X-Git-Url: https://pintos-os.org/cgi-bin/gitweb.cgi?a=blobdiff_plain;f=src%2Flanguage%2Fstats%2Ffactor.c;h=3043fced29cb69d8e5cd5215475f5820817e6dfe;hb=63aa70751714736d6577c590484ad926492b2fe2;hp=f3933268431c646e70ed741fd74b7856567ab011;hpb=e943de7a3e0645852c3b659889ff3ccf38dd43ec;p=pspp diff --git a/src/language/stats/factor.c b/src/language/stats/factor.c index f393326843..3043fced29 100644 --- a/src/language/stats/factor.c +++ b/src/language/stats/factor.c @@ -1,5 +1,6 @@ /* PSPP - a program for statistical analysis. - Copyright (C) 2009, 2010, 2011, 2012 Free Software Foundation, Inc. + 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 @@ -19,11 +20,12 @@ #include #include #include -#include -#include +#include +#include #include #include +#include "data/any-reader.h" #include "data/casegrouper.h" #include "data/casereader.h" #include "data/casewriter.h" @@ -35,6 +37,8 @@ #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" @@ -45,6 +49,7 @@ #include "output/charts/scree.h" #include "output/tab.h" + #include "gettext.h" #define _(msgid) gettext (msgid) #define N_(msgid) msgid @@ -87,7 +92,7 @@ enum print_opts PRINT_EXTRACTION = 0x0100, PRINT_INITIAL = 0x0200, PRINT_KMO = 0x0400, - PRINT_REPR = 0x0800, + PRINT_REPR = 0x0800, PRINT_FSCORE = 0x1000 }; @@ -96,6 +101,7 @@ enum rotation_type ROT_VARIMAX = 0, ROT_EQUAMAX, ROT_QUARTIMAX, + ROT_PROMAX, ROT_NONE }; @@ -131,14 +137,66 @@ quartimax_coefficients (double *x, double *y, *y = c ; } -static const rotation_coefficients rotation_coeff[3] = { +static const rotation_coefficients rotation_coeff[] = { varimax_coefficients, equamax_coefficients, - quartimax_coefficients + quartimax_coefficients, + varimax_coefficients /* PROMAX is identical to VARIMAX */ }; -struct cmd_factor +/* return diag (C'C) ^ {-0.5} */ +static gsl_matrix * +diag_rcp_sqrt (const gsl_matrix *C) +{ + int j; + 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 (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) +{ + int j; + gsl_matrix *r = gsl_matrix_calloc (CCinv->size1, CCinv->size2); + + assert (CCinv->size1 == CCinv->size2); + + for (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; @@ -152,12 +210,14 @@ struct cmd_factor 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 iterations; + int extraction_iterations; double rconverge; @@ -166,13 +226,13 @@ struct cmd_factor bool sort; }; + struct idata { /* Intermediate values used in calculation */ + struct matrix_material mm; - const gsl_matrix *corr ; /* The correlation matrix */ - gsl_matrix *cov ; /* The covariance matrix */ - const gsl_matrix *n ; /* Matrix of number of samples */ + gsl_matrix *analysis_matrix; /* A pointer to either mm.corr or mm.cov */ gsl_vector *eval ; /* The eigenvalues */ gsl_matrix *evec ; /* The eigenvectors */ @@ -182,6 +242,8 @@ struct idata gsl_vector *msr ; /* Multiple Squared Regressions */ double detR; /* The determinant of the correlation matrix */ + + struct covariance *cvm; }; static struct idata * @@ -204,10 +266,10 @@ idata_free (struct idata *id) gsl_vector_free (id->msr); gsl_vector_free (id->eval); gsl_matrix_free (id->evec); - if (id->cov != NULL) - gsl_matrix_free (id->cov); - if (id->corr != NULL) - gsl_matrix_free (CONST_CAST (gsl_matrix *, id->corr)); + if (id->mm.cov != NULL) + gsl_matrix_free (id->mm.cov); + if (id->mm.corr != NULL) + gsl_matrix_free (CONST_CAST (gsl_matrix *, id->mm.corr)); free (id); } @@ -221,7 +283,7 @@ anti_image (const gsl_matrix *m) assert (m->size1 == m->size2); a = gsl_matrix_alloc (m->size1, m->size2); - + for (i = 0; i < m->size1; ++i) { for (j = 0; j < m->size2; ++j) @@ -246,7 +308,7 @@ ssq_od_n (const gsl_matrix *m, int n) assert (m->size1 == m->size2); assert (n < m->size1); - + for (i = 0; i < m->size1; ++i) { if (i == n ) continue; @@ -302,11 +364,11 @@ dump_vector (const gsl_vector *v) #endif -static int +static int n_extracted_factors (const struct cmd_factor *factor, struct idata *idata) { int i; - + /* If there is a cached value, then return that. */ if ( idata->n_extractions != 0) return idata->n_extractions; @@ -318,7 +380,7 @@ n_extracted_factors (const struct cmd_factor *factor, struct idata *idata) idata->n_extractions = factor->n_factors; goto finish; } - + /* Use the MIN_EIGEN setting. */ for (i = 0 ; i < idata->eval->size; ++i) { @@ -353,7 +415,7 @@ struct smr_workspace { /* Copy of the subject */ gsl_matrix *m; - + gsl_matrix *inverse; gsl_permutation *perm; @@ -366,7 +428,7 @@ struct smr_workspace 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); @@ -389,13 +451,13 @@ ws_destroy (struct smr_workspace *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 + /* For an explanation of what this is doing, see http://www.visualstatistics.net/Visual%20Statistics%20Multimedia/multiple_regression_analysis.htm */ @@ -407,7 +469,7 @@ squared_multiple_correlation (const gsl_matrix *corr, int var, struct smr_worksp gsl_matrix_swap_rows (ws->m, 0, var); gsl_matrix_swap_columns (ws->m, 0, var); - rxx = gsl_matrix_submatrix (ws->m, 1, 1, ws->m->size1 - 1, ws->m->size1 - 1); + rxx = gsl_matrix_submatrix (ws->m, 1, 1, ws->m->size1 - 1, ws->m->size1 - 1); gsl_linalg_LU_decomp (&rxx.matrix, ws->perm, &signum); @@ -456,7 +518,7 @@ factor_matrix_workspace_alloc (size_t n, size_t nf) ws->eval = gsl_vector_alloc (n); ws->evec = gsl_matrix_alloc (n, n); ws->r = gsl_matrix_alloc (n, n); - + return ws; } @@ -491,10 +553,10 @@ perm_shift_apply (gsl_permutation *target, const gsl_permutation *p, } -/* +/* 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, @@ -527,7 +589,7 @@ sort_matrix_indirect (const gsl_matrix *input, gsl_permutation *perm) } } - while (column_n < m && row_n < n) + 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); @@ -536,7 +598,7 @@ sort_matrix_indirect (const gsl_matrix *input, gsl_permutation *perm) { 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; @@ -554,11 +616,11 @@ sort_matrix_indirect (const gsl_matrix *input, gsl_permutation *perm) 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); + gsl_permutation_reverse (perm); } @@ -592,7 +654,7 @@ clone_matrix (const gsl_matrix *m) } -static double +static double initial_sv (const gsl_matrix *fm) { int j, k; @@ -621,7 +683,9 @@ static void rotate (const struct cmd_factor *cf, const gsl_matrix *unrot, const gsl_vector *communalities, gsl_matrix *result, - gsl_vector *rotated_loadings + gsl_vector *rotated_loadings, + gsl_matrix *pattern_matrix, + gsl_matrix *factor_correlation_matrix ) { int j, k; @@ -658,7 +722,7 @@ rotate (const struct cmd_factor *cf, const gsl_matrix *unrot, /* Now perform the rotation iterations */ prev_sv = initial_sv (normalised); - for (i = 0 ; i < cf->iterations ; ++i) + for (i = 0 ; i < cf->rotation_iterations ; ++i) { double sv = 0.0; for (j = 0 ; j < normalised->size2; ++j) @@ -681,7 +745,7 @@ rotate (const struct cmd_factor *cf, const gsl_matrix *unrot, { 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; @@ -730,6 +794,142 @@ rotate (const struct cmd_factor *cf, const gsl_matrix *unrot, 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); + + int signum; + + int i, j; + + /* 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); + gsl_matrix *D ; + gsl_matrix *Q ; + + + /* Vector of length p containing (indexed by i) + \Sum^m_j {\lambda^2_{ij}} */ + gsl_vector *rssq = gsl_vector_calloc (unrot->size1); + + for (i = 0; i < P->size1; ++i) + { + double sum = 0; + for (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 (i = 0; i < P->size1; ++i) + { + for (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); + + 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); + + D = diag_rcp_sqrt (L); + 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 (i = 0 ; i < result->size2; ++i) @@ -740,7 +940,7 @@ rotate (const struct cmd_factor *cf, const gsl_matrix *unrot, { double s = gsl_matrix_get (result, j, i); ssq += s * s; - sum += gsl_matrix_get (result, j, i); + sum += s; } gsl_vector_set (rotated_loadings, i, ssq); @@ -761,7 +961,7 @@ rotate (const struct cmd_factor *cf, const gsl_matrix *unrot, 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, +iterate_factor_matrix (const gsl_matrix *r, gsl_vector *communalities, gsl_matrix *factors, struct factor_matrix_workspace *ws) { size_t i; @@ -809,12 +1009,15 @@ iterate_factor_matrix (const gsl_matrix *r, gsl_vector *communalities, gsl_matri 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) { - const struct dictionary *dict = dataset_dict (ds); - + struct dictionary *dict = NULL; + int n_iterations = 25; struct cmd_factor factor; factor.n_vars = 0; factor.vars = NULL; @@ -825,39 +1028,111 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) factor.extraction = EXTRACTION_PC; factor.n_factors = 0; factor.min_eigen = SYSMIS; - factor.iterations = 25; + factor.extraction_iterations = 25; + factor.rotation_iterations = 25; factor.econverge = 0.001; factor.blank = 0; factor.sort = false; factor.plot = 0; factor.rotation = ROT_VARIMAX; + factor.wv = NULL; factor.rconverge = 0.0001; - factor.wv = dict_get_weight (dict); - lex_match (lexer, T_SLASH); - if (!lex_force_match_id (lexer, "VARIABLES")) + struct matrix_reader *mr = NULL; + struct casereader *matrix_reader = NULL; + + if (lex_match_id (lexer, "VARIABLES")) { - goto error; + lex_match (lexer, T_EQUALS); + dict = dataset_dict (ds); + factor.wv = dict_get_weight (dict); + + if (!parse_variables_const (lexer, dict, &factor.vars, &factor.n_vars, + PV_NO_DUPLICATE | PV_NUMERIC)) + goto error; } + else if (lex_match_id (lexer, "MATRIX")) + { + if (! lex_force_match_id (lexer, "IN")) + goto error; + if (!lex_force_match (lexer, T_LPAREN)) + { + goto error; + } + if (lex_match_id (lexer, "CORR")) + { + } + else if (lex_match_id (lexer, "COV")) + { + } + else + { + 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; + 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; - lex_match (lexer, T_EQUALS); + matrix_reader + = any_reader_open_and_decode (fh, NULL, &dict, NULL); - if (!parse_variables_const (lexer, dict, &factor.vars, &factor.n_vars, - PV_NO_DUPLICATE | PV_NUMERIC)) - goto error; + if (! (matrix_reader && dict)) + { + goto error; + } + } - if (factor.n_vars < 2) - msg (MW, _("Factor analysis on a single variable is not useful.")); + if (! lex_force_match (lexer, T_RPAREN)) + goto error; + + mr = create_matrix_reader_from_case_reader (dict, matrix_reader, + &factor.vars, &factor.n_vars); + } + else + { + goto error; + } while (lex_token (lexer) != T_ENDCMD) { lex_match (lexer, T_SLASH); - if (lex_match_id (lexer, "PLOT")) + if (lex_match_id (lexer, "ANALYSIS")) + { + struct const_var_set *vs; + const struct variable **vars; + size_t n_vars; + bool ok; + + lex_match (lexer, T_EQUALS); + + vs = const_var_set_create_from_array (factor.vars, factor.n_vars); + 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; + } + else if (lex_match_id (lexer, "PLOT")) { lex_match (lexer, T_EQUALS); while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH) @@ -916,6 +1191,19 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) { factor.rotation = ROT_QUARTIMAX; } + else if (lex_match_id (lexer, "PROMAX")) + { + factor.promax_power = 5; + if (lex_match (lexer, T_LPAREN) + && lex_force_int (lexer)) + { + 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; @@ -926,6 +1214,7 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) goto error; } } + factor.rotation_iterations = n_iterations; } else if (lex_match_id (lexer, "CRITERIA")) { @@ -934,59 +1223,64 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) { if (lex_match_id (lexer, "FACTORS")) { - if ( lex_force_match (lexer, T_LPAREN)) + if ( lex_force_match (lexer, T_LPAREN) + && lex_force_int (lexer)) { - lex_force_int (lexer); factor.n_factors = lex_integer (lexer); lex_get (lexer); - lex_force_match (lexer, T_RPAREN); + if (! lex_force_match (lexer, T_RPAREN)) + goto error; } } else if (lex_match_id (lexer, "MINEIGEN")) { - if ( lex_force_match (lexer, T_LPAREN)) + if ( lex_force_match (lexer, T_LPAREN) + && lex_force_num (lexer)) { - lex_force_num (lexer); factor.min_eigen = lex_number (lexer); lex_get (lexer); - lex_force_match (lexer, T_RPAREN); + if (! lex_force_match (lexer, T_RPAREN)) + goto error; } } else if (lex_match_id (lexer, "ECONVERGE")) { - if ( lex_force_match (lexer, T_LPAREN)) + if ( lex_force_match (lexer, T_LPAREN) + && lex_force_num (lexer)) { - lex_force_num (lexer); factor.econverge = lex_number (lexer); lex_get (lexer); - lex_force_match (lexer, T_RPAREN); + 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); - factor.rconverge = lex_number (lexer); - lex_get (lexer); - lex_force_match (lexer, T_RPAREN); - } + { + if (lex_force_match (lexer, T_LPAREN) + && lex_force_num (lexer)) + { + 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)) + if ( lex_force_match (lexer, T_LPAREN) + && lex_force_int (lexer)) { - lex_force_int (lexer); - factor.iterations = lex_integer (lexer); + n_iterations = lex_integer (lexer); lex_get (lexer); - lex_force_match (lexer, T_RPAREN); + if (! lex_force_match (lexer, T_RPAREN)) + goto error; } } else if (lex_match_id (lexer, "DEFAULT")) { factor.n_factors = 0; factor.min_eigen = 1; - factor.iterations = 25; + n_iterations = 25; } else { @@ -1022,6 +1316,7 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) goto error; } } + factor.extraction_iterations = n_iterations; } else if (lex_match_id (lexer, "FORMAT")) { @@ -1034,12 +1329,13 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) } else if (lex_match_id (lexer, "BLANK")) { - if ( lex_force_match (lexer, T_LPAREN)) + if ( lex_force_match (lexer, T_LPAREN) + && lex_force_num (lexer)) { - lex_force_num (lexer); factor.blank = lex_number (lexer); lex_get (lexer); - lex_force_match (lexer, T_RPAREN); + if (! lex_force_match (lexer, T_RPAREN)) + goto error; } } else if (lex_match_id (lexer, "DEFAULT")) @@ -1172,13 +1468,35 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) if ( factor.rotation == ROT_NONE ) factor.print &= ~PRINT_ROTATION; - if ( ! run_factor (ds, &factor)) - goto error; + if (factor.n_vars < 2) + msg (MW, _("Factor analysis on a single variable is not useful.")); + + if (matrix_reader) + { + struct idata *id = idata_alloc (factor.n_vars); + + while (next_matrix_from_reader (&id->mm, mr, + factor.vars, factor.n_vars)) + { + do_factor_by_matrix (&factor, id); + + id->mm.corr = NULL; + id->mm.cov = NULL; + } + + idata_free (id); + } + else + if ( ! run_factor (ds, &factor)) + goto error; + + destroy_matrix_reader (mr); free (factor.vars); return CMD_SUCCESS; error: + destroy_matrix_reader (mr); free (factor.vars); return CMD_FAILURE; } @@ -1319,10 +1637,10 @@ show_communalities (const struct cmd_factor * factor, tab_text (t, c++, i + heading_rows, TAT_TITLE, var_to_string (factor->vars[i])); if (factor->print & PRINT_INITIAL) - tab_double (t, c++, i + heading_rows, 0, gsl_vector_get (initial, i), NULL); + tab_double (t, c++, i + heading_rows, 0, gsl_vector_get (initial, i), NULL, RC_OTHER); if (factor->print & PRINT_EXTRACTION) - tab_double (t, c++, i + heading_rows, 0, gsl_vector_get (extracted, i), NULL); + tab_double (t, c++, i + heading_rows, 0, gsl_vector_get (extracted, i), NULL, RC_OTHER); } tab_submit (t); @@ -1333,6 +1651,7 @@ static void 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; const int heading_columns = 1; @@ -1343,10 +1662,10 @@ 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 + else tab_title (t, _("Factor Matrix")); */ @@ -1411,7 +1730,7 @@ show_factor_matrix (const struct cmd_factor *factor, struct idata *idata, const if ( fabs (x) < factor->blank) continue; - tab_double (t, heading_columns + j, heading_rows + i, 0, x, NULL); + tab_double (t, heading_columns + j, heading_rows + i, 0, x, NULL, RC_OTHER); } } @@ -1452,7 +1771,9 @@ show_explained_variance (const struct cmd_factor * factor, struct idata *idata, nc += 3; if (factor->print & PRINT_ROTATION) - nc += 3; + { + nc += factor->rotation == ROT_PROMAX ? 1 : 3; + } /* No point having a table with only headings */ if ( nc <= heading_columns) @@ -1504,18 +1825,23 @@ show_explained_variance (const struct cmd_factor * factor, struct idata *idata, if (factor->print & PRINT_ROTATION) { - tab_joint_text (t, c, 0, c + 2, 0, TAB_CENTER | TAT_TITLE, _("Rotation Sums of Squared Loadings")); - c += 3; + const int width = factor->rotation == ROT_PROMAX ? 0 : 2; + tab_joint_text (t, c, 0, c + width, 0, TAB_CENTER | TAT_TITLE, _("Rotation Sums of Squared Loadings")); + c += width + 1; } - for (i = 0; i < (nc - heading_columns) / 3 ; ++i) + for (i = 0; i < (nc - heading_columns + 2) / 3 ; ++i) { tab_text (t, i * 3 + 1, 1, TAB_CENTER | TAT_TITLE, _("Total")); + + tab_vline (t, TAL_2, heading_columns + i * 3, 0, nr - 1); + + if (i == 2 && factor->rotation == ROT_PROMAX) + continue; + /* xgettext:no-c-format */ tab_text (t, i * 3 + 2, 1, TAB_CENTER | TAT_TITLE, _("% of Variance")); tab_text (t, i * 3 + 3, 1, TAB_CENTER | TAT_TITLE, _("Cumulative %")); - - tab_vline (t, TAL_2, heading_columns + i * 3, 0, nr - 1); } for (i = 0 ; i < initial_eigenvalues->size; ++i) @@ -1548,9 +1874,9 @@ show_explained_variance (const struct cmd_factor * factor, struct idata *idata, /* Initial Eigenvalues */ if (factor->print & PRINT_INITIAL) { - tab_double (t, c++, i + heading_rows, 0, i_lambda, NULL); - tab_double (t, c++, i + heading_rows, 0, i_percent, NULL); - tab_double (t, c++, i + heading_rows, 0, i_cum, NULL); + tab_double (t, c++, i + heading_rows, 0, i_lambda, NULL, RC_OTHER); + tab_double (t, c++, i + heading_rows, 0, i_percent, NULL, RC_OTHER); + tab_double (t, c++, i + heading_rows, 0, i_cum, NULL, RC_OTHER); } @@ -1559,9 +1885,9 @@ show_explained_variance (const struct cmd_factor * factor, struct idata *idata, if (i < idata->n_extractions) { /* Sums of squared loadings */ - tab_double (t, c++, i + heading_rows, 0, e_lambda, NULL); - tab_double (t, c++, i + heading_rows, 0, e_percent, NULL); - tab_double (t, c++, i + heading_rows, 0, e_cum, NULL); + tab_double (t, c++, i + heading_rows, 0, e_lambda, NULL, RC_OTHER); + tab_double (t, c++, i + heading_rows, 0, e_percent, NULL, RC_OTHER); + tab_double (t, c++, i + heading_rows, 0, e_cum, NULL, RC_OTHER); } } @@ -1575,9 +1901,12 @@ show_explained_variance (const struct cmd_factor * factor, struct idata *idata, if (i < idata->n_extractions) { r_cum += r_percent; - tab_double (t, c++, i + heading_rows, 0, r_lambda, NULL); - tab_double (t, c++, i + heading_rows, 0, r_percent, NULL); - tab_double (t, c++, i + heading_rows, 0, r_cum, NULL); + tab_double (t, c++, i + heading_rows, 0, r_lambda, NULL, RC_OTHER); + if (factor->rotation != ROT_PROMAX) + { + tab_double (t, c++, i + heading_rows, 0, r_percent, NULL, RC_OTHER); + tab_double (t, c++, i + heading_rows, 0, r_cum, NULL, RC_OTHER); + } } } } @@ -1587,6 +1916,67 @@ show_explained_variance (const struct cmd_factor * factor, struct idata *idata, } +static void +show_factor_correlation (const struct cmd_factor * factor, const gsl_matrix *fcm) +{ + size_t i, j; + const int heading_columns = 1; + const int heading_rows = 1; + const int nr = heading_rows + fcm->size2; + const int nc = heading_columns + fcm->size1; + struct tab_table *t = tab_create (nc, nr); + + tab_title (t, _("Factor Correlation Matrix")); + + tab_headers (t, heading_columns, 0, heading_rows, 0); + + /* Outline the box */ + tab_box (t, + TAL_2, TAL_2, + -1, -1, + 0, 0, + nc - 1, nr - 1); + + /* Vertical lines */ + tab_box (t, + -1, -1, + -1, TAL_1, + heading_columns, 0, + nc - 1, nr - 1); + + tab_hline (t, TAL_1, 0, nc - 1, heading_rows); + tab_hline (t, TAL_1, 1, nc - 1, 1); + + tab_vline (t, TAL_2, heading_columns, 0, nr - 1); + + + if ( factor->extraction == EXTRACTION_PC) + tab_text (t, 0, 0, TAB_LEFT | TAT_TITLE, _("Component")); + else + tab_text (t, 0, 0, TAB_LEFT | TAT_TITLE, _("Factor")); + + for (i = 0 ; i < fcm->size1; ++i) + { + tab_text_format (t, heading_columns + i, 0, TAB_CENTER | TAT_TITLE, _("%zu"), i + 1); + } + + for (i = 0 ; i < fcm->size2; ++i) + { + tab_text_format (t, 0, heading_rows + i, TAB_CENTER | TAT_TITLE, _("%zu"), i + 1); + } + + + for (i = 0 ; i < fcm->size1; ++i) + { + for (j = 0 ; j < fcm->size2; ++j) + tab_double (t, heading_columns + i, heading_rows +j, 0, + gsl_matrix_get (fcm, i, j), NULL, RC_OTHER); + } + + tab_submit (t); +} + + static void show_correlation_matrix (const struct cmd_factor *factor, const struct idata *idata) { @@ -1675,7 +2065,7 @@ show_correlation_matrix (const struct cmd_factor *factor, const struct idata *id for (i = 0; i < factor->n_vars; ++i) { for (j = 0; j < factor->n_vars; ++j) - tab_double (t, heading_columns + i, y + j, 0, gsl_matrix_get (idata->corr, i, j), NULL); + tab_double (t, heading_columns + i, y + j, 0, gsl_matrix_get (idata->mm.corr, i, j), NULL, RC_OTHER); } } @@ -1688,13 +2078,13 @@ show_correlation_matrix (const struct cmd_factor *factor, const struct idata *id { for (j = 0; j < factor->n_vars; ++j) { - double rho = gsl_matrix_get (idata->corr, i, j); - double w = gsl_matrix_get (idata->n, i, j); + double rho = gsl_matrix_get (idata->mm.corr, i, j); + double w = gsl_matrix_get (idata->mm.n, i, j); if (i == j) continue; - tab_double (t, heading_columns + i, y + j, 0, significance_of_correlation (rho, w), NULL); + tab_double (t, heading_columns + i, y + j, 0, significance_of_correlation (rho, w), NULL, RC_PVALUE); } } } @@ -1704,65 +2094,68 @@ show_correlation_matrix (const struct cmd_factor *factor, const struct idata *id { tab_text (t, 0, nr, TAB_LEFT | TAT_TITLE, _("Determinant")); - tab_double (t, 1, nr, 0, idata->detR, NULL); + tab_double (t, 1, nr, 0, idata->detR, NULL, RC_OTHER); } tab_submit (t); } - static void do_factor (const struct cmd_factor *factor, struct casereader *r) { struct ccase *c; - const gsl_matrix *var_matrix; - const gsl_matrix *mean_matrix; - - const gsl_matrix *analysis_matrix; struct idata *idata = idata_alloc (factor->n_vars); - struct covariance *cov = covariance_1pass_create (factor->n_vars, factor->vars, + idata->cvm = covariance_1pass_create (factor->n_vars, factor->vars, factor->wv, factor->exclude); for ( ; (c = casereader_read (r) ); case_unref (c)) { - covariance_accumulate (cov, c); + covariance_accumulate (idata->cvm, c); } - idata->cov = covariance_calculate (cov); + idata->mm.cov = covariance_calculate (idata->cvm); - if (idata->cov == NULL) + if (idata->mm.cov == NULL) { msg (MW, _("The dataset contains no complete observations. No analysis will be performed.")); - covariance_destroy (cov); + covariance_destroy (idata->cvm); goto finish; } - var_matrix = covariance_moments (cov, MOMENT_VARIANCE); - mean_matrix = covariance_moments (cov, MOMENT_MEAN); - idata->n = covariance_moments (cov, MOMENT_NONE); - + 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); - if ( factor->method == METHOD_CORR) - { - idata->corr = correlation_from_covariance (idata->cov, var_matrix); - - analysis_matrix = idata->corr; - } - else - analysis_matrix = idata->cov; + do_factor_by_matrix (factor, idata); + + finish: + 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.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; if (factor->print & PRINT_DETERMINANT || factor->print & PRINT_KMO) { int sign = 0; - const int size = idata->corr->size1; + 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->corr); + gsl_matrix_memcpy (tmp, idata->mm.corr); gsl_linalg_LU_decomp (tmp, p, &sign); idata->detR = gsl_linalg_LU_det (tmp, sign); @@ -1782,6 +2175,7 @@ do_factor (const struct cmd_factor *factor, struct casereader *r) const int nr = heading_rows + factor->n_vars; struct tab_table *t = tab_create (nc, nr); + tab_set_format (t, RC_WEIGHT, wfmt); tab_title (t, _("Descriptive Statistics")); tab_headers (t, heading_columns, 0, heading_rows, 0); @@ -1812,9 +2206,9 @@ do_factor (const struct cmd_factor *factor, struct casereader *r) const struct variable *v = factor->vars[i]; tab_text (t, 0, i + heading_rows, TAB_LEFT | TAT_TITLE, var_to_string (v)); - tab_double (t, 1, i + heading_rows, 0, gsl_matrix_get (mean_matrix, i, i), NULL); - tab_double (t, 2, i + heading_rows, 0, sqrt (gsl_matrix_get (var_matrix, i, i)), NULL); - tab_double (t, 3, i + heading_rows, 0, gsl_matrix_get (idata->n, i, i), wfmt); + tab_double (t, 1, i + heading_rows, 0, gsl_matrix_get (idata->mm.mean_matrix, i, i), NULL, RC_OTHER); + tab_double (t, 2, i + heading_rows, 0, sqrt (gsl_matrix_get (idata->mm.var_matrix, i, i)), NULL, RC_OTHER); + tab_double (t, 3, i + heading_rows, 0, gsl_matrix_get (idata->mm.n, i, i), NULL, RC_WEIGHT); } tab_submit (t); @@ -1826,7 +2220,7 @@ do_factor (const struct cmd_factor *factor, struct casereader *r) double sum_ssq_r = 0; double sum_ssq_a = 0; - double df = factor->n_vars * ( factor->n_vars - 1) / 2; + double df = factor->n_vars * (factor->n_vars - 1) / 2; double w = 0; @@ -1844,7 +2238,7 @@ do_factor (const struct cmd_factor *factor, struct casereader *r) struct tab_table *t = tab_create (nc, nr); tab_title (t, _("KMO and Bartlett's Test")); - x = clone_matrix (idata->corr); + x = clone_matrix (idata->mm.corr); gsl_linalg_cholesky_decomp (x); gsl_linalg_cholesky_invert (x); @@ -1872,7 +2266,7 @@ do_factor (const struct cmd_factor *factor, struct casereader *r) tab_text (t, 0, 0, TAT_TITLE | TAB_LEFT, _("Kaiser-Meyer-Olkin Measure of Sampling Adequacy")); - tab_double (t, 2, 0, 0, sum_ssq_r / (sum_ssq_r + sum_ssq_a), NULL); + tab_double (t, 2, 0, 0, sum_ssq_r / (sum_ssq_r + sum_ssq_a), NULL, RC_OTHER); tab_text (t, 0, 1, TAT_TITLE | TAB_LEFT, _("Bartlett's Test of Sphericity")); @@ -1881,32 +2275,33 @@ do_factor (const struct cmd_factor *factor, struct casereader *r) tab_text (t, 1, 3, TAT_TITLE, _("Sig.")); - /* The literature doesn't say what to do for the value of W when + /* The literature doesn't say what to do for the value of W when missing values are involved. The best thing I can think of is to take the mean average. */ w = 0; - for (i = 0; i < idata->n->size1; ++i) - w += gsl_matrix_get (idata->n, i, i); - w /= idata->n->size1; + for (i = 0; i < idata->mm.n->size1; ++i) + w += gsl_matrix_get (idata->mm.n, i, i); + w /= idata->mm.n->size1; xsq = w - 1 - (2 * factor->n_vars + 5) / 6.0; xsq *= -log (idata->detR); - tab_double (t, 2, 1, 0, xsq, NULL); - tab_double (t, 2, 2, 0, df, &F_8_0); - tab_double (t, 2, 3, 0, gsl_cdf_chisq_Q (xsq, df), NULL); - + tab_double (t, 2, 1, 0, xsq, NULL, RC_OTHER); + tab_double (t, 2, 2, 0, df, NULL, RC_INTEGER); + tab_double (t, 2, 3, 0, gsl_cdf_chisq_Q (xsq, df), NULL, RC_PVALUE); + tab_submit (t); } show_correlation_matrix (factor, idata); - covariance_destroy (cov); + if (idata->cvm) + covariance_destroy (idata->cvm); { - gsl_matrix *am = matrix_dup (analysis_matrix); + 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); @@ -1919,18 +2314,22 @@ do_factor (const struct cmd_factor *factor, struct casereader *r) if (idata->n_extractions == 0) { - msg (MW, _("The FACTOR criteria result in zero factors extracted. Therefore no analysis will be performed.")); + msg (MW, _("The %s criteria result in zero factors extracted. Therefore no analysis will be performed."), "FACTOR"); goto finish; } if (idata->n_extractions > factor->n_vars) { - msg (MW, _("The FACTOR criteria result in more factors than variables, which is not meaningful. No analysis will be performed.")); + msg (MW, + _("The %s criteria result in more factors than variables, which is not meaningful. No analysis will be performed."), + "FACTOR"); goto finish; } - + { 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; @@ -1943,11 +2342,11 @@ do_factor (const struct cmd_factor *factor, struct casereader *r) if ( factor->extraction == EXTRACTION_PAF) { gsl_vector *diff = gsl_vector_alloc (idata->msr->size); - struct smr_workspace *ws = ws_create (analysis_matrix); + struct smr_workspace *ws = ws_create (idata->analysis_matrix); for (i = 0 ; i < factor->n_vars ; ++i) { - double r2 = squared_multiple_correlation (analysis_matrix, i, ws); + double r2 = squared_multiple_correlation (idata->analysis_matrix, i, ws); gsl_vector_set (idata->msr, i, r2); } @@ -1955,17 +2354,17 @@ do_factor (const struct cmd_factor *factor, struct casereader *r) gsl_vector_memcpy (initial_communalities, idata->msr); - for (i = 0; i < factor->iterations; ++i) + for (i = 0; i < factor->extraction_iterations; ++i) { double min, max; gsl_vector_memcpy (diff, idata->msr); - iterate_factor_matrix (analysis_matrix, idata->msr, factor_matrix, fmw); - + 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; } @@ -1983,7 +2382,7 @@ 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); + iterate_factor_matrix (idata->analysis_matrix, extracted_communalities, factor_matrix, fmw); extracted_eigenvalues = idata->eval; @@ -1997,8 +2396,14 @@ do_factor (const struct cmd_factor *factor, struct casereader *r) { 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); + rotate (factor, factor_matrix, extracted_communalities, rotated_factors, rotated_loadings, pattern_matrix, fcm); } show_explained_variance (factor, idata, idata->eval, extracted_eigenvalues, rotated_loadings); @@ -2011,16 +2416,28 @@ do_factor (const struct cmd_factor *factor, struct casereader *r) factor->extraction == EXTRACTION_PC ? _("Component Matrix") : _("Factor Matrix"), factor_matrix); + if ( factor->rotation == ROT_PROMAX) + { + show_factor_matrix (factor, idata, _("Pattern Matrix"), pattern_matrix); + gsl_matrix_free (pattern_matrix); + } + if ( factor->rotation != ROT_NONE) { show_factor_matrix (factor, idata, - factor->extraction == EXTRACTION_PC ? _("Rotated Component Matrix") : _("Rotated Factor Matrix"), + (factor->rotation == ROT_PROMAX) ? _("Structure Matrix") : + (factor->extraction == EXTRACTION_PC ? _("Rotated Component Matrix") : + _("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); @@ -2029,11 +2446,7 @@ do_factor (const struct cmd_factor *factor, struct casereader *r) } finish: - - idata_free (idata); - - casereader_destroy (r); + return; } -