1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 2009, 2010, 2011 Free Software Foundation, Inc.
4 This program is free software: you can redistribute it and/or modify
5 it under the terms of the GNU General Public License as published by
6 the Free Software Foundation, either version 3 of the License, or
7 (at your option) any later version.
9 This program is distributed in the hope that it will be useful,
10 but WITHOUT ANY WARRANTY; without even the implied warranty of
11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12 GNU General Public License for more details.
14 You should have received a copy of the GNU General Public License
15 along with this program. If not, see <http://www.gnu.org/licenses/>. */
19 #include "math/covariance.h"
21 #include <gsl/gsl_matrix.h>
23 #include "data/case.h"
24 #include "data/variable.h"
25 #include "libpspp/assertion.h"
26 #include "libpspp/misc.h"
27 #include "math/categoricals.h"
28 #include "math/interaction.h"
29 #include "math/moments.h"
31 #include "gl/xalloc.h"
33 #define n_MOMENTS (MOMENT_VARIANCE + 1)
36 /* Create a new matrix of NEW_SIZE x NEW_SIZE and copy the elements of
37 matrix IN into it. IN must be a square matrix, and in normal usage
38 it will be smaller than NEW_SIZE.
39 IN is destroyed by this function. The return value must be destroyed
40 when no longer required.
43 resize_matrix (gsl_matrix *in, size_t new_size)
47 gsl_matrix *out = NULL;
49 assert (in->size1 == in->size2);
51 if (new_size <= in->size1)
54 out = gsl_matrix_calloc (new_size, new_size);
56 for (i = 0; i < in->size1; ++i)
58 for (j = 0; j < in->size2; ++j)
60 double x = gsl_matrix_get (in, i, j);
62 gsl_matrix_set (out, i, j, x);
73 /* The variables for which the covariance matrix is to be calculated. */
75 const struct variable *const *vars;
77 /* Categorical variables. */
78 struct categoricals *categoricals;
80 /* Array containing number of categories per categorical variable. */
83 /* Dimension of the covariance matrix. */
86 /* The weight variable (or NULL if none) */
87 const struct variable *wv;
89 /* A set of matrices containing the 0th, 1st and 2nd moments */
92 /* The class of missing values to exclude */
93 enum mv_class exclude;
95 /* An array of doubles representing the covariance matrix.
96 Only the top triangle is included, and no diagonals */
100 /* 1 for single pass algorithm;
101 2 for double pass algorithm
106 0 : No pass has been made
107 1 : First pass has been started
108 2 : Second pass has been
110 IE: How many passes have been (partially) made. */
113 /* Flags indicating that the first case has been seen */
114 bool pass_one_first_case_seen;
115 bool pass_two_first_case_seen;
120 /* Return a matrix containing the M th moments.
121 The matrix is of size NxN where N is the number of variables.
122 Each row represents the moments of a variable.
123 In the absence of missing values, the columns of this matrix will
124 be identical. If missing values are involved, then element (i,j)
125 is the moment of the i th variable, when paired with the j th variable.
128 covariance_moments (const struct covariance *cov, int m)
130 return cov->moments[m];
135 /* Create a covariance struct.
138 covariance_1pass_create (size_t n_vars, const struct variable *const *vars,
139 const struct variable *weight, enum mv_class exclude)
142 struct covariance *cov = xzalloc (sizeof *cov);
146 cov->pass_one_first_case_seen = cov->pass_two_first_case_seen = false;
151 cov->n_vars = n_vars;
154 cov->moments = xmalloc (sizeof *cov->moments * n_MOMENTS);
156 for (i = 0; i < n_MOMENTS; ++i)
157 cov->moments[i] = gsl_matrix_calloc (n_vars, n_vars);
159 cov->exclude = exclude;
161 cov->n_cm = (n_vars * (n_vars - 1) ) / 2;
164 cov->cm = xcalloc (cov->n_cm, sizeof *cov->cm);
165 cov->categoricals = NULL;
171 Create a covariance struct for a two-pass algorithm. If categorical
172 variables are involed, the dimension cannot be know until after the
173 first data pass, so the actual covariances will not be allocated
177 covariance_2pass_create (size_t n_vars, const struct variable *const *vars,
178 struct categoricals *cats,
179 const struct variable *wv, enum mv_class exclude)
182 struct covariance *cov = xmalloc (sizeof *cov);
186 cov->pass_one_first_case_seen = cov->pass_two_first_case_seen = false;
191 cov->n_vars = n_vars;
194 cov->moments = xmalloc (sizeof *cov->moments * n_MOMENTS);
196 for (i = 0; i < n_MOMENTS; ++i)
197 cov->moments[i] = gsl_matrix_calloc (n_vars, n_vars);
199 cov->exclude = exclude;
204 cov->categoricals = cats;
209 /* Return an integer, which can be used to index
210 into COV->cm, to obtain the I, J th element
211 of the covariance matrix. If COV->cm does not
212 contain that element, then a negative value
216 cm_idx (const struct covariance *cov, int i, int j)
219 const int n2j = cov->dim - 2 - j;
220 const int nj = cov->dim - 2 ;
223 assert (j < cov->dim);
228 if (j >= cov->dim - 1)
235 as -= n2j * (n2j + 1) ;
243 Returns true iff the variable corresponding to the Ith element of the covariance matrix
244 has a missing value for case C
247 is_missing (const struct covariance *cov, int i, const struct ccase *c)
249 const struct variable *var = i < cov->n_vars ?
251 categoricals_get_interaction_by_subscript (cov->categoricals, i - cov->n_vars)->vars[0];
253 const union value *val = case_data (c, var);
255 return var_is_value_missing (var, val, cov->exclude);
260 get_val (const struct covariance *cov, int i, const struct ccase *c)
262 if ( i < cov->n_vars)
264 const struct variable *var = cov->vars[i];
266 const union value *val = case_data (c, var);
271 return categoricals_get_binary_by_subscript (cov->categoricals, i - cov->n_vars, c);
276 dump_matrix (const gsl_matrix *m)
280 for (i = 0 ; i < m->size1; ++i)
282 for (j = 0 ; j < m->size2; ++j)
283 printf ("%02f ", gsl_matrix_get (m, i, j));
289 /* Call this function for every case in the data set */
291 covariance_accumulate_pass1 (struct covariance *cov, const struct ccase *c)
294 const double weight = cov->wv ? case_data (c, cov->wv)->f : 1.0;
296 assert (cov->passes == 2);
297 if (!cov->pass_one_first_case_seen)
299 assert (cov->state == 0);
303 if (cov->categoricals)
304 categoricals_update (cov->categoricals, c);
306 for (i = 0 ; i < cov->dim; ++i)
308 double v1 = get_val (cov, i, c);
310 if ( is_missing (cov, i, c))
313 for (j = 0 ; j < cov->dim; ++j)
317 if ( is_missing (cov, j, c))
320 for (m = 0 ; m <= MOMENT_MEAN; ++m)
322 double *x = gsl_matrix_ptr (cov->moments[m], i, j);
330 cov->pass_one_first_case_seen = true;
334 /* Call this function for every case in the data set */
336 covariance_accumulate_pass2 (struct covariance *cov, const struct ccase *c)
339 const double weight = cov->wv ? case_data (c, cov->wv)->f : 1.0;
341 assert (cov->passes == 2);
342 assert (cov->state >= 1);
344 if (! cov->pass_two_first_case_seen)
347 assert (cov->state == 1);
350 if (cov->categoricals)
351 categoricals_done (cov->categoricals);
353 cov->dim = cov->n_vars;
355 if (cov->categoricals)
356 cov->dim += categoricals_df_total (cov->categoricals);
358 cov->n_cm = (cov->dim * (cov->dim - 1) ) / 2;
359 cov->cm = xcalloc (cov->n_cm, sizeof *cov->cm);
361 /* Grow the moment matrices so that they're large enough to accommodate the
362 categorical elements */
363 for (i = 0; i < n_MOMENTS; ++i)
365 cov->moments[i] = resize_matrix (cov->moments[i], cov->dim);
368 /* Populate the moments matrices with the categorical value elements */
369 for (i = cov->n_vars; i < cov->dim; ++i)
371 for (j = 0 ; j < cov->dim ; ++j) /* FIXME: This is WRONG !!! */
373 double w = categoricals_get_weight_by_subscript (cov->categoricals, i - cov->n_vars);
375 gsl_matrix_set (cov->moments[MOMENT_NONE], i, j, w);
377 w = categoricals_get_sum_by_subscript (cov->categoricals, i - cov->n_vars);
379 gsl_matrix_set (cov->moments[MOMENT_MEAN], i, j, w);
383 /* FIXME: This is WRONG!! It must be fixed to properly handle missing values. For
384 now it assumes there are none */
385 for (m = 0 ; m < n_MOMENTS; ++m)
387 for (i = 0 ; i < cov->dim ; ++i)
389 double x = gsl_matrix_get (cov->moments[m], i, cov->n_vars -1);
390 for (j = cov->n_vars; j < cov->dim; ++j)
392 gsl_matrix_set (cov->moments[m], i, j, x);
397 /* Divide the means by the number of samples */
398 for (i = 0; i < cov->dim; ++i)
400 for (j = 0; j < cov->dim; ++j)
402 double *x = gsl_matrix_ptr (cov->moments[MOMENT_MEAN], i, j);
403 *x /= gsl_matrix_get (cov->moments[MOMENT_NONE], i, j);
408 for (i = 0 ; i < cov->dim; ++i)
410 double v1 = get_val (cov, i, c);
412 if ( is_missing (cov, i, c))
415 for (j = 0 ; j < cov->dim; ++j)
419 double v2 = get_val (cov, j, c);
421 const double s = pow2 (v1 - gsl_matrix_get (cov->moments[MOMENT_MEAN], i, j)) * weight;
423 if ( is_missing (cov, j, c))
427 double *x = gsl_matrix_ptr (cov->moments[MOMENT_VARIANCE], i, j);
432 (v1 - gsl_matrix_get (cov->moments[MOMENT_MEAN], i, j))
434 (v2 - gsl_matrix_get (cov->moments[MOMENT_MEAN], i, j))
438 idx = cm_idx (cov, i, j);
446 cov->pass_two_first_case_seen = true;
450 /* Call this function for every case in the data set.
451 After all cases have been passed, call covariance_calculate
454 covariance_accumulate (struct covariance *cov, const struct ccase *c)
457 const double weight = cov->wv ? case_data (c, cov->wv)->f : 1.0;
459 assert (cov->passes == 1);
461 if ( !cov->pass_one_first_case_seen)
463 assert ( cov->state == 0);
467 for (i = 0 ; i < cov->dim; ++i)
469 const union value *val1 = case_data (c, cov->vars[i]);
471 if ( is_missing (cov, i, c))
474 for (j = 0 ; j < cov->dim; ++j)
478 const union value *val2 = case_data (c, cov->vars[j]);
480 if ( is_missing (cov, j, c))
483 idx = cm_idx (cov, i, j);
486 cov->cm [idx] += val1->f * val2->f * weight;
489 for (m = 0 ; m < n_MOMENTS; ++m)
491 double *x = gsl_matrix_ptr (cov->moments[m], i, j);
499 cov->pass_one_first_case_seen = true;
504 Allocate and return a gsl_matrix containing the covariances of the
508 cm_to_gsl (struct covariance *cov)
511 gsl_matrix *m = gsl_matrix_calloc (cov->dim, cov->dim);
513 /* Copy the non-diagonal elements from cov->cm */
514 for ( j = 0 ; j < cov->dim - 1; ++j)
516 for (i = j+1 ; i < cov->dim; ++i)
518 double x = cov->cm [cm_idx (cov, i, j)];
519 gsl_matrix_set (m, i, j, x);
520 gsl_matrix_set (m, j, i, x);
524 /* Copy the diagonal elements from cov->moments[2] */
525 for (j = 0 ; j < cov->dim ; ++j)
527 double sigma = gsl_matrix_get (cov->moments[2], j, j);
528 gsl_matrix_set (m, j, j, sigma);
536 covariance_calculate_double_pass (struct covariance *cov)
539 for (i = 0 ; i < cov->dim; ++i)
541 for (j = 0 ; j < cov->dim; ++j)
544 double *x = gsl_matrix_ptr (cov->moments[MOMENT_VARIANCE], i, j);
545 *x /= gsl_matrix_get (cov->moments[MOMENT_NONE], i, j);
547 idx = cm_idx (cov, i, j);
551 *x /= gsl_matrix_get (cov->moments[MOMENT_NONE], i, j);
556 return cm_to_gsl (cov);
560 covariance_calculate_single_pass (struct covariance *cov)
565 for (m = 0; m < n_MOMENTS; ++m)
567 /* Divide the moments by the number of samples */
570 for (i = 0 ; i < cov->dim; ++i)
572 for (j = 0 ; j < cov->dim; ++j)
574 double *x = gsl_matrix_ptr (cov->moments[m], i, j);
575 *x /= gsl_matrix_get (cov->moments[0], i, j);
577 if ( m == MOMENT_VARIANCE)
578 *x -= pow2 (gsl_matrix_get (cov->moments[1], i, j));
584 /* Centre the moments */
585 for ( j = 0 ; j < cov->dim - 1; ++j)
587 for (i = j + 1 ; i < cov->dim; ++i)
589 double *x = &cov->cm [cm_idx (cov, i, j)];
591 *x /= gsl_matrix_get (cov->moments[0], i, j);
594 gsl_matrix_get (cov->moments[MOMENT_MEAN], i, j)
596 gsl_matrix_get (cov->moments[MOMENT_MEAN], j, i);
600 return cm_to_gsl (cov);
604 /* Return a pointer to gsl_matrix containing the pairwise covariances. The
605 caller owns the returned matrix and must free it when it is no longer
608 Call this function only after all data have been accumulated. */
610 covariance_calculate (struct covariance *cov)
612 if ( cov->state <= 0 )
618 return covariance_calculate_single_pass (cov);
621 return covariance_calculate_double_pass (cov);
629 Covariance computed without dividing by the sample size.
632 covariance_calculate_double_pass_unnormalized (struct covariance *cov)
635 for (i = 0 ; i < cov->dim; ++i)
637 for (j = 0 ; j < cov->dim; ++j)
640 double *x = gsl_matrix_ptr (cov->moments[MOMENT_VARIANCE], i, j);
642 idx = cm_idx (cov, i, j);
650 return cm_to_gsl (cov);
654 covariance_calculate_single_pass_unnormalized (struct covariance *cov)
658 for (i = 0 ; i < cov->dim; ++i)
660 for (j = 0 ; j < cov->dim; ++j)
662 double *x = gsl_matrix_ptr (cov->moments[MOMENT_VARIANCE], i, j);
663 *x -= pow2 (gsl_matrix_get (cov->moments[MOMENT_MEAN], i, j))
664 / gsl_matrix_get (cov->moments[MOMENT_NONE], i, j);
667 for ( j = 0 ; j < cov->dim - 1; ++j)
669 for (i = j + 1 ; i < cov->dim; ++i)
671 double *x = &cov->cm [cm_idx (cov, i, j)];
674 gsl_matrix_get (cov->moments[MOMENT_MEAN], i, j)
676 gsl_matrix_get (cov->moments[MOMENT_MEAN], j, i)
677 / gsl_matrix_get (cov->moments[MOMENT_NONE], i, j);
681 return cm_to_gsl (cov);
685 /* Return a pointer to gsl_matrix containing the pairwise covariances. The
686 caller owns the returned matrix and must free it when it is no longer
689 Call this function only after all data have been accumulated. */
691 covariance_calculate_unnormalized (struct covariance *cov)
693 if ( cov->state <= 0 )
699 return covariance_calculate_single_pass_unnormalized (cov);
702 return covariance_calculate_double_pass_unnormalized (cov);
709 /* Function to access the categoricals used by COV
710 The return value is owned by the COV
712 const struct categoricals *
713 covariance_get_categoricals (const struct covariance *cov)
715 return cov->categoricals;
719 /* Destroy the COV object */
721 covariance_destroy (struct covariance *cov)
725 categoricals_destroy (cov->categoricals);
727 for (i = 0; i < n_MOMENTS; ++i)
728 gsl_matrix_free (cov->moments[i]);
736 covariance_dim (const struct covariance * cov)