98 lines
1.9 KiB
C++
98 lines
1.9 KiB
C++
#include <cmath>
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#include <limits>
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#include "nr.h"
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using namespace std;
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namespace {
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inline void mov3(DP &a, DP &b, DP &c, const DP d, const DP e,
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const DP f)
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{
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a=d; b=e; c=f;
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}
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}
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DP NR::dbrent(const DP ax, const DP bx, const DP cx, DP f(const DP),
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DP df(const DP), const DP tol, DP &xmin)
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{
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const int ITMAX=100;
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const DP ZEPS=numeric_limits<DP>::epsilon()*1.0e-3;
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bool ok1,ok2;
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int iter;
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DP a,b,d=0.0,d1,d2,du,dv,dw,dx,e=0.0;
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DP fu,fv,fw,fx,olde,tol1,tol2,u,u1,u2,v,w,x,xm;
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a=(ax < cx ? ax : cx);
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b=(ax > cx ? ax : cx);
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x=w=v=bx;
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fw=fv=fx=f(x);
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dw=dv=dx=df(x);
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for (iter=0;iter<ITMAX;iter++) {
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xm=0.5*(a+b);
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tol1=tol*fabs(x)+ZEPS;
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tol2=2.0*tol1;
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if (fabs(x-xm) <= (tol2-0.5*(b-a))) {
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xmin=x;
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return fx;
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}
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if (fabs(e) > tol1) {
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d1=2.0*(b-a);
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d2=d1;
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if (dw != dx) d1=(w-x)*dx/(dx-dw);
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if (dv != dx) d2=(v-x)*dx/(dx-dv);
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u1=x+d1;
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u2=x+d2;
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ok1 = (a-u1)*(u1-b) > 0.0 && dx*d1 <= 0.0;
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ok2 = (a-u2)*(u2-b) > 0.0 && dx*d2 <= 0.0;
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olde=e;
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e=d;
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if (ok1 || ok2) {
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if (ok1 && ok2)
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d=(fabs(d1) < fabs(d2) ? d1 : d2);
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else if (ok1)
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d=d1;
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else
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d=d2;
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if (fabs(d) <= fabs(0.5*olde)) {
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u=x+d;
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if (u-a < tol2 || b-u < tol2)
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d=SIGN(tol1,xm-x);
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} else {
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d=0.5*(e=(dx >= 0.0 ? a-x : b-x));
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}
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} else {
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d=0.5*(e=(dx >= 0.0 ? a-x : b-x));
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}
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} else {
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d=0.5*(e=(dx >= 0.0 ? a-x : b-x));
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}
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if (fabs(d) >= tol1) {
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u=x+d;
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fu=f(u);
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} else {
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u=x+SIGN(tol1,d);
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fu=f(u);
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if (fu > fx) {
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xmin=x;
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return fx;
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}
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}
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du=df(u);
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if (fu <= fx) {
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if (u >= x) a=x; else b=x;
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mov3(v,fv,dv,w,fw,dw);
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mov3(w,fw,dw,x,fx,dx);
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mov3(x,fx,dx,u,fu,du);
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} else {
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if (u < x) a=u; else b=u;
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if (fu <= fw || w == x) {
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mov3(v,fv,dv,w,fw,dw);
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mov3(w,fw,dw,u,fu,du);
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} else if (fu < fv || v == x || v == w) {
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mov3(v,fv,dv,u,fu,du);
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}
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}
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}
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nrerror("Too many iterations in routine dbrent");
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return 0.0;
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}
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