119 lines
2.6 KiB
C++
119 lines
2.6 KiB
C++
#include <cmath>
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#include "nr.h"
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using namespace std;
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Vec_DP *x_p;
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Mat_DP *d_p;
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void NR::bsstep(Vec_IO_DP &y, Vec_IO_DP &dydx, DP &xx, const DP htry,
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const DP eps, Vec_I_DP &yscal, DP &hdid, DP &hnext,
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void derivs(const DP, Vec_I_DP &, Vec_O_DP &))
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{
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const int KMAXX=8, IMAXX=(KMAXX+1);
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const DP SAFE1=0.25, SAFE2=0.7, REDMAX=1.0e-5, REDMIN=0.7;
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const DP TINY=1.0e-30, SCALMX=0.1;
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static const int nseq_d[IMAXX]={2,4,6,8,10,12,14,16,18};
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static int first=1,kmax,kopt;
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static DP epsold = -1.0,xnew;
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static Vec_DP a(IMAXX);
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static Mat_DP alf(KMAXX,KMAXX);
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bool exitflag=false;
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int i,iq,k,kk,km,reduct;
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DP eps1,errmax,fact,h,red,scale,work,wrkmin,xest;
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Vec_INT nseq(nseq_d,IMAXX);
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Vec_DP err(KMAXX);
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int nv=y.size();
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Vec_DP yerr(nv),ysav(nv),yseq(nv);
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x_p=new Vec_DP(KMAXX);
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d_p=new Mat_DP(nv,KMAXX);
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if (eps != epsold) {
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hnext = xnew = -1.0e29;
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eps1=SAFE1*eps;
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a[0]=nseq[0]+1;
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for (k=0;k<KMAXX;k++) a[k+1]=a[k]+nseq[k+1];
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for (iq=1;iq<KMAXX;iq++) {
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for (k=0;k<iq;k++)
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alf[k][iq]=pow(eps1,(a[k+1]-a[iq+1])/
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((a[iq+1]-a[0]+1.0)*(2*k+3)));
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}
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epsold=eps;
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for (kopt=1;kopt<KMAXX-1;kopt++)
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if (a[kopt+1] > a[kopt]*alf[kopt-1][kopt]) break;
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kmax=kopt;
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}
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h=htry;
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for (i=0;i<nv;i++) ysav[i]=y[i];
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if (xx != xnew || h != hnext) {
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first=1;
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kopt=kmax;
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}
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reduct=0;
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for (;;) {
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for (k=0;k<=kmax;k++) {
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xnew=xx+h;
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if (xnew == xx) nrerror("step size underflow in bsstep");
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mmid(ysav,dydx,xx,h,nseq[k],yseq,derivs);
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xest=SQR(h/nseq[k]);
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pzextr(k,xest,yseq,y,yerr);
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if (k != 0) {
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errmax=TINY;
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for (i=0;i<nv;i++) errmax=MAX(errmax,fabs(yerr[i]/yscal[i]));
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errmax /= eps;
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km=k-1;
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err[km]=pow(errmax/SAFE1,1.0/(2*km+3));
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}
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if (k != 0 && (k >= kopt-1 || first)) {
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if (errmax < 1.0) {
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exitflag=true;
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break;
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}
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if (k == kmax || k == kopt+1) {
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red=SAFE2/err[km];
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break;
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}
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else if (k == kopt && alf[kopt-1][kopt] < err[km]) {
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red=1.0/err[km];
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break;
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}
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else if (kopt == kmax && alf[km][kmax-1] < err[km]) {
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red=alf[km][kmax-1]*SAFE2/err[km];
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break;
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}
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else if (alf[km][kopt] < err[km]) {
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red=alf[km][kopt-1]/err[km];
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break;
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}
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}
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}
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if (exitflag) break;
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red=MIN(red,REDMIN);
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red=MAX(red,REDMAX);
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h *= red;
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reduct=1;
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}
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xx=xnew;
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hdid=h;
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first=0;
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wrkmin=1.0e35;
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for (kk=0;kk<=km;kk++) {
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fact=MAX(err[kk],SCALMX);
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work=fact*a[kk+1];
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if (work < wrkmin) {
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scale=fact;
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wrkmin=work;
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kopt=kk+1;
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}
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}
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hnext=h/scale;
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if (kopt >= k && kopt != kmax && !reduct) {
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fact=MAX(scale/alf[kopt-1][kopt],SCALMX);
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if (a[kopt+1]*fact <= wrkmin) {
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hnext=h/fact;
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kopt++;
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}
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}
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delete d_p;
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delete x_p;
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}
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