94 lines
1.9 KiB
C
94 lines
1.9 KiB
C
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#include <math.h>
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#define NRANSI
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#include "nrutil.h"
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#define ITMAX 100
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#define ZEPS 1.0e-10
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#define MOV3(a,b,c, d,e,f) (a)=(d);(b)=(e);(c)=(f);
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float dbrent(float ax, float bx, float cx, float (*f)(float),
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float (*df)(float), float tol, float *xmin)
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{
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int iter,ok1,ok2;
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float a,b,d,d1,d2,du,dv,dw,dx,e=0.0;
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float 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=1;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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#undef ITMAX
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#undef ZEPS
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#undef MOV3
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#undef NRANSI
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