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broydn.c
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broydn.c
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#include "decs.h"
#define NRANSI
#include "NRUTIL.H"
#define MAXITS 200
#define EPS 1.0e-7
#define TOLF 1.0e-4
#define TOLX EPS
#define STPMX 100.0
#define TOLMIN 1.0e-6
#define FREERETURN {free_vector(fvec,1,n);free_vector(xold,1,n); \
free_vector(w,1,n);free_vector(t,1,n);free_vector(s,1,n); \
free_matrix(r,1,n,1,n);free_matrix(qt,1,n,1,n);free_vector(p,1,n); \
free_vector(g,1,n);free_vector(fvcold,1,n);free_vector(d,1,n); \
free_vector(c,1,n);return;}
void broydn(int useanalyticjac
,FTYPE parms[]
,FTYPE x[], int n, int *check
,void (*vecfunc)(int n, FTYPE parms[], FTYPE v[], FTYPE f[])
,int (*usrfun)(int n, FTYPE *parms, FTYPE *Xguess, FTYPE *spc_diff, FTYPE **alpha)
)
{
// FTYPE nrfmin(FTYPE parms[], FTYPE x[]);
// void lnsrch(int n, FTYPE xold[], FTYPE fold, FTYPE g[], FTYPE p[], FTYPE x[],
// FTYPE *f, FTYPE stpmax, int *check, FTYPE (*func)(FTYPE []));
// void qrdcmp(FTYPE **a, int n, FTYPE *c, FTYPE *d, int *sing);
// void qrupdt(FTYPE **r, FTYPE **qt, int n, FTYPE u[], FTYPE v[]);
// void rsolv(FTYPE **a, int n, FTYPE d[], FTYPE b[]);
int i,its,j,k,restrt,sing,skip;
FTYPE den,f,fold,stpmax,sum,temp,test,*c,*d,*fvcold;
FTYPE *g,*p,**qt,**r,*s,*t,*w,*xold;
// DEBUG var
FTYPE **rtest;
int qq,pp;
FTYPE jacdiff,jacavg;
c=vector(1,n);
d=vector(1,n);
fvcold=vector(1,n);
g=vector(1,n);
p=vector(1,n);
qt=matrix(1,n,1,n);
r=matrix(1,n,1,n);
// DEBUG line below
rtest=matrix(1,n,1,n);
s=vector(1,n);
t=vector(1,n);
w=vector(1,n);
xold=vector(1,n);
fvec=vector(1,n);
nn=n;
nrfuncv=vecfunc;
f=nrfmin(parms,x);
test=0.0;
for (i=1;i<=n;i++)
if (fabs(fvec[i]) > test)test=fabs(fvec[i]);
if (test < 0.01*TOLF) {
*check=0;
FREERETURN
}
for (sum=0.0,i=1;i<=n;i++) sum += SQR(x[i]);
stpmax=STPMX*FMAX(sqrt(sum),(FTYPE)n);
restrt=1;
for (its=1;its<=MAXITS;its++) {
if (restrt) {
if(useanalyticjac){
// GODMARK : why doesn't this work?
// usrfun2(n,x,fvec,rtest);
//usrfun_joninterp2(n,x,fvec,r);
(*usrfun)(n,parms,x,fvec,r);
}
else{
fdjac(n,parms,x,fvec,r,vecfunc);
/*
jacdiff=0.0;
jacavg=0.0;
for(qq=1;qq<=n;qq++) for(pp=1;pp<=n;pp++){
jacavg+=fabs(rtest[qq][pp]);
jacdiff+=fabs(rtest[qq][pp]-r[qq][pp]);
}
jacavg/=(n*n);
stderrfprintf("x=%g %g fvec=%g %g jacdiff=%g %g\n",x[1],x[2],fvec[1],fvec[2],jacdiff,jacdiff/jacavg);
*/
}
qrdcmp(r,n,c,d,&sing);
if (sing) nrerror("singular Jacobian in broydn");
for (i=1;i<=n;i++) {
for (j=1;j<=n;j++) qt[i][j]=0.0;
qt[i][i]=1.0;
}
for (k=1;k<n;k++) {
if (c[k]) {
for (j=1;j<=n;j++) {
sum=0.0;
for (i=k;i<=n;i++)
sum += r[i][k]*qt[i][j];
sum /= c[k];
for (i=k;i<=n;i++)
qt[i][j] -= sum*r[i][k];
}
}
}
for (i=1;i<=n;i++) {
r[i][i]=d[i];
for (j=1;j<i;j++) r[i][j]=0.0;
}
} else {
for (i=1;i<=n;i++) s[i]=x[i]-xold[i];
for (i=1;i<=n;i++) {
for (sum=0.0,j=i;j<=n;j++) sum += r[i][j]*s[j];
t[i]=sum;
}
skip=1;
for (i=1;i<=n;i++) {
for (sum=0.0,j=1;j<=n;j++) sum += qt[j][i]*t[j];
w[i]=fvec[i]-fvcold[i]-sum;
if (fabs(w[i]) >= EPS*(fabs(fvec[i])+fabs(fvcold[i]))) skip=0;
else w[i]=0.0;
}
if (!skip) {
for (i=1;i<=n;i++) {
for (sum=0.0,j=1;j<=n;j++) sum += qt[i][j]*w[j];
t[i]=sum;
}
for (den=0.0,i=1;i<=n;i++) den += SQR(s[i]);
for (i=1;i<=n;i++) s[i] /= den;
qrupdt(r,qt,n,t,s);
for (i=1;i<=n;i++) {
if (r[i][i] == 0.0) nrerror("r singular in broydn");
d[i]=r[i][i];
}
}
}
for (i=1;i<=n;i++) {
for (sum=0.0,j=1;j<=n;j++) sum += qt[i][j]*fvec[j];
g[i]=sum;
}
for (i=n;i>=1;i--) {
for (sum=0.0,j=1;j<=i;j++) sum += r[j][i]*g[j];
g[i]=sum;
}
for (i=1;i<=n;i++) {
xold[i]=x[i];
fvcold[i]=fvec[i];
}
fold=f;
for (i=1;i<=n;i++) {
for (sum=0.0,j=1;j<=n;j++) sum += qt[i][j]*fvec[j];
p[i] = -sum;
}
rsolv(r,n,d,p);
lnsrch(n,parms,xold,fold,g,p,x,&f,stpmax,check,nrfmin);
test=0.0;
for (i=1;i<=n;i++)
if (fabs(fvec[i]) > test) test=fabs(fvec[i]);
if (test < TOLF) {
*check=0;
FREERETURN
}
if (*check) {
if (restrt) FREERETURN
else {
test=0.0;
den=FMAX(f,0.5*n);
for (i=1;i<=n;i++) {
temp=fabs(g[i])*FMAX(fabs(x[i]),1.0)/den;
if (temp > test) test=temp;
}
if (test < TOLMIN) FREERETURN
else restrt=1;
}
} else {
restrt=0;
test=0.0;
for (i=1;i<=n;i++) {
temp=(fabs(x[i]-xold[i]))/FMAX(fabs(x[i]),1.0);
if (temp > test) test=temp;
}
if (test < TOLX) FREERETURN
}
}
nrerror("MAXITS exceeded in broydn");
FREERETURN
}
#undef MAXITS
#undef EPS
#undef TOLF
#undef TOLMIN
#undef TOLX
#undef STPMX
#undef FREERETURN
#undef NRANSI
/* (C) Copr. 1986-92 Numerical Recipes Software *1.@Q.. */