/* PSPP - a program for statistical analysis.
- Copyright (C) 2009, 2010, 2011, 2012 Free Software Foundation, Inc.
+ Copyright (C) 2009, 2010, 2011, 2012, 2014, 2015,
+ 2016, 2017 Free Software Foundation, Inc.
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
#include <gsl/gsl_vector.h>
#include <gsl/gsl_linalg.h>
#include <gsl/gsl_matrix.h>
-#include <gsl/gsl_eigen.h>
-#include <gsl/gsl_blas.h>
+#include <gsl/gsl_eigen.h>
+#include <gsl/gsl_blas.h>
#include <gsl/gsl_sort_vector.h>
#include <gsl/gsl_cdf.h>
+#include "data/any-reader.h"
#include "data/casegrouper.h"
#include "data/casereader.h"
#include "data/casewriter.h"
#include "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/tab.h"
+#include "output/pivot-table.h"
+
#include "gettext.h"
#define _(msgid) gettext (msgid)
PRINT_EXTRACTION = 0x0100,
PRINT_INITIAL = 0x0200,
PRINT_KMO = 0x0400,
- PRINT_REPR = 0x0800,
+ PRINT_REPR = 0x0800,
PRINT_FSCORE = 0x1000
};
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;
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);
*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;
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;
bool sort;
};
+
struct idata
{
/* Intermediate values used in calculation */
+ struct matrix_material mm;
- const gsl_matrix *corr ; /* The correlation matrix */
- gsl_matrix *cov ; /* The covariance matrix */
- const gsl_matrix *n ; /* Matrix of number of samples */
+ gsl_matrix *analysis_matrix; /* A pointer to either mm.corr or mm.cov */
gsl_vector *eval ; /* The eigenvalues */
gsl_matrix *evec ; /* The eigenvectors */
gsl_vector *msr ; /* Multiple Squared Regressions */
double detR; /* The determinant of the correlation matrix */
+
+ gsl_matrix *ai_cov; /* The anti-image covariance matrix */
+ gsl_matrix *ai_cor; /* The anti-image correlation matrix */
+ struct covariance *cvm;
};
static struct idata *
idata_alloc (size_t n_vars)
{
- struct idata *id = xzalloc (sizeof (*id));
+ struct idata *id = XZALLOC (struct idata);
id->n_extractions = 0;
id->msr = gsl_vector_alloc (n_vars);
gsl_vector_free (id->msr);
gsl_vector_free (id->eval);
gsl_matrix_free (id->evec);
- if (id->cov != NULL)
- gsl_matrix_free (id->cov);
- if (id->corr != NULL)
- gsl_matrix_free (CONST_CAST (gsl_matrix *, id->corr));
+ gsl_matrix_free (id->ai_cov);
+ gsl_matrix_free (id->ai_cor);
free (id);
}
-
-static gsl_matrix *
-anti_image (const gsl_matrix *m)
+/* 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, j;
- gsl_matrix *a;
+ int i;
+ double ss = 0;
assert (m->size1 == m->size2);
- a = gsl_matrix_alloc (m->size1, m->size2);
-
+ assert (j < m->size1);
+
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);
- }
+ if (i == j) continue;
+ ss += pow2 (gsl_matrix_get (m, i, j));
}
- return a;
+ return ss;
}
-
-/* Return the sum of all the elements excluding row N */
+/* Return the sum of squares of all the elements excluding row N */
static double
ssq_od_n (const gsl_matrix *m, int n)
{
assert (m->size1 == m->size2);
assert (n < m->size1);
-
+
for (i = 0; i < m->size1; ++i)
{
- if (i == n ) continue;
for (j = 0; j < m->size2; ++j)
{
+ if (i == j) continue;
ss += pow2 (gsl_matrix_get (m, i, j));
}
}
}
+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
#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,
idata->n_extractions = factor->n_factors;
goto finish;
}
-
+
/* Use the MIN_EIGEN setting. */
for (i = 0 ; i < idata->eval->size; ++i)
{
/* Returns a newly allocated matrix identical to M.
- It it the callers responsibility to free the returned value.
+ It is the callers responsibility to free the returned value.
*/
static gsl_matrix *
matrix_dup (const gsl_matrix *m)
{
/* Copy of the subject */
gsl_matrix *m;
-
+
gsl_matrix *inverse;
gsl_permutation *perm;
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);
}
-/*
+/*
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
*/
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);
ws->eval = gsl_vector_alloc (n);
ws->evec = gsl_matrix_alloc (n, n);
ws->r = gsl_matrix_alloc (n, n);
-
+
return ws;
}
}
-/*
+/*
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,
}
}
- 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);
{
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.
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);
}
}
-static double
+static double
initial_sv (const gsl_matrix *fm)
{
int j, k;
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;
}
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;
/* 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)
{
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;
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)
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;
gsl_matrix_free (h_sqrt);
gsl_matrix_free (normalised);
+ if (cf->rotation == ROT_PROMAX)
+ {
+ /* general purpose m by m matrix, where m is the number of factors */
+ gsl_matrix *mm1 = gsl_matrix_calloc (unrot->size2, unrot->size2);
+ gsl_matrix *mm2 = gsl_matrix_calloc (unrot->size2, unrot->size2);
+
+ /* general purpose m by p matrix, where p is the number of variables */
+ gsl_matrix *mp1 = gsl_matrix_calloc (unrot->size2, unrot->size1);
+
+ gsl_matrix *pm1 = gsl_matrix_calloc (unrot->size1, unrot->size2);
+
+ gsl_permutation *perm = gsl_permutation_alloc (unrot->size2);
+
+ int signum;
+
+ int i, j;
+
+ /* The following variables follow the notation by SPSS Statistical Algorithms
+ page 342 */
+ gsl_matrix *L = gsl_matrix_calloc (unrot->size2, unrot->size2);
+ gsl_matrix *P = clone_matrix (result);
+ gsl_matrix *D ;
+ gsl_matrix *Q ;
+
+
+ /* Vector of length p containing (indexed by i)
+ \Sum^m_j {\lambda^2_{ij}} */
+ gsl_vector *rssq = gsl_vector_calloc (unrot->size1);
+
+ for (i = 0; i < P->size1; ++i)
+ {
+ double sum = 0;
+ for (j = 0; j < P->size2; ++j)
+ {
+ sum += gsl_matrix_get (result, i, j)
+ * gsl_matrix_get (result, i, j);
+
+ }
+
+ gsl_vector_set (rssq, i, sqrt (sum));
+ }
+
+ for (i = 0; i < P->size1; ++i)
+ {
+ for (j = 0; j < P->size2; ++j)
+ {
+ double l = gsl_matrix_get (result, i, j);
+ double r = gsl_vector_get (rssq, i);
+ gsl_matrix_set (P, i, j, pow (fabs (l / r), cf->promax_power + 1) * r / l);
+ }
+ }
+
+ gsl_vector_free (rssq);
+
+ gsl_linalg_matmult_mod (result,
+ GSL_LINALG_MOD_TRANSPOSE,
+ result,
+ GSL_LINALG_MOD_NONE,
+ mm1);
+
+ gsl_linalg_LU_decomp (mm1, perm, &signum);
+ gsl_linalg_LU_invert (mm1, perm, mm2);
+
+ gsl_linalg_matmult_mod (mm2, GSL_LINALG_MOD_NONE,
+ result, GSL_LINALG_MOD_TRANSPOSE,
+ mp1);
+
+ gsl_linalg_matmult_mod (mp1, GSL_LINALG_MOD_NONE,
+ P, GSL_LINALG_MOD_NONE,
+ L);
+
+ D = diag_rcp_sqrt (L);
+ Q = gsl_matrix_calloc (unrot->size2, unrot->size2);
+
+ gsl_linalg_matmult_mod (L, GSL_LINALG_MOD_NONE,
+ D, GSL_LINALG_MOD_NONE,
+ Q);
+
+ gsl_matrix *QQinv = gsl_matrix_calloc (unrot->size2, unrot->size2);
+
+ gsl_linalg_matmult_mod (Q, GSL_LINALG_MOD_TRANSPOSE,
+ Q, GSL_LINALG_MOD_NONE,
+ QQinv);
+
+ gsl_linalg_cholesky_decomp (QQinv);
+ gsl_linalg_cholesky_invert (QQinv);
+
+
+ gsl_matrix *C = diag_rcp_inv_sqrt (QQinv);
+ gsl_matrix *Cinv = clone_matrix (C);
+
+ gsl_linalg_cholesky_decomp (Cinv);
+ gsl_linalg_cholesky_invert (Cinv);
+
+
+ gsl_linalg_matmult_mod (result, GSL_LINALG_MOD_NONE,
+ Q, GSL_LINALG_MOD_NONE,
+ pm1);
+
+ gsl_linalg_matmult_mod (pm1, GSL_LINALG_MOD_NONE,
+ Cinv, GSL_LINALG_MOD_NONE,
+ pattern_matrix);
+
+
+ gsl_linalg_matmult_mod (C, GSL_LINALG_MOD_NONE,
+ QQinv, GSL_LINALG_MOD_NONE,
+ mm1);
+
+ gsl_linalg_matmult_mod (mm1, GSL_LINALG_MOD_NONE,
+ C, GSL_LINALG_MOD_TRANSPOSE,
+ factor_correlation_matrix);
+
+ gsl_linalg_matmult_mod (pattern_matrix, GSL_LINALG_MOD_NONE,
+ factor_correlation_matrix, GSL_LINALG_MOD_NONE,
+ pm1);
+
+ gsl_matrix_memcpy (result, pm1);
+
+
+ gsl_matrix_free (QQinv);
+ gsl_matrix_free (C);
+ gsl_matrix_free (Cinv);
+
+ gsl_matrix_free (D);
+ gsl_matrix_free (Q);
+ gsl_matrix_free (L);
+ gsl_matrix_free (P);
+
+ gsl_permutation_free (perm);
+
+ gsl_matrix_free (mm1);
+ gsl_matrix_free (mm2);
+ gsl_matrix_free (mp1);
+ gsl_matrix_free (pm1);
+ }
+
/* reflect negative sums and populate the rotated loadings vector*/
for (i = 0 ; i < result->size2; ++i)
{
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);
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;
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;
factor.extraction = EXTRACTION_PC;
factor.n_factors = 0;
factor.min_eigen = SYSMIS;
- factor.iterations = 25;
+ factor.extraction_iterations = 25;
+ factor.rotation_iterations = 25;
factor.econverge = 0.001;
factor.blank = 0;
factor.sort = false;
factor.plot = 0;
factor.rotation = ROT_VARIMAX;
+ factor.wv = NULL;
factor.rconverge = 0.0001;
- factor.wv = dict_get_weight (dict);
-
lex_match (lexer, T_SLASH);
- if (!lex_force_match_id (lexer, "VARIABLES"))
+ struct matrix_reader *mr = NULL;
+ struct casereader *matrix_reader = NULL;
+
+ if (lex_match_id (lexer, "VARIABLES"))
{
- goto error;
+ lex_match (lexer, T_EQUALS);
+ dict = dataset_dict (ds);
+ factor.wv = dict_get_weight (dict);
+
+ if (!parse_variables_const (lexer, dict, &factor.vars, &factor.n_vars,
+ PV_NO_DUPLICATE | PV_NUMERIC))
+ goto error;
}
+ else if (lex_match_id (lexer, "MATRIX"))
+ {
+ 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, T_EQUALS);
+ matrix_reader
+ = any_reader_open_and_decode (fh, NULL, &dict, NULL);
- if (!parse_variables_const (lexer, dict, &factor.vars, &factor.n_vars,
- PV_NO_DUPLICATE | PV_NUMERIC))
- goto error;
+ if (! (matrix_reader && dict))
+ {
+ goto error;
+ }
+ }
- if (factor.n_vars < 2)
- msg (MW, _("Factor analysis on a single variable is not useful."));
+ if (! lex_force_match (lexer, T_RPAREN))
+ goto error;
+
+ mr = matrix_reader_create (dict, matrix_reader);
+ factor.vars = xmemdup (mr->cvars, mr->n_cvars * sizeof *mr->cvars);
+ factor.n_vars = mr->n_cvars;
+ }
+ else
+ {
+ goto error;
+ }
while (lex_token (lexer) != T_ENDCMD)
{
lex_match (lexer, T_SLASH);
- if (lex_match_id (lexer, "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;
+
+ if (mr)
+ {
+ free (mr->cvars);
+ mr->cvars = xmemdup (vars, n_vars * sizeof *vars);
+ mr->n_cvars = n_vars;
+ }
+ }
+ else if (lex_match_id (lexer, "PLOT"))
{
lex_match (lexer, T_EQUALS);
while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
{
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;
goto error;
}
}
+ factor.rotation_iterations = n_iterations;
}
else if (lex_match_id (lexer, "CRITERIA"))
{
{
if (lex_match_id (lexer, "FACTORS"))
{
- if ( lex_force_match (lexer, T_LPAREN))
+ if (lex_force_match (lexer, T_LPAREN)
+ && lex_force_int (lexer))
{
- lex_force_int (lexer);
factor.n_factors = lex_integer (lexer);
lex_get (lexer);
- lex_force_match (lexer, T_RPAREN);
+ if (! lex_force_match (lexer, T_RPAREN))
+ goto error;
}
}
else if (lex_match_id (lexer, "MINEIGEN"))
{
- if ( lex_force_match (lexer, T_LPAREN))
+ if (lex_force_match (lexer, T_LPAREN)
+ && lex_force_num (lexer))
{
- lex_force_num (lexer);
factor.min_eigen = lex_number (lexer);
lex_get (lexer);
- lex_force_match (lexer, T_RPAREN);
+ if (! lex_force_match (lexer, T_RPAREN))
+ goto error;
}
}
else if (lex_match_id (lexer, "ECONVERGE"))
{
- if ( lex_force_match (lexer, T_LPAREN))
+ if (lex_force_match (lexer, T_LPAREN)
+ && lex_force_num (lexer))
{
- lex_force_num (lexer);
factor.econverge = lex_number (lexer);
lex_get (lexer);
- lex_force_match (lexer, T_RPAREN);
+ if (! lex_force_match (lexer, T_RPAREN))
+ goto error;
}
}
else if (lex_match_id (lexer, "RCONVERGE"))
- {
- if ( lex_force_match (lexer, T_LPAREN))
- {
- lex_force_num (lexer);
- factor.rconverge = lex_number (lexer);
- lex_get (lexer);
- lex_force_match (lexer, T_RPAREN);
- }
+ {
+ if (lex_force_match (lexer, T_LPAREN)
+ && lex_force_num (lexer))
+ {
+ factor.rconverge = lex_number (lexer);
+ lex_get (lexer);
+ if (! lex_force_match (lexer, T_RPAREN))
+ goto error;
+ }
}
else if (lex_match_id (lexer, "ITERATE"))
{
- if ( lex_force_match (lexer, T_LPAREN))
+ if (lex_force_match (lexer, T_LPAREN)
+ && lex_force_int_range (lexer, "ITERATE", 0, INT_MAX))
{
- lex_force_int (lexer);
- factor.iterations = lex_integer (lexer);
+ n_iterations = lex_integer (lexer);
lex_get (lexer);
- lex_force_match (lexer, T_RPAREN);
+ if (! lex_force_match (lexer, T_RPAREN))
+ goto error;
}
}
else if (lex_match_id (lexer, "DEFAULT"))
{
factor.n_factors = 0;
factor.min_eigen = 1;
- factor.iterations = 25;
+ n_iterations = 25;
}
else
{
}
else if (lex_match_id (lexer, "EXTRACTION"))
{
- extraction_seen = true;
lex_match (lexer, T_EQUALS);
while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
{
goto error;
}
}
+ factor.extraction_iterations = n_iterations;
}
else if (lex_match_id (lexer, "FORMAT"))
{
}
else if (lex_match_id (lexer, "BLANK"))
{
- if ( lex_force_match (lexer, T_LPAREN))
+ if (lex_force_match (lexer, T_LPAREN)
+ && lex_force_num (lexer))
{
- lex_force_num (lexer);
factor.blank = lex_number (lexer);
lex_get (lexer);
- lex_force_match (lexer, T_RPAREN);
+ if (! lex_force_match (lexer, T_RPAREN))
+ goto error;
}
}
else if (lex_match_id (lexer, "DEFAULT"))
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;
{
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;
}
}
- 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 (matrix_reader_next (&id->mm, mr, NULL))
+ {
+ do_factor_by_matrix (&factor, id);
+
+ gsl_matrix_free (id->ai_cov);
+ id->ai_cov = NULL;
+ gsl_matrix_free (id->ai_cor);
+ id->ai_cor = NULL;
+
+ matrix_material_uninit (&id->mm);
+ }
+
+ idata_free (id);
+ }
+ else
+ if (! run_factor (ds, &factor))
+ goto error;
+ matrix_reader_destroy (mr);
free (factor.vars);
return CMD_SUCCESS;
error:
+ matrix_reader_destroy (mr);
free (factor.vars);
return CMD_FAILURE;
}
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);
/* 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;
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"));
+ struct pivot_table *table = pivot_table_create (N_("Communalities"));
- tab_headers (t, heading_columns, 0, heading_rows, 0);
-
- 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, "%s", 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"));
-
- 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);
+ struct pivot_table *table = pivot_table_create (
+ N_("Total Variance Explained"));
- tab_hline (t, TAL_1, 0, nc - 1, heading_rows);
- tab_hline (t, TAL_1, 1, nc - 1, 1);
+ 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);
- 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;
- c = 0;
+ int row = pivot_category_create_leaf (
+ components->root, pivot_value_new_integer (i + 1));
- tab_text_format (t, c++, i + heading_rows, TAB_LEFT | TAT_TITLE, _("%zu"), i + 1);
-
- i_cum += i_percent;
- e_cum += e_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);
- }
+ put_variance (table, row, phase_idx++, i_lambda, i_percent, i_cum);
-
- 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);
- }
- }
-
- if (rotated_loadings != NULL)
+ if (i < idata->n_extractions)
{
- const double r_lambda = gsl_vector_get (rotated_loadings, i);
- double r_percent = 100.0 * r_lambda / e_total ;
+ if (factor->print & PRINT_EXTRACTION)
+ put_variance (table, row, phase_idx++, e_lambda, e_percent, e_cum);
- if (factor->print & PRINT_ROTATION)
+ if (rotated_loadings != NULL && factor->print & PRINT_ROTATION)
{
- if (i < idata->n_extractions)
- {
- r_cum += r_percent;
- tab_double (t, c++, i + heading_rows, 0, r_lambda, NULL);
- tab_double (t, c++, i + heading_rows, 0, r_percent, NULL);
- tab_double (t, c++, i + heading_rows, 0, r_cum, NULL);
- }
+ 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);
-
- tab_title (t, _("Correlation Matrix"));
-
- tab_hline (t, TAL_1, 0, nc - 1, heading_rows);
-
- if (nr > heading_rows)
- {
- tab_headers (t, heading_columns, 0, heading_rows, 0);
+ struct pivot_table *table = pivot_table_create (N_("Anti-Image Matrices"));
- tab_vline (t, TAL_2, 2, 0, nr - 1);
+ add_var_dims (table, factor);
- /* Outline the box */
- tab_box (t,
- TAL_2, TAL_2,
- -1, -1,
- 0, 0,
- nc - 1, nr - 1);
+ pivot_dimension_create (table, PIVOT_AXIS_ROW, N_("Statistics"),
+ N_("Anti-image Covariance"),
+ N_("Anti-image Correlation"));
- /* 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)
{
- tab_text (t, 0, nr, TAB_LEFT | TAT_TITLE, _("Determinant"));
-
- tab_double (t, 1, nr, 0, idata->detR, NULL);
+ struct pivot_value *caption = pivot_value_new_user_text_nocopy (
+ xasprintf ("%s: %.2f", _("Determinant"), idata->detR));
+ pivot_table_set_caption (table, caption);
}
- tab_submit (t);
+ pivot_table_submit (table);
}
+static void
+show_covariance_matrix (const struct cmd_factor *factor, const struct idata *idata)
+{
+ if (!(factor->print & PRINT_COVARIANCE))
+ return;
+
+ struct pivot_table *table = pivot_table_create (N_("Covariance Matrix"));
+ add_var_dims (table, factor);
+
+ for (int i = 0; i < factor->n_vars; ++i)
+ for (int j = 0; j < factor->n_vars; ++j)
+ {
+ double cov = gsl_matrix_get (idata->mm.cov, i, j);
+ pivot_table_put2 (table, j, i, pivot_value_new_number (cov));
+ }
+
+ pivot_table_submit (table);
+}
static void
do_factor (const struct cmd_factor *factor, struct casereader *r)
{
struct ccase *c;
- 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 (cov);
+ covariance_destroy (idata->cvm);
goto finish;
}
- var_matrix = covariance_moments (cov, MOMENT_VARIANCE);
- mean_matrix = covariance_moments (cov, MOMENT_MEAN);
- idata->n = covariance_moments (cov, MOMENT_NONE);
-
+ idata->mm.var_matrix = covariance_moments (idata->cvm, MOMENT_VARIANCE);
+ idata->mm.mean_matrix = covariance_moments (idata->cvm, MOMENT_MEAN);
+ idata->mm.n = covariance_moments (idata->cvm, MOMENT_NONE);
+
+ do_factor_by_matrix (factor, idata);
- if ( factor->method == METHOD_CORR)
+ finish:
+ gsl_matrix_free (idata->mm.corr);
+ gsl_matrix_free (idata->mm.cov);
+
+ idata_free (idata);
+ casereader_destroy (r);
+}
+
+static void
+do_factor_by_matrix (const struct cmd_factor *factor, struct idata *idata)
+{
+ if (!idata->mm.cov && !(idata->mm.corr && idata->mm.var_matrix))
{
- idata->corr = correlation_from_covariance (idata->cov, var_matrix);
-
- analysis_matrix = idata->corr;
+ msg (ME, _("The dataset has no covariance matrix or a "
+ "correlation matrix along with standard deviations."));
+ return;
}
+
+ if (idata->mm.cov && !idata->mm.corr)
+ idata->mm.corr = correlation_from_covariance (idata->mm.cov, idata->mm.var_matrix);
+ if (idata->mm.corr && !idata->mm.cov)
+ idata->mm.cov = covariance_from_correlation (idata->mm.corr, idata->mm.var_matrix);
+ if (factor->method == METHOD_CORR)
+ idata->analysis_matrix = idata->mm.corr;
else
- analysis_matrix = idata->cov;
+ idata->analysis_matrix = idata->mm.cov;
+
+ gsl_matrix *r_inv;
+ r_inv = clone_matrix (idata->mm.corr);
+ gsl_linalg_cholesky_decomp (r_inv);
+ gsl_linalg_cholesky_invert (r_inv);
+
+ idata->ai_cov = anti_image_cov (r_inv);
+ idata->ai_cor = anti_image_corr (r_inv, idata);
+
+ 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);
+ }
+ gsl_matrix_free (r_inv);
if (factor->print & PRINT_DETERMINANT
|| factor->print & PRINT_KMO)
{
int sign = 0;
- const int size = idata->corr->size1;
+ const int size = idata->mm.corr->size1;
gsl_permutation *p = gsl_permutation_calloc (size);
gsl_matrix *tmp = gsl_matrix_calloc (size, size);
- gsl_matrix_memcpy (tmp, idata->corr);
+ gsl_matrix_memcpy (tmp, idata->mm.corr);
gsl_linalg_LU_decomp (tmp, p, &sign);
idata->detR = gsl_linalg_LU_det (tmp, sign);
gsl_matrix_free (tmp);
}
- if ( factor->print & PRINT_UNIVARIATE)
+ if (factor->print & PRINT_UNIVARIATE
+ && idata->mm.n && idata->mm.mean_matrix && idata->mm.var_matrix)
{
- const struct fmt_spec *wfmt = factor->wv ? var_get_print_format (factor->wv) : & F_8_0;
- const int nc = 4;
- int i;
+ struct pivot_table *table = pivot_table_create (
+ N_("Descriptive Statistics"));
+ pivot_table_set_weight_var (table, factor->wv);
- const int heading_columns = 1;
- const int heading_rows = 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);
- const int nr = heading_rows + factor->n_vars;
-
- struct tab_table *t = tab_create (nc, nr);
- tab_title (t, _("Descriptive Statistics"));
-
- 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"));
+ 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)
+ if (factor->print & PRINT_KMO && idata->mm.n)
{
- int i;
- double sum_ssq_r = 0;
- double sum_ssq_a = 0;
-
- double df = factor->n_vars * ( factor->n_vars - 1) / 2;
-
- double w = 0;
-
-
- double xsq;
-
- const int heading_columns = 2;
- const int heading_rows = 0;
-
- const int nr = heading_rows + 4;
- const int nc = heading_columns + 1;
-
- gsl_matrix *a, *x;
-
- struct tab_table *t = tab_create (nc, nr);
- tab_title (t, _("KMO and Bartlett's Test"));
-
- x = clone_matrix (idata->corr);
- gsl_linalg_cholesky_decomp (x);
- gsl_linalg_cholesky_invert (x);
-
- a = anti_image (x);
-
- for (i = 0; i < x->size1; ++i)
- {
- sum_ssq_r += ssq_od_n (x, i);
- sum_ssq_a += ssq_od_n (a, i);
- }
-
- gsl_matrix_free (a);
- gsl_matrix_free (x);
-
- 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);
-
- tab_vline (t, TAL_2, heading_columns, 0, nr - 1);
-
- tab_text (t, 0, 0, TAT_TITLE | TAB_LEFT, _("Kaiser-Meyer-Olkin Measure of Sampling Adequacy"));
-
- tab_double (t, 2, 0, 0, sum_ssq_r / (sum_ssq_r + sum_ssq_a), NULL);
-
- tab_text (t, 0, 1, TAT_TITLE | TAB_LEFT, _("Bartlett's Test of Sphericity"));
-
- tab_text (t, 1, 1, TAT_TITLE, _("Approx. Chi-Square"));
- tab_text (t, 1, 2, TAT_TITLE, _("df"));
- tab_text (t, 1, 3, TAT_TITLE, _("Sig."));
-
-
- /* The literature doesn't say what to do for the value of W when
+ 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. */
- w = 0;
- for (i = 0; i < idata->n->size1; ++i)
- w += gsl_matrix_get (idata->n, i, i);
- w /= idata->n->size1;
-
- xsq = w - 1 - (2 * factor->n_vars + 5) / 6.0;
- xsq *= -log (idata->detR);
-
- tab_double (t, 2, 1, 0, xsq, NULL);
- tab_double (t, 2, 2, 0, df, &F_8_0);
- tab_double (t, 2, 3, 0, gsl_cdf_chisq_Q (xsq, df), NULL);
-
-
- tab_submit (t);
+ 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);
- covariance_destroy (cov);
+ show_covariance_matrix (factor, idata);
+ if (idata->cvm)
+ covariance_destroy (idata->cvm);
{
- gsl_matrix *am = matrix_dup (analysis_matrix);
+ gsl_matrix *am = matrix_dup (idata->analysis_matrix);
gsl_eigen_symmv_workspace *workspace = gsl_eigen_symmv_alloc (factor->n_vars);
-
+
gsl_eigen_symmv (am, idata->eval, idata->evec, workspace);
gsl_eigen_symmv_free (workspace);
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;
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);
}
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);
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);
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);
}
-