s, c, y, t;
for (s = c = 0., i = 0; i < pt->n_rows; i++)
for (j = 0; j < pt->n_cols; j++)
{
double Xresid, Yresid;
double temp;
Xresid = PT[i] - Xbar;
Yresid = Y[j] - Ybar;
temp = (T * Xresid * Yresid
- ((S / (2. * T))
* (Xresid * Xresid * SY + Yresid * Yresid * SX)));
y = pt->mat[j + i * pt->n_cols] * temp * temp - c;
t = s + y;
c = (t - s) - y;
s = t;
}
*error = sqrt (s) / (T * T);
}
}
/* Calculate symmetric statistics and their asymptotic standard
errors. Returns 0 if none could be calculated. */
static int
calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
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])
{
int q, i;
q = MIN (pt->ns_rows, pt->ns_cols);
if (q <= 1)
return 0;
for (i = 0; i < N_SYMMETRIC; i++)
v[i] = ase[i] = t[i] = SYSMIS;
/* Phi, Cramer's V, contingency coefficient. */
if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
{
double Xp = 0.; /* Pearson chi-square. */
int r, c;
for (r = 0; r < pt->n_rows; r++)
for (c = 0; c < pt->n_cols; c++)
{
const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
const double freq = pt->mat[pt->n_cols * r + c];
const double residual = freq - expected;
Xp += residual * residual / expected;
}
if (proc->statistics & (1u << CRS_ST_PHI))
{
v[0] = sqrt (Xp / pt->total);
v[1] = sqrt (Xp / (pt->total * (q - 1)));
}
if (proc->statistics & (1u << CRS_ST_CC))
v[2] = sqrt (Xp / (Xp + pt->total));
}
if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
| (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
{
double *cum;
double Dr, Dc;
double P, Q;
double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
double btau_var;
int r, c;
Dr = Dc = pow2 (pt->total);
for (r = 0; r < pt->n_rows; r++)
Dr -= pow2 (pt->row_tot[r]);
for (c = 0; c < pt->n_cols; c++)
Dc -= pow2 (pt->col_tot[c]);
cum = xnmalloc (pt->n_cols * pt->n_rows, sizeof *cum);
for (c = 0; c < pt->n_cols; c++)
{
double ct = 0.;
for (r = 0; r < pt->n_rows; r++)
cum[c + r * pt->n_cols] = ct += pt->mat[c + r * pt->n_cols];
}
/* P and Q. */
{
int i, j;
double Cij, Dij;
P = Q = 0.;
for (i = 0; i < pt->n_rows; i++)
{
Cij = Dij = 0.;
for (j = 1; j < pt->n_cols; j++)
Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
if (i > 0)
for (j = 1; j < pt->n_cols; j++)
Dij += cum[j + (i - 1) * pt->n_cols];
for (j = 0;;)
{
double fij = pt->mat[j + i * pt->n_cols];
P += fij * Cij;
Q += fij * Dij;
if (++j == pt->n_cols)
break;
assert (j < pt->n_cols);
Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
if (i > 0)
{
Cij += cum[j - 1 + (i - 1) * pt->n_cols];
Dij -= cum[j + (i - 1) * pt->n_cols];
}
}
}
}
if (proc->statistics & (1u << CRS_ST_BTAU))
v[3] = (P - Q) / sqrt (Dr * Dc);
if (proc->statistics & (1u << CRS_ST_CTAU))
v[4] = (q * (P - Q)) / (pow2 (pt->total) * (q - 1));
if (proc->statistics & (1u << 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. */
{
int i, j;
double Cij, Dij;
btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
for (i = 0; i < pt->n_rows; i++)
{
Cij = Dij = 0.;
for (j = 1; j < pt->n_cols; j++)
Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
if (i > 0)
for (j = 1; j < pt->n_cols; j++)
Dij += cum[j + (i - 1) * pt->n_cols];
for (j = 0;;)
{
double fij = pt->mat[j + i * pt->n_cols];
if (proc->statistics & (1u << CRS_ST_BTAU))
{
const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
+ v[3] * (pt->row_tot[i] * Dc
+ pt->col_tot[j] * Dr));
btau_cum += fij * temp * temp;
}
{
const double temp = Cij - Dij;
ctau_cum += fij * temp * temp;
}
if (proc->statistics & (1u << CRS_ST_GAMMA))
{
const double temp = Q * Cij - P * Dij;
gamma_cum += fij * temp * temp;
}
if (proc->statistics & (1u << CRS_ST_D))
{
d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
- (P - Q) * (pt->total - pt->row_tot[i]));
d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
- (Q - P) * (pt->total - pt->col_tot[j]));
}
if (++j == pt->n_cols)
break;
assert (j < pt->n_cols);
Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
if (i > 0)
{
Cij += cum[j - 1 + (i - 1) * pt->n_cols];
Dij -= cum[j + (i - 1) * pt->n_cols];
}
}
}
}
btau_var = ((btau_cum
- (pt->total * pow2 (pt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
/ pow2 (Dr * Dc));
if (proc->statistics & (1u << CRS_ST_BTAU))
{
ase[3] = sqrt (btau_var);
t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / pt->total)
/ (Dr * Dc)));
}
if (proc->statistics & (1u << CRS_ST_CTAU))
{
ase[4] = ((2 * q / ((q - 1) * pow2 (pt->total)))
* sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
t[4] = v[4] / ase[4];
}
if (proc->statistics & (1u << 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) / pt->total));
}
if (proc->statistics & (1u << 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) / pt->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) / pt->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) / pt->total)));
}
free (cum);
}
/* Spearman correlation, Pearson's r. */
if (proc->statistics & (1u << CRS_ST_CORR))
{
double *R = xmalloc (sizeof *R * pt->n_rows);
double *C = xmalloc (sizeof *C * pt->n_cols);
{
double y, t, c = 0., s = 0.;
int i = 0;
for (;;)
{
R[i] = s + (pt->row_tot[i] + 1.) / 2.;
y = pt->row_tot[i] - c;
t = s + y;
c = (t - s) - y;
s = t;
if (++i == pt->n_rows)
break;
assert (i < pt->n_rows);
}
}
{
double y, t, c = 0., s = 0.;
int j = 0;
for (;;)
{
C[j] = s + (pt->col_tot[j] + 1.) / 2;
y = pt->col_tot[j] - c;
t = s + y;
c = (t - s) - y;
s = t;
if (++j == pt->n_cols)
break;
assert (j < pt->n_cols);
}
}
calc_r (pt, R, C, &v[6], &t[6], &ase[6]);
free (R);
free (C);
calc_r (pt, (double *) pt->rows, (double *) pt->cols, &v[7], &t[7], &ase[7]);
}
/* Cohen's kappa. */
if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
{
double ase_under_h0;
double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
int i, j;
for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
i < pt->ns_rows; i++, j++)
{
double prod, sum;
while (pt->col_tot[j] == 0.)
j++;
prod = pt->row_tot[i] * pt->col_tot[j];
sum = pt->row_tot[i] + pt->col_tot[j];
sum_fii += pt->mat[j + i * pt->n_cols];
sum_rici += prod;
sum_fiiri_ci += pt->mat[j + i * pt->n_cols] * sum;
sum_riciri_ci += prod * sum;
}
for (sum_fijri_ci2 = 0., i = 0; i < pt->ns_rows; i++)
for (j = 0; j < pt->ns_cols; j++)
{
double sum = pt->row_tot[i] + pt->col_tot[j];
sum_fijri_ci2 += pt->mat[j + i * pt->n_cols] * sum * sum;
}
v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
ase_under_h0 = sqrt ((pow2 (pt->total) * sum_rici
+ sum_rici * sum_rici
- pt->total * sum_riciri_ci)
/ (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
ase[8] = sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
/ pow2 (pow2 (pt->total) - sum_rici))
+ ((2. * (pt->total - sum_fii)
* (2. * sum_fii * sum_rici
- pt->total * sum_fiiri_ci))
/ pow3 (pow2 (pt->total) - sum_rici))
+ (pow2 (pt->total - sum_fii)
* (pt->total * sum_fijri_ci2 - 4.
* sum_rici * sum_rici)
/ pow4 (pow2 (pt->total) - sum_rici))));
t[8] = v[8] / ase_under_h0;
}
return 1;
}
/* Calculate risk estimate. */
static int
calc_risk (struct pivot_table *pt,
double *value, double *upper, double *lower, union value *c)
{
double f11, f12, f21, f22;
double v;
{
int i;
for (i = 0; i < 3; i++)
value[i] = upper[i] = lower[i] = SYSMIS;
}
if (pt->ns_rows != 2 || pt->ns_cols != 2)
return 0;
{
int nz_cols[2];
int i, j;
for (i = j = 0; i < pt->n_cols; i++)
if (pt->col_tot[i] != 0.)
{
nz_cols[j++] = i;
if (j == 2)
break;
}
assert (j == 2);
f11 = pt->mat[nz_cols[0]];
f12 = pt->mat[nz_cols[1]];
f21 = pt->mat[nz_cols[0] + pt->n_cols];
f22 = pt->mat[nz_cols[1] + pt->n_cols];
c[0] = pt->cols[nz_cols[0]];
c[1] = pt->cols[nz_cols[1]];
}
value[0] = (f11 * f22) / (f12 * f21);
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 1;
}
/* Calculate directional measures. */
static int
calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
double t[N_DIRECTIONAL], double sig[N_DIRECTIONAL])
{
{
int i;
for (i = 0; i < N_DIRECTIONAL; i++)
v[i] = ase[i] = t[i] = sig[i] = SYSMIS;
}
/* Lambda. */
if (proc->statistics & (1u << CRS_ST_LAMBDA))
{
double *fim = xnmalloc (pt->n_rows, sizeof *fim);
int *fim_index = xnmalloc (pt->n_rows, sizeof *fim_index);
double *fmj = xnmalloc (pt->n_cols, sizeof *fmj);
int *fmj_index = xnmalloc (pt->n_cols, sizeof *fmj_index);
double sum_fim, sum_fmj;
double rm, cm;
int rm_index, cm_index;
int i, j;
/* Find maximum for each row and their sum. */
for (sum_fim = 0., i = 0; i < pt->n_rows; i++)
{
double max = pt->mat[i * pt->n_cols];
int index = 0;
for (j = 1; j < pt->n_cols; j++)
if (pt->mat[j + i * pt->n_cols] > max)
{
max = pt->mat[j + i * pt->n_cols];
index = j;
}
sum_fim += fim[i] = max;
fim_index[i] = index;
}
/* Find maximum for each column. */
for (sum_fmj = 0., j = 0; j < pt->n_cols; j++)
{
double max = pt->mat[j];
int index = 0;
for (i = 1; i < pt->n_rows; i++)
if (pt->mat[j + i * pt->n_cols] > max)
{
max = pt->mat[j + i * pt->n_cols];
index = i;
}
sum_fmj += fmj[j] = max;
fmj_index[j] = index;
}
/* Find maximum row total. */
rm = pt->row_tot[0];
rm_index = 0;
for (i = 1; i < pt->n_rows; i++)
if (pt->row_tot[i] > rm)
{
rm = pt->row_tot[i];
rm_index = i;
}
/* Find maximum column total. */
cm = pt->col_tot[0];
cm_index = 0;
for (j = 1; j < pt->n_cols; j++)
if (pt->col_tot[j] > cm)
{
cm = pt->col_tot[j];
cm_index = j;
}
v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * pt->total - rm - cm);
v[1] = (sum_fmj - rm) / (pt->total - rm);
v[2] = (sum_fim - cm) / (pt->total - cm);
/* ASE1 for Y given PT. */
{
double accum;
accum = 0.;
for (i = 0; i < pt->n_rows; i++)
if (cm_index == fim_index[i])
accum += fim[i];
ase[2] = sqrt ((pt->total - sum_fim) * (sum_fim + cm - 2. * accum)
/ pow3 (pt->total - cm));
}
/* ASE0 for Y given PT. */
{
double accum;
for (accum = 0., i = 0; i < pt->n_rows; i++)
if (cm_index != fim_index[i])
accum += (pt->mat[i * pt->n_cols + fim_index[i]]
+ pt->mat[i * pt->n_cols + cm_index]);
t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
}
/* ASE1 for PT given Y. */
{
double accum;
accum = 0.;
for (j = 0; j < pt->n_cols; j++)
if (rm_index == fmj_index[j])
accum += fmj[j];
ase[1] = sqrt ((pt->total - sum_fmj) * (sum_fmj + rm - 2. * accum)
/ pow3 (pt->total - rm));
}
/* ASE0 for PT given Y. */
{
double accum;
for (accum = 0., j = 0; j < pt->n_cols; j++)
if (rm_index != fmj_index[j])
accum += (pt->mat[j + pt->n_cols * fmj_index[j]]
+ pt->mat[j + pt->n_cols * rm_index]);
t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / pt->total) / (pt->total - rm));
}
/* Symmetric ASE0 and ASE1. */
{
double accum0;
double accum1;
for (accum0 = accum1 = 0., i = 0; i < pt->n_rows; i++)
for (j = 0; j < pt->n_cols; j++)
{
int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
int temp1 = (i == rm_index) + (j == cm_index);
accum0 += pt->mat[j + i * pt->n_cols] * pow2 (temp0 - temp1);
accum1 += (pt->mat[j + i * pt->n_cols]
* pow2 (temp0 + (v[0] - 1.) * temp1));
}
ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
t[0] = v[0] / (sqrt (accum0 - pow2 (sum_fim + sum_fmj - cm - rm) / pt->total)
/ (2. * pt->total - rm - cm));
}
for (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, sum_fij2_ci;
double sum_ri2, sum_cj2;
for (sum_fij2_ri = sum_fij2_ci = 0., i = 0; i < pt->n_rows; i++)
for (j = 0; j < pt->n_cols; j++)
{
double temp = pow2 (pt->mat[j + i * pt->n_cols]);
sum_fij2_ri += temp / pt->row_tot[i];
sum_fij2_ci += temp / pt->col_tot[j];
}
for (sum_ri2 = 0., i = 0; i < pt->n_rows; i++)
sum_ri2 += pow2 (pt->row_tot[i]);
for (sum_cj2 = 0., j = 0; j < pt->n_cols; j++)
sum_cj2 += pow2 (pt->col_tot[j]);
v[3] = (pt->total * sum_fij2_ci - sum_ri2) / (pow2 (pt->total) - sum_ri2);
v[4] = (pt->total * sum_fij2_ri - sum_cj2) / (pow2 (pt->total) - sum_cj2);
}
}
if (proc->statistics & (1u << CRS_ST_UC))
{
double UX, UY, UXY, P;
double ase1_yx, ase1_xy, ase1_sym;
int i, j;
for (UX = 0., i = 0; i < pt->n_rows; i++)
if (pt->row_tot[i] > 0.)
UX -= pt->row_tot[i] / pt->total * log (pt->row_tot[i] / pt->total);
for (UY = 0., j = 0; j < pt->n_cols; j++)
if (pt->col_tot[j] > 0.)
UY -= pt->col_tot[j] / pt->total * log (pt->col_tot[j] / pt->total);
for (UXY = P = 0., i = 0; i < pt->n_rows; i++)
for (j = 0; j < pt->n_cols; j++)
{
double entry = pt->mat[j + i * pt->n_cols];
if (entry <= 0.)
continue;
P += entry * pow2 (log (pt->col_tot[j] * pt->row_tot[i] / (pt->total * entry)));
UXY -= entry / pt->total * log (entry / pt->total);
}
for (ase1_yx = ase1_xy = ase1_sym = 0., i = 0; i < pt->n_rows; i++)
for (j = 0; j < pt->n_cols; j++)
{
double entry = pt->mat[j + i * pt->n_cols];
if (entry <= 0.)
continue;
ase1_yx += entry * pow2 (UY * log (entry / pt->row_tot[i])
+ (UX - UXY) * log (pt->col_tot[j] / pt->total));
ase1_xy += entry * pow2 (UX * log (entry / pt->col_tot[j])
+ (UY - UXY) * log (pt->row_tot[i] / pt->total));
ase1_sym += entry * pow2 ((UXY
* log (pt->row_tot[i] * pt->col_tot[j] / pow2 (pt->total)))
- (UX + UY) * log (entry / pt->total));
}
v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
ase[5] = (2. / (pt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
t[5] = SYSMIS;
v[6] = (UX + UY - UXY) / UX;
ase[6] = sqrt (ase1_xy) / (pt->total * UX * UX);
t[6] = v[6] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UX));
v[7] = (UX + UY - UXY) / UY;
ase[7] = sqrt (ase1_yx) / (pt->total * UY * UY);
t[7] = v[7] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UY));
}
/* Somers' D. */
if (proc->statistics & (1u << 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, pt, v_dummy, ase_dummy, t_dummy,
somers_d_v, somers_d_ase, somers_d_t))
{
int i;
for (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 & (1u << CRS_ST_ETA))
{
{
double sum_Xr, sum_X2r;
double SX, SXW;
int i, j;
for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
{
sum_Xr += pt->rows[i].f * pt->row_tot[i];
sum_X2r += pow2 (pt->rows[i].f) * pt->row_tot[i];
}
SX = sum_X2r - pow2 (sum_Xr) / pt->total;
for (SXW = 0., j = 0; j < pt->n_cols; j++)
{
double cum;
for (cum = 0., i = 0; i < pt->n_rows; i++)
{
SXW += pow2 (pt->rows[i].f) * pt->mat[j + i * pt->n_cols];
cum += pt->rows[i].f * pt->mat[j + i * pt->n_cols];
}
SXW -= cum * cum / pt->col_tot[j];
}
v[11] = sqrt (1. - SXW / SX);
}
{
double sum_Yc, sum_Y2c;
double SY, SYW;
int i, j;
for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
{
sum_Yc += pt->cols[i].f * pt->col_tot[i];
sum_Y2c += pow2 (pt->cols[i].f) * pt->col_tot[i];
}
SY = sum_Y2c - sum_Yc * sum_Yc / pt->total;
for (SYW = 0., i = 0; i < pt->n_rows; i++)
{
double cum;
for (cum = 0., j = 0; j < pt->n_cols; j++)
{
SYW += pow2 (pt->cols[j].f) * pt->mat[j + i * pt->n_cols];
cum += pt->cols[j].f * pt->mat[j + i * pt->n_cols];
}
SYW -= cum * cum / pt->row_tot[i];
}
v[12] = sqrt (1. - SYW / SY);
}
}
return 1;
}
/*
Local Variables:
mode: c
End:
*/