--- /dev/null
+/* PSPP - a program for statistical analysis.
+ Copyright (C) 2009, 2010, 2011, 2012, 2014, 2015,
+ 2016, 2017 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 <http://www.gnu.org/licenses/>. */
+
+#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 <gsl/gsl_cdf.h>
+
+#include "data/any-reader.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 "language/commands/file-handle.h"
+#include "language/commands/matrix-reader.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/charts/scree.h"
+#include "output/pivot-table.h"
+
+
+#include "gettext.h"
+#define _(msgid) gettext (msgid)
+#define N_(msgid) msgid
+
+enum method
+ {
+ METHOD_CORR,
+ METHOD_COV
+ };
+
+enum missing_type
+ {
+ MISS_LISTWISE,
+ MISS_PAIRWISE,
+ MISS_MEANSUB,
+ };
+
+enum extraction_method
+ {
+ EXTRACTION_PC,
+ EXTRACTION_PAF,
+ };
+
+enum plot_opts
+ {
+ PLOT_SCREE = 0x0001,
+ PLOT_ROTATION = 0x0002
+ };
+
+enum print_opts
+ {
+ PRINT_UNIVARIATE = 1 << 0,
+ PRINT_DETERMINANT = 1 << 1,
+ PRINT_INV = 1 << 2,
+ PRINT_AIC = 1 << 3,
+ PRINT_SIG = 1 << 4,
+ PRINT_COVARIANCE = 1 << 5,
+ PRINT_CORRELATION = 1 << 6,
+ PRINT_ROTATION = 1 << 7,
+ PRINT_EXTRACTION = 1 << 8,
+ PRINT_INITIAL = 1 << 9,
+ PRINT_KMO = 1 << 10,
+ PRINT_REPR = 1 << 11,
+ PRINT_FSCORE = 1 << 12
+ };
+
+enum rotation_type
+ {
+ ROT_VARIMAX = 0,
+ ROT_EQUAMAX,
+ ROT_QUARTIMAX,
+ ROT_PROMAX,
+ ROT_NONE
+ };
+
+typedef void (*rotation_coefficients) (double *x, double *y,
+ double a, double b, double c, double d,
+ const gsl_matrix *loadings);
+
+
+static void
+varimax_coefficients (double *x, double *y,
+ double a, double b, double c, double d,
+ const gsl_matrix *loadings)
+{
+ *x = d - 2 * a * b / loadings->size1;
+ *y = c - (a * a - b * b) / loadings->size1;
+}
+
+static void
+equamax_coefficients (double *x, double *y,
+ double a, double b, double c, double d,
+ const gsl_matrix *loadings)
+{
+ *x = d - loadings->size2 * a * b / loadings->size1;
+ *y = c - loadings->size2 * (a * a - b * b) / (2 * loadings->size1);
+}
+
+static void
+quartimax_coefficients (double *x, double *y,
+ double a UNUSED, double b UNUSED, double c, double d,
+ const gsl_matrix *loadings UNUSED)
+{
+ *x = d;
+ *y = c;
+}
+
+static const rotation_coefficients rotation_coeff[] = {
+ varimax_coefficients,
+ equamax_coefficients,
+ quartimax_coefficients,
+ varimax_coefficients /* PROMAX is identical to VARIMAX */
+};
+
+
+/* return diag (C'C) ^ {-0.5} */
+static gsl_matrix *
+diag_rcp_sqrt (const gsl_matrix *C)
+{
+ gsl_matrix *d = gsl_matrix_calloc (C->size1, C->size2);
+ gsl_matrix *r = gsl_matrix_calloc (C->size1, C->size2);
+
+ assert (C->size1 == C->size2);
+
+ gsl_linalg_matmult_mod (C, GSL_LINALG_MOD_TRANSPOSE,
+ C, GSL_LINALG_MOD_NONE,
+ d);
+
+ for (int j = 0; j < d->size2; ++j)
+ {
+ double e = gsl_matrix_get (d, j, j);
+ e = 1.0 / sqrt (e);
+ gsl_matrix_set (r, j, j, e);
+ }
+
+ gsl_matrix_free (d);
+
+ return r;
+}
+
+
+
+/* return diag ((C'C)^-1) ^ {-0.5} */
+static gsl_matrix *
+diag_rcp_inv_sqrt (const gsl_matrix *CCinv)
+{
+ gsl_matrix *r = gsl_matrix_calloc (CCinv->size1, CCinv->size2);
+
+ assert (CCinv->size1 == CCinv->size2);
+
+ for (int j = 0; j < CCinv->size2; ++j)
+ {
+ double e = gsl_matrix_get (CCinv, j, j);
+ e = 1.0 / sqrt (e);
+ gsl_matrix_set (r, j, j, e);
+ }
+
+ return r;
+}
+
+
+
+
+
+struct cmd_factor
+{
+ size_t n_vars;
+ const struct variable **vars;
+
+ const struct variable *wv;
+
+ enum method method;
+ enum missing_type missing_type;
+ enum mv_class exclude;
+ enum print_opts print;
+ enum extraction_method extraction;
+ enum plot_opts plot;
+ enum rotation_type rotation;
+ int rotation_iterations;
+ int promax_power;
+
+ /* Extraction Criteria */
+ int n_factors;
+ double min_eigen;
+ double econverge;
+ int extraction_iterations;
+
+ double rconverge;
+
+ /* Format */
+ double blank;
+ bool sort;
+};
+
+
+struct idata
+{
+ /* Intermediate values used in calculation */
+ struct matrix_material mm;
+
+ gsl_matrix *analysis_matrix; /* A pointer to either mm.corr or mm.cov */
+
+ gsl_vector *eval; /* The eigenvalues */
+ gsl_matrix *evec; /* The eigenvectors */
+
+ int n_extractions;
+
+ gsl_vector *msr; /* Multiple Squared Regressions */
+
+ double detR; /* The determinant of the correlation matrix */
+
+ gsl_matrix *ai_cov; /* The anti-image covariance matrix */
+ gsl_matrix *ai_cor; /* The anti-image correlation matrix */
+ struct covariance *cvm;
+};
+
+static struct idata *
+idata_alloc (size_t n_vars)
+{
+ struct idata *id = XZALLOC (struct idata);
+
+ id->n_extractions = 0;
+ id->msr = gsl_vector_alloc (n_vars);
+
+ id->eval = gsl_vector_alloc (n_vars);
+ id->evec = gsl_matrix_alloc (n_vars, n_vars);
+
+ return id;
+}
+
+static void
+idata_free (struct idata *id)
+{
+ gsl_vector_free (id->msr);
+ gsl_vector_free (id->eval);
+ gsl_matrix_free (id->evec);
+ gsl_matrix_free (id->ai_cov);
+ gsl_matrix_free (id->ai_cor);
+
+ free (id);
+}
+
+/* Return the sum of squares of all the elements in row J excluding column J */
+static double
+ssq_row_od_n (const gsl_matrix *m, int j)
+{
+ assert (m->size1 == m->size2);
+ assert (j < m->size1);
+
+ double ss = 0;
+ for (int i = 0; i < m->size1; ++i)
+ if (i != j)
+ ss += pow2 (gsl_matrix_get (m, i, j));
+ return ss;
+}
+
+/* Return the sum of squares of all the elements excluding row N */
+static double
+ssq_od_n (const gsl_matrix *m, int n)
+{
+ assert (m->size1 == m->size2);
+ assert (n < m->size1);
+
+ double ss = 0;
+ for (int i = 0; i < m->size1; ++i)
+ for (int j = 0; j < m->size2; ++j)
+ if (i != j)
+ ss += pow2 (gsl_matrix_get (m, i, j));
+ return ss;
+}
+
+
+static gsl_matrix *
+anti_image_corr (const gsl_matrix *m, const struct idata *idata)
+{
+ assert (m->size1 == m->size2);
+
+ gsl_matrix *a = gsl_matrix_alloc (m->size1, m->size2);
+ for (int i = 0; i < m->size1; ++i)
+ for (int j = 0; j < m->size2; ++j)
+ {
+ double *p = gsl_matrix_ptr (a, i, j);
+ *p = gsl_matrix_get (m, i, j);
+ *p /= sqrt (gsl_matrix_get (m, i, i) *
+ gsl_matrix_get (m, j, j));
+ }
+
+ for (int i = 0; i < m->size1; ++i)
+ {
+ double r = ssq_row_od_n (idata->mm.corr, i);
+ double u = ssq_row_od_n (a, i);
+ gsl_matrix_set (a, i, i, r / (r + u));
+ }
+
+ return a;
+}
+
+static gsl_matrix *
+anti_image_cov (const gsl_matrix *m)
+{
+ assert (m->size1 == m->size2);
+
+ gsl_matrix *a = gsl_matrix_alloc (m->size1, m->size2);
+ for (int i = 0; i < m->size1; ++i)
+ for (int 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;
+}
+
+#if 0
+static void
+dump_matrix (const gsl_matrix *m)
+{
+ for (int i = 0; i < m->size1; ++i)
+ {
+ for (int j = 0; j < m->size2; ++j)
+ printf ("%02f ", gsl_matrix_get (m, i, j));
+ printf ("\n");
+ }
+}
+
+static void
+dump_matrix_permute (const gsl_matrix *m, const gsl_permutation *p)
+{
+ for (int i = 0; i < m->size1; ++i)
+ {
+ for (int j = 0; j < m->size2; ++j)
+ printf ("%02f ", gsl_matrix_get (m, gsl_permutation_get (p, i), j));
+ printf ("\n");
+ }
+}
+
+
+static void
+dump_vector (const gsl_vector *v)
+{
+ for (size_t i = 0; i < v->size; ++i)
+ printf ("%02f\n", gsl_vector_get (v, i));
+ printf ("\n");
+}
+#endif
+
+
+static int
+n_extracted_factors (const struct cmd_factor *factor, struct idata *idata)
+{
+ /* If there is a cached value, then return that. */
+ if (idata->n_extractions != 0)
+ return idata->n_extractions;
+
+ /* Otherwise, if the number of factors has been explicitly requested,
+ use that. */
+ if (factor->n_factors > 0)
+ {
+ idata->n_extractions = factor->n_factors;
+ goto finish;
+ }
+
+ /* Use the MIN_EIGEN setting. */
+ for (int i = 0; i < idata->eval->size; ++i)
+ {
+ double evali = fabs (gsl_vector_get (idata->eval, i));
+
+ idata->n_extractions = i;
+
+ if (evali < factor->min_eigen)
+ goto finish;
+ }
+
+ finish:
+ return idata->n_extractions;
+}
+
+
+/* Returns a newly allocated matrix identical to M.
+ It is the callers responsibility to free the returned value.
+*/
+static gsl_matrix *
+matrix_dup (const gsl_matrix *m)
+{
+ gsl_matrix *n = gsl_matrix_alloc (m->size1, m->size2);
+ gsl_matrix_memcpy (n, m);
+ return n;
+}
+
+
+struct smr_workspace
+{
+ /* Copy of the subject */
+ gsl_matrix *m;
+
+ gsl_matrix *inverse;
+
+ gsl_permutation *perm;
+
+ gsl_matrix *result1;
+ gsl_matrix *result2;
+};
+
+
+static struct smr_workspace *ws_create (const gsl_matrix *input)
+{
+ struct smr_workspace *ws = xmalloc (sizeof (*ws));
+
+ ws->m = gsl_matrix_alloc (input->size1, input->size2);
+ ws->inverse = gsl_matrix_calloc (input->size1 - 1, input->size2 - 1);
+ ws->perm = gsl_permutation_alloc (input->size1 - 1);
+ ws->result1 = gsl_matrix_calloc (input->size1 - 1, 1);
+ ws->result2 = gsl_matrix_calloc (1, 1);
+
+ return ws;
+}
+
+static void
+ws_destroy (struct smr_workspace *ws)
+{
+ gsl_matrix_free (ws->result2);
+ gsl_matrix_free (ws->result1);
+ gsl_permutation_free (ws->perm);
+ gsl_matrix_free (ws->inverse);
+ gsl_matrix_free (ws->m);
+
+ free (ws);
+}
+
+
+/*
+ Return the square of the regression coefficient for VAR regressed against all other variables.
+ */
+static double
+squared_multiple_correlation (const gsl_matrix *corr, int var, struct smr_workspace *ws)
+{
+ /* For an explanation of what this is doing, see
+ http://www.visualstatistics.net/Visual%20Statistics%20Multimedia/multiple_regression_analysis.htm
+ */
+
+ gsl_matrix_memcpy (ws->m, corr);
+
+ gsl_matrix_swap_rows (ws->m, 0, var);
+ gsl_matrix_swap_columns (ws->m, 0, var);
+
+ gsl_matrix_view rxx = gsl_matrix_submatrix (ws->m, 1, 1, ws->m->size1 - 1, ws->m->size1 - 1);
+
+ int signum = 0;
+ gsl_linalg_LU_decomp (&rxx.matrix, ws->perm, &signum);
+
+ gsl_linalg_LU_invert (&rxx.matrix, ws->perm, ws->inverse);
+
+ gsl_matrix_const_view rxy = gsl_matrix_const_submatrix (ws->m, 1, 0, ws->m->size1 - 1, 1);
+ gsl_matrix_const_view ryx = gsl_matrix_const_submatrix (ws->m, 0, 1, 1, ws->m->size1 - 1);
+
+ gsl_blas_dgemm (CblasNoTrans, CblasNoTrans,
+ 1.0, ws->inverse, &rxy.matrix, 0.0, ws->result1);
+
+ gsl_blas_dgemm (CblasNoTrans, CblasNoTrans,
+ 1.0, &ryx.matrix, ws->result1, 0.0, ws->result2);
+
+ return gsl_matrix_get (ws->result2, 0, 0);
+}
+
+
+
+static double the_communality (const gsl_matrix *evec, const gsl_vector *eval, int n, int n_factors);
+
+
+struct factor_matrix_workspace
+{
+ size_t n_factors;
+ gsl_eigen_symmv_workspace *eigen_ws;
+
+ gsl_vector *eval;
+ gsl_matrix *evec;
+
+ gsl_matrix *gamma;
+
+ gsl_matrix *r;
+};
+
+static struct factor_matrix_workspace *
+factor_matrix_workspace_alloc (size_t n, size_t nf)
+{
+ struct factor_matrix_workspace *ws = xmalloc (sizeof (*ws));
+
+ ws->n_factors = nf;
+ ws->gamma = gsl_matrix_calloc (nf, nf);
+ ws->eigen_ws = gsl_eigen_symmv_alloc (n);
+ ws->eval = gsl_vector_alloc (n);
+ ws->evec = gsl_matrix_alloc (n, n);
+ ws->r = gsl_matrix_alloc (n, n);
+
+ return ws;
+}
+
+static void
+factor_matrix_workspace_free (struct factor_matrix_workspace *ws)
+{
+ gsl_eigen_symmv_free (ws->eigen_ws);
+ gsl_vector_free (ws->eval);
+ gsl_matrix_free (ws->evec);
+ gsl_matrix_free (ws->gamma);
+ gsl_matrix_free (ws->r);
+ free (ws);
+}
+
+/*
+ Shift P left by OFFSET places, and overwrite TARGET
+ with the shifted result.
+ Positions in TARGET less than OFFSET are unchanged.
+*/
+static void
+perm_shift_apply (gsl_permutation *target, const gsl_permutation *p,
+ size_t offset)
+{
+ assert (target->size == p->size);
+ assert (offset <= target->size);
+
+ for (size_t i = 0; i < target->size - offset; ++i)
+ target->data[i] = p->data [i + offset];
+}
+
+
+/*
+ Indirectly sort the rows of matrix INPUT, storing the sort order in PERM.
+ The sort criteria are as follows:
+
+ Rows are sorted on the first column, until the absolute value of an
+ element in a subsequent column is greater than that of the first
+ column. Thereafter, rows will be sorted on the second column,
+ until the absolute value of an element in a subsequent column
+ exceeds that of the second column ...
+*/
+static void
+sort_matrix_indirect (const gsl_matrix *input, gsl_permutation *perm)
+{
+ assert (perm->size == input->size1);
+
+ const size_t n = perm->size;
+ const size_t m = input->size2;
+ gsl_permutation *p = gsl_permutation_alloc (n);
+
+ /* Copy INPUT into MAT, discarding the sign */
+ gsl_matrix *mat = gsl_matrix_alloc (n, m);
+ for (int i = 0; i < mat->size1; ++i)
+ for (int j = 0; j < mat->size2; ++j)
+ gsl_matrix_set (mat, i, j, fabs (gsl_matrix_get (input, i, j)));
+
+ int column_n = 0;
+ int row_n = 0;
+ while (column_n < m && row_n < n)
+ {
+ gsl_vector_const_view columni = gsl_matrix_const_column (mat, column_n);
+ gsl_sort_vector_index (p, &columni.vector);
+
+ int i;
+ for (i = 0; i < n; ++i)
+ {
+ gsl_vector_view row = gsl_matrix_row (mat, p->data[n - 1 - i]);
+ size_t maxindex = gsl_vector_max_index (&row.vector);
+
+ if (maxindex > column_n)
+ break;
+
+ /* All subsequent elements of this row, are of no interest.
+ So set them all to a highly negative value */
+ for (int j = column_n + 1; j < row.vector.size; ++j)
+ gsl_vector_set (&row.vector, j, -DBL_MAX);
+ }
+
+ perm_shift_apply (perm, p, row_n);
+ row_n += i;
+
+ column_n++;
+ }
+
+ gsl_permutation_free (p);
+ gsl_matrix_free (mat);
+
+ assert (0 == gsl_permutation_valid (perm));
+
+ /* We want the biggest value to be first */
+ gsl_permutation_reverse (perm);
+}
+
+
+static void
+drot_go (double phi, double *l0, double *l1)
+{
+ double r0 = cos (phi) * *l0 + sin (phi) * *l1;
+ double r1 = - sin (phi) * *l0 + cos (phi) * *l1;
+
+ *l0 = r0;
+ *l1 = r1;
+}
+
+
+static gsl_matrix *
+clone_matrix (const gsl_matrix *m)
+{
+ gsl_matrix *c = gsl_matrix_calloc (m->size1, m->size2);
+
+ for (int j = 0; j < c->size1; ++j)
+ for (int k = 0; k < c->size2; ++k)
+ gsl_matrix_set (c, j, k, gsl_matrix_get (m, j, k));
+
+ return c;
+}
+
+
+static double
+initial_sv (const gsl_matrix *fm)
+{
+ double sv = 0.0;
+ for (int j = 0; j < fm->size2; ++j)
+ {
+ double l4s = 0;
+ double l2s = 0;
+
+ for (int 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 struct cmd_factor *cf, const gsl_matrix *unrot,
+ const gsl_vector *communalities,
+ gsl_matrix *result,
+ gsl_vector *rotated_loadings,
+ gsl_matrix *pattern_matrix,
+ gsl_matrix *factor_correlation_matrix)
+{
+ /* First get a normalised version of UNROT */
+ gsl_matrix *normalised = gsl_matrix_calloc (unrot->size1, unrot->size2);
+ gsl_matrix *h_sqrt = gsl_matrix_calloc (communalities->size, communalities->size);
+ gsl_matrix *h_sqrt_inv;
+
+ /* H is the diagonal matrix containing the absolute values of the communalities */
+ for (int i = 0; i < communalities->size; ++i)
+ {
+ double *ptr = gsl_matrix_ptr (h_sqrt, i, i);
+ *ptr = fabs (gsl_vector_get (communalities, i));
+ }
+
+ /* Take the square root of the communalities */
+ gsl_linalg_cholesky_decomp (h_sqrt);
+
+ /* Save a copy of h_sqrt and invert it */
+ h_sqrt_inv = clone_matrix (h_sqrt);
+ gsl_linalg_cholesky_decomp (h_sqrt_inv);
+ gsl_linalg_cholesky_invert (h_sqrt_inv);
+
+ /* normalised vertion is H^{1/2} x UNROT */
+ gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, h_sqrt_inv, unrot, 0.0, normalised);
+
+ gsl_matrix_free (h_sqrt_inv);
+
+ /* Now perform the rotation iterations */
+ double prev_sv = initial_sv (normalised);
+ for (int i = 0; i < cf->rotation_iterations; ++i)
+ {
+ double sv = 0.0;
+ for (int j = 0; j < normalised->size2; ++j)
+ {
+ /* These variables relate to the convergence criterium */
+ double l4s = 0;
+ double l2s = 0;
+
+ for (int k = j + 1; k < normalised->size2; ++k)
+ {
+ double a = 0.0;
+ double b = 0.0;
+ double c = 0.0;
+ double d = 0.0;
+ for (int p = 0; p < normalised->size1; ++p)
+ {
+ double jv = gsl_matrix_get (normalised, p, j);
+ double kv = gsl_matrix_get (normalised, p, k);
+
+ double u = jv * jv - kv * kv;
+ double v = 2 * jv * kv;
+ a += u;
+ b += v;
+ c += u * u - v * v;
+ d += 2 * u * v;
+ }
+
+ double x, y;
+ rotation_coeff [cf->rotation] (&x, &y, a, b, c, d, normalised);
+ double 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 (int 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);
+
+ if (cf->rotation == ROT_PROMAX)
+ {
+ /* general purpose m by m matrix, where m is the number of factors */
+ gsl_matrix *mm1 = gsl_matrix_calloc (unrot->size2, unrot->size2);
+ gsl_matrix *mm2 = gsl_matrix_calloc (unrot->size2, unrot->size2);
+
+ /* general purpose m by p matrix, where p is the number of variables */
+ gsl_matrix *mp1 = gsl_matrix_calloc (unrot->size2, unrot->size1);
+
+ gsl_matrix *pm1 = gsl_matrix_calloc (unrot->size1, unrot->size2);
+
+ gsl_permutation *perm = gsl_permutation_alloc (unrot->size2);
+
+
+ /* The following variables follow the notation by SPSS Statistical
+ Algorithms page 342. */
+ gsl_matrix *L = gsl_matrix_calloc (unrot->size2, unrot->size2);
+ gsl_matrix *P = clone_matrix (result);
+
+ /* Vector of length p containing (indexed by i)
+ \Sum^m_j {\lambda^2_{ij}} */
+ gsl_vector *rssq = gsl_vector_calloc (unrot->size1);
+
+ for (int i = 0; i < P->size1; ++i)
+ {
+ double sum = 0;
+ for (int j = 0; j < P->size2; ++j)
+ sum += gsl_matrix_get (result, i, j) * gsl_matrix_get (result, i, j);
+ gsl_vector_set (rssq, i, sqrt (sum));
+ }
+
+ for (int i = 0; i < P->size1; ++i)
+ {
+ for (int j = 0; j < P->size2; ++j)
+ {
+ double l = gsl_matrix_get (result, i, j);
+ double r = gsl_vector_get (rssq, i);
+ gsl_matrix_set (P, i, j, pow (fabs (l / r), cf->promax_power + 1) * r / l);
+ }
+ }
+
+ gsl_vector_free (rssq);
+
+ gsl_linalg_matmult_mod (result,
+ GSL_LINALG_MOD_TRANSPOSE,
+ result,
+ GSL_LINALG_MOD_NONE,
+ mm1);
+
+ int signum;
+ gsl_linalg_LU_decomp (mm1, perm, &signum);
+ gsl_linalg_LU_invert (mm1, perm, mm2);
+
+ gsl_linalg_matmult_mod (mm2, GSL_LINALG_MOD_NONE,
+ result, GSL_LINALG_MOD_TRANSPOSE,
+ mp1);
+
+ gsl_linalg_matmult_mod (mp1, GSL_LINALG_MOD_NONE,
+ P, GSL_LINALG_MOD_NONE,
+ L);
+
+ gsl_matrix *D = diag_rcp_sqrt (L);
+ gsl_matrix *Q = gsl_matrix_calloc (unrot->size2, unrot->size2);
+
+ gsl_linalg_matmult_mod (L, GSL_LINALG_MOD_NONE,
+ D, GSL_LINALG_MOD_NONE,
+ Q);
+
+ gsl_matrix *QQinv = gsl_matrix_calloc (unrot->size2, unrot->size2);
+
+ gsl_linalg_matmult_mod (Q, GSL_LINALG_MOD_TRANSPOSE,
+ Q, GSL_LINALG_MOD_NONE,
+ QQinv);
+
+ gsl_linalg_cholesky_decomp (QQinv);
+ gsl_linalg_cholesky_invert (QQinv);
+
+
+ gsl_matrix *C = diag_rcp_inv_sqrt (QQinv);
+ gsl_matrix *Cinv = clone_matrix (C);
+
+ gsl_linalg_cholesky_decomp (Cinv);
+ gsl_linalg_cholesky_invert (Cinv);
+
+
+ gsl_linalg_matmult_mod (result, GSL_LINALG_MOD_NONE,
+ Q, GSL_LINALG_MOD_NONE,
+ pm1);
+
+ gsl_linalg_matmult_mod (pm1, GSL_LINALG_MOD_NONE,
+ Cinv, GSL_LINALG_MOD_NONE,
+ pattern_matrix);
+
+
+ gsl_linalg_matmult_mod (C, GSL_LINALG_MOD_NONE,
+ QQinv, GSL_LINALG_MOD_NONE,
+ mm1);
+
+ gsl_linalg_matmult_mod (mm1, GSL_LINALG_MOD_NONE,
+ C, GSL_LINALG_MOD_TRANSPOSE,
+ factor_correlation_matrix);
+
+ gsl_linalg_matmult_mod (pattern_matrix, GSL_LINALG_MOD_NONE,
+ factor_correlation_matrix, GSL_LINALG_MOD_NONE,
+ pm1);
+
+ gsl_matrix_memcpy (result, pm1);
+
+
+ gsl_matrix_free (QQinv);
+ gsl_matrix_free (C);
+ gsl_matrix_free (Cinv);
+
+ gsl_matrix_free (D);
+ gsl_matrix_free (Q);
+ gsl_matrix_free (L);
+ gsl_matrix_free (P);
+
+ gsl_permutation_free (perm);
+
+ gsl_matrix_free (mm1);
+ gsl_matrix_free (mm2);
+ gsl_matrix_free (mp1);
+ gsl_matrix_free (pm1);
+ }
+
+
+ /* reflect negative sums and populate the rotated loadings vector*/
+ for (int i = 0; i < result->size2; ++i)
+ {
+ double ssq = 0.0;
+ double sum = 0.0;
+ for (int j = 0; j < result->size1; ++j)
+ {
+ double s = gsl_matrix_get (result, j, i);
+ ssq += s * s;
+ sum += s;
+ }
+
+ gsl_vector_set (rotated_loadings, i, ssq);
+
+ if (sum < 0)
+ for (int j = 0; j < result->size1; ++j)
+ {
+ double *lambda = gsl_matrix_ptr (result, j, i);
+ *lambda = - *lambda;
+ }
+ }
+}
+
+/*
+ Get an approximation for the factor matrix into FACTORS, and the communalities into COMMUNALITIES.
+ R is the matrix to be analysed.
+ WS is a pointer to a structure which must have been initialised with factor_matrix_workspace_init.
+ */
+static void
+iterate_factor_matrix (const gsl_matrix *r, gsl_vector *communalities, gsl_matrix *factors,
+ struct factor_matrix_workspace *ws)
+{
+ assert (r->size1 == r->size2);
+ assert (r->size1 == communalities->size);
+
+ assert (factors->size1 == r->size1);
+ assert (factors->size2 == ws->n_factors);
+
+ gsl_matrix_memcpy (ws->r, r);
+
+ /* Apply Communalities to diagonal of correlation matrix */
+ for (size_t i = 0; i < communalities->size; ++i)
+ {
+ double *x = gsl_matrix_ptr (ws->r, i, i);
+ *x = gsl_vector_get (communalities, i);
+ }
+
+ gsl_eigen_symmv (ws->r, ws->eval, ws->evec, ws->eigen_ws);
+
+ gsl_matrix_view mv = gsl_matrix_submatrix (ws->evec, 0, 0, ws->evec->size1, ws->n_factors);
+
+ /* Gamma is the diagonal matrix containing the absolute values of the eigenvalues */
+ for (size_t i = 0; i < ws->n_factors; ++i)
+ {
+ double *ptr = gsl_matrix_ptr (ws->gamma, i, i);
+ *ptr = fabs (gsl_vector_get (ws->eval, i));
+ }
+
+ /* Take the square root of gamma */
+ gsl_linalg_cholesky_decomp (ws->gamma);
+
+ gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, &mv.matrix, ws->gamma, 0.0, factors);
+
+ for (size_t i = 0; i < r->size1; ++i)
+ {
+ double h = the_communality (ws->evec, ws->eval, i, ws->n_factors);
+ gsl_vector_set (communalities, i, h);
+ }
+}
+
+
+
+static bool run_factor (struct dataset *ds, const struct cmd_factor *factor);
+
+static void do_factor_by_matrix (const struct cmd_factor *factor, struct idata *idata);
+
+
+
+int
+cmd_factor (struct lexer *lexer, struct dataset *ds)
+{
+ int n_iterations = 25;
+
+ struct cmd_factor factor = {
+ .n_vars = 0,
+ .vars = NULL,
+ .method = METHOD_CORR,
+ .missing_type = MISS_LISTWISE,
+ .exclude = MV_ANY,
+ .print = PRINT_INITIAL | PRINT_EXTRACTION | PRINT_ROTATION,
+ .extraction = EXTRACTION_PC,
+ .n_factors = 0,
+ .min_eigen = SYSMIS,
+ .extraction_iterations = 25,
+ .rotation_iterations = 25,
+ .econverge = 0.001,
+
+ .blank = 0,
+ .sort = false,
+ .plot = 0,
+ .rotation = ROT_VARIMAX,
+ .wv = NULL,
+
+ .rconverge = 0.0001,
+ };
+
+ lex_match (lexer, T_SLASH);
+
+ struct dictionary *dict = NULL;
+ struct matrix_reader *mr = NULL;
+ struct casereader *matrix_reader = NULL;
+
+ int vars_start, vars_end;
+ if (lex_match_id (lexer, "VARIABLES"))
+ {
+ lex_match (lexer, T_EQUALS);
+ dict = dataset_dict (ds);
+ factor.wv = dict_get_weight (dict);
+
+ vars_start = lex_ofs (lexer);
+ if (!parse_variables_const (lexer, dict, &factor.vars, &factor.n_vars,
+ PV_NO_DUPLICATE | PV_NUMERIC))
+ goto error;
+ vars_end = lex_ofs (lexer) - 1;
+ }
+ else if (lex_match_id (lexer, "MATRIX"))
+ {
+ lex_match (lexer, T_EQUALS);
+ if (!lex_force_match_phrase (lexer, "IN("))
+ goto error;
+ if (!lex_match_id (lexer, "CORR") && !lex_match_id (lexer, "COV"))
+ {
+ lex_error (lexer, _("Matrix input for %s must be either COV or CORR"),
+ "FACTOR");
+ goto error;
+ }
+ if (!lex_force_match (lexer, T_EQUALS))
+ goto error;
+ vars_start = lex_ofs (lexer);
+ if (lex_match (lexer, T_ASTERISK))
+ {
+ dict = dataset_dict (ds);
+ matrix_reader = casereader_clone (dataset_source (ds));
+ }
+ else
+ {
+ struct file_handle *fh = fh_parse (lexer, FH_REF_FILE, NULL);
+ if (fh == NULL)
+ goto error;
+
+ matrix_reader = any_reader_open_and_decode (fh, NULL, &dict, NULL);
+
+ if (!(matrix_reader && dict))
+ goto error;
+ }
+ vars_end = lex_ofs (lexer) - 1;
+
+ if (!lex_force_match (lexer, T_RPAREN))
+ {
+ casereader_destroy (matrix_reader);
+ goto error;
+ }
+
+ mr = matrix_reader_create (dict, matrix_reader);
+ factor.vars = xmemdup (mr->cvars, mr->n_cvars * sizeof *mr->cvars);
+ factor.n_vars = mr->n_cvars;
+ }
+ else
+ goto error;
+
+ while (lex_token (lexer) != T_ENDCMD)
+ {
+ lex_match (lexer, T_SLASH);
+
+ if (lex_match_id (lexer, "ANALYSIS"))
+ {
+ struct const_var_set *vs;
+ const struct variable **vars;
+ size_t n_vars;
+
+ lex_match (lexer, T_EQUALS);
+
+ vars_start = lex_ofs (lexer);
+ vs = const_var_set_create_from_array (factor.vars, factor.n_vars);
+ vars_end = lex_ofs (lexer) - 1;
+ bool ok = parse_const_var_set_vars (lexer, vs, &vars, &n_vars,
+ PV_NO_DUPLICATE | PV_NUMERIC);
+ const_var_set_destroy (vs);
+
+ if (!ok)
+ goto error;
+
+ free (factor.vars);
+ factor.vars = vars;
+ factor.n_vars = n_vars;
+
+ if (mr)
+ {
+ free (mr->cvars);
+ mr->cvars = xmemdup (vars, n_vars * sizeof *vars);
+ mr->n_cvars = n_vars;
+ }
+ }
+ else if (lex_match_id (lexer, "PLOT"))
+ {
+ lex_match (lexer, T_EQUALS);
+ while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
+ {
+ if (lex_match_id (lexer, "EIGEN"))
+ {
+ factor.plot |= PLOT_SCREE;
+ }
+#if FACTOR_FULLY_IMPLEMENTED
+ else if (lex_match_id (lexer, "ROTATION"))
+ {
+ }
+#endif
+ else
+ {
+ lex_error_expecting (lexer, "EIGEN"
+#if FACTOR_FULLY_IMPLEMENTED
+ , "ROTATION"
+#endif
+ );
+ goto error;
+ }
+ }
+ }
+ else if (lex_match_id (lexer, "METHOD"))
+ {
+ lex_match (lexer, T_EQUALS);
+ while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
+ {
+ if (lex_match_id (lexer, "COVARIANCE"))
+ factor.method = METHOD_COV;
+ else if (lex_match_id (lexer, "CORRELATION"))
+ factor.method = METHOD_CORR;
+ else
+ {
+ lex_error_expecting (lexer, "COVARIANCE", "CORRELATION");
+ goto error;
+ }
+ }
+ }
+ else if (lex_match_id (lexer, "ROTATION"))
+ {
+ 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"))
+ factor.rotation = ROT_VARIMAX;
+ else if (lex_match_id (lexer, "EQUAMAX"))
+ factor.rotation = ROT_EQUAMAX;
+ else if (lex_match_id (lexer, "QUARTIMAX"))
+ factor.rotation = ROT_QUARTIMAX;
+ else if (lex_match_id (lexer, "PROMAX"))
+ {
+ factor.promax_power = 5;
+ if (lex_match (lexer, T_LPAREN))
+ {
+ if (!lex_force_int (lexer))
+ goto error;
+ factor.promax_power = lex_integer (lexer);
+ lex_get (lexer);
+ if (!lex_force_match (lexer, T_RPAREN))
+ goto error;
+ }
+ factor.rotation = ROT_PROMAX;
+ }
+ else if (lex_match_id (lexer, "NOROTATE"))
+ factor.rotation = ROT_NONE;
+ else
+ {
+ lex_error_expecting (lexer, "DEFAULT", "VARIMAX", "EQUAMAX",
+ "QUARTIMAX", "PROMAX", "NOROTATE");
+ goto error;
+ }
+ }
+ factor.rotation_iterations = n_iterations;
+ }
+ else if (lex_match_id (lexer, "CRITERIA"))
+ {
+ 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, T_LPAREN)
+ || !lex_force_int (lexer))
+ goto error;
+ factor.n_factors = lex_integer (lexer);
+ lex_get (lexer);
+ if (!lex_force_match (lexer, T_RPAREN))
+ goto error;
+ }
+ else if (lex_match_id (lexer, "MINEIGEN"))
+ {
+ if (!lex_force_match (lexer, T_LPAREN)
+ || !lex_force_num (lexer))
+ goto error;
+ factor.min_eigen = lex_number (lexer);
+ lex_get (lexer);
+ if (!lex_force_match (lexer, T_RPAREN))
+ goto error;
+ }
+ else if (lex_match_id (lexer, "ECONVERGE"))
+ {
+ if (!lex_force_match (lexer, T_LPAREN)
+ || !lex_force_num (lexer))
+ goto error;
+ factor.econverge = lex_number (lexer);
+ lex_get (lexer);
+ if (!lex_force_match (lexer, T_RPAREN))
+ goto error;
+ }
+ else if (lex_match_id (lexer, "RCONVERGE"))
+ {
+ if (!lex_force_match (lexer, T_LPAREN)
+ || !lex_force_num (lexer))
+ goto error;
+ factor.rconverge = lex_number (lexer);
+ lex_get (lexer);
+ if (!lex_force_match (lexer, T_RPAREN))
+ goto error;
+ }
+ else if (lex_match_id (lexer, "ITERATE"))
+ {
+ if (!lex_force_match (lexer, T_LPAREN)
+ || !lex_force_int_range (lexer, "ITERATE", 0, INT_MAX))
+ goto error;
+ n_iterations = lex_integer (lexer);
+ lex_get (lexer);
+ if (!lex_force_match (lexer, T_RPAREN))
+ goto error;
+ }
+ else if (lex_match_id (lexer, "DEFAULT"))
+ {
+ factor.n_factors = 0;
+ factor.min_eigen = 1;
+ n_iterations = 25;
+ }
+ else
+ {
+ lex_error_expecting (lexer, "FACTORS", "MINEIGEN",
+ "ECONVERGE", "RCONVERGE", "ITERATE",
+ "DEFAULT");
+ goto error;
+ }
+ }
+ }
+ else if (lex_match_id (lexer, "EXTRACTION"))
+ {
+ lex_match (lexer, T_EQUALS);
+ while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
+ {
+ if (lex_match_id (lexer, "PAF"))
+ factor.extraction = EXTRACTION_PAF;
+ else if (lex_match_id (lexer, "PC"))
+ factor.extraction = EXTRACTION_PC;
+ else if (lex_match_id (lexer, "PA1"))
+ factor.extraction = EXTRACTION_PC;
+ else if (lex_match_id (lexer, "DEFAULT"))
+ factor.extraction = EXTRACTION_PC;
+ else
+ {
+ lex_error_expecting (lexer, "PAF", "PC", "PA1", "DEFAULT");
+ goto error;
+ }
+ }
+ factor.extraction_iterations = n_iterations;
+ }
+ else if (lex_match_id (lexer, "FORMAT"))
+ {
+ lex_match (lexer, T_EQUALS);
+ while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
+ {
+ if (lex_match_id (lexer, "SORT"))
+ factor.sort = true;
+ else if (lex_match_id (lexer, "BLANK"))
+ {
+ if (!lex_force_match (lexer, T_LPAREN)
+ || !lex_force_num (lexer))
+ goto error;
+ factor.blank = lex_number (lexer);
+ lex_get (lexer);
+ if (!lex_force_match (lexer, T_RPAREN))
+ goto error;
+ }
+ else if (lex_match_id (lexer, "DEFAULT"))
+ {
+ factor.blank = 0;
+ factor.sort = false;
+ }
+ else
+ {
+ lex_error_expecting (lexer, "SORT", "BLANK", "DEFAULT");
+ goto error;
+ }
+ }
+ }
+ else if (lex_match_id (lexer, "PRINT"))
+ {
+ factor.print = 0;
+ 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_UNIVARIATE;
+ else if (lex_match_id (lexer, "DET"))
+ factor.print |= PRINT_DETERMINANT;
+#if FACTOR_FULLY_IMPLEMENTED
+ else if (lex_match_id (lexer, "INV"))
+ {
+ }
+#endif
+ else if (lex_match_id (lexer, "AIC"))
+ factor.print |= PRINT_AIC;
+ else if (lex_match_id (lexer, "SIG"))
+ factor.print |= PRINT_SIG;
+ else if (lex_match_id (lexer, "CORRELATION"))
+ factor.print |= PRINT_CORRELATION;
+ else if (lex_match_id (lexer, "COVARIANCE"))
+ factor.print |= PRINT_COVARIANCE;
+ else if (lex_match_id (lexer, "ROTATION"))
+ factor.print |= PRINT_ROTATION;
+ else if (lex_match_id (lexer, "EXTRACTION"))
+ factor.print |= PRINT_EXTRACTION;
+ else if (lex_match_id (lexer, "INITIAL"))
+ factor.print |= PRINT_INITIAL;
+ 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, "FSCORE"))
+ {
+ }
+#endif
+ else if (lex_match (lexer, T_ALL))
+ factor.print = -1;
+ else if (lex_match_id (lexer, "DEFAULT"))
+ {
+ factor.print |= PRINT_INITIAL;
+ factor.print |= PRINT_EXTRACTION;
+ factor.print |= PRINT_ROTATION;
+ }
+ else
+ {
+ lex_error_expecting (lexer, "UNIVARIATE", "DET", "AIC", "SIG",
+ "CORRELATION", "COVARIANCE", "ROTATION",
+ "EXTRACTION", "INITIAL", "KMO", "ALL",
+ "DEFAULT");
+ goto error;
+ }
+ }
+ }
+ else if (lex_match_id (lexer, "MISSING"))
+ {
+ lex_match (lexer, T_EQUALS);
+ while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
+ {
+ if (lex_match_id (lexer, "INCLUDE"))
+ factor.exclude = MV_SYSTEM;
+ else if (lex_match_id (lexer, "EXCLUDE"))
+ factor.exclude = MV_ANY;
+ else if (lex_match_id (lexer, "LISTWISE"))
+ factor.missing_type = MISS_LISTWISE;
+ else if (lex_match_id (lexer, "PAIRWISE"))
+ factor.missing_type = MISS_PAIRWISE;
+ else if (lex_match_id (lexer, "MEANSUB"))
+ factor.missing_type = MISS_MEANSUB;
+ else
+ {
+ lex_error_expecting (lexer, "INCLUDE", "EXCLUDE", "LISTWISE",
+ "PAIRRWISE", "MEANSUB");
+ goto error;
+ }
+ }
+ }
+ else
+ {
+ lex_error_expecting (lexer, "ANALYSIS", "PLOT", "METHOD", "ROTATION",
+ "CRITERIA", "EXTRACTION", "FORMAT", "PRINT",
+ "MISSING");
+ goto error;
+ }
+ }
+
+ if (factor.rotation == ROT_NONE)
+ factor.print &= ~PRINT_ROTATION;
+
+ assert (factor.n_vars > 0);
+ if (factor.n_vars < 2)
+ lex_ofs_msg (lexer, SW, vars_start, vars_end,
+ _("Factor analysis on a single variable is not useful."));
+
+ if (matrix_reader)
+ {
+ struct idata *id = idata_alloc (factor.n_vars);
+
+ while (matrix_reader_next (&id->mm, mr, NULL))
+ {
+ do_factor_by_matrix (&factor, id);
+
+ gsl_matrix_free (id->ai_cov);
+ id->ai_cov = NULL;
+ gsl_matrix_free (id->ai_cor);
+ id->ai_cor = NULL;
+
+ matrix_material_uninit (&id->mm);
+ }
+
+ idata_free (id);
+ }
+ else
+ if (!run_factor (ds, &factor))
+ goto error;
+
+ matrix_reader_destroy (mr);
+ free (factor.vars);
+ return CMD_SUCCESS;
+
+error:
+ matrix_reader_destroy (mr);
+ free (factor.vars);
+ return CMD_FAILURE;
+}
+
+static void do_factor (const struct cmd_factor *factor, struct casereader *group);
+
+
+static bool
+run_factor (struct dataset *ds, const struct cmd_factor *factor)
+{
+ struct dictionary *dict = dataset_dict (ds);
+ bool ok;
+ struct casereader *group;
+
+ struct casegrouper *grouper = casegrouper_create_splits (proc_open (ds), dict);
+
+ while (casegrouper_get_next_group (grouper, &group))
+ {
+ if (factor->missing_type == MISS_LISTWISE)
+ group = casereader_create_filter_missing (group, factor->vars, factor->n_vars,
+ factor->exclude,
+ NULL, NULL);
+ do_factor (factor, group);
+ }
+
+ ok = casegrouper_destroy (grouper);
+ ok = proc_commit (ds) && ok;
+
+ return ok;
+}
+
+
+/* Return the communality of variable N, calculated to N_FACTORS */
+static double
+the_communality (const gsl_matrix *evec, const gsl_vector *eval, int n, int n_factors)
+{
+ assert (n >= 0);
+ assert (n < eval->size);
+ assert (n < evec->size1);
+ assert (n_factors <= eval->size);
+
+ double comm = 0;
+ for (size_t i = 0; i < n_factors; ++i)
+ {
+ double evali = fabs (gsl_vector_get (eval, i));
+
+ double eveci = gsl_matrix_get (evec, n, i);
+
+ comm += pow2 (eveci) * evali;
+ }
+
+ return comm;
+}
+
+/* Return the communality of variable N, calculated to N_FACTORS */
+static double
+communality (const struct idata *idata, int n, int n_factors)
+{
+ return the_communality (idata->evec, idata->eval, n, n_factors);
+}
+
+
+static void
+show_scree (const struct cmd_factor *f, const struct idata *idata)
+{
+ struct scree *s;
+ const char *label;
+
+ if (!(f->plot & PLOT_SCREE))
+ return;
+
+
+ label = f->extraction == EXTRACTION_PC ? _("Component Number") : _("Factor Number");
+
+ s = scree_create (idata->eval, label);
+
+ scree_submit (s);
+}
+
+static void
+show_communalities (const struct cmd_factor * factor,
+ const gsl_vector *initial, const gsl_vector *extracted)
+{
+ if (!(factor->print & (PRINT_INITIAL | PRINT_EXTRACTION)))
+ return;
+
+ struct pivot_table *table = pivot_table_create (N_("Communalities"));
+
+ struct pivot_dimension *communalities = pivot_dimension_create (
+ table, PIVOT_AXIS_COLUMN, N_("Communalities"));
+ if (factor->print & PRINT_INITIAL)
+ pivot_category_create_leaves (communalities->root, N_("Initial"));
+ if (factor->print & PRINT_EXTRACTION)
+ pivot_category_create_leaves (communalities->root, N_("Extraction"));
+
+ struct pivot_dimension *variables = pivot_dimension_create (
+ table, PIVOT_AXIS_ROW, N_("Variables"));
+
+ for (size_t i = 0; i < factor->n_vars; ++i)
+ {
+ int row = pivot_category_create_leaf (
+ variables->root, pivot_value_new_variable (factor->vars[i]));
+
+ int col = 0;
+ if (factor->print & PRINT_INITIAL)
+ pivot_table_put2 (table, col++, row, pivot_value_new_number (
+ gsl_vector_get (initial, i)));
+ if (factor->print & PRINT_EXTRACTION)
+ pivot_table_put2 (table, col++, row, pivot_value_new_number (
+ gsl_vector_get (extracted, i)));
+ }
+
+ pivot_table_submit (table);
+}
+
+static struct pivot_dimension *
+create_numeric_dimension (struct pivot_table *table,
+ enum pivot_axis_type axis_type, const char *name,
+ size_t n, bool show_label)
+{
+ struct pivot_dimension *d = pivot_dimension_create (table, axis_type, name);
+ d->root->show_label = show_label;
+ for (int i = 0; i < n; ++i)
+ pivot_category_create_leaf (d->root, pivot_value_new_integer (i + 1));
+ return d;
+}
+
+static void
+show_factor_matrix (const struct cmd_factor *factor, const struct idata *idata, const char *title, const gsl_matrix *fm)
+{
+ struct pivot_table *table = pivot_table_create (title);
+
+ const int n_factors = idata->n_extractions;
+ create_numeric_dimension (
+ table, PIVOT_AXIS_COLUMN,
+ factor->extraction == EXTRACTION_PC ? N_("Component") : N_("Factor"),
+ n_factors, true);
+
+ struct pivot_dimension *variables = pivot_dimension_create (
+ table, PIVOT_AXIS_ROW, N_("Variables"));
+
+ /* Initialise to the identity permutation */
+ gsl_permutation *perm = gsl_permutation_calloc (factor->n_vars);
+
+ if (factor->sort)
+ sort_matrix_indirect (fm, perm);
+
+ for (size_t i = 0; i < factor->n_vars; ++i)
+ {
+ const int matrix_row = perm->data[i];
+
+ int var_idx = pivot_category_create_leaf (
+ variables->root, pivot_value_new_variable (factor->vars[matrix_row]));
+
+ for (size_t j = 0; j < n_factors; ++j)
+ {
+ double x = gsl_matrix_get (fm, matrix_row, j);
+ if (fabs (x) < factor->blank)
+ continue;
+
+ pivot_table_put2 (table, j, var_idx, pivot_value_new_number (x));
+ }
+ }
+
+ gsl_permutation_free (perm);
+
+ pivot_table_submit (table);
+}
+
+static void
+put_variance (struct pivot_table *table, int row, int phase_idx,
+ double lambda, double percent, double cum)
+{
+ double entries[] = { lambda, percent, cum };
+ for (size_t i = 0; i < sizeof entries / sizeof *entries; i++)
+ pivot_table_put3 (table, i, phase_idx, row,
+ pivot_value_new_number (entries[i]));
+}
+
+static void
+show_explained_variance (const struct cmd_factor * factor,
+ const struct idata *idata,
+ const gsl_vector *initial_eigenvalues,
+ const gsl_vector *extracted_eigenvalues,
+ const gsl_vector *rotated_loadings)
+{
+ if (!(factor->print & (PRINT_INITIAL | PRINT_EXTRACTION | PRINT_ROTATION)))
+ return;
+
+ struct pivot_table *table = pivot_table_create (
+ N_("Total Variance Explained"));
+
+ pivot_dimension_create (table, PIVOT_AXIS_COLUMN, N_("Statistics"),
+ N_("Total"), PIVOT_RC_OTHER,
+ /* xgettext:no-c-format */
+ N_("% of Variance"), PIVOT_RC_PERCENT,
+ /* xgettext:no-c-format */
+ N_("Cumulative %"), PIVOT_RC_PERCENT);
+
+ struct pivot_dimension *phase = pivot_dimension_create (
+ table, PIVOT_AXIS_COLUMN, N_("Phase"));
+ if (factor->print & PRINT_INITIAL)
+ pivot_category_create_leaves (phase->root, N_("Initial Eigenvalues"));
+
+ if (factor->print & PRINT_EXTRACTION)
+ pivot_category_create_leaves (phase->root,
+ N_("Extraction Sums of Squared Loadings"));
+
+ if (factor->print & PRINT_ROTATION)
+ pivot_category_create_leaves (phase->root,
+ N_("Rotation Sums of Squared Loadings"));
+
+ struct pivot_dimension *components = pivot_dimension_create (
+ table, PIVOT_AXIS_ROW,
+ factor->extraction == EXTRACTION_PC ? N_("Component") : N_("Factor"));
+
+ double i_total = 0.0;
+ for (size_t i = 0; i < initial_eigenvalues->size; ++i)
+ i_total += gsl_vector_get (initial_eigenvalues, i);
+
+ double e_total = (factor->extraction == EXTRACTION_PAF
+ ? factor->n_vars
+ : i_total);
+
+ double i_cum = 0.0;
+ double e_cum = 0.0;
+ double r_cum = 0.0;
+ for (size_t i = 0; i < factor->n_vars; ++i)
+ {
+ const double i_lambda = gsl_vector_get (initial_eigenvalues, i);
+ double i_percent = 100.0 * i_lambda / i_total;
+ i_cum += i_percent;
+
+ const double e_lambda = gsl_vector_get (extracted_eigenvalues, i);
+ double e_percent = 100.0 * e_lambda / e_total;
+ e_cum += e_percent;
+
+ int row = pivot_category_create_leaf (
+ components->root, pivot_value_new_integer (i + 1));
+
+ int phase_idx = 0;
+
+ /* Initial Eigenvalues */
+ if (factor->print & PRINT_INITIAL)
+ put_variance (table, row, phase_idx++, i_lambda, i_percent, i_cum);
+
+ if (i < idata->n_extractions)
+ {
+ if (factor->print & PRINT_EXTRACTION)
+ put_variance (table, row, phase_idx++, e_lambda, e_percent, e_cum);
+
+ if (rotated_loadings != NULL && factor->print & PRINT_ROTATION)
+ {
+ double r_lambda = gsl_vector_get (rotated_loadings, i);
+ double r_percent = 100.0 * r_lambda / e_total;
+ if (factor->rotation == ROT_PROMAX)
+ r_lambda = r_percent = SYSMIS;
+
+ r_cum += r_percent;
+ put_variance (table, row, phase_idx++, r_lambda, r_percent,
+ r_cum);
+ }
+ }
+ }
+
+ pivot_table_submit (table);
+}
+
+static void
+show_factor_correlation (const struct cmd_factor * factor, const gsl_matrix *fcm)
+{
+ struct pivot_table *table = pivot_table_create (
+ N_("Factor Correlation Matrix"));
+
+ create_numeric_dimension (
+ table, PIVOT_AXIS_ROW,
+ factor->extraction == EXTRACTION_PC ? N_("Component") : N_("Factor"),
+ fcm->size2, true);
+
+ create_numeric_dimension (table, PIVOT_AXIS_COLUMN, N_("Factor 2"),
+ fcm->size1, false);
+
+ for (size_t i = 0; i < fcm->size1; ++i)
+ for (size_t j = 0; j < fcm->size2; ++j)
+ pivot_table_put2 (table, j, i,
+ pivot_value_new_number (gsl_matrix_get (fcm, i, j)));
+
+ pivot_table_submit (table);
+}
+
+static void
+add_var_dims (struct pivot_table *table, const struct cmd_factor *factor)
+{
+ for (int i = 0; i < 2; i++)
+ {
+ struct pivot_dimension *d = pivot_dimension_create (
+ table, i ? PIVOT_AXIS_ROW : PIVOT_AXIS_COLUMN,
+ N_("Variables"));
+
+ for (size_t j = 0; j < factor->n_vars; j++)
+ pivot_category_create_leaf (
+ d->root, pivot_value_new_variable (factor->vars[j]));
+ }
+}
+
+static void
+show_aic (const struct cmd_factor *factor, const struct idata *idata)
+{
+ if ((factor->print & PRINT_AIC) == 0)
+ return;
+
+ struct pivot_table *table = pivot_table_create (N_("Anti-Image Matrices"));
+
+ add_var_dims (table, factor);
+
+ pivot_dimension_create (table, PIVOT_AXIS_ROW, N_("Statistics"),
+ N_("Anti-image Covariance"),
+ N_("Anti-image Correlation"));
+
+ for (size_t i = 0; i < factor->n_vars; ++i)
+ for (size_t j = 0; j < factor->n_vars; ++j)
+ {
+ double cov = gsl_matrix_get (idata->ai_cov, i, j);
+ pivot_table_put3 (table, i, j, 0, pivot_value_new_number (cov));
+
+ double corr = gsl_matrix_get (idata->ai_cor, i, j);
+ pivot_table_put3 (table, i, j, 1, pivot_value_new_number (corr));
+ }
+
+ pivot_table_submit (table);
+}
+
+static void
+show_correlation_matrix (const struct cmd_factor *factor, const struct idata *idata)
+{
+ if (!(factor->print & (PRINT_CORRELATION | PRINT_SIG | PRINT_DETERMINANT)))
+ return;
+
+ struct pivot_table *table = pivot_table_create (N_("Correlation Matrix"));
+
+ if (factor->print & (PRINT_CORRELATION | PRINT_SIG))
+ {
+ add_var_dims (table, factor);
+
+ struct pivot_dimension *statistics = pivot_dimension_create (
+ table, PIVOT_AXIS_ROW, N_("Statistics"));
+ if (factor->print & PRINT_CORRELATION)
+ pivot_category_create_leaves (statistics->root, N_("Correlation"),
+ PIVOT_RC_CORRELATION);
+ if (factor->print & PRINT_SIG)
+ pivot_category_create_leaves (statistics->root, N_("Sig. (1-tailed)"),
+ PIVOT_RC_SIGNIFICANCE);
+
+ int stat_idx = 0;
+ if (factor->print & PRINT_CORRELATION)
+ {
+ for (int i = 0; i < factor->n_vars; ++i)
+ for (int j = 0; j < factor->n_vars; ++j)
+ {
+ double corr = gsl_matrix_get (idata->mm.corr, i, j);
+ pivot_table_put3 (table, j, i, stat_idx,
+ pivot_value_new_number (corr));
+ }
+ stat_idx++;
+ }
+
+ if (factor->print & PRINT_SIG)
+ {
+ for (int i = 0; i < factor->n_vars; ++i)
+ for (int j = 0; j < factor->n_vars; ++j)
+ if (i != j)
+ {
+ double rho = gsl_matrix_get (idata->mm.corr, i, j);
+ double w = gsl_matrix_get (idata->mm.n, i, j);
+ double sig = significance_of_correlation (rho, w);
+ pivot_table_put3 (table, j, i, stat_idx,
+ pivot_value_new_number (sig));
+ }
+ stat_idx++;
+ }
+ }
+
+ if (factor->print & PRINT_DETERMINANT)
+ {
+ struct pivot_value *caption = pivot_value_new_user_text_nocopy (
+ xasprintf ("%s: %.2f", _("Determinant"), idata->detR));
+ pivot_table_set_caption (table, caption);
+ }
+
+ pivot_table_submit (table);
+}
+
+static void
+show_covariance_matrix (const struct cmd_factor *factor, const struct idata *idata)
+{
+ if (!(factor->print & PRINT_COVARIANCE))
+ return;
+
+ struct pivot_table *table = pivot_table_create (N_("Covariance Matrix"));
+ add_var_dims (table, factor);
+
+ for (int i = 0; i < factor->n_vars; ++i)
+ for (int j = 0; j < factor->n_vars; ++j)
+ {
+ double cov = gsl_matrix_get (idata->mm.cov, i, j);
+ pivot_table_put2 (table, j, i, pivot_value_new_number (cov));
+ }
+
+ pivot_table_submit (table);
+}
+
+
+static void
+do_factor (const struct cmd_factor *factor, struct casereader *r)
+{
+ struct ccase *c;
+ struct idata *idata = idata_alloc (factor->n_vars);
+
+ idata->cvm = covariance_1pass_create (factor->n_vars, factor->vars,
+ factor->wv, factor->exclude, true);
+
+ for (; (c = casereader_read (r)); case_unref (c))
+ {
+ covariance_accumulate (idata->cvm, c);
+ }
+
+ idata->mm.cov = covariance_calculate (idata->cvm);
+
+ if (idata->mm.cov == NULL)
+ {
+ msg (MW, _("The dataset contains no complete observations. No analysis will be performed."));
+ covariance_destroy (idata->cvm);
+ goto finish;
+ }
+
+ idata->mm.var_matrix = covariance_moments (idata->cvm, MOMENT_VARIANCE);
+ idata->mm.mean_matrix = covariance_moments (idata->cvm, MOMENT_MEAN);
+ idata->mm.n = covariance_moments (idata->cvm, MOMENT_NONE);
+
+ do_factor_by_matrix (factor, idata);
+
+ finish:
+ gsl_matrix_free (idata->mm.corr);
+ gsl_matrix_free (idata->mm.cov);
+
+ idata_free (idata);
+ casereader_destroy (r);
+}
+
+static void
+do_factor_by_matrix (const struct cmd_factor *factor, struct idata *idata)
+{
+ if (!idata->mm.cov && !(idata->mm.corr && idata->mm.var_matrix))
+ {
+ msg (ME, _("The dataset has no covariance matrix or a "
+ "correlation matrix along with standard deviations."));
+ return;
+ }
+
+ if (idata->mm.cov && !idata->mm.corr)
+ idata->mm.corr = correlation_from_covariance (idata->mm.cov, idata->mm.var_matrix);
+ if (idata->mm.corr && !idata->mm.cov)
+ idata->mm.cov = covariance_from_correlation (idata->mm.corr, idata->mm.var_matrix);
+ if (factor->method == METHOD_CORR)
+ idata->analysis_matrix = idata->mm.corr;
+ else
+ idata->analysis_matrix = idata->mm.cov;
+
+ gsl_matrix *r_inv;
+ r_inv = clone_matrix (idata->mm.corr);
+ gsl_linalg_cholesky_decomp (r_inv);
+ gsl_linalg_cholesky_invert (r_inv);
+
+ idata->ai_cov = anti_image_cov (r_inv);
+ idata->ai_cor = anti_image_corr (r_inv, idata);
+
+ double sum_ssq_r = 0;
+ double sum_ssq_a = 0;
+ for (int i = 0; i < r_inv->size1; ++i)
+ {
+ sum_ssq_r += ssq_od_n (idata->mm.corr, i);
+ sum_ssq_a += ssq_od_n (idata->ai_cor, i);
+ }
+
+ gsl_matrix_free (r_inv);
+
+ if (factor->print & PRINT_DETERMINANT
+ || factor->print & PRINT_KMO)
+ {
+ int sign = 0;
+
+ const int size = idata->mm.corr->size1;
+ gsl_permutation *p = gsl_permutation_calloc (size);
+ gsl_matrix *tmp = gsl_matrix_calloc (size, size);
+ gsl_matrix_memcpy (tmp, idata->mm.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
+ && idata->mm.n && idata->mm.mean_matrix && idata->mm.var_matrix)
+ {
+ struct pivot_table *table = pivot_table_create (
+ N_("Descriptive Statistics"));
+ pivot_table_set_weight_var (table, factor->wv);
+
+ pivot_dimension_create (table, PIVOT_AXIS_COLUMN, N_("Statistics"),
+ N_("Mean"), PIVOT_RC_OTHER,
+ N_("Std. Deviation"), PIVOT_RC_OTHER,
+ N_("Analysis N"), PIVOT_RC_COUNT);
+
+ struct pivot_dimension *variables = pivot_dimension_create (
+ table, PIVOT_AXIS_ROW, N_("Variables"));
+
+ for (size_t i = 0; i < factor->n_vars; ++i)
+ {
+ const struct variable *v = factor->vars[i];
+
+ int row = pivot_category_create_leaf (
+ variables->root, pivot_value_new_variable (v));
+
+ double entries[] = {
+ gsl_matrix_get (idata->mm.mean_matrix, i, i),
+ sqrt (gsl_matrix_get (idata->mm.var_matrix, i, i)),
+ gsl_matrix_get (idata->mm.n, i, i),
+ };
+ for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
+ pivot_table_put2 (table, j, row,
+ pivot_value_new_number (entries[j]));
+ }
+
+ pivot_table_submit (table);
+ }
+
+ if (factor->print & PRINT_KMO && idata->mm.n)
+ {
+ struct pivot_table *table = pivot_table_create (
+ N_("KMO and Bartlett's Test"));
+
+ struct pivot_dimension *statistics = pivot_dimension_create (
+ table, PIVOT_AXIS_ROW, N_("Statistics"),
+ N_("Kaiser-Meyer-Olkin Measure of Sampling Adequacy"), PIVOT_RC_OTHER);
+ pivot_category_create_group (
+ statistics->root, N_("Bartlett's Test of Sphericity"),
+ N_("Approx. Chi-Square"), PIVOT_RC_OTHER,
+ N_("df"), PIVOT_RC_INTEGER,
+ N_("Sig."), PIVOT_RC_SIGNIFICANCE);
+
+ /* 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. */
+ double w = 0;
+ for (int i = 0; i < idata->mm.n->size1; ++i)
+ w += gsl_matrix_get (idata->mm.n, i, i);
+ w /= idata->mm.n->size1;
+
+ double xsq = ((w - 1 - (2 * factor->n_vars + 5) / 6.0)
+ * -log (idata->detR));
+ double df = factor->n_vars * (factor->n_vars - 1) / 2;
+ double entries[] = {
+ sum_ssq_r / (sum_ssq_r + sum_ssq_a),
+ xsq,
+ df,
+ gsl_cdf_chisq_Q (xsq, df)
+ };
+ for (size_t i = 0; i < sizeof entries / sizeof *entries; i++)
+ pivot_table_put1 (table, i, pivot_value_new_number (entries[i]));
+
+ pivot_table_submit (table);
+ }
+
+ show_correlation_matrix (factor, idata);
+ show_covariance_matrix (factor, idata);
+ if (idata->cvm)
+ covariance_destroy (idata->cvm);
+
+ {
+ gsl_matrix *am = matrix_dup (idata->analysis_matrix);
+ gsl_eigen_symmv_workspace *workspace = gsl_eigen_symmv_alloc (factor->n_vars);
+
+ 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);
+
+ idata->n_extractions = n_extracted_factors (factor, idata);
+
+ if (idata->n_extractions == 0)
+ {
+ msg (MW, _("The %s criteria result in zero factors extracted. Therefore no analysis will be performed."), "FACTOR");
+ return;
+ }
+
+ if (idata->n_extractions > factor->n_vars)
+ {
+ msg (MW,
+ _("The %s criteria result in more factors than variables, which is not meaningful. No analysis will be performed."),
+ "FACTOR");
+ return;
+ }
+
+ {
+ gsl_matrix *rotated_factors = NULL;
+ gsl_matrix *pattern_matrix = NULL;
+ gsl_matrix *fcm = NULL;
+ gsl_vector *rotated_loadings = NULL;
+
+ const gsl_vector *extracted_eigenvalues = NULL;
+ gsl_vector *initial_communalities = gsl_vector_alloc (factor->n_vars);
+ gsl_vector *extracted_communalities = gsl_vector_alloc (factor->n_vars);
+ struct factor_matrix_workspace *fmw = factor_matrix_workspace_alloc (idata->msr->size, idata->n_extractions);
+ gsl_matrix *factor_matrix = gsl_matrix_calloc (factor->n_vars, fmw->n_factors);
+
+ if (factor->extraction == EXTRACTION_PAF)
+ {
+ gsl_vector *diff = gsl_vector_alloc (idata->msr->size);
+ struct smr_workspace *ws = ws_create (idata->analysis_matrix);
+
+ for (size_t i = 0; i < factor->n_vars; ++i)
+ {
+ double r2 = squared_multiple_correlation (idata->analysis_matrix, i, ws);
+
+ gsl_vector_set (idata->msr, i, r2);
+ }
+ ws_destroy (ws);
+
+ gsl_vector_memcpy (initial_communalities, idata->msr);
+
+ for (size_t i = 0; i < factor->extraction_iterations; ++i)
+ {
+ double min, max;
+ gsl_vector_memcpy (diff, idata->msr);
+
+ iterate_factor_matrix (idata->analysis_matrix, idata->msr, factor_matrix, fmw);
+
+ gsl_vector_sub (diff, idata->msr);
+
+ gsl_vector_minmax (diff, &min, &max);
+
+ if (fabs (min) < factor->econverge && fabs (max) < factor->econverge)
+ break;
+ }
+ gsl_vector_free (diff);
+
+
+
+ gsl_vector_memcpy (extracted_communalities, idata->msr);
+ extracted_eigenvalues = fmw->eval;
+ }
+ else if (factor->extraction == EXTRACTION_PC)
+ {
+ for (size_t i = 0; i < factor->n_vars; ++i)
+ gsl_vector_set (initial_communalities, i, communality (idata, i, factor->n_vars));
+
+ gsl_vector_memcpy (extracted_communalities, initial_communalities);
+
+ iterate_factor_matrix (idata->analysis_matrix, extracted_communalities, factor_matrix, fmw);
+
+
+ extracted_eigenvalues = idata->eval;
+ }
+
+
+ show_aic (factor, idata);
+ show_communalities (factor, initial_communalities, extracted_communalities);
+
+ if (factor->rotation != ROT_NONE)
+ {
+ rotated_factors = gsl_matrix_calloc (factor_matrix->size1, factor_matrix->size2);
+ rotated_loadings = gsl_vector_calloc (factor_matrix->size2);
+ if (factor->rotation == ROT_PROMAX)
+ {
+ pattern_matrix = gsl_matrix_calloc (factor_matrix->size1, factor_matrix->size2);
+ fcm = gsl_matrix_calloc (factor_matrix->size2, factor_matrix->size2);
+ }
+
+
+ rotate (factor, factor_matrix, extracted_communalities, rotated_factors, rotated_loadings, pattern_matrix, fcm);
+ }
+
+ show_explained_variance (factor, idata, idata->eval, extracted_eigenvalues, rotated_loadings);
+
+ factor_matrix_workspace_free (fmw);
+
+ show_scree (factor, idata);
+
+ show_factor_matrix (factor, idata,
+ (factor->extraction == EXTRACTION_PC
+ ? N_("Component Matrix") : N_("Factor Matrix")),
+ factor_matrix);
+
+ if (factor->rotation == ROT_PROMAX)
+ {
+ show_factor_matrix (factor, idata, N_("Pattern Matrix"),
+ pattern_matrix);
+ gsl_matrix_free (pattern_matrix);
+ }
+
+ if (factor->rotation != ROT_NONE)
+ {
+ show_factor_matrix (factor, idata,
+ (factor->rotation == ROT_PROMAX
+ ? N_("Structure Matrix")
+ : factor->extraction == EXTRACTION_PC
+ ? N_("Rotated Component Matrix")
+ : N_("Rotated Factor Matrix")),
+ rotated_factors);
+
+ gsl_matrix_free (rotated_factors);
+ }
+
+ if (factor->rotation == ROT_PROMAX)
+ {
+ show_factor_correlation (factor, fcm);
+ gsl_matrix_free (fcm);
+ }
+
+ gsl_matrix_free (factor_matrix);
+ gsl_vector_free (rotated_loadings);
+ gsl_vector_free (initial_communalities);
+ gsl_vector_free (extracted_communalities);
+ }
+}
+
+
projects / pspp / blobdiff