X-Git-Url: https://pintos-os.org/cgi-bin/gitweb.cgi?a=blobdiff_plain;f=src%2Flanguage%2Fstats%2Ffactor.c;h=cf67ecd8d4de1f8f82528bd1de9cf9662e7e0a16;hb=0200682d517fd4b7cfc4e333378de03bcf74be43;hp=d50d6ad3fdf2c5b6eb6c86bbbe3e3044a893f4ac;hpb=2b5831d68df1824881f9117bf2297957a6e49f64;p=pspp diff --git a/src/language/stats/factor.c b/src/language/stats/factor.c index d50d6ad3fd..cf67ecd8d4 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 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 @@ -16,38 +17,38 @@ #include - #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" +#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/chart-item.h" +#include "output/charts/scree.h" +#include "output/pivot-table.h" -#include - -#include -#include -#include -#include -#include -#include -#include - -#include -#include -#include -#include -#include -#include - -#include -#include - -#include - -#include -#include #include "gettext.h" #define _(msgid) gettext (msgid) @@ -91,7 +92,7 @@ enum print_opts PRINT_EXTRACTION = 0x0100, PRINT_INITIAL = 0x0200, PRINT_KMO = 0x0400, - PRINT_REPR = 0x0800, + PRINT_REPR = 0x0800, PRINT_FSCORE = 0x1000 }; @@ -100,18 +101,19 @@ 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 ); + const gsl_matrix *loadings); static void varimax_coefficients (double *x, double *y, double a, double b, double c, double d, - const gsl_matrix *loadings ) + const gsl_matrix *loadings) { *x = d - 2 * a * b / loadings->size1; *y = c - (a * a - b * b) / loadings->size1; @@ -120,7 +122,7 @@ varimax_coefficients (double *x, double *y, static void equamax_coefficients (double *x, double *y, double a, double b, double c, double d, - const gsl_matrix *loadings ) + const gsl_matrix *loadings) { *x = d - loadings->size2 * a * b / loadings->size1; *y = c - loadings->size2 * (a * a - b * b) / (2 * loadings->size1); @@ -135,14 +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; @@ -156,12 +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; @@ -170,13 +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 */ - const 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 */ @@ -184,6 +240,12 @@ struct idata 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 * @@ -206,10 +268,106 @@ 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) +{ + int i; + double ss = 0; + assert (m->size1 == m->size2); + + assert (j < m->size1); + + for (i = 0; i < m->size1; ++i) + { + if (i == j) continue; + 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) +{ + int i, j; + double ss = 0; + assert (m->size1 == m->size2); + + assert (n < m->size1); + + for (i = 0; i < m->size1; ++i) + { + for (j = 0; j < m->size2; ++j) + { + if (i == j) continue; + ss += pow2 (gsl_matrix_get (m, i, j)); + } + } + + return ss; +} + + +static gsl_matrix * +anti_image_corr (const gsl_matrix *m, const struct idata *idata) +{ + int i, j; + gsl_matrix *a; + assert (m->size1 == m->size2); + + a = gsl_matrix_alloc (m->size1, m->size2); + + for (i = 0; i < m->size1; ++i) + { + for (j = 0; j < m->size2; ++j) + { + double *p = gsl_matrix_ptr (a, i, j); + *p = gsl_matrix_get (m, i, j); + *p /= sqrt (gsl_matrix_get (m, i, i) * + gsl_matrix_get (m, j, j)); + } + } + + for (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) +{ + int i, j; + gsl_matrix *a; + assert (m->size1 == m->size2); + + a = gsl_matrix_alloc (m->size1, m->size2); + + for (i = 0; i < m->size1; ++i) + { + for (j = 0; j < m->size2; ++j) + { + double *p = gsl_matrix_ptr (a, i, j); + *p = gsl_matrix_get (m, i, j); + *p /= gsl_matrix_get (m, i, i); + *p /= gsl_matrix_get (m, j, j); + } + } + + return a; +} #if 0 static void @@ -225,7 +383,6 @@ dump_matrix (const gsl_matrix *m) } } - static void dump_matrix_permute (const gsl_matrix *m, const gsl_permutation *p) { @@ -253,13 +410,13 @@ 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) + if (idata->n_extractions != 0) return idata->n_extractions; /* Otherwise, if the number of factors has been explicitly requested, @@ -269,7 +426,7 @@ 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) { @@ -304,7 +461,7 @@ struct smr_workspace { /* Copy of the subject */ gsl_matrix *m; - + gsl_matrix *inverse; gsl_permutation *perm; @@ -317,7 +474,7 @@ 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); @@ -340,13 +497,13 @@ 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 */ @@ -358,7 +515,7 @@ 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); @@ -407,7 +564,7 @@ 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; } @@ -442,10 +599,10 @@ 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, @@ -478,7 +635,7 @@ 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); @@ -487,8 +644,8 @@ 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 ) + + if (maxindex > column_n) break; /* All subsequent elements of this row, are of no interest. @@ -505,11 +662,11 @@ sort_matrix_indirect (const gsl_matrix *input, gsl_permutation *perm) gsl_permutation_free (p); gsl_matrix_free (mat); - - assert ( 0 == gsl_permutation_valid (perm)); + + assert (0 == gsl_permutation_valid (perm)); /* We want the biggest value to be first */ - gsl_permutation_reverse (perm); + gsl_permutation_reverse (perm); } @@ -543,7 +700,7 @@ clone_matrix (const gsl_matrix *m) } -static double +static double initial_sv (const gsl_matrix *fm) { int j, k; @@ -563,7 +720,7 @@ initial_sv (const gsl_matrix *fm) l4s += lambda_4; l2s += lambda_sq; } - sv += ( fm->size1 * l4s - (l2s * l2s) ) / (fm->size1 * fm->size1 ); + sv += (fm->size1 * l4s - (l2s * l2s)) / (fm->size1 * fm->size1); } return sv; } @@ -572,7 +729,9 @@ 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; @@ -609,7 +768,7 @@ 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) @@ -632,7 +791,7 @@ 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; @@ -646,7 +805,7 @@ rotate (const struct cmd_factor *cf, const gsl_matrix *unrot, phi = atan2 (x, y) / 4.0 ; /* Don't bother rotating if the angle is small */ - if ( fabs (sin (phi) ) <= pow (10.0, -15.0)) + if (fabs (sin (phi)) <= pow (10.0, -15.0)) continue; for (p = 0; p < normalised->size1; ++p) @@ -666,10 +825,10 @@ rotate (const struct cmd_factor *cf, const gsl_matrix *unrot, l2s += lambda_sq; } } - sv += ( normalised->size1 * l4s - (l2s * l2s) ) / (normalised->size1 * normalised->size1 ); + sv += (normalised->size1 * l4s - (l2s * l2s)) / (normalised->size1 * normalised->size1); } - if ( fabs (sv - prev_sv) <= cf->rconverge) + if (fabs (sv - prev_sv) <= cf->rconverge) break; prev_sv = sv; @@ -679,6 +838,143 @@ rotate (const struct cmd_factor *cf, const gsl_matrix *unrot, 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); + + 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*/ @@ -690,12 +986,12 @@ 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); - if ( sum < 0 ) + if (sum < 0) for (j = 0 ; j < result->size1; ++j) { double *lambda = gsl_matrix_ptr (result, j, i); @@ -711,7 +1007,7 @@ 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; @@ -759,13 +1055,15 @@ 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) { - bool extraction_seen = false; - 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; @@ -776,42 +1074,115 @@ 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); - lex_match (lexer, '/'); + struct matrix_reader *mr = NULL; + struct casereader *matrix_reader = NULL; - if (!lex_force_match_id (lexer, "VARIABLES")) + 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")) + { + lex_match (lexer, T_EQUALS); + 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, '='); + 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; - while (lex_token (lexer) != '.') + mr = create_matrix_reader_from_case_reader (dict, matrix_reader, + &factor.vars, &factor.n_vars); + } + else { - lex_match (lexer, '/'); + 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, '='); - while (lex_token (lexer) != '.' && lex_token (lexer) != '/') + lex_match (lexer, T_EQUALS); + while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH) { if (lex_match_id (lexer, "EIGEN")) { @@ -831,8 +1202,8 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) } else if (lex_match_id (lexer, "METHOD")) { - lex_match (lexer, '='); - while (lex_token (lexer) != '.' && lex_token (lexer) != '/') + lex_match (lexer, T_EQUALS); + while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH) { if (lex_match_id (lexer, "COVARIANCE")) { @@ -851,8 +1222,8 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) } else if (lex_match_id (lexer, "ROTATION")) { - lex_match (lexer, '='); - while (lex_token (lexer) != '.' && lex_token (lexer) != '/') + lex_match (lexer, T_EQUALS); + while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH) { /* VARIMAX and DEFAULT are defaults */ if (lex_match_id (lexer, "VARIMAX") || lex_match_id (lexer, "DEFAULT")) @@ -867,6 +1238,19 @@ 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; @@ -877,67 +1261,73 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) goto error; } } + factor.rotation_iterations = n_iterations; } else if (lex_match_id (lexer, "CRITERIA")) { - lex_match (lexer, '='); - while (lex_token (lexer) != '.' && lex_token (lexer) != '/') + lex_match (lexer, T_EQUALS); + while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH) { if (lex_match_id (lexer, "FACTORS")) { - if ( lex_force_match (lexer, '(')) + if (lex_force_match (lexer, T_LPAREN) + && lex_force_int (lexer)) { - lex_force_int (lexer); factor.n_factors = lex_integer (lexer); lex_get (lexer); - lex_force_match (lexer, ')'); + if (! lex_force_match (lexer, T_RPAREN)) + goto error; } } else if (lex_match_id (lexer, "MINEIGEN")) { - if ( lex_force_match (lexer, '(')) + 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, ')'); + if (! lex_force_match (lexer, T_RPAREN)) + goto error; } } else if (lex_match_id (lexer, "ECONVERGE")) { - if ( lex_force_match (lexer, '(')) + 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, ')'); + if (! lex_force_match (lexer, T_RPAREN)) + goto error; } } 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, ')'); - } + { + 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, '(')) + 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, ')'); + 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 { @@ -948,9 +1338,8 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) } else if (lex_match_id (lexer, "EXTRACTION")) { - extraction_seen = true; - lex_match (lexer, '='); - while (lex_token (lexer) != '.' && lex_token (lexer) != '/') + lex_match (lexer, T_EQUALS); + while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH) { if (lex_match_id (lexer, "PAF")) { @@ -974,11 +1363,12 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) goto error; } } + factor.extraction_iterations = n_iterations; } else if (lex_match_id (lexer, "FORMAT")) { - lex_match (lexer, '='); - while (lex_token (lexer) != '.' && lex_token (lexer) != '/') + lex_match (lexer, T_EQUALS); + while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH) { if (lex_match_id (lexer, "SORT")) { @@ -986,12 +1376,13 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) } else if (lex_match_id (lexer, "BLANK")) { - if ( lex_force_match (lexer, '(')) + 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, ')'); + if (! lex_force_match (lexer, T_RPAREN)) + goto error; } } else if (lex_match_id (lexer, "DEFAULT")) @@ -1009,8 +1400,8 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) else if (lex_match_id (lexer, "PRINT")) { factor.print = 0; - lex_match (lexer, '='); - while (lex_token (lexer) != '.' && lex_token (lexer) != '/') + lex_match (lexer, T_EQUALS); + while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH) { if (lex_match_id (lexer, "UNIVARIATE")) { @@ -1024,10 +1415,11 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) else if (lex_match_id (lexer, "INV")) { } +#endif else if (lex_match_id (lexer, "AIC")) { + factor.print |= PRINT_AIC; } -#endif else if (lex_match_id (lexer, "SIG")) { factor.print |= PRINT_SIG; @@ -1036,11 +1428,10 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) { factor.print |= PRINT_CORRELATION; } -#if FACTOR_FULLY_IMPLEMENTED else if (lex_match_id (lexer, "COVARIANCE")) { + factor.print |= PRINT_COVARIANCE; } -#endif else if (lex_match_id (lexer, "ROTATION")) { factor.print |= PRINT_ROTATION; @@ -1053,10 +1444,11 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) { factor.print |= PRINT_INITIAL; } -#if FACTOR_FULLY_IMPLEMENTED else if (lex_match_id (lexer, "KMO")) { + factor.print |= PRINT_KMO; } +#if FACTOR_FULLY_IMPLEMENTED else if (lex_match_id (lexer, "REPR")) { } @@ -1083,8 +1475,8 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) } else if (lex_match_id (lexer, "MISSING")) { - lex_match (lexer, '='); - while (lex_token (lexer) != '.' && lex_token (lexer) != '/') + lex_match (lexer, T_EQUALS); + while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH) { if (lex_match_id (lexer, "INCLUDE")) { @@ -1120,16 +1512,50 @@ cmd_factor (struct lexer *lexer, struct dataset *ds) } } - if ( factor.rotation == ROT_NONE ) + 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 (factor.n_vars < 1) + { + msg (ME, _("Factor analysis without variables is not possible.")); + goto error; + } + + 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); + + gsl_matrix_free (id->ai_cov); + id->ai_cov = NULL; + gsl_matrix_free (id->ai_cor); + id->ai_cor = NULL; + gsl_matrix_free (id->mm.corr); + id->mm.corr = NULL; + gsl_matrix_free (id->mm.cov); + 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; } @@ -1148,7 +1574,7 @@ run_factor (struct dataset *ds, const struct cmd_factor *factor) while (casegrouper_get_next_group (grouper, &group)) { - if ( factor->missing_type == MISS_LISTWISE ) + if (factor->missing_type == MISS_LISTWISE) group = casereader_create_filter_missing (group, factor->vars, factor->n_vars, factor->exclude, NULL, NULL); @@ -1189,19 +1615,19 @@ the_communality (const gsl_matrix *evec, const gsl_vector *eval, int n, int n_fa /* Return the communality of variable N, calculated to N_FACTORS */ static double -communality (struct idata *idata, int n, int n_factors) +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, struct idata *idata) +show_scree (const struct cmd_factor *f, const struct idata *idata) { struct scree *s; const char *label ; - if ( !(f->plot & PLOT_SCREE) ) + if (!(f->plot & PLOT_SCREE)) return; @@ -1216,583 +1642,530 @@ static void show_communalities (const struct cmd_factor * factor, const gsl_vector *initial, const gsl_vector *extracted) { - int i; - int c = 0; - const int heading_columns = 1; - int nc = heading_columns; - const int heading_rows = 1; - const int nr = heading_rows + factor->n_vars; - struct tab_table *t; - - if (factor->print & PRINT_EXTRACTION) - nc++; - - if (factor->print & PRINT_INITIAL) - nc++; - - /* No point having a table with only headings */ - if (nc <= 1) + if (!(factor->print & (PRINT_INITIAL | PRINT_EXTRACTION))) return; - t = tab_create (nc, nr); - - tab_title (t, _("Communalities")); - - tab_headers (t, heading_columns, 0, heading_rows, 0); + struct pivot_table *table = pivot_table_create (N_("Communalities")); - c = 1; + struct pivot_dimension *communalities = pivot_dimension_create ( + table, PIVOT_AXIS_COLUMN, N_("Communalities")); if (factor->print & PRINT_INITIAL) - tab_text (t, c++, 0, TAB_CENTER | TAT_TITLE, _("Initial")); - + pivot_category_create_leaves (communalities->root, N_("Initial")); if (factor->print & PRINT_EXTRACTION) - tab_text (t, c++, 0, TAB_CENTER | TAT_TITLE, _("Extraction")); - - /* 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_vline (t, TAL_2, heading_columns, 0, nr - 1); - - for (i = 0 ; i < factor->n_vars; ++i) + 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) { - c = 0; - tab_text (t, c++, i + heading_rows, TAT_TITLE, var_to_string (factor->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) - tab_double (t, c++, i + heading_rows, 0, gsl_vector_get (initial, i), NULL); - + pivot_table_put2 (table, col++, row, pivot_value_new_number ( + gsl_vector_get (initial, i))); if (factor->print & PRINT_EXTRACTION) - tab_double (t, c++, i + heading_rows, 0, gsl_vector_get (extracted, i), NULL); + pivot_table_put2 (table, col++, row, pivot_value_new_number ( + gsl_vector_get (extracted, i))); } - tab_submit (t); + 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, struct idata *idata, const char *title, const gsl_matrix *fm) +show_factor_matrix (const struct cmd_factor *factor, const struct idata *idata, const char *title, const gsl_matrix *fm) { - int i; - const int n_factors = idata->n_extractions; - - const int heading_columns = 1; - const int heading_rows = 2; - const int nr = heading_rows + factor->n_vars; - const int nc = heading_columns + n_factors; - gsl_permutation *perm; + struct pivot_table *table = pivot_table_create (title); - 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); - - if ( factor->extraction == EXTRACTION_PC ) - tab_joint_text (t, - 1, 0, - nc - 1, 0, - TAB_CENTER | TAT_TITLE, _("Component")); - else - tab_joint_text (t, - 1, 0, - nc - 1, 0, - TAB_CENTER | TAT_TITLE, _("Factor")); - - - tab_hline (t, TAL_1, heading_columns, nc - 1, 1); - - - /* 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, 1, - nc - 1, nr - 1); - - tab_hline (t, TAL_1, 0, nc - 1, heading_rows); - tab_vline (t, TAL_2, heading_columns, 0, nr - 1); + 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 */ - perm = gsl_permutation_calloc (factor->n_vars); + gsl_permutation *perm = gsl_permutation_calloc (factor->n_vars); - if ( factor->sort) + if (factor->sort) sort_matrix_indirect (fm, perm); - for (i = 0 ; i < n_factors; ++i) - { - tab_text_format (t, heading_columns + i, 1, TAB_CENTER | TAT_TITLE, _("%d"), i + 1); - } - - for (i = 0 ; i < factor->n_vars; ++i) + for (size_t i = 0 ; i < factor->n_vars; ++i) { - int j; const int matrix_row = perm->data[i]; - tab_text (t, 0, i + heading_rows, TAT_TITLE, var_to_string (factor->vars[matrix_row])); - for (j = 0 ; j < n_factors; ++j) + 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) + if (fabs (x) < factor->blank) continue; - tab_double (t, heading_columns + j, heading_rows + i, 0, x, NULL); + pivot_table_put2 (table, j, var_idx, pivot_value_new_number (x)); } } gsl_permutation_free (perm); - tab_submit (t); + 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, struct idata *idata, +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) { - size_t i; - int c = 0; - const int heading_columns = 1; - const int heading_rows = 2; - const int nr = heading_rows + factor->n_vars; - - struct tab_table *t ; - - double i_total = 0.0; - double i_cum = 0.0; - - double e_total = 0.0; - double e_cum = 0.0; - - double r_cum = 0.0; - - int nc = heading_columns; - - if (factor->print & PRINT_EXTRACTION) - nc += 3; - - if (factor->print & PRINT_INITIAL) - nc += 3; - - if (factor->print & PRINT_ROTATION) - nc += 3; - - /* No point having a table with only headings */ - if ( nc <= heading_columns) + if (!(factor->print & (PRINT_INITIAL | PRINT_EXTRACTION | PRINT_ROTATION))) return; - t = tab_create (nc, nr); - - tab_title (t, _("Total Variance Explained")); + struct pivot_table *table = pivot_table_create ( + N_("Total Variance Explained")); - tab_headers (t, heading_columns, 0, heading_rows, 0); + 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); - /* 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, 1, TAB_LEFT | TAT_TITLE, _("Component")); - else - tab_text (t, 0, 1, TAB_LEFT | TAT_TITLE, _("Factor")); - - c = 1; + struct pivot_dimension *phase = pivot_dimension_create ( + table, PIVOT_AXIS_COLUMN, N_("Phase")); if (factor->print & PRINT_INITIAL) - { - tab_joint_text (t, c, 0, c + 2, 0, TAB_CENTER | TAT_TITLE, _("Initial Eigenvalues")); - c += 3; - } + pivot_category_create_leaves (phase->root, N_("Initial Eigenvalues")); if (factor->print & PRINT_EXTRACTION) - { - tab_joint_text (t, c, 0, c + 2, 0, TAB_CENTER | TAT_TITLE, _("Extraction Sums of Squared Loadings")); - c += 3; - } + pivot_category_create_leaves (phase->root, + N_("Extraction Sums of Squared Loadings")); 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; - } + pivot_category_create_leaves (phase->root, + N_("Rotation Sums of Squared Loadings")); - for (i = 0; i < (nc - heading_columns) / 3 ; ++i) - { - tab_text (t, i * 3 + 1, 1, TAB_CENTER | TAT_TITLE, _("Total")); - /* 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 %")); + struct pivot_dimension *components = pivot_dimension_create ( + table, PIVOT_AXIS_ROW, + factor->extraction == EXTRACTION_PC ? N_("Component") : N_("Factor")); - tab_vline (t, TAL_2, heading_columns + i * 3, 0, nr - 1); - } - - for (i = 0 ; i < initial_eigenvalues->size; ++i) + double i_total = 0.0; + for (size_t i = 0 ; i < initial_eigenvalues->size; ++i) i_total += gsl_vector_get (initial_eigenvalues, i); - if ( factor->extraction == EXTRACTION_PAF) - { - e_total = factor->n_vars; - } - else - { - e_total = i_total; - } + double e_total = (factor->extraction == EXTRACTION_PAF + ? factor->n_vars + : i_total); - for (i = 0 ; i < factor->n_vars; ++i) + 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; - 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); + int row = pivot_category_create_leaf ( + components->root, pivot_value_new_integer (i + 1)); - i_cum += i_percent; - e_cum += e_percent; - r_cum += r_percent; + int phase_idx = 0; /* 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); - } - - - if (factor->print & PRINT_EXTRACTION) - { - 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); - } - } + put_variance (table, row, phase_idx++, i_lambda, i_percent, i_cum); - if (factor->print & PRINT_ROTATION) - { - if (i < idata->n_extractions) - { - tab_double (t, c++, i + heading_rows, 0, r_lambda, NULL); - tab_double (t, c++, i + heading_rows, 0, r_percent, NULL); - tab_double (t, c++, i + heading_rows, 0, r_cum, NULL); - } - } + if (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); + } + } } - tab_submit (t); + pivot_table_submit (table); } - static void -show_correlation_matrix (const struct cmd_factor *factor, const struct idata *idata) +show_factor_correlation (const struct cmd_factor * factor, const gsl_matrix *fcm) { - struct tab_table *t ; - size_t i, j; - int y_pos_corr = -1; - int y_pos_sig = -1; - int suffix_rows = 0; + struct pivot_table *table = pivot_table_create ( + N_("Factor Correlation Matrix")); - const int heading_rows = 1; - const int heading_columns = 2; + create_numeric_dimension ( + table, PIVOT_AXIS_ROW, + factor->extraction == EXTRACTION_PC ? N_("Component") : N_("Factor"), + fcm->size2, true); - int nc = heading_columns ; - int nr = heading_rows ; - int n_data_sets = 0; + create_numeric_dimension (table, PIVOT_AXIS_COLUMN, N_("Factor 2"), + fcm->size1, false); - if (factor->print & PRINT_CORRELATION) - { - y_pos_corr = n_data_sets; - n_data_sets++; - nc = heading_columns + factor->n_vars; - } + 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))); - if (factor->print & PRINT_SIG) - { - y_pos_sig = n_data_sets; - n_data_sets++; - nc = heading_columns + factor->n_vars; - } + pivot_table_submit (table); +} - nr += n_data_sets * factor->n_vars; +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")); - if (factor->print & PRINT_DETERMINANT) - suffix_rows = 1; + for (size_t j = 0; j < factor->n_vars; j++) + pivot_category_create_leaf ( + d->root, pivot_value_new_variable (factor->vars[j])); + } +} - /* If the table would contain only headings, don't bother rendering it */ - if (nr <= heading_rows && suffix_rows == 0) +static void +show_aic (const struct cmd_factor *factor, const struct idata *idata) +{ + if ((factor->print & PRINT_AIC) == 0) return; - t = tab_create (nc, nr + suffix_rows); + struct pivot_table *table = pivot_table_create (N_("Anti-Image Matrices")); - tab_title (t, _("Correlation Matrix")); + add_var_dims (table, factor); - tab_hline (t, TAL_1, 0, nc - 1, heading_rows); - - if (nr > heading_rows) - { - tab_headers (t, heading_columns, 0, heading_rows, 0); + pivot_dimension_create (table, PIVOT_AXIS_ROW, N_("Statistics"), + N_("Anti-image Covariance"), + N_("Anti-image Correlation")); - tab_vline (t, TAL_2, 2, 0, nr - 1); - - /* 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); + 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)); + } - for (i = 0; i < factor->n_vars; ++i) - tab_text (t, heading_columns + i, 0, TAT_TITLE, var_to_string (factor->vars[i])); + 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; - for (i = 0 ; i < n_data_sets; ++i) - { - int y = heading_rows + i * factor->n_vars; - size_t v; - for (v = 0; v < factor->n_vars; ++v) - tab_text (t, 1, y + v, TAT_TITLE, var_to_string (factor->vars[v])); + struct pivot_table *table = pivot_table_create (N_("Correlation Matrix")); - tab_hline (t, TAL_1, 0, nc - 1, y); - } + 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) - { - const double y = heading_rows + y_pos_corr; - tab_text (t, 0, y, TAT_TITLE, _("Correlations")); - - 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); - } - } - + pivot_category_create_leaves (statistics->root, N_("Correlation"), + PIVOT_RC_CORRELATION); if (factor->print & PRINT_SIG) - { - const double y = heading_rows + y_pos_sig * factor->n_vars; - tab_text (t, 0, y, TAT_TITLE, _("Sig. 1-tailed")); + pivot_category_create_leaves (statistics->root, N_("Sig. (1-tailed)"), + PIVOT_RC_SIGNIFICANCE); - for (i = 0; i < factor->n_vars; ++i) - { - 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); - - if (i == j) - continue; + 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++; + } - tab_double (t, heading_columns + i, y + j, 0, significance_of_correlation (rho, w), NULL); - } - } - } + 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) - { - int sign = 0; - double det = 0.0; + table->caption = pivot_value_new_user_text_nocopy ( + xasprintf ("%s: %.2f", _("Determinant"), idata->detR)); - const int size = idata->corr->size1; - gsl_permutation *p = gsl_permutation_calloc (size); - gsl_matrix *tmp = gsl_matrix_calloc (size, size); - gsl_matrix_memcpy (tmp, idata->corr); + pivot_table_submit (table); +} - gsl_linalg_LU_decomp (tmp, p, &sign); - det = gsl_linalg_LU_det (tmp, sign); - gsl_permutation_free (p); - gsl_matrix_free (tmp); +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); - tab_text (t, 0, nr, TAB_LEFT | TAT_TITLE, _("Determinant")); - tab_double (t, 1, nr, 0, det, NULL); - } + 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)); + } - tab_submit (t); + pivot_table_submit (table); } - 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, - factor->wv, factor->exclude); + idata->cvm = covariance_1pass_create (factor->n_vars, factor->vars, + factor->wv, factor->exclude, true); - for ( ; (c = casereader_read (r) ); case_unref (c)) + 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 (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); + + 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); +} - if ( factor->method == METHOD_CORR) +static void +do_factor_by_matrix (const struct cmd_factor *factor, struct idata *idata) +{ + if (!idata->mm.cov && !idata->mm.corr) { - idata->corr = correlation_from_covariance (idata->cov, var_matrix); - analysis_matrix = idata->corr; + msg (ME, _("The dataset has no complete covariance or correlation matrix.")); + 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 - analysis_matrix = idata->cov; + idata->analysis_matrix = idata->mm.cov; - if ( factor->print & PRINT_UNIVARIATE) - { - const int nc = 4; - int i; - const struct fmt_spec *wfmt = factor->wv ? var_get_print_format (factor->wv) : & F_8_0; + 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); - const int heading_columns = 1; - const int heading_rows = 1; + int i; + double sum_ssq_r = 0; + double sum_ssq_a = 0; + for (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); + } - const int nr = heading_rows + factor->n_vars; + gsl_matrix_free (r_inv); - struct tab_table *t = tab_create (nc, nr); - tab_title (t, _("Descriptive Statistics")); + if (factor->print & PRINT_DETERMINANT + || factor->print & PRINT_KMO) + { + int sign = 0; - tab_headers (t, heading_columns, 0, heading_rows, 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); - /* Outline the box */ - tab_box (t, - TAL_2, TAL_2, - -1, -1, - 0, 0, - nc - 1, nr - 1); + gsl_linalg_LU_decomp (tmp, p, &sign); + idata->detR = gsl_linalg_LU_det (tmp, sign); + gsl_permutation_free (p); + gsl_matrix_free (tmp); + } - /* Vertical lines */ - tab_box (t, - -1, -1, - -1, TAL_1, - heading_columns, 0, - nc - 1, nr - 1); + if (factor->print & PRINT_UNIVARIATE) + { + struct pivot_table *table = pivot_table_create ( + N_("Descriptive Statistics")); + pivot_table_set_weight_var (table, factor->wv); - tab_hline (t, TAL_1, 0, nc - 1, heading_rows); - tab_vline (t, TAL_2, heading_columns, 0, nr - 1); + 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); - tab_text (t, 1, 0, TAB_CENTER | TAT_TITLE, _("Mean")); - tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("Std. Deviation")); - tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("Analysis N")); + struct pivot_dimension *variables = pivot_dimension_create ( + table, PIVOT_AXIS_ROW, N_("Variables")); for (i = 0 ; i < factor->n_vars; ++i) { 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); + 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])); } - tab_submit (t); + pivot_table_submit (table); + } + + if (factor->print & PRINT_KMO) + { + 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 (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); -#if 1 { + gsl_matrix *am = matrix_dup (idata->analysis_matrix); gsl_eigen_symmv_workspace *workspace = gsl_eigen_symmv_alloc (factor->n_vars); - - gsl_eigen_symmv (matrix_dup (analysis_matrix), idata->eval, idata->evec, workspace); + + gsl_eigen_symmv (am, idata->eval, idata->evec, workspace); gsl_eigen_symmv_free (workspace); + gsl_matrix_free (am); } gsl_eigen_symmv_sort (idata->eval, idata->evec, GSL_EIGEN_SORT_ABS_DESC); -#endif idata->n_extractions = n_extracted_factors (factor, idata); if (idata->n_extractions == 0) { - msg (MW, _("The FACTOR criteria result in zero factors extracted. Therefore no analysis will be performed.")); - goto finish; + 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 FACTOR criteria result in more factors than variables, which is not meaningful. No analysis will be performed.")); - goto finish; + 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; @@ -1802,14 +2175,14 @@ do_factor (const struct cmd_factor *factor, struct casereader *r) 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) + 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); } @@ -1817,18 +2190,18 @@ 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) + + if (fabs (min) < factor->econverge && fabs (max) < factor->econverge) break; } gsl_vector_free (diff); @@ -1845,22 +2218,28 @@ 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; } + show_aic (factor, idata); show_communalities (factor, initial_communalities, extracted_communalities); - - if ( factor->rotation != ROT_NONE) + 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); + rotate (factor, factor_matrix, extracted_communalities, rotated_factors, rotated_loadings, pattern_matrix, fcm); } show_explained_variance (factor, idata, idata->eval, extracted_eigenvalues, rotated_loadings); @@ -1870,30 +2249,41 @@ do_factor (const struct cmd_factor *factor, struct casereader *r) show_scree (factor, idata); show_factor_matrix (factor, idata, - factor->extraction == EXTRACTION_PC ? _("Component Matrix") : _("Factor Matrix"), + (factor->extraction == EXTRACTION_PC + ? N_("Component Matrix") : N_("Factor Matrix")), factor_matrix); - if ( factor->rotation != ROT_NONE) + 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->extraction == EXTRACTION_PC ? _("Rotated Component Matrix") : _("Rotated Factor Matrix"), + (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); } - - finish: - - idata_free (idata); - - casereader_destroy (r); } -