+++ /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/data-io/file-handle.h"
-#include "language/data-io/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