/* PSPP - a program for statistical analysis.
- Copyright (C) 2009, 2010 Free Software Foundation, Inc.
+ Copyright (C) 2009, 2010, 2011, 2012 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 <gsl/gsl_vector.h>
#include <gsl/gsl_linalg.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_eigen.h>
#include <gsl/gsl_blas.h>
#include <gsl/gsl_sort_vector.h>
-
-#include <math/covariance.h>
-
-#include <math/correlation.h>
-#include <math/moments.h>
-#include <data/procedure.h>
-#include <language/lexer/variable-parser.h>
-#include <language/lexer/value-parser.h>
-#include <language/command.h>
-#include <language/lexer/lexer.h>
-
-#include <data/casegrouper.h>
-#include <data/casereader.h>
-#include <data/casewriter.h>
-#include <data/dictionary.h>
-#include <data/format.h>
-#include <data/subcase.h>
-
-#include <libpspp/misc.h>
-#include <libpspp/message.h>
-
-#include <output/tab.h>
-
-#include <output/charts/scree.h>
-#include <output/chart-item.h>
+#include <gsl/gsl_cdf.h>
+
+#include "data/casegrouper.h"
+#include "data/casereader.h"
+#include "data/casewriter.h"
+#include "data/dataset.h"
+#include "data/dictionary.h"
+#include "data/format.h"
+#include "data/subcase.h"
+#include "language/command.h"
+#include "language/lexer/lexer.h"
+#include "language/lexer/value-parser.h"
+#include "language/lexer/variable-parser.h"
+#include "libpspp/cast.h"
+#include "libpspp/message.h"
+#include "libpspp/misc.h"
+#include "math/correlation.h"
+#include "math/covariance.h"
+#include "math/moments.h"
+#include "output/chart-item.h"
+#include "output/charts/scree.h"
+#include "output/tab.h"
#include "gettext.h"
#define _(msgid) gettext (msgid)
double econverge;
int iterations;
+ double rconverge;
+
/* Format */
double blank;
bool sort;
/* Intermediate values used in calculation */
const gsl_matrix *corr ; /* The correlation matrix */
- const gsl_matrix *cov ; /* The covariance matrix */
+ gsl_matrix *cov ; /* The covariance matrix */
const gsl_matrix *n ; /* Matrix of number of samples */
gsl_vector *eval ; /* The eigenvalues */
int n_extractions;
gsl_vector *msr ; /* Multiple Squared Regressions */
+
+ double detR; /* The determinant of the correlation matrix */
};
static struct idata *
gsl_vector_free (id->msr);
gsl_vector_free (id->eval);
gsl_matrix_free (id->evec);
+ if (id->cov != NULL)
+ gsl_matrix_free (id->cov);
+ if (id->corr != NULL)
+ gsl_matrix_free (CONST_CAST (gsl_matrix *, id->corr));
free (id);
}
+static gsl_matrix *
+anti_image (const gsl_matrix *m)
+{
+ int i, j;
+ gsl_matrix *a;
+ assert (m->size1 == m->size2);
+
+ a = gsl_matrix_alloc (m->size1, m->size2);
+
+ for (i = 0; i < m->size1; ++i)
+ {
+ for (j = 0; j < m->size2; ++j)
+ {
+ double *p = gsl_matrix_ptr (a, i, j);
+ *p = gsl_matrix_get (m, i, j);
+ *p /= gsl_matrix_get (m, i, i);
+ *p /= gsl_matrix_get (m, j, j);
+ }
+ }
+
+ return a;
+}
+
+
+/* Return the sum of all the elements excluding row N */
+static double
+ssq_od_n (const gsl_matrix *m, int n)
+{
+ int i, j;
+ double ss = 0;
+ assert (m->size1 == m->size2);
+
+ assert (n < m->size1);
+
+ for (i = 0; i < m->size1; ++i)
+ {
+ if (i == n ) continue;
+ for (j = 0; j < m->size2; ++j)
+ {
+ ss += pow2 (gsl_matrix_get (m, i, j));
+ }
+ }
+
+ return ss;
+}
+
+
+
+#if 0
static void
dump_matrix (const gsl_matrix *m)
{
}
}
-
static void
dump_matrix_permute (const gsl_matrix *m, const gsl_permutation *p)
{
}
printf ("\n");
}
+#endif
static int
}
+static double
+initial_sv (const gsl_matrix *fm)
+{
+ int j, k;
+
+ double sv = 0.0;
+ for (j = 0 ; j < fm->size2; ++j)
+ {
+ double l4s = 0;
+ double l2s = 0;
+
+ for (k = j + 1 ; k < fm->size2; ++k)
+ {
+ double lambda = gsl_matrix_get (fm, k, j);
+ double lambda_sq = lambda * lambda;
+ double lambda_4 = lambda_sq * lambda_sq;
+
+ l4s += lambda_4;
+ l2s += lambda_sq;
+ }
+ sv += ( fm->size1 * l4s - (l2s * l2s) ) / (fm->size1 * fm->size1 );
+ }
+ return sv;
+}
+
static void
-rotate (const gsl_matrix *unrot, const gsl_vector *communalities, enum rotation_type rot_type,
+rotate (const struct cmd_factor *cf, const gsl_matrix *unrot,
+ const gsl_vector *communalities,
gsl_matrix *result,
gsl_vector *rotated_loadings
)
{
int j, k;
int i;
+ double prev_sv;
/* First get a normalised version of UNROT */
gsl_matrix *normalised = gsl_matrix_calloc (unrot->size1, unrot->size2);
gsl_matrix_free (h_sqrt_inv);
+
/* Now perform the rotation iterations */
- for (i = 0 ; i < 25 ; ++i)
+
+ prev_sv = initial_sv (normalised);
+ for (i = 0 ; i < cf->iterations ; ++i)
{
+ double sv = 0.0;
for (j = 0 ; j < normalised->size2; ++j)
{
+ /* These variables relate to the convergence criterium */
+ double l4s = 0;
+ double l2s = 0;
+
for (k = j + 1 ; k < normalised->size2; ++k)
{
int p;
double d = 0.0;
double x, y;
double phi;
+
for (p = 0; p < normalised->size1; ++p)
{
double jv = gsl_matrix_get (normalised, p, j);
d += 2 * u * v;
}
- rotation_coeff [rot_type] (&x, &y, a, b, c, d, normalised);
+ rotation_coeff [cf->rotation] (&x, &y, a, b, c, d, normalised);
phi = atan2 (x, y) / 4.0 ;
-
+
+ /* Don't bother rotating if the angle is small */
+ if ( fabs (sin (phi) ) <= pow (10.0, -15.0))
+ continue;
+
for (p = 0; p < normalised->size1; ++p)
{
double *lambda0 = gsl_matrix_ptr (normalised, p, j);
double *lambda1 = gsl_matrix_ptr (normalised, p, k);
drot_go (phi, lambda0, lambda1);
}
+
+ /* Calculate the convergence criterium */
+ {
+ double lambda = gsl_matrix_get (normalised, k, j);
+ double lambda_sq = lambda * lambda;
+ double lambda_4 = lambda_sq * lambda_sq;
+
+ l4s += lambda_4;
+ l2s += lambda_sq;
+ }
}
+ sv += ( normalised->size1 * l4s - (l2s * l2s) ) / (normalised->size1 * normalised->size1 );
}
+
+ if ( fabs (sv - prev_sv) <= cf->rconverge)
+ break;
+
+ prev_sv = sv;
}
gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0,
h_sqrt, normalised, 0.0, result);
gsl_matrix_free (h_sqrt);
+ gsl_matrix_free (normalised);
/* reflect negative sums and populate the rotated loadings vector*/
factor.min_eigen = SYSMIS;
factor.iterations = 25;
factor.econverge = 0.001;
+
factor.blank = 0;
factor.sort = false;
factor.plot = 0;
factor.rotation = ROT_VARIMAX;
+ factor.rconverge = 0.0001;
+
factor.wv = dict_get_weight (dict);
- lex_match (lexer, '/');
+ lex_match (lexer, T_SLASH);
if (!lex_force_match_id (lexer, "VARIABLES"))
{
goto error;
}
- lex_match (lexer, '=');
+ lex_match (lexer, T_EQUALS);
if (!parse_variables_const (lexer, dict, &factor.vars, &factor.n_vars,
PV_NO_DUPLICATE | PV_NUMERIC))
if (factor.n_vars < 2)
msg (MW, _("Factor analysis on a single variable is not useful."));
- while (lex_token (lexer) != '.')
+ while (lex_token (lexer) != T_ENDCMD)
{
- lex_match (lexer, '/');
+ lex_match (lexer, T_SLASH);
if (lex_match_id (lexer, "PLOT"))
{
- lex_match (lexer, '=');
- while (lex_token (lexer) != '.' && lex_token (lexer) != '/')
+ lex_match (lexer, T_EQUALS);
+ while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
{
if (lex_match_id (lexer, "EIGEN"))
{
}
else if (lex_match_id (lexer, "METHOD"))
{
- lex_match (lexer, '=');
- while (lex_token (lexer) != '.' && lex_token (lexer) != '/')
+ lex_match (lexer, T_EQUALS);
+ while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
{
if (lex_match_id (lexer, "COVARIANCE"))
{
}
else if (lex_match_id (lexer, "ROTATION"))
{
- lex_match (lexer, '=');
- while (lex_token (lexer) != '.' && lex_token (lexer) != '/')
+ lex_match (lexer, T_EQUALS);
+ while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
{
/* VARIMAX and DEFAULT are defaults */
if (lex_match_id (lexer, "VARIMAX") || lex_match_id (lexer, "DEFAULT"))
}
else if (lex_match_id (lexer, "CRITERIA"))
{
- lex_match (lexer, '=');
- while (lex_token (lexer) != '.' && lex_token (lexer) != '/')
+ lex_match (lexer, T_EQUALS);
+ while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
{
if (lex_match_id (lexer, "FACTORS"))
{
- if ( lex_force_match (lexer, '('))
+ if ( lex_force_match (lexer, T_LPAREN))
{
lex_force_int (lexer);
factor.n_factors = lex_integer (lexer);
lex_get (lexer);
- lex_force_match (lexer, ')');
+ lex_force_match (lexer, T_RPAREN);
}
}
else if (lex_match_id (lexer, "MINEIGEN"))
{
- if ( lex_force_match (lexer, '('))
+ if ( lex_force_match (lexer, T_LPAREN))
{
lex_force_num (lexer);
factor.min_eigen = lex_number (lexer);
lex_get (lexer);
- lex_force_match (lexer, ')');
+ lex_force_match (lexer, T_RPAREN);
}
}
else if (lex_match_id (lexer, "ECONVERGE"))
{
- if ( lex_force_match (lexer, '('))
+ if ( lex_force_match (lexer, T_LPAREN))
{
lex_force_num (lexer);
factor.econverge = lex_number (lexer);
lex_get (lexer);
- lex_force_match (lexer, ')');
+ lex_force_match (lexer, T_RPAREN);
+ }
+ }
+ else if (lex_match_id (lexer, "RCONVERGE"))
+ {
+ if ( lex_force_match (lexer, T_LPAREN))
+ {
+ lex_force_num (lexer);
+ factor.rconverge = lex_number (lexer);
+ lex_get (lexer);
+ lex_force_match (lexer, T_RPAREN);
}
}
else if (lex_match_id (lexer, "ITERATE"))
{
- if ( lex_force_match (lexer, '('))
+ if ( lex_force_match (lexer, T_LPAREN))
{
lex_force_int (lexer);
factor.iterations = lex_integer (lexer);
lex_get (lexer);
- lex_force_match (lexer, ')');
+ lex_force_match (lexer, T_RPAREN);
}
}
else if (lex_match_id (lexer, "DEFAULT"))
else if (lex_match_id (lexer, "EXTRACTION"))
{
extraction_seen = true;
- lex_match (lexer, '=');
- while (lex_token (lexer) != '.' && lex_token (lexer) != '/')
+ lex_match (lexer, T_EQUALS);
+ while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
{
if (lex_match_id (lexer, "PAF"))
{
}
else if (lex_match_id (lexer, "FORMAT"))
{
- lex_match (lexer, '=');
- while (lex_token (lexer) != '.' && lex_token (lexer) != '/')
+ lex_match (lexer, T_EQUALS);
+ while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
{
if (lex_match_id (lexer, "SORT"))
{
}
else if (lex_match_id (lexer, "BLANK"))
{
- if ( lex_force_match (lexer, '('))
+ if ( lex_force_match (lexer, T_LPAREN))
{
lex_force_num (lexer);
factor.blank = lex_number (lexer);
lex_get (lexer);
- lex_force_match (lexer, ')');
+ lex_force_match (lexer, T_RPAREN);
}
}
else if (lex_match_id (lexer, "DEFAULT"))
else if (lex_match_id (lexer, "PRINT"))
{
factor.print = 0;
- lex_match (lexer, '=');
- while (lex_token (lexer) != '.' && lex_token (lexer) != '/')
+ lex_match (lexer, T_EQUALS);
+ while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
{
if (lex_match_id (lexer, "UNIVARIATE"))
{
{
factor.print |= PRINT_INITIAL;
}
-#if FACTOR_FULLY_IMPLEMENTED
else if (lex_match_id (lexer, "KMO"))
{
+ factor.print |= PRINT_KMO;
}
+#if FACTOR_FULLY_IMPLEMENTED
else if (lex_match_id (lexer, "REPR"))
{
}
}
else if (lex_match_id (lexer, "MISSING"))
{
- lex_match (lexer, '=');
- while (lex_token (lexer) != '.' && lex_token (lexer) != '/')
+ lex_match (lexer, T_EQUALS);
+ while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
{
if (lex_match_id (lexer, "INCLUDE"))
{
tab_title (t, _("Factor Matrix"));
*/
- tab_title (t, title);
+ tab_title (t, "%s", title);
tab_headers (t, heading_columns, 0, heading_rows, 0);
const double e_lambda = gsl_vector_get (extracted_eigenvalues, i);
double e_percent = 100.0 * e_lambda / e_total ;
- const double r_lambda = gsl_vector_get (rotated_loadings, i);
- double r_percent = 100.0 * r_lambda / e_total ;
-
c = 0;
- tab_text_format (t, c++, i + heading_rows, TAB_LEFT | TAT_TITLE, _("%d"), i + 1);
+ tab_text_format (t, c++, i + heading_rows, TAB_LEFT | TAT_TITLE, _("%zu"), i + 1);
i_cum += i_percent;
e_cum += e_percent;
- r_cum += r_percent;
/* Initial Eigenvalues */
if (factor->print & PRINT_INITIAL)
}
}
- if (factor->print & PRINT_ROTATION)
- {
- if (i < idata->n_extractions)
- {
- tab_double (t, c++, i + heading_rows, 0, r_lambda, NULL);
- tab_double (t, c++, i + heading_rows, 0, r_percent, NULL);
- tab_double (t, c++, i + heading_rows, 0, r_cum, NULL);
- }
- }
+ if (rotated_loadings != NULL)
+ {
+ const double r_lambda = gsl_vector_get (rotated_loadings, i);
+ double r_percent = 100.0 * r_lambda / e_total ;
+ if (factor->print & PRINT_ROTATION)
+ {
+ if (i < idata->n_extractions)
+ {
+ r_cum += r_percent;
+ tab_double (t, c++, i + heading_rows, 0, r_lambda, NULL);
+ tab_double (t, c++, i + heading_rows, 0, r_percent, NULL);
+ tab_double (t, c++, i + heading_rows, 0, r_cum, NULL);
+ }
+ }
+ }
}
tab_submit (t);
if (factor->print & PRINT_SIG)
{
const double y = heading_rows + y_pos_sig * factor->n_vars;
- tab_text (t, 0, y, TAT_TITLE, _("Sig. 1-tailed"));
+ tab_text (t, 0, y, TAT_TITLE, _("Sig. (1-tailed)"));
for (i = 0; i < factor->n_vars; ++i)
{
if (factor->print & PRINT_DETERMINANT)
{
- int sign = 0;
- double det = 0.0;
-
- const int size = idata->corr->size1;
- gsl_permutation *p = gsl_permutation_calloc (size);
- gsl_matrix *tmp = gsl_matrix_calloc (size, size);
- gsl_matrix_memcpy (tmp, idata->corr);
-
- gsl_linalg_LU_decomp (tmp, p, &sign);
- det = gsl_linalg_LU_det (tmp, sign);
- gsl_permutation_free (p);
- gsl_matrix_free (tmp);
-
-
tab_text (t, 0, nr, TAB_LEFT | TAT_TITLE, _("Determinant"));
- tab_double (t, 1, nr, 0, det, NULL);
+
+ tab_double (t, 1, nr, 0, idata->detR, NULL);
}
tab_submit (t);
const gsl_matrix *analysis_matrix;
struct idata *idata = idata_alloc (factor->n_vars);
- struct covariance *cov = covariance_create (factor->n_vars, factor->vars,
+ struct covariance *cov = covariance_1pass_create (factor->n_vars, factor->vars,
factor->wv, factor->exclude);
for ( ; (c = casereader_read (r) ); case_unref (c))
idata->cov = covariance_calculate (cov);
+ if (idata->cov == NULL)
+ {
+ msg (MW, _("The dataset contains no complete observations. No analysis will be performed."));
+ goto finish;
+ }
+
var_matrix = covariance_moments (cov, MOMENT_VARIANCE);
mean_matrix = covariance_moments (cov, MOMENT_MEAN);
idata->n = covariance_moments (cov, MOMENT_NONE);
+
if ( factor->method == METHOD_CORR)
{
idata->corr = correlation_from_covariance (idata->cov, var_matrix);
+
analysis_matrix = idata->corr;
}
else
analysis_matrix = idata->cov;
+
+ if (factor->print & PRINT_DETERMINANT
+ || factor->print & PRINT_KMO)
+ {
+ int sign = 0;
+
+ const int size = idata->corr->size1;
+ gsl_permutation *p = gsl_permutation_calloc (size);
+ gsl_matrix *tmp = gsl_matrix_calloc (size, size);
+ gsl_matrix_memcpy (tmp, idata->corr);
+
+ gsl_linalg_LU_decomp (tmp, p, &sign);
+ idata->detR = gsl_linalg_LU_det (tmp, sign);
+ gsl_permutation_free (p);
+ gsl_matrix_free (tmp);
+ }
+
if ( factor->print & PRINT_UNIVARIATE)
{
+ const struct fmt_spec *wfmt = factor->wv ? var_get_print_format (factor->wv) : & F_8_0;
const int nc = 4;
int i;
- const struct fmt_spec *wfmt = factor->wv ? var_get_print_format (factor->wv) : & F_8_0;
-
const int heading_columns = 1;
const int heading_rows = 1;
tab_submit (t);
}
+ if (factor->print & PRINT_KMO)
+ {
+ int i;
+ double sum_ssq_r = 0;
+ double sum_ssq_a = 0;
+
+ double df = factor->n_vars * ( factor->n_vars - 1) / 2;
+
+ double w = 0;
+
+
+ double xsq;
+
+ const int heading_columns = 2;
+ const int heading_rows = 0;
+
+ const int nr = heading_rows + 4;
+ const int nc = heading_columns + 1;
+
+ gsl_matrix *a, *x;
+
+ struct tab_table *t = tab_create (nc, nr);
+ tab_title (t, _("KMO and Bartlett's Test"));
+
+ x = clone_matrix (idata->corr);
+ gsl_linalg_cholesky_decomp (x);
+ gsl_linalg_cholesky_invert (x);
+
+ a = anti_image (x);
+
+ for (i = 0; i < x->size1; ++i)
+ {
+ sum_ssq_r += ssq_od_n (x, i);
+ sum_ssq_a += ssq_od_n (a, i);
+ }
+
+ gsl_matrix_free (a);
+ gsl_matrix_free (x);
+
+ tab_headers (t, heading_columns, 0, heading_rows, 0);
+
+ /* Outline the box */
+ tab_box (t,
+ TAL_2, TAL_2,
+ -1, -1,
+ 0, 0,
+ nc - 1, nr - 1);
+
+ tab_vline (t, TAL_2, heading_columns, 0, nr - 1);
+
+ tab_text (t, 0, 0, TAT_TITLE | TAB_LEFT, _("Kaiser-Meyer-Olkin Measure of Sampling Adequacy"));
+
+ tab_double (t, 2, 0, 0, sum_ssq_r / (sum_ssq_r + sum_ssq_a), NULL);
+
+ tab_text (t, 0, 1, TAT_TITLE | TAB_LEFT, _("Bartlett's Test of Sphericity"));
+
+ tab_text (t, 1, 1, TAT_TITLE, _("Approx. Chi-Square"));
+ tab_text (t, 1, 2, TAT_TITLE, _("df"));
+ tab_text (t, 1, 3, TAT_TITLE, _("Sig."));
+
+
+ /* The literature doesn't say what to do for the value of W when
+ missing values are involved. The best thing I can think of
+ is to take the mean average. */
+ w = 0;
+ for (i = 0; i < idata->n->size1; ++i)
+ w += gsl_matrix_get (idata->n, i, i);
+ w /= idata->n->size1;
+
+ xsq = w - 1 - (2 * factor->n_vars + 5) / 6.0;
+ xsq *= -log (idata->detR);
+
+ tab_double (t, 2, 1, 0, xsq, NULL);
+ tab_double (t, 2, 2, 0, df, &F_8_0);
+ tab_double (t, 2, 3, 0, gsl_cdf_chisq_Q (xsq, df), NULL);
+
+
+ tab_submit (t);
+ }
+
show_correlation_matrix (factor, idata);
+ covariance_destroy (cov);
-#if 1
{
+ gsl_matrix *am = matrix_dup (analysis_matrix);
gsl_eigen_symmv_workspace *workspace = gsl_eigen_symmv_alloc (factor->n_vars);
- gsl_eigen_symmv (matrix_dup (analysis_matrix), idata->eval, idata->evec, workspace);
+ gsl_eigen_symmv (am, idata->eval, idata->evec, workspace);
gsl_eigen_symmv_free (workspace);
+ gsl_matrix_free (am);
}
gsl_eigen_symmv_sort (idata->eval, idata->evec, GSL_EIGEN_SORT_ABS_DESC);
-#endif
idata->n_extractions = n_extracted_factors (factor, idata);
rotated_factors = gsl_matrix_calloc (factor_matrix->size1, factor_matrix->size2);
rotated_loadings = gsl_vector_calloc (factor_matrix->size2);
- rotate (factor_matrix, extracted_communalities, factor->rotation, rotated_factors, rotated_loadings);
+ rotate (factor, factor_matrix, extracted_communalities, rotated_factors, rotated_loadings);
}
show_explained_variance (factor, idata, idata->eval, extracted_eigenvalues, rotated_loadings);
+ gsl_matrix_free (factor_matrix);
+ gsl_vector_free (rotated_loadings);
gsl_vector_free (initial_communalities);
gsl_vector_free (extracted_communalities);
}
casereader_destroy (r);
}
+
+
+
projects / pspp / blobdiff