File: [local] / OpenXM / src / hgm / mh / src / rk.c (download)
Revision 1.18, Wed Mar 2 01:09:36 2016 UTC (8 years, 6 months ago) by takayama
Branch: MAIN
CVS Tags: HEAD Changes since 1.17: +4 -4
lines
Undo the previous commit. MH_Dp = 1 is necessary for a long step of gsl RK.
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/*
License: LGPL
Ref: Copied from this11/misc-2011/A1/wishart/Prog
$OpenXM: OpenXM/src/hgm/mh/src/rk.c,v 1.18 2016/03/02 01:09:36 takayama Exp $
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
#include "sfile.h"
#include "mh.h"
#include "t-gsl_errno.h"
#include "t-gsl_odeiv.h"
extern int MH_RANK;
extern int MH_M;
extern MH_RF mh_rf;
char *MH_Gfname;
char *MH_Dfname;
extern int MH_Mg;
extern double *MH_Beta; extern double *MH_Ng; extern double MH_X0g;
extern int MH_RawName;
double MH_Hg = 0.001;
static struct SFILE *Gf =NULL;
static struct SFILE *Df =NULL;
int MH_P95=0;
int MH_Verbose=0;
int MH_strategy=STRATEGY_DEFAULT; /* 0: rk4, 1:a-rk4 (adaptive) */
double MH_abserr = 1e-10;
double MH_relerr = MH_RELERR_DEFAULT ;
/* D_i = MH_abserr + MH_relerr*|y_i|
If observed error E > D*110/100, the stepsize will be decreased.
cf. GSL, 26.3 Adaptive Step-size control.
*/
int mh_rf_for_gsl(double t,const double y[],double f[],void *params) {
(*mh_rf)(t,(double *)y,MH_RANK,f,MH_RANK);
return(GSL_SUCCESS);
}
static int mypower(int x,int n) {
int a,i;
a = 1;
for (i=0; i<n; i++) a = a*x;
return(a);
}
int mh_gopen_file() {
FILE *fp;
char fname[1024];
int i;
extern int MH_byFile;
Gf=NULL;
Df=NULL;
if (MH_Verbose) {
oxprintfe("MH_Gfname=%s\n",MH_Gfname);
oxprintfe("MH_Dfname=%s\n",MH_Dfname);
}
if (MH_RANK != mypower(2,MH_Mg)) {
oxprintfe("rk.c MH_RANK=%d is not equal to 2^MH_Mg=%d. input_data_file is broken.\n",MH_RANK,mypower(2,MH_Mg));
mh_usage();
mh_exit(-1);
}
if (MH_Dfname != NULL) {
if (!MH_RawName) {
sprintf(&(MH_Dfname[strlen(MH_Dfname)]),"-m%d-n%lf-x0%lf-b",MH_Mg,*MH_Ng,MH_X0g);
for (i=0; i<MH_Mg; i++) {
sprintf(&(MH_Dfname[strlen(MH_Dfname)]),"%lf,",MH_Beta[i]);
}
sprintf(&(MH_Dfname[strlen(MH_Dfname)]),".txt");
}
Df = mh_fopen(MH_Dfname,"w",MH_byFile);
if (Df == NULL) {
oxprintfe("Error to open the file %s\n",MH_Dfname);
return(-1);
}
}
if (MH_Gfname != NULL) {
Gf = mh_fopen(MH_Gfname,"w",MH_byFile);
if (Gf == NULL) {
oxprintfe("Error to open the file %s\n",MH_Gfname);
return(-1);
}
}else return(1);
if (MH_byFile) {
sprintf(fname,"%s-gp.txt",MH_Gfname);
fp = fopen(fname,"w");
fprintf(fp,"set xrange [0:20]\n");
fprintf(fp,"set yrange [0:1.2]\n");
fprintf(fp,"plot \"%s\" title \"by hg\" with lines\n",MH_Gfname);
fclose(fp);
}
return(0);
}
/*
Runge-Kutta
y_{n+1} = y_n + 1/6 k_1 + 1/3 k_2 + 1/3 k_3 + 1/6 k_4
k_1 = h f(x_n, y_n)
k_2 = h f(x_n + 1/2 h, y_n + 1/2 k_1)
k_3 = h f(x_n + 1/2 h, y_n + 1/2 k_2)
k_4 = h f(x_n + h, y_n + k_3)
*/
/* ベクトル値関数 rk is defined in tmp-code-?.c,
f(x, y) (x : scalar, y : vector) */
static void show_v(double x,double *v, int n)
{
int i;
static int counter=0;
extern int MH_Dp;
char swork[MH_SSIZE];
if (MH_Dp <= 0) return;
if ((counter % MH_Dp) != 0) { counter++; return;} else counter=1;
sprintf(swork,"%lf\n",x); mh_fputs(swork,Df);
for (i = 0; i < n; i++) {sprintf(swork," %le\n", v[i]); mh_fputs(swork,Df);}
}
struct MH_RESULT mh_rkmain(double x0,double y0[],double xn)
{
static int initialized=0;
int i;
double h;
double x;
char swork[MH_SSIZE];
struct MH_RESULT result;
extern int MH_deallocate;
/*
double y[MH_RANK];
double k1[MH_RANK], k2[MH_RANK], k3[MH_RANK], k4[MH_RANK];
double temp[MH_RANK];
double ty[MH_RANK];
*/
static double *y,*k1,*k2,*k3,*k4,*temp,*ty;
if (MH_deallocate && initialized) {
if (y) mh_free(y);
if (k1) mh_free(k1);
if (k2) mh_free(k2);
if (k3) mh_free(k3);
if (k4) mh_free(k4);
if (temp) mh_free(temp);
if (ty) mh_free(ty);
y = k1 = k2 = k3 = k4 = temp = ty = NULL;
initialized=0;
return(result);
}
if (!initialized) {
y = (double *)mh_malloc(sizeof(double)*MH_RANK);
k1 = (double *)mh_malloc(sizeof(double)*MH_RANK);
k2 = (double *)mh_malloc(sizeof(double)*MH_RANK);
k3 = (double *)mh_malloc(sizeof(double)*MH_RANK);
k4 = (double *)mh_malloc(sizeof(double)*MH_RANK);
temp = (double *)mh_malloc(sizeof(double)*MH_RANK);
ty = (double *)mh_malloc(sizeof(double)*MH_RANK);
initialized=1;
}
h = MH_Hg;
for (i = 0; i < MH_RANK; i++)
y[i] = y0[i];
if (MH_strategy == 0) {
for (x = x0; (h>0?(x<xn):(x>xn)); x += h) {
if (Df) show_v(x,y, MH_RANK);
if (Gf) {
sprintf(swork,"%lf %le\n",x,y[0]);
mh_fputs(swork,Gf);
}
/* Output 95% point */
if (MH_P95) {
if ((MH_P95==1) && (y[0] >= 0.95)) {
oxprintf("x=%le, y[0]=%lf\n",x,y[0]);
MH_P95=2;
}else if ((MH_P95==2) && (y[0] >=0.9500000001)) {
oxprintf("x=%le, y[0]=%lf\n",x,y[0]);
MH_P95=0;
}
}
(*mh_rf)(x, y, MH_RANK, temp, MH_RANK);
for (i = 0; i < MH_RANK; i++)
k1[i] = h * temp[i];
for (i = 0; i < MH_RANK; i++)
ty[i] = y[i] + 0.5 * k1[i];
(*mh_rf)(x + 0.5 * h, ty, MH_RANK, temp, MH_RANK);
for (i = 0; i < MH_RANK; i++)
k2[i] = h * temp[i];
for (i = 0; i < MH_RANK; i++)
ty[i] = y[i] + 0.5 * k2[i];
(*mh_rf)(x + 0.5 * h, ty, MH_RANK, temp, MH_RANK);
for (i = 0; i < MH_RANK; i++)
k3[i] = h * temp[i];
for (i = 0; i < MH_RANK; i++)
ty[i] = y[i] + k3[i];
(*mh_rf)(x + h, ty, MH_RANK, temp, MH_RANK);
for (i = 0; i < MH_RANK; i++)
k4[i] = h * temp[i];
for (i = 0; i < MH_RANK; i++)
y[i] = y[i] + 1.0/6.0 * k1[i] + 1.0/3.0 * k2[i] + 1.0/3.0 * k3[i] + 1.0/6.0 * k4[i];
}
}else
{
extern int MH_Dp;
double dh;
double mh_dp_orig;
double x1;
const gsl_odeiv_step_type *T = gsl_odeiv_step_rkf45;
gsl_odeiv_step *s = gsl_odeiv_step_alloc(T, MH_RANK);
gsl_odeiv_control *c = gsl_odeiv_control_y_new(MH_abserr, MH_relerr);
/* We should use the relative error.
hgm.cwishart(m=5,n=20,beta=c(1,2,3,4,5),x=20,x0=2,approxdeg=20);
0.977
hgm.cwishart(m=8,n=20,beta=c(1,2,3,4,5,5.6,5.7,5.8),x=30,x0=1,approxdeg=20);
0.962 (non-gsl) or 0.969 (gsl, abs error 0.0, relative error 1e-10),
NaN abs=0, rel=1e-5 or abs=1e-18, rel=1e-6
./mh causes NaN when rel error is 1e-10 on old 32bit machines.
*/
gsl_odeiv_evolve *e = gsl_odeiv_evolve_alloc(MH_RANK);
gsl_odeiv_system sys = {mh_rf_for_gsl, NULL, 0, NULL};
sys.dimension = MH_RANK;
/* oxprintf("MH_RANK=%d\n",MH_RANK); */
if (x0 >= xn) {oxprintfe("Error: x0 < x must hold.\n"); mh_exit(-30);}
x = x0;
if (MH_Dp > 0) dh = MH_Dp*h; else dh=xn-x0;
mh_dp_orig = MH_Dp; MH_Dp=1;
while (x < xn) {
if (Df) show_v(x,y, MH_RANK);
if (Gf) {
sprintf(swork,"%lf %le\n",x,y[0]);
mh_fputs(swork,Gf);
}
/* Output 95% point */
if (MH_P95) {
if ((MH_P95==1) && (y[0] >= 0.95)) {
oxprintf("x=%le, y[0]=%lf\n",x,y[0]);
MH_P95=2;
}else if ((MH_P95==2) && (y[0] >=0.9500000001)) {
oxprintf("x=%le, y[0]=%lf\n",x,y[0]);
MH_P95=0;
}
}
x1 = x+dh;
while ((x < x1) && (x < xn)) {
int status = gsl_odeiv_evolve_apply(e, c, s, &sys, &x, x1, &h, y);
if (status != GSL_SUCCESS) {
oxprintfe("gsl_odeiv_evolve_apply failed.\n");
break;
}
}
}
gsl_odeiv_evolve_free(e);
gsl_odeiv_control_free(c);
gsl_odeiv_step_free(s);
MH_Dp=mh_dp_orig;
}
if (MH_Verbose) oxprintf("x=%lf, y[0]=%lg\n",x,y[0]);
result.x = x;
result.rank = MH_RANK;
result.y = (double *)mh_malloc(sizeof(double)*MH_RANK); /* todo, how to free it */
for (i=0; i<MH_RANK; i++) (result.y)[i] = y[i];
result.size=2;
result.sfpp = (struct SFILE **)mh_malloc(sizeof(struct SFILE *)*(result.size)); /* todo, free */
(result.sfpp)[0] = Df;
(result.sfpp)[1] = Gf;
return result;
}
/*
rk4 MH_strategy==0;
a-rk4 MH_strategy==1; adaptive
a-rk4-m MH_strategy==2; adaptive and multiply
*/
void mh_set_strategy(int s,double err[2]) {
MH_strategy = s;
if (err[0] >= 0.0) MH_abserr = err[0];
if (err[1] >= 0.0) MH_relerr = err[1];
}