From: John Darrington Date: Sat, 17 Oct 2009 09:12:56 +0000 (+0200) Subject: Add a two pass algorithm to calculate covariance matrices. X-Git-Tag: fc11-i386-build23^0 X-Git-Url: https://pintos-os.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=3bbe45fcc70f8d059b4bf6715d629209b50fa48e;p=pspp-builds.git Add a two pass algorithm to calculate covariance matrices. The single pass algorithm, although faster, is numerically unstable. Furthermore, at can't reasonably be achieved when categorical variables are involved. This change implements a two pass algorithm and allows the caller to choose which algorithm (s)he prefers. --- diff --git a/src/language/stats/correlations.c b/src/language/stats/correlations.c index e397dae5..277cfea5 100644 --- a/src/language/stats/correlations.c +++ b/src/language/stats/correlations.c @@ -325,15 +325,25 @@ run_corr (struct casereader *r, const struct corr_opts *opts, const struct corr const gsl_matrix *cov_matrix; gsl_matrix *corr_matrix; struct covariance *cov = covariance_create (corr->n_vars_total, corr->vars, - opts->wv, opts->exclude); + opts->wv, opts->exclude, 2); + + struct casereader *rc = casereader_clone (r); for ( ; (c = casereader_read (r) ); case_unref (c)) { - covariance_accumulate (cov, c); + covariance_accumulate_pass1 (cov, c); + } + + for ( ; (c = casereader_read (rc) ); case_unref (c)) + { + covariance_accumulate_pass2 (cov, c); } cov_matrix = covariance_calculate (cov); + casereader_destroy (rc); + + samples_matrix = covariance_moments (cov, MOMENT_NONE); var_matrix = covariance_moments (cov, MOMENT_VARIANCE); mean_matrix = covariance_moments (cov, MOMENT_MEAN); diff --git a/src/math/covariance.c b/src/math/covariance.c index 32cda24c..1548187b 100644 --- a/src/math/covariance.c +++ b/src/math/covariance.c @@ -16,6 +16,7 @@ #include +#include #include "covariance.h" #include #include "moments.h" @@ -56,6 +57,23 @@ struct covariance 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; }; @@ -79,10 +97,16 @@ covariance_moments (const struct covariance *cov, int m) */ struct covariance * covariance_create (size_t n_vars, const struct variable **vars, - const struct variable *weight, enum mv_class exclude) + const struct variable *weight, enum mv_class exclude, + short passes) { size_t i; struct covariance *cov = xmalloc (sizeof *cov); + assert (passes == 1 || passes == 2); + cov->passes = passes; + cov->state = 0; + cov->pass_one_first_case_seen = cov->pass_two_first_case_seen = false; + cov->vars = xmalloc (sizeof *cov->vars * n_vars); cov->wv = weight; @@ -175,14 +199,148 @@ cm_idx (const struct covariance *cov, int i, int j) return i - 1 + as; } +static 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"); + } +} + +/* 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_data (c, cov->wv)->f : 1.0; + + assert (cov->passes == 2); + if (!cov->pass_one_first_case_seen) + { + assert (cov->state == 0); + cov->state = 1; + } + + for (i = 0 ; i < cov->n_vars; ++i) + { + const union value *val1 = case_data (c, cov->vars[i]); + + if ( var_is_value_missing (cov->vars[i], val1, cov->exclude)) + continue; + + for (j = 0 ; j < cov->n_vars; ++j) + { + double pwr = 1.0; + const union value *val2 = case_data (c, cov->vars[j]); + + if ( var_is_value_missing (cov->vars[j], val2, cov->exclude)) + continue; + + for (m = 0 ; m <= MOMENT_MEAN; ++m) + { + double *x = gsl_matrix_ptr (cov->moments[m], i, j); + + *x += pwr * weight; + pwr *= val1->f; + } + } + } + + 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_data (c, cov->wv)->f : 1.0; + + assert (cov->passes == 2); + assert (cov->state >= 1); + + if (! cov->pass_two_first_case_seen) + { + assert (cov->state == 1); + cov->state = 2; + + /* Divide the means by the number of samples */ + for (i = 0; i < cov->n_vars; ++i) + { + for (j = 0; j < cov->n_vars; ++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->n_vars; ++i) + { + const union value *val1 = case_data (c, cov->vars[i]); + + if ( var_is_value_missing (cov->vars[i], val1, cov->exclude)) + continue; + + for (j = 0 ; j < cov->n_vars; ++j) + { + int idx; + double ss ; + const union value *val2 = case_data (c, cov->vars[j]); + + const double s = pow2 (val1->f - gsl_matrix_get (cov->moments[MOMENT_MEAN], i, j)) * weight; + + if ( var_is_value_missing (cov->vars[j], val2, cov->exclude)) + continue; + + { + double *x = gsl_matrix_ptr (cov->moments[MOMENT_VARIANCE], i, j); + *x += s; + } + + ss = + (val1->f - gsl_matrix_get (cov->moments[MOMENT_MEAN], i, j)) + * + (val2->f - 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; + assert (cov->passes == 1); + + if ( !cov->pass_one_first_case_seen) + { + assert ( cov->state == 0); + cov->state = 1; + } + for (i = 0 ; i < cov->n_vars; ++i) { const union value *val1 = case_data (c, cov->vars[i]); @@ -214,6 +372,8 @@ covariance_accumulate (struct covariance *cov, const struct ccase *c) } } } + + cov->pass_one_first_case_seen = true; } @@ -249,14 +409,32 @@ cm_to_gsl (struct covariance *cov) } +static const gsl_matrix * +covariance_calculate_double_pass (struct covariance *cov) +{ + size_t i, j; + for (i = 0 ; i < cov->n_vars; ++i) + { + for (j = 0 ; j < cov->n_vars; ++j) + { + int idx; + double *x = gsl_matrix_ptr (cov->moments[MOMENT_VARIANCE], i, j); + *x /= gsl_matrix_get (cov->moments[MOMENT_NONE], i, j); + + 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); +} -/* - 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) +static const gsl_matrix * +covariance_calculate_single_pass (struct covariance *cov) { size_t i, j; size_t m; @@ -300,6 +478,33 @@ covariance_calculate (struct covariance *cov) } + +/* + 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) +{ + assert ( cov->state > 0 ); + + switch (cov->passes) + { + case 1: + return covariance_calculate_single_pass (cov); + break; + case 2: + return covariance_calculate_double_pass (cov); + break; + default: + NOT_REACHED (); + } +} + + + + /* Destroy the COV object */ void covariance_destroy (struct covariance *cov) diff --git a/src/math/covariance.h b/src/math/covariance.h index ee096af6..8855433e 100644 --- a/src/math/covariance.h +++ b/src/math/covariance.h @@ -28,13 +28,17 @@ struct variable; struct ccase ; struct covariance * covariance_create (size_t n_vars, const struct variable **vars, - const struct variable *wv, enum mv_class excl); + const struct variable *wv, enum mv_class excl, + short passes); + struct covariance * covariance_2pass_create (size_t n_vars, const struct variable **vars, size_t n_catvars, const struct variable **catvars, const struct variable *weight, enum mv_class excl); void covariance_accumulate (struct covariance *, const struct ccase *); +void covariance_accumulate_pass1 (struct covariance *, const struct ccase *); +void covariance_accumulate_pass2 (struct covariance *, const struct ccase *); const gsl_matrix * covariance_calculate (struct covariance *cov);