+++ /dev/null
-/* PSPP - a program for statistical analysis.
- Copyright (C) 2005 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 <http://www.gnu.org/licenses/>. */
-
-#include <config.h>
-#include <gsl/gsl_fit.h>
-#include <gsl/gsl_multifit.h>
-
-#include <gsl/gsl_blas.h>
-#include <gsl/gsl_cblas.h>
-
-
-
-/*
- Find the least-squares estimate of b for the linear model:
-
- Y = Xb + Z
-
- where Y is an n-by-1 column vector, X is an n-by-p matrix of
- independent variables, b is a p-by-1 vector of regression coefficients,
- and Z is an n-by-1 normally-distributed random vector with independent
- identically distributed components with mean 0.
-
- This estimate is found via the sweep operator or singular-value
- decomposition with gsl.
-
-
- References:
-
- 1. Matrix Computations, third edition. GH Golub and CF Van Loan.
- The Johns Hopkins University Press. 1996. ISBN 0-8018-5414-8.
-
- 2. Numerical Analysis for Statisticians. K Lange. Springer. 1999.
- ISBN 0-387-94979-8.
-
- 3. Numerical Linear Algebra for Applications in Statistics. JE Gentle.
- Springer. 1998. ISBN 0-387-98542-5.
-*/
-
-#include <math/linreg/linreg.h>
-#include <math/coefficient.h>
-#include <gsl/gsl_errno.h>
-#include <linreg/sweep.h>
-/*
- Get the mean and standard deviation of a vector
- of doubles via a form of the Kalman filter as
- described on page 32 of [3].
- */
-static int
-linreg_mean_std (gsl_vector_const_view v, double *mp, double *sp, double *ssp)
-{
- size_t i;
- double j = 0.0;
- double d;
- double tmp;
- double mean;
- double variance;
-
- mean = gsl_vector_get (&v.vector, 0);
- variance = 0;
- for (i = 1; i < v.vector.size; i++)
- {
- j = (double) i + 1.0;
- tmp = gsl_vector_get (&v.vector, i);
- d = (tmp - mean) / j;
- mean += d;
- variance += j * (j - 1.0) * d * d;
- }
- *mp = mean;
- *sp = sqrt (variance / (j - 1.0));
- *ssp = variance;
-
- return GSL_SUCCESS;
-}
-
-/*
- Set V to contain an array of pointers to the variables
- used in the model. V must be at least C->N_COEFFS in length.
- The return value is the number of distinct variables found.
- */
-int
-pspp_linreg_get_vars (const void *c_, const struct variable **v)
-{
- const pspp_linreg_cache *c = c_;
- const struct variable *tmp;
- int i;
- int j;
- int result = 0;
-
- /*
- Make sure the caller doesn't try to sneak a variable
- into V that is not in the model.
- */
- for (i = 0; i < c->n_coeffs; i++)
- {
- v[i] = NULL;
- }
- for (j = 0; j < c->n_coeffs; j++)
- {
- tmp = pspp_coeff_get_var (c->coeff[j], 0);
- assert (tmp != NULL);
- /* Repeated variables are likely to bunch together, at the end
- of the array. */
- i = result - 1;
- while (i >= 0 && v[i] != tmp)
- {
- i--;
- }
- if (i < 0 && result < c->n_coeffs)
- {
- v[result] = tmp;
- result++;
- }
- }
- return result;
-}
-
-/*
- Allocate a pspp_linreg_cache and return a pointer
- to it. n is the number of cases, p is the number of
- independent variables.
- */
-pspp_linreg_cache *
-pspp_linreg_cache_alloc (size_t n, size_t p)
-{
- pspp_linreg_cache *c;
-
- c = (pspp_linreg_cache *) malloc (sizeof (pspp_linreg_cache));
- c->depvar = NULL;
- c->indep_means = gsl_vector_alloc (p);
- c->indep_std = gsl_vector_alloc (p);
- c->ssx = gsl_vector_alloc (p); /* Sums of squares for the
- independent variables.
- */
- c->ss_indeps = gsl_vector_alloc (p); /* Sums of squares for the
- model parameters.
- */
- c->cov = gsl_matrix_alloc (p + 1, p + 1); /* Covariance matrix. */
- c->n_obs = n;
- c->n_indeps = p;
- /*
- Default settings.
- */
- c->method = PSPP_LINREG_SWEEP;
- c->predict = pspp_linreg_predict;
- c->residual = pspp_linreg_residual; /* The procedure to compute my
- residuals. */
- c->get_vars = pspp_linreg_get_vars; /* The procedure that returns
- pointers to model
- variables. */
- c->resid = NULL; /* The variable storing my residuals. */
- c->pred = NULL; /* The variable storing my predicted values. */
-
- return c;
-}
-
-bool
-pspp_linreg_cache_free (void *m)
-{
- int i;
-
- pspp_linreg_cache *c = m;
- if (c != NULL)
- {
- gsl_vector_free (c->indep_means);
- gsl_vector_free (c->indep_std);
- gsl_vector_free (c->ss_indeps);
- gsl_matrix_free (c->cov);
- gsl_vector_free (c->ssx);
- for (i = 0; i < c->n_coeffs; i++)
- {
- pspp_coeff_free (c->coeff[i]);
- }
- free (c->coeff);
- free (c);
- }
- return true;
-}
-
-/*
- Fit the linear model via least squares. All pointers passed to pspp_linreg
- are assumed to be allocated to the correct size and initialized to the
- values as indicated by opts.
- */
-int
-pspp_linreg (const gsl_vector * Y, const gsl_matrix * X,
- const pspp_linreg_opts * opts, pspp_linreg_cache * cache)
-{
- int rc;
- gsl_matrix *design = NULL;
- gsl_matrix_view xtx;
- gsl_matrix_view xm;
- gsl_matrix_view xmxtx;
- gsl_vector_view xty;
- gsl_vector_view xi;
- gsl_vector_view xj;
- gsl_vector *param_estimates;
-
- size_t i;
- size_t j;
- double tmp;
- double m;
- double s;
- double ss;
-
- if (cache == NULL)
- {
- return GSL_EFAULT;
- }
- if (opts->get_depvar_mean_std)
- {
- linreg_mean_std (gsl_vector_const_subvector (Y, 0, Y->size),
- &m, &s, &ss);
- cache->depvar_mean = m;
- cache->depvar_std = s;
- cache->sst = ss;
- }
- for (i = 0; i < cache->n_indeps; i++)
- {
- if (opts->get_indep_mean_std[i])
- {
- linreg_mean_std (gsl_matrix_const_column (X, i), &m, &s, &ss);
- gsl_vector_set (cache->indep_means, i, m);
- gsl_vector_set (cache->indep_std, i, s);
- gsl_vector_set (cache->ssx, i, ss);
- }
- }
- cache->dft = cache->n_obs - 1;
- cache->dfm = cache->n_indeps;
- cache->dfe = cache->dft - cache->dfm;
- cache->n_coeffs = X->size2;
- cache->intercept = 0.0;
-
- if (cache->method == PSPP_LINREG_SWEEP)
- {
- gsl_matrix *sw;
- /*
- Subtract the means to improve the condition of the design
- matrix. This requires copying X and Y. We do not divide by the
- standard deviations of the independent variables here since doing
- so would cause a miscalculation of the residual sums of
- squares. Dividing by the standard deviation is done GSL's linear
- regression functions, so if the design matrix has a poor
- condition, use QR decomposition.
-
- The design matrix here does not include a column for the intercept
- (i.e., a column of 1's). If using PSPP_LINREG_QR, we need that column,
- so design is allocated here when sweeping, or below if using QR.
- */
- design = gsl_matrix_alloc (X->size1, X->size2);
- for (i = 0; i < X->size2; i++)
- {
- m = gsl_vector_get (cache->indep_means, i);
- for (j = 0; j < X->size1; j++)
- {
- tmp = (gsl_matrix_get (X, j, i) - m);
- gsl_matrix_set (design, j, i, tmp);
- }
- }
- sw = gsl_matrix_calloc (cache->n_indeps + 1, cache->n_indeps + 1);
- xtx = gsl_matrix_submatrix (sw, 0, 0, cache->n_indeps, cache->n_indeps);
-
- for (i = 0; i < xtx.matrix.size1; i++)
- {
- tmp = gsl_vector_get (cache->ssx, i);
- gsl_matrix_set (&(xtx.matrix), i, i, tmp);
- xi = gsl_matrix_column (design, i);
- for (j = (i + 1); j < xtx.matrix.size2; j++)
- {
- xj = gsl_matrix_column (design, j);
- gsl_blas_ddot (&(xi.vector), &(xj.vector), &tmp);
- gsl_matrix_set (&(xtx.matrix), i, j, tmp);
- }
- }
-
- gsl_matrix_set (sw, cache->n_indeps, cache->n_indeps, cache->sst);
- xty = gsl_matrix_column (sw, cache->n_indeps);
- /*
- This loop starts at 1, with i=0 outside the loop, so we can get
- the model sum of squares due to the first independent variable.
- */
- xi = gsl_matrix_column (design, 0);
- gsl_blas_ddot (&(xi.vector), Y, &tmp);
- gsl_vector_set (&(xty.vector), 0, tmp);
- tmp *= tmp / gsl_vector_get (cache->ssx, 0);
- gsl_vector_set (cache->ss_indeps, 0, tmp);
- for (i = 1; i < cache->n_indeps; i++)
- {
- xi = gsl_matrix_column (design, i);
- gsl_blas_ddot (&(xi.vector), Y, &tmp);
- gsl_vector_set (&(xty.vector), i, tmp);
- }
-
- /*
- Sweep on the matrix sw, which contains XtX, XtY and YtY.
- */
- reg_sweep (sw);
- cache->sse = gsl_matrix_get (sw, cache->n_indeps, cache->n_indeps);
- cache->mse = cache->sse / cache->dfe;
- /*
- Get the intercept.
- */
- m = cache->depvar_mean;
- for (i = 0; i < cache->n_indeps; i++)
- {
- tmp = gsl_matrix_get (sw, i, cache->n_indeps);
- cache->coeff[i]->estimate = tmp;
- m -= tmp * gsl_vector_get (cache->indep_means, i);
- }
- /*
- Get the covariance matrix of the parameter estimates.
- Only the upper triangle is necessary.
- */
-
- /*
- The loops below do not compute the entries related
- to the estimated intercept.
- */
- for (i = 0; i < cache->n_indeps; i++)
- for (j = i; j < cache->n_indeps; j++)
- {
- tmp = -1.0 * cache->mse * gsl_matrix_get (sw, i, j);
- gsl_matrix_set (cache->cov, i + 1, j + 1, tmp);
- }
- /*
- Get the covariances related to the intercept.
- */
- xtx = gsl_matrix_submatrix (sw, 0, 0, cache->n_indeps, cache->n_indeps);
- xmxtx = gsl_matrix_submatrix (cache->cov, 0, 1, 1, cache->n_indeps);
- xm = gsl_matrix_view_vector (cache->indep_means, 1, cache->n_indeps);
- rc = gsl_blas_dsymm (CblasRight, CblasUpper, cache->mse,
- &xtx.matrix, &xm.matrix, 0.0, &xmxtx.matrix);
- if (rc == GSL_SUCCESS)
- {
- tmp = cache->mse / cache->n_obs;
- for (i = 1; i < 1 + cache->n_indeps; i++)
- {
- tmp -= gsl_matrix_get (cache->cov, 0, i)
- * gsl_vector_get (cache->indep_means, i - 1);
- }
- gsl_matrix_set (cache->cov, 0, 0, tmp);
-
- cache->intercept = m;
- }
- else
- {
- fprintf (stderr, "%s:%d:gsl_blas_dsymm: %s\n",
- __FILE__, __LINE__, gsl_strerror (rc));
- exit (rc);
- }
- gsl_matrix_free (sw);
- }
- else if (cache->method == PSPP_LINREG_CONDITIONAL_INVERSE)
- {
- /*
- Use the SVD of X^T X to find a conditional inverse of X^TX. If
- the SVD is X^T X = U D V^T, then set the conditional inverse
- to (X^T X)^c = V D^- U^T. D^- is defined as follows: If entry
- (i, i) has value sigma_i, then entry (i, i) of D^- is 1 /
- sigma_i if sigma_i > 0, and 0 otherwise. Then solve the normal
- equations by setting the estimated parameter vector to
- (X^TX)^c X^T Y.
- */
- }
- else
- {
- gsl_multifit_linear_workspace *wk;
- /*
- Use QR decomposition via GSL.
- */
-
- param_estimates = gsl_vector_alloc (1 + X->size2);
- design = gsl_matrix_alloc (X->size1, 1 + X->size2);
-
- for (j = 0; j < X->size1; j++)
- {
- gsl_matrix_set (design, j, 0, 1.0);
- for (i = 0; i < X->size2; i++)
- {
- tmp = gsl_matrix_get (X, j, i);
- gsl_matrix_set (design, j, i + 1, tmp);
- }
- }
-
- wk = gsl_multifit_linear_alloc (design->size1, design->size2);
- rc = gsl_multifit_linear (design, Y, param_estimates,
- cache->cov, &(cache->sse), wk);
- for (i = 0; i < cache->n_coeffs; i++)
- {
- cache->coeff[i]->estimate = gsl_vector_get (param_estimates, i + 1);
- }
- cache->intercept = gsl_vector_get (param_estimates, 0);
- if (rc == GSL_SUCCESS)
- {
- gsl_multifit_linear_free (wk);
- gsl_vector_free (param_estimates);
- }
- else
- {
- fprintf (stderr, "%s:%d: gsl_multifit_linear returned %d\n",
- __FILE__, __LINE__, rc);
- }
- }
-
-
- cache->ssm = cache->sst - cache->sse;
- /*
- Get the remaining sums of squares for the independent
- variables.
- */
- m = 0;
- for (i = 1; i < cache->n_indeps; i++)
- {
- j = i - 1;
- m += gsl_vector_get (cache->ss_indeps, j);
- tmp = cache->ssm - m;
- gsl_vector_set (cache->ss_indeps, i, tmp);
- }
-
- gsl_matrix_free (design);
- return GSL_SUCCESS;
-}
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