/* PSPP - a program for statistical analysis.
- Copyright (C) 2009 Free Software Foundation, Inc.
+ Copyright (C) 2009, 2010, 2011 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
#include <config.h>
-#include "covariance.h"
-#include <gl/xalloc.h>
-#include "moments.h"
+#include "math/covariance.h"
+
#include <gsl/gsl_matrix.h>
-#include <data/case.h>
-#include <data/variable.h>
-#include <libpspp/misc.h>
+
+#include "data/case.h"
+#include "data/variable.h"
+#include "libpspp/assertion.h"
+#include "libpspp/misc.h"
+#include "math/categoricals.h"
+#include "math/interaction.h"
+#include "math/moments.h"
+
+#include "gl/xalloc.h"
#define n_MOMENTS (MOMENT_VARIANCE + 1)
+/* Create a new matrix of NEW_SIZE x NEW_SIZE and copy the elements of
+ matrix IN into it. IN must be a square matrix, and in normal usage
+ it will be smaller than NEW_SIZE.
+ IN is destroyed by this function. The return value must be destroyed
+ when no longer required.
+*/
+static gsl_matrix *
+resize_matrix (gsl_matrix *in, size_t new_size)
+{
+ size_t i, j;
+
+ gsl_matrix *out = NULL;
+
+ assert (in->size1 == in->size2);
+
+ if (new_size <= in->size1)
+ return in;
+
+ out = gsl_matrix_calloc (new_size, new_size);
+
+ for (i = 0; i < in->size1; ++i)
+ {
+ for (j = 0; j < in->size2; ++j)
+ {
+ double x = gsl_matrix_get (in, i, j);
+
+ gsl_matrix_set (out, i, j, x);
+ }
+ }
+
+ gsl_matrix_free (in);
+
+ return out;
+}
+
struct covariance
{
- /* The variables for which the covariance matrix is to be calculated */
+ /* True if the covariances are centerered. (ie Real covariances) */
+ bool centered;
+
+ /* The variables for which the covariance matrix is to be calculated. */
size_t n_vars;
- const struct variable **vars;
-
+ const struct variable *const *vars;
+
+ /* Categorical variables. */
+ struct categoricals *categoricals;
+
+ /* Array containing number of categories per categorical variable. */
+ size_t *n_categories;
+
+ /* Dimension of the covariance matrix. */
+ size_t dim;
+
/* The weight variable (or NULL if none) */
const struct variable *wv;
Only the top triangle is included, and no diagonals */
double *cm;
int n_cm;
+
+ /* 1 for single pass algorithm;
+ 2 for double pass algorithm
+ */
+ short passes;
+
+ /*
+ 0 : No pass has been made
+ 1 : First pass has been started
+ 2 : Second pass has been
+
+ IE: How many passes have been (partially) made. */
+ short state;
+
+ /* Flags indicating that the first case has been seen */
+ bool pass_one_first_case_seen;
+ bool pass_two_first_case_seen;
+
+ gsl_matrix *unnormalised;
};
be identical. If missing values are involved, then element (i,j)
is the moment of the i th variable, when paired with the j th variable.
*/
-const gsl_matrix *
+gsl_matrix *
covariance_moments (const struct covariance *cov, int m)
{
return cov->moments[m];
-/* Create a covariance struct */
+/* Create a covariance struct.
+ */
struct covariance *
-covariance_create (size_t n_vars, const struct variable **vars,
- const struct variable *weight, enum mv_class exclude)
+covariance_1pass_create (size_t n_vars, const struct variable *const *vars,
+ const struct variable *weight, enum mv_class exclude,
+ bool centered)
{
size_t i;
- struct covariance *cov = xmalloc (sizeof *cov);
- cov->vars = xmalloc (sizeof *cov->vars * n_vars);
+ struct covariance *cov = XZALLOC (struct covariance);
+
+ cov->centered = centered;
+ cov->passes = 1;
+ cov->state = 0;
+ cov->pass_one_first_case_seen = cov->pass_two_first_case_seen = false;
+
+ cov->vars = vars;
cov->wv = weight;
cov->n_vars = n_vars;
+ cov->dim = n_vars;
+
+ cov->moments = xmalloc (sizeof *cov->moments * n_MOMENTS);
+
+ for (i = 0; i < n_MOMENTS; ++i)
+ cov->moments[i] = gsl_matrix_calloc (n_vars, n_vars);
+
+ cov->exclude = exclude;
+
+ cov->n_cm = (n_vars * (n_vars - 1)) / 2;
+
+
+ cov->cm = xcalloc (cov->n_cm, sizeof *cov->cm);
+ cov->categoricals = NULL;
+
+ return cov;
+}
+
+/*
+ Create a covariance struct for a two-pass algorithm. If categorical
+ variables are involed, the dimension cannot be know until after the
+ first data pass, so the actual covariances will not be allocated
+ until then.
+ */
+struct covariance *
+covariance_2pass_create (size_t n_vars, const struct variable *const *vars,
+ struct categoricals *cats,
+ const struct variable *wv, enum mv_class exclude,
+ bool centered)
+{
+ size_t i;
+ struct covariance *cov = xmalloc (sizeof *cov);
- for (i = 0; i < n_vars; ++i)
- cov->vars[i] = vars[i];
+ cov->centered = centered;
+ cov->passes = 2;
+ cov->state = 0;
+ cov->pass_one_first_case_seen = cov->pass_two_first_case_seen = false;
+
+ cov->vars = vars;
+
+ cov->wv = wv;
+ cov->n_vars = n_vars;
+ cov->dim = n_vars;
cov->moments = xmalloc (sizeof *cov->moments * n_MOMENTS);
-
+
for (i = 0; i < n_MOMENTS; ++i)
cov->moments[i] = gsl_matrix_calloc (n_vars, n_vars);
cov->exclude = exclude;
- cov->n_cm = (n_vars * (n_vars - 1) ) / 2;
+ cov->n_cm = -1;
+ cov->cm = NULL;
- cov->cm = xcalloc (sizeof *cov->cm, cov->n_cm);
+ cov->categoricals = cats;
+ cov->unnormalised = NULL;
return cov;
}
-/* Return an integer, which can be used to index
+/* Return an integer, which can be used to index
into COV->cm, to obtain the I, J th element
of the covariance matrix. If COV->cm does not
contain that element, then a negative value
cm_idx (const struct covariance *cov, int i, int j)
{
int as;
- const int n2j = cov->n_vars - 2 - j;
- const int nj = cov->n_vars - 2 ;
-
+ const int n2j = cov->dim - 2 - j;
+ const int nj = cov->dim - 2 ;
+
assert (i >= 0);
- assert (j < cov->n_vars);
+ assert (j < cov->dim);
- if ( i == 0)
+ if (i == 0)
return -1;
- if (j >= cov->n_vars - 1)
+ if (j >= cov->dim - 1)
return -1;
- if ( i <= j)
+ if (i <= j)
return -1 ;
as = nj * (nj + 1) ;
- as -= n2j * (n2j + 1) ;
+ as -= n2j * (n2j + 1) ;
as /= 2;
return i - 1 + as;
}
+/*
+ Returns true iff the variable corresponding to the Ith element of the covariance matrix
+ has a missing value for case C
+*/
+static bool
+is_missing (const struct covariance *cov, int i, const struct ccase *c)
+{
+ const struct variable *var = i < cov->n_vars ?
+ cov->vars[i] :
+ categoricals_get_interaction_by_subscript (cov->categoricals, i - cov->n_vars)->vars[0];
+
+ const union value *val = case_data (c, var);
+
+ return (var_is_value_missing (var, val) & cov->exclude) != 0;
+}
+
+
+static double
+get_val (const struct covariance *cov, int i, const struct ccase *c)
+{
+ if (i < cov->n_vars)
+ {
+ const struct variable *var = cov->vars[i];
+
+ const union value *val = case_data (c, var);
+
+ return val->f;
+ }
+
+ return categoricals_get_effects_code_for_case (cov->categoricals, i - cov->n_vars, c);
+}
+
+#if 0
+void
+dump_matrix (const gsl_matrix *m)
+{
+ size_t i, j;
+
+ for (i = 0 ; i < m->size1; ++i)
+ {
+ for (j = 0 ; j < m->size2; ++j)
+ printf ("%02f ", gsl_matrix_get (m, i, j));
+ printf ("\n");
+ }
+}
+#endif
+
+/* Call this function for every case in the data set */
+void
+covariance_accumulate_pass1 (struct covariance *cov, const struct ccase *c)
+{
+ size_t i, j, m;
+ const double weight = cov->wv ? case_num (c, cov->wv) : 1.0;
+
+ assert (cov->passes == 2);
+ if (!cov->pass_one_first_case_seen)
+ {
+ assert (cov->state == 0);
+ cov->state = 1;
+ }
+
+ if (cov->categoricals)
+ categoricals_update (cov->categoricals, c);
+
+ for (i = 0 ; i < cov->dim; ++i)
+ {
+ double v1 = get_val (cov, i, c);
+
+ if (is_missing (cov, i, c))
+ continue;
+
+ for (j = 0 ; j < cov->dim; ++j)
+ {
+ double pwr = 1.0;
+
+ if (is_missing (cov, j, c))
+ continue;
+
+ for (m = 0 ; m <= MOMENT_MEAN; ++m)
+ {
+ double *x = gsl_matrix_ptr (cov->moments[m], i, j);
+
+ *x += pwr * weight;
+ pwr *= v1;
+ }
+ }
+ }
+
+ cov->pass_one_first_case_seen = true;
+}
+
+
/* Call this function for every case in the data set */
void
+covariance_accumulate_pass2 (struct covariance *cov, const struct ccase *c)
+{
+ size_t i, j;
+ const double weight = cov->wv ? case_num (c, cov->wv) : 1.0;
+
+ assert (cov->passes == 2);
+ assert (cov->state >= 1);
+
+ if (! cov->pass_two_first_case_seen)
+ {
+ size_t m;
+ assert (cov->state == 1);
+ cov->state = 2;
+
+ if (cov->categoricals)
+ categoricals_done (cov->categoricals);
+
+ cov->dim = cov->n_vars;
+
+ if (cov->categoricals)
+ cov->dim += categoricals_df_total (cov->categoricals);
+
+ cov->n_cm = (cov->dim * (cov->dim - 1)) / 2;
+ cov->cm = xcalloc (cov->n_cm, sizeof *cov->cm);
+
+ /* Grow the moment matrices so that they're large enough to accommodate the
+ categorical elements */
+ for (i = 0; i < n_MOMENTS; ++i)
+ {
+ cov->moments[i] = resize_matrix (cov->moments[i], cov->dim);
+ }
+
+ /* Populate the moments matrices with the categorical value elements */
+ for (i = cov->n_vars; i < cov->dim; ++i)
+ {
+ for (j = 0 ; j < cov->dim ; ++j) /* FIXME: This is WRONG !!! */
+ {
+ double w = categoricals_get_weight_by_subscript (cov->categoricals, i - cov->n_vars);
+
+ gsl_matrix_set (cov->moments[MOMENT_NONE], i, j, w);
+
+ w = categoricals_get_sum_by_subscript (cov->categoricals, i - cov->n_vars);
+
+ gsl_matrix_set (cov->moments[MOMENT_MEAN], i, j, w);
+ }
+ }
+
+ /* FIXME: This is WRONG!! It must be fixed to properly handle missing values. For
+ now it assumes there are none */
+ for (m = 0 ; m < n_MOMENTS; ++m)
+ {
+ for (i = 0 ; i < cov->dim ; ++i)
+ {
+ double x = gsl_matrix_get (cov->moments[m], i, cov->n_vars -1);
+ for (j = cov->n_vars; j < cov->dim; ++j)
+ {
+ gsl_matrix_set (cov->moments[m], i, j, x);
+ }
+ }
+ }
+
+ /* Divide the means by the number of samples */
+ for (i = 0; i < cov->dim; ++i)
+ {
+ for (j = 0; j < cov->dim; ++j)
+ {
+ double *x = gsl_matrix_ptr (cov->moments[MOMENT_MEAN], i, j);
+ *x /= gsl_matrix_get (cov->moments[MOMENT_NONE], i, j);
+ }
+ }
+ }
+
+ for (i = 0 ; i < cov->dim; ++i)
+ {
+ double v1 = get_val (cov, i, c);
+
+ if (is_missing (cov, i, c))
+ continue;
+
+ for (j = 0 ; j < cov->dim; ++j)
+ {
+ int idx;
+ double ss ;
+ double v2 = get_val (cov, j, c);
+
+ const double s = pow2 (v1 - gsl_matrix_get (cov->moments[MOMENT_MEAN], i, j)) * weight;
+
+ if (is_missing (cov, j, c))
+ continue;
+
+ {
+ double *x = gsl_matrix_ptr (cov->moments[MOMENT_VARIANCE], i, j);
+ *x += s;
+ }
+
+ ss =
+ (v1 - gsl_matrix_get (cov->moments[MOMENT_MEAN], i, j))
+ *
+ (v2 - gsl_matrix_get (cov->moments[MOMENT_MEAN], i, j))
+ * weight
+ ;
+
+ idx = cm_idx (cov, i, j);
+ if (idx >= 0)
+ {
+ cov->cm [idx] += ss;
+ }
+ }
+ }
+
+ cov->pass_two_first_case_seen = true;
+}
+
+
+/* Call this function for every case in the data set.
+ After all cases have been passed, call covariance_calculate
+ */
+void
covariance_accumulate (struct covariance *cov, const struct ccase *c)
{
size_t i, j, m;
- const double weight = cov->wv ? case_data (c, cov->wv)->f : 1.0;
+ const double weight = cov->wv ? case_num (c, cov->wv) : 1.0;
+
+ assert (cov->passes == 1);
- for (i = 0 ; i < cov->n_vars; ++i)
+ if (!cov->pass_one_first_case_seen)
+ {
+ assert (cov->state == 0);
+ cov->state = 1;
+ }
+
+ for (i = 0 ; i < cov->dim; ++i)
{
const union value *val1 = case_data (c, cov->vars[i]);
- if ( var_is_value_missing (cov->vars[i], val1, cov->exclude))
+ if (is_missing (cov, i, c))
continue;
- for (j = 0 ; j < cov->n_vars; ++j)
+ for (j = 0 ; j < cov->dim; ++j)
{
double pwr = 1.0;
int idx;
const union value *val2 = case_data (c, cov->vars[j]);
- if ( var_is_value_missing (cov->vars[j], val2, cov->exclude))
+ if (is_missing (cov, j, c))
continue;
idx = cm_idx (cov, i, j);
if (idx >= 0)
{
- cov->cm [idx] += val1->f * val2->f;
+ cov->cm [idx] += val1->f * val2->f * weight;
}
for (m = 0 ; m < n_MOMENTS; ++m)
}
}
}
+
+ cov->pass_one_first_case_seen = true;
}
-/*
+/*
Allocate and return a gsl_matrix containing the covariances of the
data.
*/
cm_to_gsl (struct covariance *cov)
{
int i, j;
- gsl_matrix *m = gsl_matrix_calloc (cov->n_vars, cov->n_vars);
+ gsl_matrix *m = gsl_matrix_calloc (cov->dim, cov->dim);
/* Copy the non-diagonal elements from cov->cm */
- for ( j = 0 ; j < cov->n_vars - 1; ++j)
+ for (j = 0 ; j < cov->dim - 1; ++j)
{
- for (i = j+1 ; i < cov->n_vars; ++i)
+ for (i = j+1 ; i < cov->dim; ++i)
{
double x = cov->cm [cm_idx (cov, i, j)];
gsl_matrix_set (m, i, j, x);
}
/* Copy the diagonal elements from cov->moments[2] */
- for (j = 0 ; j < cov->n_vars ; ++j)
+ for (j = 0 ; j < cov->dim ; ++j)
{
double sigma = gsl_matrix_get (cov->moments[2], j, j);
gsl_matrix_set (m, j, j, sigma);
}
+static gsl_matrix *
+covariance_calculate_double_pass (struct covariance *cov)
+{
+ size_t i, j;
+ for (i = 0 ; i < cov->dim; ++i)
+ {
+ for (j = 0 ; j < cov->dim; ++j)
+ {
+ int idx;
+ double *x = gsl_matrix_ptr (cov->moments[MOMENT_VARIANCE], i, j);
+ *x /= gsl_matrix_get (cov->moments[MOMENT_NONE], i, j);
-/*
- Return a pointer to gsl_matrix containing the pairwise covariances.
- The matrix remains owned by the COV object, and must not be freed.
- Call this function only after all data have been accumulated.
-*/
-const gsl_matrix *
-covariance_calculate (struct covariance *cov)
+ idx = cm_idx (cov, i, j);
+ if (idx >= 0)
+ {
+ x = &cov->cm [idx];
+ *x /= gsl_matrix_get (cov->moments[MOMENT_NONE], i, j);
+ }
+ }
+ }
+
+ return cm_to_gsl (cov);
+}
+
+static gsl_matrix *
+covariance_calculate_single_pass (struct covariance *cov)
{
size_t i, j;
size_t m;
for (m = 0; m < n_MOMENTS; ++m)
{
/* Divide the moments by the number of samples */
- if ( m > 0)
+ if (m > 0)
{
- for (i = 0 ; i < cov->n_vars; ++i)
+ for (i = 0 ; i < cov->dim; ++i)
{
- for (j = 0 ; j < cov->n_vars; ++j)
+ for (j = 0 ; j < cov->dim; ++j)
{
double *x = gsl_matrix_ptr (cov->moments[m], i, j);
*x /= gsl_matrix_get (cov->moments[0], i, j);
- if ( m == MOMENT_VARIANCE)
+ if (m == MOMENT_VARIANCE)
*x -= pow2 (gsl_matrix_get (cov->moments[1], i, j));
}
}
}
}
- /* Centre the moments */
- for ( j = 0 ; j < cov->n_vars - 1; ++j)
+ if (cov->centered)
{
- for (i = j + 1 ; i < cov->n_vars; ++i)
+ /* Centre the moments */
+ for (j = 0 ; j < cov->dim - 1; ++j)
{
- double *x = &cov->cm [cm_idx (cov, i, j)];
-
- *x /= gsl_matrix_get (cov->moments[0], i, j);
+ for (i = j + 1 ; i < cov->dim; ++i)
+ {
+ double *x = &cov->cm [cm_idx (cov, i, j)];
- *x -=
- gsl_matrix_get (cov->moments[MOMENT_MEAN], i, j)
- *
- gsl_matrix_get (cov->moments[MOMENT_MEAN], j, i);
+ *x /= gsl_matrix_get (cov->moments[0], i, j);
+
+ *x -=
+ gsl_matrix_get (cov->moments[MOMENT_MEAN], i, j)
+ *
+ gsl_matrix_get (cov->moments[MOMENT_MEAN], j, i);
+ }
+ }
+ }
+
+ return cm_to_gsl (cov);
+}
+
+
+/* Return a pointer to gsl_matrix containing the pairwise covariances. The
+ caller owns the returned matrix and must free it when it is no longer
+ needed.
+
+ Call this function only after all data have been accumulated. */
+gsl_matrix *
+covariance_calculate (struct covariance *cov)
+{
+ if (cov->state <= 0)
+ return NULL;
+
+ switch (cov->passes)
+ {
+ case 1:
+ return covariance_calculate_single_pass (cov);
+ break;
+ case 2:
+ return covariance_calculate_double_pass (cov);
+ break;
+ default:
+ NOT_REACHED ();
+ }
+}
+
+/*
+ Covariance computed without dividing by the sample size.
+ */
+static gsl_matrix *
+covariance_calculate_double_pass_unnormalized (struct covariance *cov)
+{
+ return cm_to_gsl (cov);
+}
+
+static gsl_matrix *
+covariance_calculate_single_pass_unnormalized (struct covariance *cov)
+{
+ size_t i, j;
+
+ if (cov->centered)
+ {
+ for (i = 0 ; i < cov->dim; ++i)
+ {
+ for (j = 0 ; j < cov->dim; ++j)
+ {
+ double *x = gsl_matrix_ptr (cov->moments[MOMENT_VARIANCE], i, j);
+ *x -= pow2 (gsl_matrix_get (cov->moments[MOMENT_MEAN], i, j))
+ / gsl_matrix_get (cov->moments[MOMENT_NONE], i, j);
+ }
+ }
+
+ for (j = 0 ; j < cov->dim - 1; ++j)
+ {
+ for (i = j + 1 ; i < cov->dim; ++i)
+ {
+ double *x = &cov->cm [cm_idx (cov, i, j)];
+
+ *x -=
+ gsl_matrix_get (cov->moments[MOMENT_MEAN], i, j)
+ *
+ gsl_matrix_get (cov->moments[MOMENT_MEAN], j, i)
+ / gsl_matrix_get (cov->moments[MOMENT_NONE], i, j);
+ }
}
}
}
+/* Return a pointer to gsl_matrix containing the pairwise covariances. The
+ returned matrix is owned by the structure, and must not be freed.
+
+ Call this function only after all data have been accumulated. */
+const gsl_matrix *
+covariance_calculate_unnormalized (struct covariance *cov)
+{
+ if (cov->state <= 0)
+ return NULL;
+
+ if (cov->unnormalised != NULL)
+ return cov->unnormalised;
+
+ switch (cov->passes)
+ {
+ case 1:
+ cov->unnormalised = covariance_calculate_single_pass_unnormalized (cov);
+ break;
+ case 2:
+ cov->unnormalised = covariance_calculate_double_pass_unnormalized (cov);
+ break;
+ default:
+ NOT_REACHED ();
+ }
+
+ return cov->unnormalised;
+}
+
+/* Function to access the categoricals used by COV
+ The return value is owned by the COV
+*/
+const struct categoricals *
+covariance_get_categoricals (const struct covariance *cov)
+{
+ return cov->categoricals;
+}
+
+
/* Destroy the COV object */
void
covariance_destroy (struct covariance *cov)
{
size_t i;
- free (cov->vars);
+
+ categoricals_destroy (cov->categoricals);
for (i = 0; i < n_MOMENTS; ++i)
gsl_matrix_free (cov->moments[i]);
+ gsl_matrix_free (cov->unnormalised);
free (cov->moments);
free (cov->cm);
free (cov);
}
+
+size_t
+covariance_dim (const struct covariance * cov)
+{
+ return (cov->dim);
+}
+
+\f
+
+/*
+ Routines to assist debugging.
+ The following are not thoroughly tested and in certain respects
+ unreliable. They should only be
+ used for aids to development. Not as user accessible code.
+*/
+
+#include "libpspp/str.h"
+#include "output/pivot-table.h"
+#include "data/format.h"
+
+
+/* Create a table which can be populated with the encodings for
+ the covariance matrix COV */
+struct pivot_table *
+covariance_dump_enc_header (const struct covariance *cov)
+{
+ struct pivot_table *table = pivot_table_create ("Covariance Encoding");
+
+ struct pivot_dimension *factors = pivot_dimension_create (
+ table, PIVOT_AXIS_COLUMN, "Factor");
+ for (size_t i = 0 ; i < cov->n_vars; ++i)
+ pivot_category_create_leaf (factors->root,
+ pivot_value_new_variable (cov->vars[i]));
+ for (size_t i = 0, n = 0; i < cov->dim - cov->n_vars; n++)
+ {
+ const struct interaction *iact =
+ categoricals_get_interaction_by_subscript (cov->categoricals, i);
+
+ struct string str = DS_EMPTY_INITIALIZER;
+ interaction_to_string (iact, &str);
+ struct pivot_category *group = pivot_category_create_group__ (
+ factors->root,
+ pivot_value_new_user_text_nocopy (ds_steal_cstr (&str)));
+
+ int df = categoricals_df (cov->categoricals, n);
+ for (int j = 0; j < df; j++)
+ pivot_category_create_leaf_rc (group, pivot_value_new_integer (j),
+ PIVOT_RC_INTEGER);
+
+ i += df;
+ }
+
+ struct pivot_dimension *matrix = pivot_dimension_create (
+ table, PIVOT_AXIS_ROW, "Matrix", "Matrix");
+ matrix->hide_all_labels = true;
+
+ return table;
+}
+
+
+/*
+ Append table T, which should have been returned by covariance_dump_enc_header
+ with an entry corresponding to case C for the covariance matrix COV
+ */
+void
+covariance_dump_enc (const struct covariance *cov, const struct ccase *c,
+ struct pivot_table *table)
+{
+ int row = pivot_category_create_leaf (
+ table->dimensions[1]->root,
+ pivot_value_new_integer (table->dimensions[1]->n_leaves));
+
+ for (int i = 0 ; i < cov->dim; ++i)
+ pivot_table_put2 (
+ table, i, row, pivot_value_new_number (get_val (cov, i, c)));
+}
projects / pspp / blobdiff