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optimization.cpp
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//
// C++ Implementation: optimization
//
// Description:
//
//
// Author: BUI Quang Minh, Steffen Klaere, Arndt von Haeseler <minh.bui@univie.ac.at>, (C) 2008
//
// Copyright: See COPYING file that comes with this distribution
//
//
#include "optimization.h"
#include <cmath>
#include <stdio.h>
#include <stdlib.h>
#include <iostream>
#include "lbfgsb/lbfgsb_new.h"
#include "tools.h"
using namespace std;
const double ERROR_X = 1.0e-4;
double ran1(long *idum);
double *new_vector(long nl, long nh);
void free_vector(double *v, long nl, long nh);
double **new_matrix(long nrl, long nrh, long ncl, long nch);
void free_matrix(double **m, long nrl, long nrh, long ncl, long nch);
void fixBound(double x[], double lower[], double upper[], int n);
#define NR_END 1
#define FREE_ARG char*
#define GET_PSUM \
for (n=1;n<=ndim;n++) {\
for (sum=0.0,m=1;m<=mpts;m++) sum += p[m][n];\
psum[n]=sum;}
/*
#define IA 16807
#define IM 2147483647
#define AM (1.0/IM)
#define IQ 127773
#define IR 2836
#define NTAB 32
#define NDIV (1+(IM-1)/NTAB)
#define EPS 1.2e-7
#define RNMX (1.0-EPS)
double ran1(long *idum) {
int j;
long k;
static long iy=0;
static long iv[NTAB];
double temp;
if (*idum <= 0 || !iy) {
if (-(*idum) < 1) *idum=1;
else *idum = -(*idum);
for (j=NTAB+7;j>=0;j--) {
k=(*idum)/IQ;
*idum=IA*(*idum-k*IQ)-IR*k;
if (*idum < 0) *idum += IM;
if (j < NTAB) iv[j] = *idum;
}
iy=iv[0];
}
k=(*idum)/IQ;
*idum=IA*(*idum-k*IQ)-IR*k;
if (*idum < 0) *idum += IM;
j=iy/NDIV;
iy=iv[j];
iv[j] = *idum;
if ((temp=AM*iy) > RNMX) return RNMX;
else return temp;
}
#undef IA
#undef IM
#undef AM
#undef IQ
#undef IR
#undef NTAB
#undef NDIV
#undef EPS
#undef RNMX
*/
long idum = 123456;
double tt;
void nrerror(const char *error_text)
/* Numerical Recipes standard error handler */
{
cerr << "NUMERICAL ERROR: " << error_text << endl;
//exit(1);
abort();
}
double *new_vector(long nl, long nh)
/* allocate a double vector with subscript range v[nl..nh] */
{
double *v;
v=(double *)malloc((size_t) ((nh-nl+1+NR_END)*sizeof(double)));
if (!v) nrerror("allocation failure in vector()");
return v-nl+NR_END;
}
double **new_matrix(long nrl, long nrh, long ncl, long nch)
/* allocate a double matrix with subscript range m[nrl..nrh][ncl..nch] */
{
long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;
double **m;
/* allocate pointers to rows */
m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
if (!m) nrerror("allocation failure 1 in matrix()");
m += NR_END;
m -= nrl;
/* allocate rows and set pointers to them */
m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
m[nrl] += NR_END;
m[nrl] -= ncl;
for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;
/* return pointer to array of pointers to rows */
return m;
}
void free_vector(double *v, long nl, long nh)
/* free a double vector allocated with vector() */
{
free((FREE_ARG) (v+nl-NR_END));
}
void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
/* free a double matrix allocated by dmatrix() */
{
free((FREE_ARG) (m[nrl]+ncl-NR_END));
free((FREE_ARG) (m+nrl-NR_END));
}
void fixBound(double x[], double lower[], double upper[], int n) {
for (int i = 1; i <= n; i++) {
if (x[i] < lower[i])
x[i] = lower[i];
else if (x[i] > upper[i])
x[i] = upper[i];
}
}
/**********************************************
Optimization routines
**********************************************/
Optimization::Optimization()
{
}
Optimization::~Optimization()
{
}
/*****************************************************
One dimensional optimization with Brent method
*****************************************************/
#define ITMAX 100
#define CGOLD 0.3819660
#define GOLD 1.618034
#define GLIMIT 100.0
#define TINY 1.0e-20
#define ZEPS 1.0e-10
#define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);
#define SIGN(a,b) ((b) >= 0.0 ? fabs(a) : -fabs(a))
#define TRY_AITKEN 0
/* Brents method in one dimension */
double Optimization::brent_opt (double ax, double bx, double cx, double tol,
double *foptx, double *f2optx, double fax, double fbx, double fcx) {
int iter;
double a,b,d=0,etemp,fu,fv,fw,fx,p,q,r,tol1,tol2,u,v,w,x,xm;
double xw,wv,vx;
double e=0.0;
a=(ax < cx ? ax : cx);
b=(ax > cx ? ax : cx);
x=bx;
fx=fbx;
if (fax < fcx) {
w=ax;
fw=fax;
v=cx;
fv=fcx;
} else {
w=cx;
fw=fcx;
v=ax;
fv=fax;
}
#if TRY_AITKEN
double delta = 0; //change in U
double lastDelta = 0; //previous change in U
double lastU = 0; //previous value of U
#endif
for (iter=1;iter<=ITMAX;iter++) {
xm=0.5*(a+b);
tol2=2.0*(tol1=tol*fabs(x)+ZEPS);
if (fabs(x-xm) <= (tol2-0.5*(b-a))) {
*foptx = fx;
xw = x-w;
wv = w-v;
vx = v-x;
*f2optx = 2.0*(fv*xw + fx*wv + fw*vx)/
(v*v*xw + x*x*wv + w*w*vx);
return x;
}
if (fabs(e) > tol1) {
r=(x-w)*(fx-fv);
q=(x-v)*(fx-fw);
p=(x-v)*q-(x-w)*r;
q=2.0*(q-r);
if (q > 0.0)
p = -p;
q=fabs(q);
etemp=e;
e=d;
if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))
d=CGOLD*(e=(x >= xm ? a-x : b-x));
else {
d=p/q;
u=x+d;
if (u-a < tol2 || b-u < tol2)
d=SIGN(tol1,xm-x);
}
} else {
d=CGOLD*(e=(x >= xm ? a-x : b-x));
}
u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));
fu=computeFunction(u);
#if TRY_AITKEN
//In a Nutshell, Aitken's sequence accelerator constructs
//an auxiliary sequence, using
//"the main sequence, minus the square of the delta divided
// by the delta of the delta".
double aitken = 0;
bool haveAitken = false;
if (iter>=2) {
lastDelta = delta;
delta = u - lastU;
//For now. Later, use a calculated tolerance
if (iter>=3 && 0.00001 < fabs(delta-lastDelta) && 0.00001 < fabs(delta) ) {
haveAitken = true;
aitken = u - ( delta * delta ) / (delta - lastDelta);
}
}
cout.precision(6);
if (!haveAitken) {
cout << "f(" << u << ")=" << fu << endl;
} else {
cout << "f(" << u << ")=" << fu << ", A=" << aitken << ", f(A)=" << computeFunction(aitken) << endl;
}
lastU = u;
#endif
if (fu <= fx) {
if (u >= x)
a=x;
else
b=x;
SHFT(v,w,x,u)
SHFT(fv,fw,fx,fu)
} else {
if (u < x)
a=u;
else
b=u;
if (fu <= fw || w == x) {
v=w;
w=u;
fv=fw;
fw=fu;
} else
if (fu <= fv || v == x || v == w) {
v=u;
fv=fu;
}
}
}
*foptx = fx;
xw = x-w;
wv = w-v;
vx = v-x;
*f2optx = 2.0*(fv*xw + fx*wv + fw*vx)/(v*v*xw + x*x*wv + w*w*vx);
return x;
}
#undef ITMAX
#undef CGOLD
#undef ZEPS
#undef SHFT
#undef SIGN
#undef GOLD
#undef GLIMIT
#undef TINY
double Optimization::minimizeOneDimen(double xmin, double xguess, double xmax, double tolerance, double *fx, double *f2x) {
double eps, optx, ax, bx, cx, fa, fb, fc;
//int converged; /* not converged error flag */
/* first attempt to bracketize minimum */
if (xguess < xmin) xguess = xmin;
if (xguess > xmax) xguess = xmax;
eps = xguess*tolerance*50.0;
ax = xguess - eps;
if (ax < xmin) ax = xmin;
bx = xguess;
cx = xguess + eps;
if (cx > xmax) cx = xmax;
/* check if this works */
// compute fb first to save some computation, if any
fb = computeFunction(bx);
fa = (ax<bx) ? computeFunction(ax) : fb;
fc = (bx<cx) ? computeFunction(cx) : fb;
/* if it works use these borders else be conservative */
if ((fa < fb) || (fc < fb)) {
if (ax != xmin) fa = computeFunction(xmin);
if (cx != xmax) fc = computeFunction(xmax);
ax = xmin;
cx = xmax;
}
/*
const int MAX_ROUND = 10;
for (i = 0; ((fa < fb-tolerance) || (fc < fb-tolerance)) && (i<MAX_ROUND); i++) {
// brent method require that fb is smaller than both fa and fc
// find some random values until fb achieve this
bx = (((double)rand()) / RAND_MAX)*(cx-ax) + ax;
fb = computeFunction(bx);
}*/
/*
if ((fa < fb) || (fc < fb)) {
if (fa < fc) { bx = ax; fb = fa; } else { bx = cx; fb = fc; }
//cout << "WARNING: Initial value for Brent method is set at bound " << bx << endl;
}*/
// optx = brent_opt(xmin, xguess, xmax, tolerance, fx, f2x, fa, fb, fc);
//} else
optx = brent_opt(ax, bx, cx, tolerance, fx, f2x, fa, fb, fc);
if (*fx > fb) // if worse, return initial value
{
*fx = computeFunction(bx);
return bx;
}
return optx; /* return optimal x */
}
double Optimization::minimizeOneDimenSafeMode(double xmin, double xguess, double xmax, double tolerance, double *f)
{
double ferror;
double optx = minimizeOneDimen(xmin, xguess, xmax, tolerance, f, &ferror);
double fnew;
// check value at the boundary
if ((optx < xmax) && (fnew = computeFunction(xmax)) <= *f+tolerance) {
//if (verbose_mode >= VB_MAX)
//cout << "Note from Newton safe mode: " << optx << " (" << f << ") -> " << xmax << " ("<< fnew << ")" << endl;
optx = xmax;
*f = fnew;
}
if ((optx > xmin) && (fnew = computeFunction(xmin)) <= *f+tolerance) {
//if (verbose_mode >= VB_MAX)
//cout << "Note from Newton safe mode: " << optx << " -> " << xmin << endl;
optx = xmin;
*f = fnew;
}
return optx;
}
/*****************************************************
One dimensional optimization with Newton Raphson
only applicable if 1st and 2nd derivatives are easy to compute
*****************************************************/
double Optimization::minimizeNewtonSafeMode(double xmin, double xguess, double xmax, double tolerance, double &f)
{
double optx = minimizeNewton(xmin, xguess, xmax, tolerance, f);
double fnew;
// check value at the boundary
if ((optx < xmax) && (fnew = computeFunction(xmax)) <= f+tolerance) {
//if (verbose_mode >= VB_MAX)
//cout << "Note from Newton safe mode: " << optx << " (" << f << ") -> " << xmax << " ("<< fnew << ")" << endl;
optx = xmax;
f = fnew;
}
if ((optx > xmin) && (fnew = computeFunction(xmin)) <= f+tolerance) {
//if (verbose_mode >= VB_MAX)
//cout << "Note from Newton safe mode: " << optx << " -> " << xmin << endl;
optx = xmin;
f = fnew;
}
return optx;
}
double Optimization::minimizeNewton(double x1, double xguess, double x2, double xacc, double &d2l, int maxNRStep)
{
int j;
double df,dx,dxold,f;
double temp,xh,xl,rts, rts_old, xinit;
rts = xguess;
if (rts < x1) rts = x1;
if (rts > x2) rts = x2;
xinit = xguess;
// finit = fold = fm = computeFuncDerv(rts,f,df);
computeFuncDerv(rts,f,df);
d2l = df;
if (!isfinite(f) || !isfinite(df)) {
nrerror("Wrong computeFuncDerv");
}
if (df >= 0.0 && fabs(f) < xacc) return rts;
if (f < 0.0) {
xl = rts;
xh = x2;
} else {
xh = rts;
xl = x1;
}
dx=dxold=fabs(xh-xl);
for (j=1;j<=maxNRStep;j++) {
rts_old = rts;
if (
(df <= 0.0) // function is concave
// || (fm > fold + xacc) // increasing
|| (((rts-xh)*df-f)*((rts-xl)*df-f) >= 0.0) // out of bound
//|| (fabs(2.0*f) > fabs(dxold*df)) // converge too slow
) {
dxold=dx;
dx=0.5*(xh-xl);
rts=xl+dx;
d2l = df;
if (xl == rts) return rts;
} else {
dxold=dx;
dx=f/df;
temp=rts;
rts -= dx;
d2l = df;
if (temp == rts) return rts;
}
if (fabs(dx) < xacc || (j == maxNRStep)) {
// if (fm > finit) {
// // happen in rare cases that it is worse than starting point: revert init value
// fm = computeFunction(xinit);
// return xinit;
// }
return rts_old;
// return rts;
}
// fold = fm;
// fm = computeFuncDerv(rts,f,df);
computeFuncDerv(rts,f,df);
if (!isfinite(f) || !isfinite(df)) nrerror("Wrong computeFuncDerv");
if (df > 0.0 && fabs(f) < xacc) {
d2l = df;
// if (fm > finit) {
// // happen in rare cases that it is worse than starting point: revert init value
// fm = computeFunction(xinit);
// return xinit;
// }
return rts;
}
if (f < 0.0)
xl=rts;
else if (f > 0.0)
xh=rts;
}
nrerror("Maximum number of iterations exceeded in minimizeNewton");
d2l = 0.0;
return 0.0;
}
double Optimization::minimizeNewton(double x1, double xguess, double x2, double xacc, int maxNRStep)
{
double var;
double optx = minimizeNewton(x1, xguess, x2, xacc, var, maxNRStep);
return optx;
}
/*****************************************************
Multi dimensional optimization with Newton Raphson
only applicable if 1st and 2nd derivatives are easy to compute
*****************************************************/
int matinv (double x[], int n, int m, double space[]);
double Optimization::minimizeNewtonMulti(double *x1, double *xguess, double *x2, double xacc, int N, int maxNRStep)
{
int i, step;
int N_2 = N*N;
double df[N_2], dx[N], dxold[N], f[N+1], space[N];
double temp, xh[N], xl[N], rts[N], rts_old[N];
for (i = 0; i < N; i++) {
rts[i] = xguess[i];
if (rts[i] < x1[i]) rts[i] = x1[i];
if (rts[i] > x2[i]) rts[i] = x2[i];
}
computeFuncDervMulti(rts, f, df);
double score = f[N];
// double score = targetFunk(rts-1);
// cout << "Newton step 0: " << score << endl;
bool stop = true;
for (i = 0; i < N; i++) {
if (!(fabs(f[i]) < xacc))
stop = false;
xl[i] = x1[i];
xh[i] = x2[i];
// if (f[i] < 0.0) {
// xl[i] = rts[i];
// xh[i] = x2[i];
// } else {
// xh[i] = rts[i];
// xl[i] = x1[i];
// }
dx[i] = dxold[i] = fabs(xh[i]-xl[i]);
}
if (stop) {
memcpy(xguess, rts, sizeof(double)*N);
return score;
}
for (step = 1; step <= maxNRStep; step++) {
memcpy(rts_old, rts, sizeof(double)*N);
// first compute inverse of hessian matrix
matinv(df, N, N, space);
// now take the product
for (i = 0; i < N; i++) {
space[i] = 0.0;
for (int k = 0; k < N; k++) {
space[i] += df[i*N+k] * f[k];
}
}
// identify alpha to be not out of bound
double alpha;
for (alpha = 1.0; alpha > xacc; alpha *= 0.5) {
bool ok_bound = true;
for (i = 0; i < N; i++)
if (rts[i]-alpha*space[i] < xl[i] || rts[i]-alpha*space[i] > xh[i]) {
ok_bound = false;
break;
}
if (ok_bound) break;
}
do {
stop = true;
for (i = 0; i < N; i++) {
dxold[i] = dx[i];
dx[i] = alpha*space[i];
temp=rts[i];
rts[i] -= dx[i];
if (fabs(dx[i]) >= xacc && (step != maxNRStep)) {
stop = false;
} else {
rts[i] = rts_old[i];
}
}
double new_score = targetFunk(rts-1);
if (new_score <= score) break;
// score increased, reduce step size by half
memcpy(rts, rts_old, sizeof(double)*N);
alpha *= 0.5;
} while (!stop);
if (stop) {
break;
}
computeFuncDervMulti(rts, f, df);
score = f[N];
// double score = targetFunk(rts-1);
// cout << "Newton step " << step << ": " << score << endl;
// for (i = 0; i < N; i++) cout << " " << rts[i];
// cout << endl;
stop = true;
for (i = 0; i < N; i++) {
if (!(fabs(f[i]) < xacc)) {
stop = false;
}
// if (f[i] < 0.0)
// xl[i] = rts[i];
// else
// xh[i] = rts[i];
}
if (stop)
break;
}
// copy returned x-value
memcpy(xguess, rts, sizeof(double)*N);
if (stop)
return score;
cout << "Maximum number of iterations exceeded in minimizeNewtonMulti" << endl;
return score;
}
/*****************************************************
Multi dimensional optimization with BFGS method
*****************************************************/
#define ALF 1.0e-4
#define TOLX 1.0e-7
//static double maxarg1,maxarg2;
//#define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1) > (maxarg2) ?\
// (maxarg1) : (maxarg2))
void Optimization::lnsrch(int n, double xold[], double fold, double g[], double p[], double x[],
double *f, double stpmax, int *check, double lower[], double upper[]) {
int i;
double a,alam,alam2=0,alamin,b,disc,f2=0,fold2=0,rhs1,rhs2,slope,sum,temp,
test,tmplam;
*check=0;
for (sum=0.0,i=1;i<=n;i++) sum += p[i]*p[i];
sum=sqrt(sum);
if (sum > stpmax)
for (i=1;i<=n;i++) p[i] *= stpmax/sum;
for (slope=0.0,i=1;i<=n;i++)
slope += g[i]*p[i];
test=0.0;
for (i=1;i<=n;i++) {
temp=fabs(p[i])/max(fabs(xold[i]),1.0);
if (temp > test) test=temp;
}
alamin=TOLX/test;
alam=1.0;
bool first_time = true;
for (;;) {
// for (; alam >= alamin;) {
// bool out_of_bound = false;
// for (i=1;i<=n;i++) {
// x[i]=xold[i]+alam*p[i];
// if (x[i] < lower[i] || x[i] > upper[i]) {
// out_of_bound = true;
// break;
// }
// }
// if (out_of_bound)
// alam *= 0.5;
// else
// break;
// }
for (i=1;i<=n;i++) x[i]=xold[i]+alam*p[i];
fixBound(x, lower, upper, n);
//checkRange(x);
*f=targetFunk(x);
if (alam < alamin) {
for (i=1;i<=n;i++) x[i]=xold[i];
*check=1;
return;
} else if (*f <= fold+ALF*alam*slope) return;
else {
if (first_time)
tmplam = -slope/(2.0*(*f-fold-slope));
else {
rhs1 = *f-fold-alam*slope;
rhs2=f2-fold2-alam2*slope;
a=(rhs1/(alam*alam)-rhs2/(alam2*alam2))/(alam-alam2);
b=(-alam2*rhs1/(alam*alam)+alam*rhs2/(alam2*alam2))/(alam-alam2);
if (a == 0.0) tmplam = -slope/(2.0*b);
else {
disc=b*b-3.0*a*slope;
if (disc<0.0) //nrerror("Roundoff problem in lnsrch.");
tmplam = 0.5 * alam;
else if (b <= 0.0) tmplam=(-b+sqrt(disc))/(3.0*a);
else tmplam = -slope/(b+sqrt(disc));
}
if (tmplam>0.5*alam)
tmplam=0.5*alam;
}
}
alam2=alam;
f2 = *f;
fold2=fold;
alam=max(tmplam,0.1*alam);
first_time = false;
}
}
#undef ALF
#undef TOLX
const int MAX_ITER = 3;
extern double random_double(int *rstream);
bool Optimization::restartParameters(double guess[], int ndim, double lower[], double upper[], bool bound_check[], int iteration) {
int i;
bool restart = false;
if (iteration <= MAX_ITER) {
for (i = 1; i <= ndim; i++) {
if (bound_check[i]) {
if (fabs(guess[i]-lower[i]) < 1e-4 || fabs(guess[i]-upper[i]) < 1e-4) {
restart = true;
break;
} // if (fabs...
} // if bound_check
} // for
} // if iteration
if (restart) {
// TODO: Dominik observed that this warning is printed even during model
// testing. A quieter solution might be preferred.
cout << "Restart estimation at the boundary... " << std::endl;
for (i = 1; i <= ndim; i++) {
guess[i] = random_double() * (upper[i] - lower[i])/3 + lower[i];
}
}
return (restart);
}
double Optimization::minimizeMultiDimen(double guess[], int ndim, double lower[], double upper[], bool bound_check[], double gtol, double *hessian) {
int i, iter;
double fret, minf = 1e+12;
double *minx = new double [ndim+1];
int count = 0;
bool restart;
do {
dfpmin(guess, ndim, lower, upper, gtol, &iter, &fret, hessian);
if (fret < minf) {
minf = fret;
for (i = 1; i <= ndim; i++) {
minx[i] = guess[i];
}
}
count++;
// restart the search if at the boundary
// it's likely to end at a local optimum at the boundary
restart = restartParameters(guess,ndim,lower,upper,bound_check,count);
} while (restart);
if (count > 1) {
for (i = 1; i <= ndim; i++) {
guess[i] = minx[i];
}
fret = minf;
}
delete [] minx;
return fret;
}
#define ITMAX 200
#define SQR(a) ((a)*(a))
#define EPS 3.0e-8
#define TOLX (4*EPS)
#define STPMX 100.0
#define FREEALL free_vector(xi,1,n);free_vector(pnew,1,n); \
free_matrix(hessin,1,n,1,n);free_vector(hdg,1,n);free_vector(g,1,n); \
free_vector(dg,1,n);
void Optimization::dfpmin(double p[], int n, double lower[], double upper[]
, double gtol, int *iter, double *fret, double *hessian) {
int check,i,its,j;
double den,fac,fad,fae,fp,stpmax,sum=0.0,sumdg,sumxi,temp,test;
double *dg,*g,*hdg,**hessin,*pnew,*xi;
dg=new_vector(1,n);
g=new_vector(1,n);
hdg=new_vector(1,n);
hessin=new_matrix(1,n,1,n);
pnew=new_vector(1,n);
xi=new_vector(1,n);
fp = derivativeFunk(p,g);
for (i=1;i<=n;++i)
{
xi[i] = -g[i];
sum += p[i]*p[i];
}
if (hessian) {
int pos = 0;
for (i=1; i<=n; i++) {
for (j=1; j<=n; j++, ++pos) {
hessin[i][j] = hessian[pos];
}
}
} else {
for (i=1;i<=n;i++) {
for (j=1;j<=n;j++) {
hessin[i][j]=0.0;
}
hessin[i][i]=1.0;
}
}
//checkBound(p, xi, lower, upper, n);
//checkDirection(p, xi);
stpmax=STPMX*max(sqrt(sum),(double)n);
for (its=1;its<=ITMAX;its++) {
*iter=its;
lnsrch(n,p,fp,g,xi,pnew,fret,stpmax,&check, lower, upper);
fp = *fret;
for (i=1;i<=n;i++) {
xi[i]=pnew[i]-p[i];
p[i]=pnew[i];
}
test=0.0;
for (i=1;i<=n;i++) {
temp=fabs(xi[i])/max(fabs(p[i]),1.0);
if (temp > test) test=temp;
}
if (test < TOLX) {
FREEALL
return;
}
for (i=1;i<=n;i++) dg[i]=g[i];
derivativeFunk(p,g);
test=0.0;
den=max(fabs(*fret),1.0); // fix bug found by Tung, as also suggested by NR author
for (i=1;i<=n;i++) {
temp=fabs(g[i])*max(fabs(p[i]),1.0)/den;
if (temp > test) test=temp;
}
if (test < gtol) {
FREEALL
return;
}
for (i=1;i<=n;i++) {
dg[i]=g[i]-dg[i];
}
for (i=1;i<=n;i++) {
hdg[i]=0.0;
for (j=1;j<=n;j++) {
hdg[i] += hessin[i][j]*dg[j];
}
}
fac=fae=sumdg=sumxi=0.0;
for (i=1;i<=n;i++) {
fac += dg[i]*xi[i];
fae += dg[i]*hdg[i];
sumdg += SQR(dg[i]);
sumxi += SQR(xi[i]);
}
if (fac*fac > EPS*sumdg*sumxi)
{
fac=1.0/fac;
fad=1.0/fae;
for (i=1;i<=n;i++) {
dg[i]=fac*xi[i]-fad*hdg[i];
}
for (i=1;i<=n;i++) {
for (j=1;j<=n;j++) {
hessin[i][j] += fac*xi[i]*xi[j]
-fad*hdg[i]*hdg[j]+fae*dg[i]*dg[j];
}
}
}
for (i=1;i<=n;i++) {
xi[i]=0.0;
for (j=1;j<=n;j++) xi[i] -= hessin[i][j]*g[j];
}
//checkBound(p, xi, lower, upper, n);
//checkDirection(p, xi);
//if (*iter > 200) cout << "iteration=" << *iter << endl;
}
// BQM: disable this message!
//nrerror("too many iterations in dfpmin");
FREEALL
}
#undef ITMAX
#undef SQR
#undef EPS
#undef TOLX
#undef STPMX
#undef FREEALL
#undef FMAX
/**
the approximated derivative function
@param x the input vector x
@param dfx the derivative at x
@return the function value at x
*/
double Optimization::derivativeFunk(double x[], double dfx[]) {
/*
if (!checkRange(x))
return INFINITIVE;
*/
int ndim = getNDim();
double *h = new double[ndim+1];
double temp;
int dim;
double fx = targetFunk(x);
for (dim = 1; dim <= ndim; dim++ ){
temp = x[dim];
h[dim] = ERROR_X * fabs(temp);
if (h[dim] == 0.0) h[dim] = ERROR_X;
x[dim] = temp + h[dim];
h[dim] = x[dim] - temp;
dfx[dim] = (targetFunk(x));
x[dim] = temp;
}
for (dim = 1; dim <= ndim; dim++ )
dfx[dim] = (dfx[dim] - fx) / h[dim];
delete [] h;
return fx;
}
/*#define NRANSI
#define ITMAX 100
#define CGOLD 0.3819660
#define ZEPS 1.0e-10
#define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);
#define SIGN(a,b) ((b) >= 0.0 ? fabs(a) : -fabs(a))
double Optimization::brent(double ax, double bx, double cx, double tol,
double *xmin)
{
int iter;
double a,b,d=0.0,etemp,fu,fv,fw,fx,p,q,r,tol1,tol2,u,v,w,x,xm;
double e=0.0;
a=(ax < cx ? ax : cx);
b=(ax > cx ? ax : cx);
x=w=v=bx;
fw=fv=fx=computeFunction(x);
for (iter=1;iter<=ITMAX;iter++) {
xm=0.5*(a+b);
tol2=2.0*(tol1=tol*fabs(x)+ZEPS);
if (fabs(x-xm) <= (tol2-0.5*(b-a))) {
*xmin=x;
return fx;
}
if (fabs(e) > tol1) {
r=(x-w)*(fx-fv);
q=(x-v)*(fx-fw);
p=(x-v)*q-(x-w)*r;
q=2.0*(q-r);
if (q > 0.0) p = -p;
q=fabs(q);
etemp=e;
e=d;
if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))
d=CGOLD*(e=(x >= xm ? a-x : b-x));
else {
d=p/q;
u=x+d;
if (u-a < tol2 || b-u < tol2)
d=SIGN(tol1,xm-x);
}
} else {
d=CGOLD*(e=(x >= xm ? a-x : b-x));
}
u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));
fu=computeFunction(u);
if (fu <= fx) {
if (u >= x) a=x; else b=x;
SHFT(v,w,x,u)
SHFT(fv,fw,fx,fu)
} else {
if (u < x) a=u; else b=u;
if (fu <= fw || w == x) {
v=w;
w=u;
fv=fw;
fw=fu;
} else if (fu <= fv || v == x || v == w) {