int newton_min_func(double (*funcpt)(double *,int),double *xi,int N,double *dx,double fsval,double *xf) {
int rcode,iter;
int i,siter,retval;
double gtol,stol;
double fx,num,den,stop0,maxstep,fxf;
double *jac,*hess,*scheck,*xc,*L,*step;
jac = (double*) malloc(sizeof(double) *N);
scheck = (double*) malloc(sizeof(double) *N);
xc = (double*) malloc(sizeof(double) *N);
step = (double*) malloc(sizeof(double) *N);
hess = (double*) malloc(sizeof(double) *N * N);
L = (double*) malloc(sizeof(double) *N * N);
rcode = 0;
iter = 0;
siter = (int) SETITER;
gtol = pow((double) FDVAL,1.0/3.0);
stol = gtol * gtol;
fx = funcpt(xi,N);
jacobian_fd(funcpt,xi,N,jac);
//set values
maxstep = 1.0;
for(i = 0; i < N;++i) {
dx[i] = 1.0 / dx[i];
}
//Check Stop0
if (fabs(fx) > fabs(fsval)) {
den = fabs(fx);
} else {
den = fabs(fsval);
}
for(i = 0; i < N;++i) {
if (fabs(xi[i]) > 1.0 / fabs(dx[i])) {
num = fabs(xi[i]);
} else {
num = 1.0 / fabs(dx[i]);
}
scheck[i] = fabs(jac[i]) * num / den;
}
stop0 = array_max_abs(scheck,N);
if (stop0 <= gtol * 1e-03) {
rcode = 1;
for(i = 0; i < N;++i) {
xf[i] = xi[i];
}
return rcode;
}
hessian_fd(funcpt,xi,N,hess);
for(i = 0; i < N;++i) {
xc[i] = xi[i];
}
while (rcode == 0 && iter < siter) {
modelhess(hess,N,dx,L);
scale(jac,1,N,-1.0);
linsolve_lower(L,N,jac,step);
scale(jac,1,N,-1.0);
retval = lnsrch(funcpt,xc,jac,step,N,maxstep,dx,stol,xf);
fxf = funcpt(xf,N);
jacobian_fd(funcpt,xf,N,jac);
rcode = stopcheck(fxf,N,xc,xf,jac,dx,fsval,gtol,stol,retval);
hessian_fd(funcpt,xf,N,hess);
for(i = 0; i < N;++i) {
xc[i] = xf[i];
}
}
free(jac);
free(hess);
free(scheck);
free(xc);
free(L);
free(step);
return rcode;
}
void ML_multi_QuasiNewton::dfpmin(v_ratep_type& p,
const double gtol,
int& iter,
double& fret,
ptr_eval_func func,
ptr_eval_gradient_func dfunc
// double func(const v_ratep_type& p),
// void dfunc(const v_ratep_type& in,
// v_ratep_type& out)
)
{
// from Press et al 2002
const int ITMAX = 200;
const double EPS=std::numeric_limits<double>::epsilon();
const double TOLX = 4.0*EPS, STPMX = 100.0;
bool check;
int i, its, j;
double den, fac, fad, fae, fp, stpmax, sum=0.0, sumdg, sumxi, temp, test;
int n = p.size();
v_ratep_type dg(n), g(n), hdg(n), pnew(n), xi(n);
std::vector<v_ratep_type> hessin;
hessin.resize(n);
for (int i = 0; i < n; ++i) hessin[i].resize(n);
fp = (this->*func)(p); // fp = func(p);
(this->*dfunc)(p, g); // dfunc(p, g);
for (i = 0; i < n; ++i) {
for (j = 0; j < n; ++j) hessin[i][j] = 0.0;
hessin[i][i] = 1.0;
xi[i] = -g[i];
sum += p[i]*p[i];
}
stpmax = STPMX * MAX(std::sqrt(sum), double(n));
for (its = 0; its < ITMAX; ++its) {
iter = its;
lnsrch(p, fp, g, xi, pnew, fret, stpmax, check, func);
fp = fret;
for (i = 0; i < n; ++i) {
xi[i] = pnew[i] - p[i];
p[i] = pnew[i];
}
test = 0.0;
for (i = 0; i < n; ++i) {
temp = std::abs(xi[i]) / MAX(std::abs(p[i]), 1.0);
if (temp > test) test = temp;
}
if (test < TOLX)
return;
for (i = 0; i < n; ++i) dg[i] = g[i];
(this->*dfunc)(p, g); // dfunc(p, g);
test = 0.0;
den = MAX(fret, 1.0);
for (i = 0; i < n; ++i) {
temp = std::abs(g[i])*MAX(std::abs(p[i]), 1.0)/den;
if (temp > test) test = temp;
}
if (test < gtol)
return;
for (i = 0; i < n; ++i) dg[i] = g[i] - dg[i];
for (i = 0; i < n; ++i) {
hdg[i] = 0.0;
for (j = 0; j < n; ++j) hdg[i] += hessin[i][j]*dg[j];
}
fac = fae = sumdg = sumxi = 0.0;
for (i = 0; i < n; ++i) {
fac += dg[i]*xi[i];
fae += dg[i]*hdg[i];
sumdg += SQR(dg[i]);
sumxi += SQR(xi[i]);
}
if (fac > std::sqrt(EPS*sumdg*sumxi)) {
fac = 1.0 / fac;
fad = 1.0 / fae;
for (i = 0; i < n; ++i) dg[i] = fac*xi[i] - fad*hdg[i];
for (i = 0; i < n; ++i) {
for (j = i; j < n; ++j) {
hessin[i][j] += fac*xi[i]*xi[j] -
fad*hdg[i]*hdg[j] +
fae*dg[i]*dg[j];
hessin[j][i] = hessin[i][j];
}
}
}
for (i = 0; i < n; ++i) {
xi[i] = 0.0;
for (j = 0; j < n; ++j) xi[i] -= hessin[i][j]*g[j];
}
}
std::cerr << "dfpmin(): too many iterations" << std::endl;
assert(false);
}
