From: John Darrington Date: Wed, 23 Dec 2009 17:39:31 +0000 (+0100) Subject: First attempt at FACTOR command X-Git-Tag: lenny-x64-build83~3 X-Git-Url: https://pintos-os.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=816e076775c2c0ba944f1f03d99db611c24c8c2c;p=pspp-builds.git First attempt at FACTOR command --- diff --git a/src/language/command.def b/src/language/command.def index 066ecf92..d51f3295 100644 --- a/src/language/command.def +++ b/src/language/command.def @@ -106,6 +106,7 @@ DEF_CMD (S_DATA, 0, "DESCRIPTIVES", cmd_descriptives) DEF_CMD (S_DATA, 0, "EXAMINE", cmd_examine) DEF_CMD (S_DATA, 0, "EXECUTE", cmd_execute) DEF_CMD (S_DATA, 0, "EXPORT", cmd_export) +DEF_CMD (S_DATA, 0, "FACTOR", cmd_factor) DEF_CMD (S_DATA, 0, "FILTER", cmd_filter) DEF_CMD (S_DATA, 0, "FLIP", cmd_flip) DEF_CMD (S_DATA, 0, "FREQUENCIES", cmd_frequencies) @@ -175,7 +176,6 @@ UNIMPL_CMD ("DETECTANOMALY", "Find unusual cases") UNIMPL_CMD ("DISCRIMINANT", "Linear discriminant analysis") UNIMPL_CMD ("EDIT", "obsolete") UNIMPL_CMD ("END FILE TYPE", "Ends complex data input") -UNIMPL_CMD ("FACTOR", "Factor analysis") UNIMPL_CMD ("FILE TYPE", "Complex data input") UNIMPL_CMD ("FIT", "Goodness of Fit") UNIMPL_CMD ("GENLOG", "Categorical model fitting") diff --git a/src/language/stats/automake.mk b/src/language/stats/automake.mk index 05e8bcf9..21e3f0ae 100644 --- a/src/language/stats/automake.mk +++ b/src/language/stats/automake.mk @@ -28,6 +28,7 @@ language_stats_sources = \ src/language/stats/sort-cases.c \ src/language/stats/sort-criteria.c \ src/language/stats/sort-criteria.h \ + src/language/stats/factor.c \ src/language/stats/flip.c \ src/language/stats/freq.c \ src/language/stats/freq.h \ diff --git a/src/language/stats/factor.c b/src/language/stats/factor.c new file mode 100644 index 00000000..15d9c129 --- /dev/null +++ b/src/language/stats/factor.c @@ -0,0 +1,1433 @@ +/* PSPP - a program for statistical analysis. + Copyright (C) 2009 Free Software Foundation, Inc. + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see . */ + +#include + + +#include +#include +#include +#include +#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) +#define N_(msgid) msgid + +enum method + { + METHOD_CORR, + METHOD_COV + }; + +enum missing_type + { + MISS_LISTWISE, + MISS_PAIRWISE, + MISS_MEANSUB, + }; + +enum extraction_method + { + EXTRACTION_PC, + EXTRACTION_PAF, + }; + +enum print_opts + { + PRINT_UNIVARIATE = 0x0001, + PRINT_DETERMINANT = 0x0002, + PRINT_INV = 0x0004, + PRINT_AIC = 0x0008, + PRINT_SIG = 0x0010, + PRINT_COVARIANCE = 0x0020, + PRINT_CORRELATION = 0x0040, + PRINT_ROTATION = 0x0080, + PRINT_EXTRACTION = 0x0100, + PRINT_INITIAL = 0x0200, + PRINT_KMO = 0x0400, + PRINT_REPR = 0x0800, + PRINT_FSCORE = 0x1000 + }; + + +struct cmd_factor +{ + size_t n_vars; + const struct variable **vars; + + const struct variable *wv; + + enum method method; + enum missing_type missing_type; + enum mv_class exclude; + enum print_opts print; + enum extraction_method extraction; + + /* Extraction Criteria */ + int n_factors; + double min_eigen; + double econverge; + int iterations; + + /* Format */ + double blank; + bool sort; +}; + +struct idata +{ + /* Intermediate values used in calculation */ + + gsl_vector *eval ; /* The eigenvalues */ + gsl_matrix *evec ; /* The eigenvectors */ + + int n_extractions; + + gsl_vector *msr ; /* Multiple Squared Regressions */ +}; + +static struct idata * +idata_alloc (size_t n_vars) +{ + struct idata *id = xmalloc (sizeof (*id)); + + id->n_extractions = 0; + id->msr = gsl_vector_alloc (n_vars); + + id->eval = gsl_vector_alloc (n_vars); + id->evec = gsl_matrix_alloc (n_vars, n_vars); + + return id; +} + +static void +idata_free (struct idata *id) +{ + gsl_vector_free (id->msr); + gsl_vector_free (id->eval); + gsl_matrix_free (id->evec); + + free (id); +} + + +static void +dump_matrix (const gsl_matrix *m) +{ + size_t i, j; + + for (i = 0 ; i < m->size1; ++i) + { + for (j = 0 ; j < m->size2; ++j) + printf ("%02f ", gsl_matrix_get (m, i, j)); + printf ("\n"); + } +} + + +static void +dump_matrix_permute (const gsl_matrix *m, const gsl_permutation *p) +{ + size_t i, j; + + for (i = 0 ; i < m->size1; ++i) + { + for (j = 0 ; j < m->size2; ++j) + printf ("%02f ", gsl_matrix_get (m, gsl_permutation_get (p, i), j)); + printf ("\n"); + } +} + + +static void +dump_vector (const gsl_vector *v) +{ + size_t i; + for (i = 0 ; i < v->size; ++i) + { + printf ("%02f\n", gsl_vector_get (v, i)); + } + printf ("\n"); +} + + +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; + + /* Otherwise, if the number of factors has been explicitly requested, + use that. */ + if (factor->n_factors > 0) + { + idata->n_extractions = factor->n_factors; + goto finish; + } + + /* Use the MIN_EIGEN setting. */ + for (i = 0 ; i < idata->eval->size; ++i) + { + double evali = fabs (gsl_vector_get (idata->eval, i)); + + idata->n_extractions = i; + + if (evali < factor->min_eigen) + goto finish; + } + + finish: + return idata->n_extractions; +} + + +/* Returns a newly allocated matrix identical to M. + It it the callers responsibility to free the returned value. +*/ +static gsl_matrix * +matrix_dup (const gsl_matrix *m) +{ + gsl_matrix *n = gsl_matrix_alloc (m->size1, m->size2); + + gsl_matrix_memcpy (n, m); + + return n; +} + + +struct smr_workspace +{ + /* Copy of the subject */ + gsl_matrix *m; + + gsl_matrix *inverse; + + gsl_permutation *perm; + + gsl_matrix *result1; + gsl_matrix *result2; +}; + + +static struct smr_workspace *ws_create (const gsl_matrix *input) +{ + struct smr_workspace *ws = xmalloc (sizeof (*ws)); + + ws->m = gsl_matrix_alloc (input->size1, input->size2); + ws->inverse = gsl_matrix_calloc (input->size1 - 1, input->size2 - 1); + ws->perm = gsl_permutation_alloc (input->size1 - 1); + ws->result1 = gsl_matrix_calloc (input->size1 - 1, 1); + ws->result2 = gsl_matrix_calloc (1, 1); + + return ws; +} + +static void +ws_destroy (struct smr_workspace *ws) +{ + gsl_matrix_free (ws->result2); + gsl_matrix_free (ws->result1); + gsl_permutation_free (ws->perm); + gsl_matrix_free (ws->inverse); + gsl_matrix_free (ws->m); + + free (ws); +} + + +/* + Return the square of the regression coefficient for VAR regressed against all other variables. + */ +static double +squared_multiple_correlation (const gsl_matrix *analysis_matrix, int var, struct smr_workspace *ws) +{ + /* For an explanation of what this is doing, see + http://www.visualstatistics.net/Visual%20Statistics%20Multimedia/multiple_regression_analysis.htm + */ + + int signum = 0; + gsl_matrix_view rxx; + + gsl_matrix_memcpy (ws->m, analysis_matrix); + + 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); + + gsl_linalg_LU_decomp (&rxx.matrix, ws->perm, &signum); + + gsl_linalg_LU_invert (&rxx.matrix, ws->perm, ws->inverse); + + { + gsl_matrix_const_view rxy = gsl_matrix_const_submatrix (ws->m, 1, 0, ws->m->size1 - 1, 1); + gsl_matrix_const_view ryx = gsl_matrix_const_submatrix (ws->m, 0, 1, 1, ws->m->size1 - 1); + + gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, + 1.0, ws->inverse, &rxy.matrix, 0.0, ws->result1); + + gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, + 1.0, &ryx.matrix, ws->result1, 0.0, ws->result2); + } + + return gsl_matrix_get (ws->result2, 0, 0); +} + + + +static double the_communality (const gsl_matrix *evec, const gsl_vector *eval, int n, int n_factors); + + +struct factor_matrix_workspace +{ + size_t n_factors; + gsl_eigen_symmv_workspace *eigen_ws; + + gsl_vector *eval ; + gsl_matrix *evec ; + + gsl_matrix *gamma ; + + gsl_matrix *r; +}; + +static struct factor_matrix_workspace * +factor_matrix_workspace_alloc (size_t n, size_t nf) +{ + struct factor_matrix_workspace *ws = xmalloc (sizeof (*ws)); + + ws->n_factors = nf; + ws->gamma = gsl_matrix_calloc (nf, nf); + ws->eigen_ws = gsl_eigen_symmv_alloc (n); + ws->eval = gsl_vector_alloc (n); + ws->evec = gsl_matrix_alloc (n, n); + ws->r = gsl_matrix_alloc (n, n); + + return ws; +} + +static void +factor_matrix_workspace_free (struct factor_matrix_workspace *ws) +{ + gsl_eigen_symmv_free (ws->eigen_ws); + gsl_vector_free (ws->eval); + gsl_matrix_free (ws->evec); + gsl_matrix_free (ws->gamma); + gsl_matrix_free (ws->r); + free (ws); +} + +/* + Shift P left by OFFSET places, and overwrite TARGET + with the shifted result. + Positions in TARGET less than OFFSET are unchanged. +*/ +static void +perm_shift_apply (gsl_permutation *target, const gsl_permutation *p, + size_t offset) +{ + size_t i; + assert (target->size == p->size); + assert (offset <= target->size); + + for (i = 0; i < target->size - offset; ++i) + { + target->data[i] = p->data [i + offset]; + } +} + + +/* + Indirectly sort the rows of matrix INPUT, storing the sort order in PERM. + The sort criteria are as follows: + + Rows are sorted on the first column, until the absolute value of an + element in a subsequent column is greater than that of the first + column. Thereafter, rows will be sorted on the second column, + until the absolute value of an element in a subsequent column + exceeds that of the second column ... +*/ +static void +sort_matrix_indirect (const gsl_matrix *input, gsl_permutation *perm) +{ + const size_t n = perm->size; + const size_t m = input->size2; + int i, j; + gsl_matrix *mat ; + int column_n = 0; + int row_n = 0; + gsl_permutation *p; + + assert (perm->size == input->size1); + + p = gsl_permutation_alloc (n); + + /* Copy INPUT into MAT, discarding the sign */ + mat = gsl_matrix_alloc (n, m); + for (i = 0 ; i < mat->size1; ++i) + { + for (j = 0 ; j < mat->size2; ++j) + { + double x = gsl_matrix_get (input, i, j); + gsl_matrix_set (mat, i, j, fabs (x)); + } + } + + 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); + + for (i = 0 ; i < n; ++i) + { + gsl_vector_view row = gsl_matrix_row (mat, p->data[n - 1 - i]); + size_t maxindex = gsl_vector_max_index (&row.vector); + + if ( maxindex > column_n ) + break; + + /* All subsequent elements of this row, are of no interest. + So set them all to a highly negative value */ + for (j = column_n + 1; j < row.vector.size ; ++j) + gsl_vector_set (&row.vector, j, -DBL_MAX); + } + + perm_shift_apply (perm, p, row_n); + row_n += i; + + column_n++; + } + + gsl_permutation_free (p); + gsl_matrix_free (mat); + + assert ( 0 == gsl_permutation_valid (perm)); + + /* We want the biggest value to be first */ + gsl_permutation_reverse (perm); +} + + +/* + Get an approximation for the factor matrix into FACTORS, and the communalities into COMMUNALITIES. + R is the matrix to be analysed. + WS is a pointer to a structure which must have been initialised with factor_matrix_workspace_init. + */ +static void +iterate_factor_matrix (const gsl_matrix *r, gsl_vector *communalities, gsl_matrix *factors, struct factor_matrix_workspace *ws) +{ + size_t i; + gsl_matrix_view mv ; + + assert (r->size1 == r->size2); + assert (r->size1 == communalities->size); + + assert (factors->size1 == r->size1); + assert (factors->size2 == ws->n_factors); + + gsl_matrix_memcpy (ws->r, r); + + /* Apply Communalities to diagonal of correlation matrix */ + for (i = 0 ; i < communalities->size ; ++i) + { + double *x = gsl_matrix_ptr (ws->r, i, i); + *x = gsl_vector_get (communalities, i); + } + + gsl_eigen_symmv (ws->r, ws->eval, ws->evec, ws->eigen_ws); + + mv = gsl_matrix_submatrix (ws->evec, 0, 0, ws->evec->size1, ws->n_factors); + + /* Gamma is the diagonal matrix containing the absolute values of the eigenvalues */ + for (i = 0 ; i < ws->n_factors ; ++i) + { + double *ptr = gsl_matrix_ptr (ws->gamma, i, i); + *ptr = fabs (gsl_vector_get (ws->eval, i)); + } + + /* Take the square root of gamma */ + gsl_linalg_cholesky_decomp (ws->gamma); + + gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, + 1.0, &mv.matrix, ws->gamma, 0.0, factors); + + for (i = 0 ; i < r->size1 ; ++i) + { + double h = the_communality (ws->evec, ws->eval, i, ws->n_factors); + gsl_vector_set (communalities, i, h); + } +} + + + +static bool run_factor (struct dataset *ds, const struct cmd_factor *factor); + + +int +cmd_factor (struct lexer *lexer, struct dataset *ds) +{ + bool extraction_seen = false; + const struct dictionary *dict = dataset_dict (ds); + + struct cmd_factor factor; + factor.method = METHOD_CORR; + factor.missing_type = MISS_LISTWISE; + factor.exclude = MV_ANY; + factor.print = PRINT_INITIAL | PRINT_EXTRACTION | PRINT_ROTATION; + factor.extraction = EXTRACTION_PC; + factor.n_factors = 0; + factor.min_eigen = SYSMIS; + factor.iterations = 25; + factor.econverge = 0.001; + factor.blank = 0; + factor.sort = false; + + factor.wv = dict_get_weight (dict); + + lex_match (lexer, '/'); + + if (!lex_force_match_id (lexer, "VARIABLES")) + { + goto error; + } + + lex_match (lexer, '='); + + if (!parse_variables_const (lexer, dict, &factor.vars, &factor.n_vars, + PV_NO_DUPLICATE | PV_NUMERIC)) + goto error; + + while (lex_token (lexer) != '.') + { + lex_match (lexer, '/'); + +#if FACTOR_FULLY_IMPLEMENTED + if (lex_match_id (lexer, "PLOT")) + { + lex_match (lexer, '='); + while (lex_token (lexer) != '.' && lex_token (lexer) != '/') + { + if (lex_match_id (lexer, "EIGEN")) + { + } + else if (lex_match_id (lexer, "ROTATION")) + { + } + else + { + lex_error (lexer, NULL); + goto error; + } + } + } + else +#endif + if (lex_match_id (lexer, "METHOD")) + { + lex_match (lexer, '='); + while (lex_token (lexer) != '.' && lex_token (lexer) != '/') + { + if (lex_match_id (lexer, "COVARIANCE")) + { + factor.method = METHOD_COV; + } + else if (lex_match_id (lexer, "CORRELATION")) + { + factor.method = METHOD_CORR; + } + else + { + lex_error (lexer, NULL); + goto error; + } + } + } +#if FACTOR_FULLY_IMPLEMENTED + else if (lex_match_id (lexer, "ROTATION")) + { + lex_match (lexer, '='); + while (lex_token (lexer) != '.' && lex_token (lexer) != '/') + { + if (lex_match_id (lexer, "VARIMAX")) + { + } + else if (lex_match_id (lexer, "DEFAULT")) + { + } + else + { + lex_error (lexer, NULL); + goto error; + } + } + } +#endif + else if (lex_match_id (lexer, "CRITERIA")) + { + lex_match (lexer, '='); + while (lex_token (lexer) != '.' && lex_token (lexer) != '/') + { + if (lex_match_id (lexer, "FACTORS")) + { + if ( lex_force_match (lexer, '(')) + { + lex_force_int (lexer); + factor.n_factors = lex_integer (lexer); + lex_get (lexer); + lex_force_match (lexer, ')'); + } + } + else if (lex_match_id (lexer, "MINEIGEN")) + { + if ( lex_force_match (lexer, '(')) + { + lex_force_num (lexer); + factor.min_eigen = lex_number (lexer); + lex_get (lexer); + lex_force_match (lexer, ')'); + } + } + else if (lex_match_id (lexer, "ECONVERGE")) + { + if ( lex_force_match (lexer, '(')) + { + lex_force_num (lexer); + factor.econverge = lex_number (lexer); + lex_get (lexer); + lex_force_match (lexer, ')'); + } + } + else if (lex_match_id (lexer, "ITERATE")) + { + if ( lex_force_match (lexer, '(')) + { + lex_force_int (lexer); + factor.iterations = lex_integer (lexer); + lex_get (lexer); + lex_force_match (lexer, ')'); + } + } + else if (lex_match_id (lexer, "DEFAULT")) + { + factor.n_factors = 0; + factor.min_eigen = 1; + factor.iterations = 25; + } + else + { + lex_error (lexer, NULL); + goto error; + } + } + } + else if (lex_match_id (lexer, "EXTRACTION")) + { + extraction_seen = true; + lex_match (lexer, '='); + while (lex_token (lexer) != '.' && lex_token (lexer) != '/') + { + if (lex_match_id (lexer, "PAF")) + { + factor.extraction = EXTRACTION_PAF; + } + else if (lex_match_id (lexer, "PC")) + { + factor.extraction = EXTRACTION_PC; + } + else if (lex_match_id (lexer, "PA1")) + { + factor.extraction = EXTRACTION_PC; + } + else if (lex_match_id (lexer, "DEFAULT")) + { + factor.extraction = EXTRACTION_PC; + } + else + { + lex_error (lexer, NULL); + goto error; + } + } + } + else if (lex_match_id (lexer, "FORMAT")) + { + lex_match (lexer, '='); + while (lex_token (lexer) != '.' && lex_token (lexer) != '/') + { + if (lex_match_id (lexer, "SORT")) + { + factor.sort = true; + } + else if (lex_match_id (lexer, "BLANK")) + { + if ( lex_force_match (lexer, '(')) + { + lex_force_num (lexer); + factor.blank = lex_number (lexer); + lex_get (lexer); + lex_force_match (lexer, ')'); + } + } + else if (lex_match_id (lexer, "DEFAULT")) + { + factor.blank = 0; + factor.sort = false; + } + else + { + lex_error (lexer, NULL); + goto error; + } + } + } + else if (lex_match_id (lexer, "PRINT")) + { + factor.print = 0; + lex_match (lexer, '='); + while (lex_token (lexer) != '.' && lex_token (lexer) != '/') + { + if (lex_match_id (lexer, "UNIVARIATE")) + { + factor.print |= PRINT_UNIVARIATE; + } + else if (lex_match_id (lexer, "DET")) + { + factor.print |= PRINT_DETERMINANT; + } +#if FACTOR_FULLY_IMPLEMENTED + else if (lex_match_id (lexer, "INV")) + { + } + else if (lex_match_id (lexer, "AIC")) + { + } + else if (lex_match_id (lexer, "SIG")) + { + } + else if (lex_match_id (lexer, "COVARIANCE")) + { + } + else if (lex_match_id (lexer, "CORRELATION")) + { + } +#endif + else if (lex_match_id (lexer, "ROTATION")) + { + factor.print |= PRINT_ROTATION; + } + else if (lex_match_id (lexer, "EXTRACTION")) + { + factor.print |= PRINT_EXTRACTION; + } + else if (lex_match_id (lexer, "INITIAL")) + { + factor.print |= PRINT_INITIAL; + } +#if FACTOR_FULLY_IMPLEMENTED + else if (lex_match_id (lexer, "KMO")) + { + } + else if (lex_match_id (lexer, "REPR")) + { + } + else if (lex_match_id (lexer, "FSCORE")) + { + } +#endif + else if (lex_match (lexer, T_ALL)) + { + factor.print = 0xFFFF; + } + else if (lex_match_id (lexer, "DEFAULT")) + { + factor.print |= PRINT_INITIAL ; + factor.print |= PRINT_EXTRACTION ; + factor.print |= PRINT_ROTATION ; + } + else + { + lex_error (lexer, NULL); + goto error; + } + } + } + else if (lex_match_id (lexer, "MISSING")) + { + lex_match (lexer, '='); + while (lex_token (lexer) != '.' && lex_token (lexer) != '/') + { + if (lex_match_id (lexer, "INCLUDE")) + { + factor.exclude = MV_SYSTEM; + } + else if (lex_match_id (lexer, "EXCLUDE")) + { + factor.exclude = MV_ANY; + } + else if (lex_match_id (lexer, "LISTWISE")) + { + factor.missing_type = MISS_LISTWISE; + } + else if (lex_match_id (lexer, "PAIRWISE")) + { + factor.missing_type = MISS_PAIRWISE; + } + else if (lex_match_id (lexer, "MEANSUB")) + { + factor.missing_type = MISS_MEANSUB; + } + else + { + lex_error (lexer, NULL); + goto error; + } + } + } + else + { + lex_error (lexer, NULL); + goto error; + } + } + + if ( ! run_factor (ds, &factor)) + goto error; + + free (factor.vars); + return CMD_SUCCESS; + + error: + free (factor.vars); + return CMD_FAILURE; +} + +static void do_factor (const struct cmd_factor *factor, struct casereader *group); + + +static bool +run_factor (struct dataset *ds, const struct cmd_factor *factor) +{ + struct dictionary *dict = dataset_dict (ds); + bool ok; + struct casereader *group; + + struct casegrouper *grouper = casegrouper_create_splits (proc_open (ds), dict); + + while (casegrouper_get_next_group (grouper, &group)) + { + if ( factor->missing_type == MISS_LISTWISE ) + group = casereader_create_filter_missing (group, factor->vars, factor->n_vars, + factor->exclude, + NULL, NULL); + do_factor (factor, group); + } + + ok = casegrouper_destroy (grouper); + ok = proc_commit (ds) && ok; + + return ok; +} + + +/* Return the communality of variable N, calculated to N_FACTORS */ +static double +the_communality (const gsl_matrix *evec, const gsl_vector *eval, int n, int n_factors) +{ + size_t i; + + double comm = 0; + + assert (n >= 0); + assert (n < eval->size); + assert (n < evec->size1); + assert (n_factors <= eval->size); + + for (i = 0 ; i < n_factors; ++i) + { + double evali = fabs (gsl_vector_get (eval, i)); + + double eveci = gsl_matrix_get (evec, n, i); + + comm += pow2 (eveci) * evali; + } + + return comm; +} + +/* Return the communality of variable N, calculated to N_FACTORS */ +static double +communality (struct idata *idata, int n, int n_factors) +{ + return the_communality (idata->evec, idata->eval, n, n_factors); +} + + + +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) + return; + + t = tab_create (nc, nr, 0); + + tab_title (t, _("Communalities")); + + tab_dim (t, tab_natural_dimensions, NULL); + + tab_headers (t, heading_columns, 0, heading_rows, 0); + + c = 1; + if (factor->print & PRINT_INITIAL) + tab_text (t, c++, 0, TAB_CENTER | TAT_TITLE, _("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) + { + c = 0; + 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); + + if (factor->print & PRINT_EXTRACTION) + tab_double (t, c++, i + heading_rows, 0, gsl_vector_get (extracted, i), NULL); + } + + tab_submit (t); +} + + +static void +show_factor_matrix (const struct cmd_factor *factor, struct idata *idata, const gsl_matrix *fm) +{ + int i; + const int n_factors = n_extracted_factors (factor, idata); + + 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 tab_table *t = tab_create (nc, nr, 0); + + if ( factor->extraction == EXTRACTION_PC ) + tab_title (t, _("Component Matrix")); + else + tab_title (t, _("Factor Matrix")); + + tab_dim (t, tab_natural_dimensions, NULL); + + 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); + + + { + gsl_vector_const_view r1 = gsl_matrix_const_row (fm, 0); + gsl_vector_const_view r2 = gsl_matrix_const_row (fm, 1); + + dump_vector (&r1.vector); + dump_vector (&r2.vector); + } + + /* Initialise to the identity permutation */ + perm = gsl_permutation_calloc (factor->n_vars); + + 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) + { + 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) + { + double x = gsl_matrix_get (fm, matrix_row, j); + + if ( fabs (x) < factor->blank) + continue; + + tab_double (t, heading_columns + j, heading_rows + i, 0, x, NULL); + } + } + + gsl_permutation_free (perm); + + tab_submit (t); +} + + +static void +show_explained_variance (const struct cmd_factor * factor, struct idata *idata, + const gsl_vector *initial_eigenvalues, + const gsl_vector *extracted_eigenvalues) +{ + 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; + + 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) + return; + + t = tab_create (nc, nr, 0); + + tab_title (t, _("Total Variance Explained")); + + tab_dim (t, tab_natural_dimensions, NULL); + + 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, 1, TAB_LEFT | TAT_TITLE, _("Component")); + else + tab_text (t, 0, 1, TAB_LEFT | TAT_TITLE, _("Factor")); + + c = 1; + if (factor->print & PRINT_INITIAL) + { + tab_joint_text (t, c, 0, c + 2, 0, TAB_CENTER | TAT_TITLE, _("Initial Eigenvalues")); + c += 3; + } + + 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; + } + + if (factor->print & PRINT_ROTATION) + { + printf ("C is %d\n", c); + tab_joint_text (t, c, 0, c + 2, 0, TAB_CENTER | TAT_TITLE, _("Rotation Sums of Squared Loadings")); + c += 3; + } + + for (i = 0; i < (nc - heading_columns) / 3 ; ++i) + { + tab_text (t, i * 3 + 1, 1, TAB_CENTER | TAT_TITLE, _("Total")); + 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) + i_total += gsl_vector_get (initial_eigenvalues, i); + + if ( factor->extraction == EXTRACTION_PAF) + { + e_total = factor->n_vars; + } + else + { + e_total = i_total; + } + + + for (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 ; + + const double e_lambda = gsl_vector_get (extracted_eigenvalues, i); + double e_percent = 100.0 * e_lambda / e_total ; + + c = 0; + + tab_text_format (t, c++, i + heading_rows, TAB_LEFT | TAT_TITLE, _("%d"), i + 1); + + i_cum += i_percent; + e_cum += e_percent; + + /* 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 < n_extracted_factors (factor, idata)) + { + /* 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_submit (t); +} + + + +static void +do_factor (const struct cmd_factor *factor, struct casereader *r) +{ + struct ccase *c; + const gsl_matrix *cov_matrix; + const gsl_matrix *var_matrix; + const gsl_matrix *mean_matrix; + const gsl_matrix *n_matrix; + + const gsl_matrix *analysis_matrix; + struct idata *idata; + + struct covariance *cov = covariance_create (factor->n_vars, factor->vars, + factor->wv, factor->exclude); + + for ( ; (c = casereader_read (r) ); case_unref (c)) + { + covariance_accumulate (cov, c); + } + + cov_matrix = covariance_calculate (cov); + + var_matrix = covariance_moments (cov, MOMENT_VARIANCE); + mean_matrix = covariance_moments (cov, MOMENT_MEAN); + n_matrix = covariance_moments (cov, MOMENT_NONE); + + if ( factor->method == METHOD_CORR) + { + analysis_matrix = correlation_from_covariance (cov_matrix, var_matrix); + } + else + analysis_matrix = cov_matrix; + + 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; + + + const int heading_columns = 1; + const int heading_rows = 1; + + const int nr = heading_rows + factor->n_vars; + + struct tab_table *t = tab_create (nc, nr, 0); + tab_title (t, _("Descriptive Statistics")); + tab_dim (t, tab_natural_dimensions, NULL); + + 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_vline (t, TAL_2, heading_columns, 0, nr - 1); + + 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")); + + 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 (n_matrix, i, i), wfmt); + } + + tab_submit (t); + } + + if ( factor->print & PRINT_DETERMINANT) + { + const int nc = 2; + const int heading_columns = 0; + const int heading_rows = 0; + const int nr = 1; + struct tab_table *t ; + + int sign = 0; + double det = 0.0; + const int size = analysis_matrix->size1; + gsl_permutation *p = gsl_permutation_calloc (size); + gsl_matrix *tmp = gsl_matrix_calloc (size, size); + + gsl_matrix_memcpy (tmp, analysis_matrix); + gsl_linalg_LU_decomp (tmp, p, &sign); + det = gsl_linalg_LU_det (tmp, sign); + gsl_permutation_free (p); + gsl_matrix_free (tmp); + + t = tab_create (nc, nr, 0); + + if ( factor->method == METHOD_CORR) + tab_title (t, _("Correlation Matrix")); + else + tab_title (t, _("Covariance Matrix")); + + tab_dim (t, tab_natural_dimensions, NULL); + + tab_headers (t, heading_columns, 0, heading_rows, 0); + + tab_hline (t, TAL_1, 0, nc - 1, heading_rows); + + tab_text (t, 0, 0, TAB_LEFT | TAT_TITLE, _("Determinant")); + tab_double (t, 1, 0, 0, det, NULL); + + tab_submit (t); + } + + + idata = idata_alloc (factor->n_vars); + + +#if 1 + { + 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_free (workspace); + } + + gsl_eigen_symmv_sort (idata->eval, idata->evec, GSL_EIGEN_SORT_ABS_DESC); +#endif + + { + const gsl_vector *extracted_eigenvalues = NULL; + gsl_vector *initial_communalities = gsl_vector_alloc (factor->n_vars); + gsl_vector *extracted_communalities = gsl_vector_alloc (factor->n_vars); + size_t i; + struct factor_matrix_workspace *fmw = factor_matrix_workspace_alloc (idata->msr->size, n_extracted_factors (factor, idata)); + gsl_matrix *factor_matrix = gsl_matrix_calloc (factor->n_vars, fmw->n_factors); + + if ( factor->extraction == EXTRACTION_PAF) + { + gsl_vector *diff = gsl_vector_alloc (idata->msr->size); + struct smr_workspace *ws = ws_create (analysis_matrix); + + for (i = 0 ; i < factor->n_vars ; ++i) + { + double r2 = squared_multiple_correlation (analysis_matrix, i, ws); + + gsl_vector_set (idata->msr, i, r2); + } + ws_destroy (ws); + + gsl_vector_memcpy (initial_communalities, idata->msr); + + for (i = 0; i < factor->iterations; ++i) + { + double min, max; + gsl_vector_memcpy (diff, idata->msr); + + iterate_factor_matrix (analysis_matrix, idata->msr, factor_matrix, fmw); + + gsl_vector_sub (diff, idata->msr); + + gsl_vector_minmax (diff, &min, &max); + + if ( fabs (min) < factor->econverge && fabs (max) < factor->econverge) + break; + } + gsl_vector_free (diff); + + gsl_vector_memcpy (extracted_communalities, idata->msr); + extracted_eigenvalues = fmw->eval; + } + else if (factor->extraction == EXTRACTION_PC) + { + for (i = 0 ; i < factor->n_vars; ++i) + { + gsl_vector_set (initial_communalities, i, communality (idata, i, factor->n_vars)); + } + gsl_vector_memcpy (extracted_communalities, initial_communalities); + + iterate_factor_matrix (analysis_matrix, extracted_communalities, factor_matrix, fmw); + extracted_eigenvalues = idata->eval; + } + + show_communalities (factor, initial_communalities, extracted_communalities); + + show_explained_variance (factor, idata, idata->eval, extracted_eigenvalues); + + factor_matrix_workspace_free (fmw); + + show_factor_matrix (factor, idata, factor_matrix); + + gsl_vector_free (initial_communalities); + gsl_vector_free (extracted_communalities); + } + + idata_free (idata); + + casereader_destroy (r); +}