Multivariate Gaussian Code using GSL
카테고리 없음 2011. 6. 11. 16:29Source code by Ralph Silva
from here
Makefile
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 | /*************************************************************************************** * Multivariate Normal density function and random number generator * Multivariate Student t density function and random number generator * Wishart random number generator * Using GSL -> www.gnu.org/software/gsl * * Copyright (C) 2006 Ralph dos Santos Silva * * 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA * * AUTHOR * Ralph dos Santos Silva, [EMAIL PROTECTED] * March, 2006 ***************************************************************************************/#include <math.h>#include <gsl/gsl_sf_gamma.h>#include <gsl/gsl_rng.h>#include <gsl/gsl_randist.h>#include <gsl/gsl_vector.h>#include <gsl/gsl_matrix.h>#include <gsl/gsl_blas.h>#include <gsl/gsl_linalg.h>/*****************************************************************************************************************//*****************************************************************************************************************/int rmvnorm(const gsl_rng *r, const int n, const gsl_vector *mean, const gsl_matrix *var, gsl_vector *result){ /* multivariate normal distribution random number generator */ /* * n dimension of the random vetor * mean vector of means of size n * var variance matrix of dimension n x n * result output variable with a sigle random vector normal distribution generation */ int k; gsl_matrix *work = gsl_matrix_alloc(n,n); gsl_matrix_memcpy(work,var); gsl_linalg_cholesky_decomp(work); for(k=0; k<n; k++) gsl_vector_set( result, k, gsl_ran_ugaussian(r) ); gsl_blas_dtrmv(CblasLower, CblasNoTrans, CblasNonUnit, work, result); gsl_vector_add(result,mean); gsl_matrix_free(work); return 0;}/*****************************************************************************************************************//*****************************************************************************************************************/double dmvnorm(const int n, const gsl_vector *x, const gsl_vector *mean, const gsl_matrix *var){ /* multivariate normal density function */ /* * n dimension of the random vetor * mean vector of means of size n * var variance matrix of dimension n x n */ int s; double ax,ay; gsl_vector *ym, *xm; gsl_matrix *work = gsl_matrix_alloc(n,n), *winv = gsl_matrix_alloc(n,n); gsl_permutation *p = gsl_permutation_alloc(n); gsl_matrix_memcpy( work, var ); gsl_linalg_LU_decomp( work, p, &s ); gsl_linalg_LU_invert( work, p, winv ); ax = gsl_linalg_LU_det( work, s ); gsl_matrix_free( work ); gsl_permutation_free( p ); xm = gsl_vector_alloc(n); gsl_vector_memcpy( xm, x); gsl_vector_sub( xm, mean ); ym = gsl_vector_alloc(n); gsl_blas_dsymv(CblasUpper,1.0,winv,xm,0.0,ym); gsl_matrix_free( winv ); gsl_blas_ddot( xm, ym, &ay); gsl_vector_free(xm); gsl_vector_free(ym); ay = exp(-0.5*ay)/sqrt( pow((2*M_PI),n)*ax ); return ay;}/*****************************************************************************************************************//*****************************************************************************************************************/int rmvt(const gsl_rng *r, const int n, const gsl_vector *location, const gsl_matrix *scale, const int dof, gsl_vector *result){ /* multivariate Student t distribution random number generator */ /* * n dimension of the random vetor * location vector of locations of size n * scale scale matrix of dimension n x n * dof degrees of freedom * result output variable with a single random vector normal distribution generation */ int k; gsl_matrix *work = gsl_matrix_alloc(n,n); double ax = 0.5*dof; ax = gsl_ran_gamma(r,ax,(1/ax)); /* gamma distribution */ gsl_matrix_memcpy(work,scale); gsl_matrix_scale(work,(1/ax)); /* scaling the matrix */ gsl_linalg_cholesky_decomp(work); for(k=0; k<n; k++) gsl_vector_set( result, k, gsl_ran_ugaussian(r) ); gsl_blas_dtrmv(CblasLower, CblasNoTrans, CblasNonUnit, work, result); gsl_vector_add(result, location); gsl_matrix_free(work); return 0;}/*****************************************************************************************************************//*****************************************************************************************************************/double dmvt(const int n, const gsl_vector *x, const gsl_vector *location, const gsl_matrix *scale, const int dof){ /* multivariate Student t density function */ /* * n dimension of the random vetor * location vector of locations of size n * scale scale matrix of dimension n x n * dof degrees of freedom */ int s; double ax,ay,az=0.5*(dof + n); gsl_vector *ym, *xm; gsl_matrix *work = gsl_matrix_alloc(n,n), *winv = gsl_matrix_alloc(n,n); gsl_permutation *p = gsl_permutation_alloc(n); gsl_matrix_memcpy( work, scale ); gsl_linalg_LU_decomp( work, p, &s ); gsl_linalg_LU_invert( work, p, winv ); ax = gsl_linalg_LU_det( work, s ); gsl_matrix_free( work ); gsl_permutation_free( p ); xm = gsl_vector_alloc(n); gsl_vector_memcpy( xm, x); gsl_vector_sub( xm, location ); ym = gsl_vector_alloc(n); gsl_blas_dsymv(CblasUpper,1.0,winv,xm,0.0,ym); gsl_matrix_free( winv ); gsl_blas_ddot( xm, ym, &ay); gsl_vector_free(xm); gsl_vector_free(ym); ay = pow((1+ay/dof),-az)*gsl_sf_gamma(az)/(gsl_sf_gamma(0.5*dof)*sqrt( pow((dof*M_PI),n)*ax )); return ay;}/*****************************************************************************************************************//*****************************************************************************************************************/int rwishart(const gsl_rng *r, const int n, const int dof, const gsl_matrix *scale, gsl_matrix *result){ /* Wishart distribution random number generator */ /* * n gives the dimension of the random matrix * dof degrees of freedom * scale scale matrix of dimension n x n * result output variable with a single random matrix Wishart distribution generation */ int k,l; gsl_matrix *work = gsl_matrix_calloc(n,n); for(k=0; k<n; k++){ gsl_matrix_set( work, k, k, sqrt( gsl_ran_chisq( r, (dof-k) ) ) ); for(l=0; l<k; l++){ gsl_matrix_set( work, k, l, gsl_ran_ugaussian(r) ); } } gsl_matrix_memcpy(result,scale); gsl_linalg_cholesky_decomp(result); gsl_blas_dtrmm(CblasLeft,CblasLower,CblasNoTrans,CblasNonUnit,1.0,result,work); gsl_blas_dsyrk(CblasUpper,CblasNoTrans,1.0,work,0.0,result); return 0;}/*************************************************************************************** * Multivariate Normal density function and random number generator * Multivariate Student t density function and random number generator * Wishart random number generator * Using GSL -> www.gnu.org/software/gsl * * Copyright (C) 2006 Ralph dos Santos Silva * * 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA * * AUTHOR * Ralph dos Santos Silva, [EMAIL PROTECTED] * March, 2006 ***************************************************************************************/int rmvnorm(const gsl_rng *r, const int n, const gsl_vector *mean, const gsl_matrix *var, gsl_vector *result);double dmvnorm(const int n, const gsl_vector *x, const gsl_vector *mean, const gsl_matrix *var);int rmvt(const gsl_rng *r, const int n, const gsl_vector *location, const gsl_matrix *scale, const int dof, gsl_vector *result);double dmvt(const int n, const gsl_vector *x, const gsl_vector *locationn, const gsl_matrix *scale, const int dof);int rwishart(const gsl_rng *r, const int n, const int dof, const gsl_matrix *scale, gsl_matrix *result);/*************************************************************************************** * A testing program for multivariate distributions * Using GSL -> www.gnu.org/software/gsl * Copyright (C) 2006 Ralph dos Santos Silva * * 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA * * AUTHOR * Ralph dos Santos Silva, [EMAIL PROTECTED] * March, 2006 ***************************************************************************************/#include <stdio.h>#include <stdlib.h>#include <stddef.h>#include <time.h>#include <math.h>/* GSL - GNU Scientific Library *//* #define GSL_CHECK_RANGE_OFF */#include <gsl/gsl_math.h>#include <gsl/gsl_rng.h>#include <gsl/gsl_cdf.h>/* ----------------------------- */#include <gsl/gsl_vector.h>#include <gsl/gsl_matrix.h>/* ----------------------------- */#include "rmv.h"int main(){ FILE *f; int k; unsigned long int initime; double result; gsl_vector *x = gsl_vector_calloc(3), *mean = gsl_vector_calloc(3); gsl_matrix *m = gsl_matrix_alloc(3,3), *rm = gsl_matrix_alloc(3,3); gsl_rng *r; time(&initime); r = gsl_rng_alloc(gsl_rng_mt19937); gsl_rng_set(r, initime); printf("The SEED is %li.\n\n",initime); gsl_matrix_set(m,0,0, 1.0); gsl_matrix_set(m,0,1, 0.2); gsl_matrix_set(m,0,2,-0.9); gsl_matrix_set(m,1,0, 0.2); gsl_matrix_set(m,1,1, 1.0); gsl_matrix_set(m,1,2, 0.1); gsl_matrix_set(m,2,0,-0.9); gsl_matrix_set(m,2,1, 0.1); gsl_matrix_set(m,2,2, 1.0); gsl_vector_set(x,0,0.1); gsl_vector_set(x,1,0.1); gsl_vector_set(x,2,0.1); result = dmvnorm(3,x,mean,m); fprintf(stdout,"norm = %g\n", result); gsl_vector_set(x,0,0.1); gsl_vector_set(x,1,0.1); gsl_vector_set(x,2,0.1); result = dmvt(3,x,mean,m,5); fprintf(stdout,"t = %g\n", result); f = fopen("test-n.txt","w"); for(k=0; k<10; k++){ rmvnorm(r,3,mean,m,x); fprintf(f, "%g %g %g\n",gsl_vector_get(x,0),gsl_vector_get(x,1),gsl_vector_get(x,2)); } fclose(f); f = fopen("test-t.txt","w"); for(k=0; k<10; k++){ rmvt(r,3,mean,m,5,x); fprintf(f, "%g %g %g\n",gsl_vector_get(x,0),gsl_vector_get(x,1),gsl_vector_get(x,2)); } fclose(f); f = fopen("test-w.txt","w"); for(k=0; k<1000; k++){ rwishart(r,3,5,m,rm); fprintf(f, "%g %g %g\n",gsl_matrix_get(rm,0,0),gsl_matrix_get(rm,0,1),gsl_matrix_get(rm,0,2)); fprintf(f, "%g %g %g\n",gsl_matrix_get(rm,1,0),gsl_matrix_get(rm,1,1),gsl_matrix_get(rm,1,2)); fprintf(f, "%g %g %g\n",gsl_matrix_get(rm,2,0),gsl_matrix_get(rm,2,1),gsl_matrix_get(rm,2,2)); } fclose(f); return 0;} |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | # Copyright (C) 2006 Ralph dos Santos Silva#LIBDIR = /home/rsilva1/local/libsunLIBDIR = /usr/libINCLUDEDIR = /usr/includeLIBGSL = -lgslLIBCBLAS = -lcblasLIBATLAS = -latlasLIBMATH = -lmCFLAGS = -O2 -static -g -Wall -W -DHAVE_INLINE -I$(INCLUDEDIR)CC = gcc.c.o: $(CC) $(CFLAGS) -c $<all: test.o rmv.o $(CC) -o test test.o rmv.o -L$(LIBDIR) $(LIBGSL) $(LIBCBLAS) $(LIBATLAS) $(LIBMATH) clean: rm -f *.o test |