X-Git-Url: https://pintos-os.org/cgi-bin/gitweb.cgi?a=blobdiff_plain;f=src%2Flanguage%2Fstats%2Ffactor.c;h=d50d6ad3fdf2c5b6eb6c86bbbe3e3044a893f4ac;hb=add3ba666ddc4f88fbf0934184c82e35c0787795;hp=0679c5f506bff96006e576a0e2d2c3968427bfc0;hpb=c74561b1a11c7ee5540336646f1f928bcbb77a05;p=pspp diff --git a/src/language/stats/factor.c b/src/language/stats/factor.c index 0679c5f506..d50d6ad3fd 100644 --- a/src/language/stats/factor.c +++ b/src/language/stats/factor.c @@ -95,6 +95,52 @@ enum print_opts PRINT_FSCORE = 0x1000 }; +enum rotation_type + { + ROT_VARIMAX = 0, + ROT_EQUAMAX, + ROT_QUARTIMAX, + 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[3] = { + varimax_coefficients, + equamax_coefficients, + quartimax_coefficients +}; + struct cmd_factor { @@ -109,6 +155,7 @@ struct cmd_factor enum print_opts print; enum extraction_method extraction; enum plot_opts plot; + enum rotation_type rotation; /* Extraction Criteria */ int n_factors; @@ -116,6 +163,8 @@ struct cmd_factor double econverge; int iterations; + double rconverge; + /* Format */ double blank; bool sort; @@ -162,6 +211,7 @@ idata_free (struct idata *id) } +#if 0 static void dump_matrix (const gsl_matrix *m) { @@ -200,6 +250,7 @@ dump_vector (const gsl_vector *v) } printf ("\n"); } +#endif static int @@ -462,13 +513,206 @@ sort_matrix_indirect (const gsl_matrix *input, gsl_permutation *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) +{ + int j, k; + gsl_matrix *c = gsl_matrix_calloc (m->size1, m->size2); + + for (j = 0 ; j < c->size1; ++j) + { + for (k = 0 ; k < c->size2; ++k) + { + const double *v = gsl_matrix_const_ptr (m, j, k); + gsl_matrix_set (c, j, k, *v); + } + } + + return c; +} + + +static double +initial_sv (const gsl_matrix *fm) +{ + int j, k; + + double sv = 0.0; + for (j = 0 ; j < fm->size2; ++j) + { + double l4s = 0; + double l2s = 0; + + for (k = j + 1 ; k < fm->size2; ++k) + { + double lambda = gsl_matrix_get (fm, k, j); + double lambda_sq = lambda * lambda; + double lambda_4 = lambda_sq * lambda_sq; + + l4s += lambda_4; + l2s += lambda_sq; + } + sv += ( fm->size1 * l4s - (l2s * l2s) ) / (fm->size1 * fm->size1 ); + } + return sv; +} + +static void +rotate (const struct cmd_factor *cf, const gsl_matrix *unrot, + const gsl_vector *communalities, + gsl_matrix *result, + gsl_vector *rotated_loadings + ) +{ + int j, k; + int i; + double prev_sv; + + /* First get a normalised version of UNROT */ + gsl_matrix *normalised = gsl_matrix_calloc (unrot->size1, unrot->size2); + gsl_matrix *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 (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 */ + + prev_sv = initial_sv (normalised); + for (i = 0 ; i < cf->iterations ; ++i) + { + double sv = 0.0; + for (j = 0 ; j < normalised->size2; ++j) + { + /* These variables relate to the convergence criterium */ + double l4s = 0; + double l2s = 0; + + for (k = j + 1 ; k < normalised->size2; ++k) + { + int p; + double a = 0.0; + double b = 0.0; + double c = 0.0; + double d = 0.0; + double x, y; + double phi; + + for (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; + } + + rotation_coeff [cf->rotation] (&x, &y, a, b, c, d, normalised); + + phi = atan2 (x, y) / 4.0 ; + + /* Don't bother rotating if the angle is small */ + if ( fabs (sin (phi) ) <= pow (10.0, -15.0)) + continue; + + for (p = 0; p < normalised->size1; ++p) + { + double *lambda0 = gsl_matrix_ptr (normalised, p, j); + double *lambda1 = gsl_matrix_ptr (normalised, p, k); + drot_go (phi, lambda0, lambda1); + } + + /* Calculate the convergence criterium */ + { + double lambda = gsl_matrix_get (normalised, k, j); + double lambda_sq = lambda * lambda; + double lambda_4 = lambda_sq * lambda_sq; + + l4s += lambda_4; + l2s += lambda_sq; + } + } + sv += ( normalised->size1 * l4s - (l2s * l2s) ) / (normalised->size1 * normalised->size1 ); + } + + if ( fabs (sv - prev_sv) <= cf->rconverge) + break; + + prev_sv = sv; + } + + gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, + h_sqrt, normalised, 0.0, result); + + gsl_matrix_free (h_sqrt); + + + /* reflect negative sums and populate the rotated loadings vector*/ + for (i = 0 ; i < result->size2; ++i) + { + double ssq = 0.0; + double sum = 0.0; + for (j = 0 ; j < result->size1; ++j) + { + double s = gsl_matrix_get (result, j, i); + ssq += s * s; + sum += gsl_matrix_get (result, j, i); + } + + gsl_vector_set (rotated_loadings, i, ssq); + + if ( sum < 0 ) + for (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) +iterate_factor_matrix (const gsl_matrix *r, gsl_vector *communalities, gsl_matrix *factors, + struct factor_matrix_workspace *ws) { size_t i; gsl_matrix_view mv ; @@ -502,8 +746,7 @@ iterate_factor_matrix (const gsl_matrix *r, gsl_vector *communalities, gsl_matri /* 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); + gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, &mv.matrix, ws->gamma, 0.0, factors); for (i = 0 ; i < r->size1 ; ++i) { @@ -524,6 +767,8 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) const struct dictionary *dict = dataset_dict (ds); struct cmd_factor factor; + factor.n_vars = 0; + factor.vars = NULL; factor.method = METHOD_CORR; factor.missing_type = MISS_LISTWISE; factor.exclude = MV_ANY; @@ -533,9 +778,13 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) factor.min_eigen = SYSMIS; factor.iterations = 25; factor.econverge = 0.001; + factor.blank = 0; factor.sort = false; factor.plot = 0; + factor.rotation = ROT_VARIMAX; + + factor.rconverge = 0.0001; factor.wv = dict_get_weight (dict); @@ -600,17 +849,27 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) } } } -#if FACTOR_FULLY_IMPLEMENTED else if (lex_match_id (lexer, "ROTATION")) { lex_match (lexer, '='); while (lex_token (lexer) != '.' && lex_token (lexer) != '/') { - if (lex_match_id (lexer, "VARIMAX")) + /* 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, "DEFAULT")) + 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, "NOROTATE")) { + factor.rotation = ROT_NONE; } else { @@ -619,7 +878,6 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) } } } -#endif else if (lex_match_id (lexer, "CRITERIA")) { lex_match (lexer, '='); @@ -655,6 +913,16 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) lex_force_match (lexer, ')'); } } + else if (lex_match_id (lexer, "RCONVERGE")) + { + if ( lex_force_match (lexer, '(')) + { + lex_force_num (lexer); + factor.rconverge = lex_number (lexer); + lex_get (lexer); + lex_force_match (lexer, ')'); + } + } else if (lex_match_id (lexer, "ITERATE")) { if ( lex_force_match (lexer, '(')) @@ -852,6 +1120,9 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) } } + if ( factor.rotation == ROT_NONE ) + factor.print &= ~PRINT_ROTATION; + if ( ! run_factor (ds, &factor)) goto error; @@ -1010,7 +1281,7 @@ show_communalities (const struct cmd_factor * factor, static void -show_factor_matrix (const struct cmd_factor *factor, struct idata *idata, const gsl_matrix *fm) +show_factor_matrix (const struct cmd_factor *factor, struct idata *idata, const char *title, const gsl_matrix *fm) { int i; const int n_factors = idata->n_extractions; @@ -1023,10 +1294,14 @@ show_factor_matrix (const struct cmd_factor *factor, struct idata *idata, const struct tab_table *t = tab_create (nc, nr); + /* if ( factor->extraction == EXTRACTION_PC ) tab_title (t, _("Component Matrix")); else tab_title (t, _("Factor Matrix")); + */ + + tab_title (t, title); tab_headers (t, heading_columns, 0, heading_rows, 0); @@ -1100,7 +1375,8 @@ show_factor_matrix (const struct cmd_factor *factor, struct idata *idata, const static void show_explained_variance (const struct cmd_factor * factor, struct idata *idata, const gsl_vector *initial_eigenvalues, - const gsl_vector *extracted_eigenvalues) + const gsl_vector *extracted_eigenvalues, + const gsl_vector *rotated_loadings) { size_t i; int c = 0; @@ -1116,6 +1392,8 @@ show_explained_variance (const struct cmd_factor * factor, struct idata *idata, double e_total = 0.0; double e_cum = 0.0; + double r_cum = 0.0; + int nc = heading_columns; if (factor->print & PRINT_EXTRACTION) @@ -1203,7 +1481,6 @@ show_explained_variance (const struct cmd_factor * factor, struct idata *idata, e_total = i_total; } - for (i = 0 ; i < factor->n_vars; ++i) { const double i_lambda = gsl_vector_get (initial_eigenvalues, i); @@ -1212,12 +1489,16 @@ show_explained_variance (const struct cmd_factor * factor, struct idata *idata, const double e_lambda = gsl_vector_get (extracted_eigenvalues, i); double e_percent = 100.0 * e_lambda / e_total ; + const double r_lambda = gsl_vector_get (rotated_loadings, i); + double r_percent = 100.0 * r_lambda / e_total ; + c = 0; tab_text_format (t, c++, i + heading_rows, TAB_LEFT | TAT_TITLE, _("%d"), i + 1); i_cum += i_percent; e_cum += e_percent; + r_cum += r_percent; /* Initial Eigenvalues */ if (factor->print & PRINT_INITIAL) @@ -1227,6 +1508,7 @@ show_explained_variance (const struct cmd_factor * factor, struct idata *idata, tab_double (t, c++, i + heading_rows, 0, i_cum, NULL); } + if (factor->print & PRINT_EXTRACTION) { if (i < idata->n_extractions) @@ -1237,6 +1519,17 @@ show_explained_variance (const struct cmd_factor * factor, struct idata *idata, tab_double (t, c++, i + heading_rows, 0, e_cum, NULL); } } + + if (factor->print & PRINT_ROTATION) + { + if (i < idata->n_extractions) + { + tab_double (t, c++, i + heading_rows, 0, r_lambda, NULL); + tab_double (t, c++, i + heading_rows, 0, r_percent, NULL); + tab_double (t, c++, i + heading_rows, 0, r_cum, NULL); + } + } + } tab_submit (t); @@ -1391,7 +1684,7 @@ do_factor (const struct cmd_factor *factor, struct casereader *r) const gsl_matrix *analysis_matrix; struct idata *idata = idata_alloc (factor->n_vars); - struct covariance *cov = covariance_create (factor->n_vars, factor->vars, + struct covariance *cov = covariance_1pass_create (factor->n_vars, factor->vars, factor->wv, factor->exclude); for ( ; (c = casereader_read (r) ); case_unref (c)) @@ -1401,6 +1694,12 @@ do_factor (const struct cmd_factor *factor, struct casereader *r) idata->cov = covariance_calculate (cov); + if (idata->cov == NULL) + { + msg (MW, _("The dataset contains no complete observations. No analysis will be performed.")); + goto finish; + } + var_matrix = covariance_moments (cov, MOMENT_VARIANCE); mean_matrix = covariance_moments (cov, MOMENT_MEAN); idata->n = covariance_moments (cov, MOMENT_NONE); @@ -1493,6 +1792,9 @@ do_factor (const struct cmd_factor *factor, struct casereader *r) } { + gsl_matrix *rotated_factors = 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); @@ -1531,6 +1833,8 @@ do_factor (const struct cmd_factor *factor, struct casereader *r) } gsl_vector_free (diff); + + gsl_vector_memcpy (extracted_communalities, idata->msr); extracted_eigenvalues = fmw->eval; } @@ -1542,18 +1846,43 @@ do_factor (const struct cmd_factor *factor, struct casereader *r) gsl_vector_memcpy (extracted_communalities, initial_communalities); iterate_factor_matrix (analysis_matrix, extracted_communalities, factor_matrix, fmw); + + extracted_eigenvalues = idata->eval; } + show_communalities (factor, initial_communalities, extracted_communalities); - show_explained_variance (factor, idata, idata->eval, extracted_eigenvalues); + + if ( factor->rotation != ROT_NONE) + { + rotated_factors = gsl_matrix_calloc (factor_matrix->size1, factor_matrix->size2); + rotated_loadings = gsl_vector_calloc (factor_matrix->size2); + + rotate (factor, factor_matrix, extracted_communalities, rotated_factors, rotated_loadings); + } + + 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_matrix); + show_factor_matrix (factor, idata, + factor->extraction == EXTRACTION_PC ? _("Component Matrix") : _("Factor Matrix"), + factor_matrix); + + if ( factor->rotation != ROT_NONE) + { + show_factor_matrix (factor, idata, + factor->extraction == EXTRACTION_PC ? _("Rotated Component Matrix") : _("Rotated Factor Matrix"), + rotated_factors); + + gsl_matrix_free (rotated_factors); + } + + gsl_vector_free (initial_communalities); gsl_vector_free (extracted_communalities); @@ -1565,3 +1894,6 @@ do_factor (const struct cmd_factor *factor, struct casereader *r) casereader_destroy (r); } + + +