--- /dev/null
+/* lib/linreg/linreg.c
+
+ Copyright (C) 2005 Free Software Foundation, Inc.
+ Written by Jason H. Stover.
+
+ 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 2 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, write to the Free Software
+ Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
+ 02111-1307, USA.
+*/
+
+/*
+ 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 "pspp_linreg.h"
+#include <gsl/gsl_errno.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;
+}
+
+/*
+ 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 *cache;
+
+ cache = (pspp_linreg_cache *) malloc (sizeof (pspp_linreg_cache));
+ cache->param_estimates = gsl_vector_alloc (p + 1);
+ cache->indep_means = gsl_vector_alloc (p);
+ cache->indep_std = gsl_vector_alloc (p);
+ cache->ssx = gsl_vector_alloc (p); /* Sums of squares for the independent
+ variables.
+ */
+ cache->ss_indeps = gsl_vector_alloc (p); /* Sums of squares for the model
+ parameters.
+ */
+ cache->cov = gsl_matrix_alloc (p + 1, p + 1); /* Covariance matrix. */
+ cache->n_obs = n;
+ cache->n_indeps = p;
+ /*
+ Default settings.
+ */
+ cache->method = PSPP_LINREG_SWEEP;
+
+ return cache;
+}
+
+void
+pspp_linreg_cache_free (pspp_linreg_cache * cache)
+{
+ gsl_vector_free (cache->param_estimates);
+ gsl_vector_free (cache->indep_means);
+ gsl_vector_free (cache->indep_std);
+ gsl_vector_free (cache->ss_indeps);
+ gsl_matrix_free (cache->cov);
+ free (cache);
+}
+
+/*
+ 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;
+ gsl_matrix_view xtx;
+ gsl_matrix_view xm;
+ gsl_matrix_view xmxtx;
+ gsl_vector_view xty;
+ gsl_vector_view xi;
+ gsl_vector_view xj;
+
+ size_t i;
+ size_t j;
+ double tmp;
+ double m;
+ double s;
+ double ss;
+ double mse;
+
+ 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;
+ 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 very 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.
+ */
+ pspp_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);
+ gsl_vector_set (cache->param_estimates, i + 1, 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);
+
+ gsl_vector_set (cache->param_estimates, 0, m);
+ }
+ else
+ {
+ fprintf (stderr, "%s:%d:gsl_blas_dsymm: %s\n",
+ __FILE__, __LINE__, gsl_strerror (rc));
+ exit (rc);
+ }
+ gsl_matrix_free (sw);
+ }
+ else
+ {
+ /*
+ Use QR decomposition via GSL. This section has not been tested.
+ */
+ 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);
+ }
+ }
+ gsl_multifit_linear_workspace *wk =
+ gsl_multifit_linear_alloc (design->size1, design->size2);
+ rc = gsl_multifit_linear (design, Y, cache->param_estimates,
+ cache->cov, &(cache->sse), wk);
+ if (rc == GSL_SUCCESS)
+ {
+ gsl_multifit_linear_free (wk);
+ }
+ 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;
+}
--- /dev/null
+/* lib/linreg/linreg.c
+
+ Copyright (C) 2005 Free Software Foundation, Inc.
+ Written by Jason H Stover.
+
+ 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 2 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, write to the Free Software
+ Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
+ 02111-1307, USA.
+ */
+
+/*
+ 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.
+
+
+ References:
+
+ Matrix Computations, third edition. GH Golub and CF Van Loan.
+ The Johns Hopkins University Press. 1996. ISBN 0-8018-5414-8.
+
+ Numerical Analysis for Statisticians. K Lange. Springer. 1999.
+ ISBN 0-387-94979-8.
+
+ Numerical Linear Algebra for Applications in Statistics. JE Gentle.
+ Springer. 1998. ISBN 0-387-98542-5.
+ */
+#ifndef PSPP_LINREG_H
+#define PSPP_LINREG_H
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_fit.h>
+#include <gsl/gsl_multifit.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_cblas.h>
+enum
+{
+ PSPP_LINREG_SWEEP,
+ PSPP_LINREG_SVD
+};
+
+/*
+ Cache for the relevant data from the model. There are several
+ members which the caller may not use, and which could use a lot of
+ storage. Therefore non-essential members of the struct will be
+ allocated only when requested.
+ */
+struct pspp_linreg_cache_struct
+{
+ int n_obs; /* Number of observations. */
+ int n_indeps; /* Number of independent variables. */
+ gsl_vector *depvar;
+ gsl_matrix *indepvar;
+ gsl_vector *residuals;
+ gsl_vector *param_estimates;
+ int method; /* Method to use to estimate parameters. */
+ /*
+ Means and standard deviations of the variables.
+ If these pointers are null when pspp_linreg() is
+ called, pspp_linreg() will compute their values.
+
+ Entry i of indep_means is the mean of independent
+ variable i, whose observations are stored in column i
+ of indepvar.
+ */
+ double depvar_mean;
+ double depvar_std;
+ gsl_vector *indep_means;
+ gsl_vector *indep_std;
+
+ /*
+ Sums of squares.
+ */
+ double ssm; /* Sums of squares for the overall model. */
+ gsl_vector *ss_indeps; /* Sums of squares from each
+ independent variable.
+ */
+ double sst; /* Sum of squares total. */
+ double sse; /* Sum of squares error. */
+ double mse; /* Mean squared error. This is just sse / dfe, but
+ since it is the best unbiased estimate of the population
+ variance, it has its own entry here.
+ */
+ gsl_vector *ssx; /* Centered sums of squares for independent variables,
+ i.e. \sum (x[i] - mean(x))^2.
+ */
+ double ssy; /* Centered sums of squares for dependent variable. */
+ /*
+ Covariance matrix of the parameter estimates.
+ */
+ gsl_matrix *cov;
+ /*
+ Degrees of freedom.
+ */
+ double dft;
+ double dfe;
+ double dfm;
+
+ /*
+ 'Hat' or Hessian matrix, i.e. (X'X)^{-1}, where X is our
+ design matrix.
+ */
+ gsl_matrix *hat;
+};
+typedef struct pspp_linreg_cache_struct pspp_linreg_cache;
+
+/*
+ Options describing what special values should be computed.
+ */
+struct pspp_linreg_opts_struct
+{
+ int resid; /* Should the residuals be returned? */
+
+ int get_depvar_mean_std;
+ int *get_indep_mean_std; /* Array of booleans dictating which
+ independent variables need their means
+ and standard deviations computed within
+ pspp_linreg. This array MUST be of
+ length n_indeps. If element i is 1,
+ pspp_linreg will compute the mean and
+ variance of indpendent variable i. If
+ element i is 0, it will not compute the
+ mean and standard deviation, and assume
+ the values are stored.
+ cache->indep_mean[i] is the mean and
+ cache->indep_std[i] is the sample
+ standard deviation.
+ */
+};
+typedef struct pspp_linreg_opts_struct pspp_linreg_opts;
+
+int pspp_reg_sweep (gsl_matrix * A);
+
+pspp_linreg_cache *pspp_linreg_cache_alloc (size_t n, size_t p);
+
+void pspp_linreg_cache_free (pspp_linreg_cache * cache);
+
+int pspp_linreg (const gsl_vector * Y, const gsl_matrix * X,
+ const pspp_linreg_opts * opts, pspp_linreg_cache * cache);
+#endif
--- /dev/null
+/* lib/linreg/sweep.c
+
+ Copyright (C) 2005 Free Software Foundation, Inc.
+ Written by Jason H Stover.
+
+ 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 2 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, write to the Free Software
+ Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
+ 02111-1307, USA.
+ */
+
+/*
+ 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, which is a modification
+ of Gauss-Jordan pivoting.
+
+
+ References:
+
+ Matrix Computations, third edition. GH Golub and CF Van Loan.
+ The Johns Hopkins University Press. 1996. ISBN 0-8018-5414-8.
+
+ Numerical Analysis for Statisticians. K Lange. Springer. 1999.
+ ISBN 0-387-94979-8.
+
+ Numerical Linear Algebra for Applications in Statistics. JE Gentle.
+ Springer. 1998. ISBN 0-387-98542-5.
+ */
+
+#include "pspp_linreg.h"
+
+/*
+ The matrix A will be overwritten. In ordinary uses of the sweep
+ operator, A will be the matrix
+
+ __ __
+ |X'X X'Y|
+ | |
+ |Y'X Y'Y|
+ -- --
+
+ X refers to the design matrix and Y to the vector of dependent
+ observations. pspp_reg_sweep sweeps on the diagonal elements of
+ X'X.
+
+ The matrix A is assumed to be symmetric, so the sweep operation is
+ performed only for the upper triangle of A.
+ */
+
+int
+pspp_reg_sweep (gsl_matrix * A)
+{
+ double sweep_element;
+ double tmp;
+ int i;
+ int j;
+ int k;
+ gsl_matrix *B;
+
+ if (A != NULL)
+ {
+ if (A->size1 == A->size2)
+ {
+ B = gsl_matrix_alloc (A->size1, A->size2);
+ for (k = 0; k < (A->size1 - 1); k++)
+ {
+ sweep_element = gsl_matrix_get (A, k, k);
+ if (fabs (sweep_element) > GSL_DBL_MIN)
+ {
+ tmp = -1.0 / sweep_element;
+ gsl_matrix_set (B, k, k, tmp);
+ /*
+ Rows before current row k.
+ */
+ for (i = 0; i < k; i++)
+ {
+ for (j = i; j < A->size2; j++)
+ {
+ /*
+ Use only the upper triangle of A.
+ */
+ if (j < k)
+ {
+ tmp = gsl_matrix_get (A, i, j) -
+ gsl_matrix_get (A, i, k)
+ * gsl_matrix_get (A, j, k) / sweep_element;
+ gsl_matrix_set (B, i, j, tmp);
+ }
+ else if (j > k)
+ {
+ tmp = gsl_matrix_get (A, i, j) -
+ gsl_matrix_get (A, i, k)
+ * gsl_matrix_get (A, k, j) / sweep_element;
+ gsl_matrix_set (B, i, j, tmp);
+ }
+ else
+ {
+ tmp = gsl_matrix_get (A, i, k) / sweep_element;
+ gsl_matrix_set (B, i, j, tmp);
+ }
+ }
+ }
+ /*
+ Current row k.
+ */
+ for (j = k + 1; j < A->size1; j++)
+ {
+ tmp = gsl_matrix_get (A, k, j) / sweep_element;
+ gsl_matrix_set (B, k, j, tmp);
+ }
+ /*
+ Rows after the current row k.
+ */
+ for (i = k + 1; i < A->size1; i++)
+ {
+ for (j = i; j < A->size2; j++)
+ {
+ tmp = gsl_matrix_get (A, i, j) -
+ gsl_matrix_get (A, k, i)
+ * gsl_matrix_get (A, k, j) / sweep_element;
+ gsl_matrix_set (B, i, j, tmp);
+ }
+ }
+ }
+ for (i = 0; i < A->size1; i++)
+ for (j = i; j < A->size2; j++)
+ {
+ gsl_matrix_set (A, i, j, gsl_matrix_get (B, i, j));
+ }
+ }
+ gsl_matrix_free (B);
+ return GSL_SUCCESS;
+ }
+ return GSL_ENOTSQR;
+ }
+ return GSL_EFAULT;
+}
projects / pspp-builds.git / commitdiff