void powell(float* p, float **xi, int n, float ftol, int *iter, float *fret,
float (*func)(float [], void*),void* args)
{
void linmin(float p[], float xi[], int n, float *fret,
float (*func)(float [], void*),void* args);
int i,ibig,j;
float del,fp,fptt,t,*pt,*ptt,*xit;
// return;
pt=vector(1,n);
ptt=vector(1,n);
xit=vector(1,n);
*fret=(*func)(p,args);
for (j=1; j<=n; j++) pt[j]=p[j];
for (*iter=1;; ++(*iter)) {
fp=(*fret);
ibig=0;
del=0.0;
for (i=1; i<=n; i++) {
for (j=1; j<=n; j++) xit[j]=xi[j][i];
fptt=(*fret);
linmin(p,xit,n,fret,func,args);
if (fptt-(*fret) > del) {
del=fptt-(*fret);
ibig=i;
}
}
if (2.0*(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))+TINY) {
free_vector(xit,1,n);
free_vector(ptt,1,n);
free_vector(pt,1,n);
return;
}
if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");
for (j=1; j<=n; j++) {
ptt[j]=2.0*p[j]-pt[j];
xit[j]=p[j]-pt[j];
pt[j]=p[j];
}
fptt=(*func)(ptt,args);
if (fptt < fp) {
t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);
if (t < 0.0) {
linmin(p,xit,n,fret,func,args);
for (j=1; j<=n; j++) {
xi[j][ibig]=xi[j][n];
xi[j][n]=xit[j];
}
}
}
}
}
bool PreconditionedConjugateGradientType::improve_energy(bool verbose) {
iter++;
//printf("I am running ConjugateGradient::improve_energy\n");
const double E0 = energy();
if (E0 != E0) {
// There is no point continuing, since we're starting with a NaN!
// So we may as well quit here.
if (verbose) {
printf("The initial energy is a NaN, so I'm quitting early.\n");
f.print_summary("has nan:", E0);
fflush(stdout);
}
return false;
}
double beta;
{
// Note: my notation vaguely follows that of
// [wikipedia](http://en.wikipedia.org/wiki/Nonlinear_conjugate_gradient_method).
// I use the Polak-Ribiere method, with automatic direction reset.
// Note that we could save some memory by using Fletcher-Reeves, and
// it seems worth implementing that as an option for
// memory-constrained problems (then we wouldn't need to store oldgrad).
pgrad(); // compute pgrad first, since that computes both.
beta = -pgrad().dot(-grad() - oldgrad)/oldgradsqr;
oldgrad = -grad();
if (beta < 0 || beta != beta || oldgradsqr == 0) beta = 0;
if (verbose) printf("beta = %g\n", beta);
oldgradsqr = -pgrad().dot(oldgrad);
direction = -pgrad() + beta*direction;
// Let's immediately free the cached gradient stored internally!
invalidate_cache();
} // free g and pg!
const double gdotd = oldgrad.dot(direction);
Minimizer lm = linmin(f, gd, kT, x, direction, -gdotd, &step);
for (int i=0; i<100 && lm.improve_energy(verbose); i++) {
if (verbose) lm.print_info("\t");
}
if (verbose) {
//lm->print_info();
print_info();
printf("grad*dir/oldgrad*dir = %g\n", grad().dot(direction)/gdotd);
}
return (energy() < E0 || beta != 0);
}
void frprmn(vectorN &p, int n, m_real ftol, int &iter, m_real &fret,
m_real (*func) (vectorN const&),
m_real (*dfunc) (vectorN const&,vectorN&))
{
m_real gg, gam, fp, dgg;
static vectorN g; g.setSize(n);
static vectorN h; h.setSize(n);
static vectorN xi; xi.setSize(n);
fp = (*dfunc) (p, xi);
for (int j=0; j<n; j++)
{
g[j] = -xi[j];
xi[j] = h[j] = g[j];
}
for (iter=0; iter<ITMAX; iter++)
{
linmin(p, xi, n, fret, func);
if (2.0 * fabs(fret - fp) <= ftol * (fabs(fret) + fabs(fp) + EPS_jhm)) return;
fp = (*dfunc) (p, xi);
dgg = gg = 0.0;
for (int j=0; j<n; j++)
{
gg += g[j] * g[j];
dgg += (xi[j] + g[j]) * xi[j];
}
if (gg == 0.0) return;
gam = dgg / gg;
for (int j=0; j<n; j++)
{
g[j] = -xi[j];
xi[j] = h[j] = g[j] + gam * h[j];
}
}
error("Too many iterations in frprmn");
}
void gradient_descent(vectorN &p, int n, m_real ftol, int &iter, m_real &fret,
m_real (*func) (vectorN const&),
m_real (*dfunc) (vectorN const&,vectorN&))
{
m_real fp;
static vectorN xi; xi.setSize(n);
for (iter=0; iter<ITMAX; iter++)
{
fp = (*dfunc) (p, xi);
linmin(p, xi, n, fret, func);
if (2.0 * fabs(fret - fp) <= ftol * (fabs(fret) + fabs(fp) + EPS_jhm))
return;
}
error("Too many iterations in gradient_descent");
}
void frprmn(double p[], int n, double ftol, int *iter, double *fret,
double (*func)(double []), void (*dfunc)(double [], double []))
{
void linmin(double p[], double xi[], int n, double *fret,
double (*func)(double []));
int j,its;
double gg,gam,fp,dgg;
double *g,*h,*xi;
g=dvector(1,n);
h=dvector(1,n);
xi=dvector(1,n);
fp=(*func)(p);
(*dfunc)(p,xi);
for (j=1;j<=n;j++) {
g[j] = -xi[j];
xi[j]=h[j]=g[j];
}
for (its=1;its<=ITMAX;its++) {
*iter=its;
linmin(p,xi,n,fret,func);
if (2.0*fabs(*fret-fp) <= ftol*(fabs(*fret)+fabs(fp)+EPS)) {
FREEALL
return;
}
fp= *fret;
(*dfunc)(p,xi);
dgg=gg=0.0;
for (j=1;j<=n;j++) {
gg += g[j]*g[j];
dgg += (xi[j]+g[j])*xi[j];
}
if (gg == 0.0) {
FREEALL
return;
}
double FletcherMinimizer::Minimize(double ftol)
{
LineMinimizer linmin(*func);
if (point.Length() == 0)
return fmin = f(point);
// Initialize direction vector
linmin.line.Dimension(point.Length());
// Evaluate function and derivatives
fmin = f(point);
while (true)
{
df(point, linmin.line, 0.1);
// Minimizing so go against gradient
linmin.line.Negate();
h = linmin.line;
g = linmin.line;
iter = 1;
while (true)
{
linmin.point = point;
linmin.Bracket(0, 1);
linmin.Brent(ftol);
// If values tested while evaluating derivative
// are closer to minimum than those found by
// descending gradient, use those as starting points!
if (func->dfmin < linmin.fmin)
{
linmin.point = point;
linmin.line = func->dpmin;
linmin.line.Subtract(point);
linmin.Bracket(0,1);
linmin.Brent(ftol);
point = linmin.point;
fmin = linmin.fmin;
break;
};
point = linmin.point;
if (2.0 * fabs(linmin.fmin - fmin) <= ftol * (fabs(linmin.fmin) + fabs(fmin) + ZEPS))
return fmin = linmin.fmin;
fmin = linmin.fmin;
df(point, linmin.line, 0.1);
double dgg = 0.0, gg = 0.0;
for (int j = 0; j < linmin.line.Length(); j++)
{
gg += g[j] * g[j];
dgg += (linmin.line[j] + g[j]) * linmin.line[j];
}
// Gradient is exactly zero
if (gg == 0.0)
return fmin;
double gamma = dgg / gg;
for (int j = 0; j < linmin.line.Length(); j++)
{
g[j] = -linmin.line[j];
h[j] = g[j] + gamma * h[j];
linmin.line[j] = h[j];
}
// Normalize direction vector to avoid degenerate cases
double norm = linmin.line.SumSquares();
if (norm > 1.0)
{
norm = sqrt (1.0 / norm);
g.Multiply(norm);
h.Multiply(norm);
linmin.line.Multiply(norm);
}
if (iter == ITMAX)
error("Fletcher.Minimizer -- Failed to converge after %d iterations", ITMAX);
iter++;
}
}
}
double PowellMinimizer::Minimize(double ftol)
{
LineMinimizer linmin(*func);
Vector pstart;
fmin = f(point);
iter = 1;
while (true)
{
pstart = point;
double fstart = fmin;
double ybig = 0;
int ibig = 0;
// Try all the directions in the current set
for (int i = 0; i < directions.rows; i++)
{
linmin.point = point;
linmin.line = directions[i];
linmin.Bracket(0, 1);
linmin.Brent(ftol);
if ((fmin - linmin.fmin) > ybig)
{
ibig = i;
ybig = fmin - linmin.fmin;
}
fmin = linmin.fmin;
point = linmin.point;
}
// are we done?
if (2 * (fstart - fmin) <= ftol * (fabs(fstart) + fabs(fmin)))
return fmin;
if (iter == ITMAX)
error("Powell.Minimize - Exceeding maximum iterations");
// Average direction moved
linmin.line = point;
linmin.line.Subtract(pstart);
// Extrapolated point
linmin.point.Add(linmin.line);
double fextra = f(linmin.point);
if (fextra < fstart)
{
double avgdir = fstart - fmin - ybig;
double newdir = fstart - fextra;
double promise = 2.0 * (fstart - 2.0 * fmin + fextra) *
avgdir * avgdir - ybig * newdir * newdir;
if (promise < 0.0)
{
linmin.Bracket(0,1);
linmin.Brent(ftol);
directions.SwapRows(ibig, directions.rows);
directions[directions.rows - 1] = linmin.line;
}
}
iter++;
}
}
void PowellMin (TSIL_REAL p[],
TSIL_REAL **xi,
int n,
TSIL_REAL ftol,
int *iter,
TSIL_REAL *fret,
TSIL_REAL (*func)(TSIL_REAL []))
{
int i, ibig, j;
TSIL_REAL del, fp, fptt, t, *pt, *ptt, *xit;
pt = (TSIL_REAL *) calloc (n, sizeof(TSIL_REAL));
ptt = (TSIL_REAL *) calloc (n, sizeof(TSIL_REAL));
xit = (TSIL_REAL *) calloc (n, sizeof(TSIL_REAL));
*fret = (*func)(p);
/* printf("Initial fret = %Lf\n", *fret); */
for (j=0; j<n; j++) pt[j] = p[j];
for (*iter=1; ; ++(*iter)) {
fp = *fret;
ibig = 0;
del = 0.0;
for (i=0; i<n; i++) {
for (j=0; j<n; j++) xit[j] = xi[j][i];
fptt = *fret;
linmin (p, xit, n, fret, func);
if (fptt - *fret > del) {
del = fptt - *fret;
ibig = i;
}
}
if (2.0L*(fp-(*fret)) <= ftol*(TSIL_FABS(fp)+TSIL_FABS(*fret))+TINY) {
/* printf("Powell exiting...\n"); */
/* printf("fp = %Lf\n", fp); */
/* printf("fret = %Lf\n", *fret); */
free (xit);
free (ptt);
free (pt);
return;
}
if (*iter == ITMAX)
TSIL_Error ("PowellMin", "Max iterations exceeded", 42);
for (j=0; j<n; j++) {
ptt[j] = 2.0L*p[j] - pt[j];
xit[j] = p[j] - pt[j];
pt[j] = p[j];
}
fptt = (*func)(ptt);
if (fptt < fp) {
t = 2.0L*(fp - 2.0L*(*fret) + fptt)*TSIL_POW(fp - (*fret) - del, 2)
- del*TSIL_POW(fp - fptt, 2);
if (t < 0.0) {
linmin (p, xit, n, fret, func);
for (j=0; j<n; j++) {
xi[j][ibig] = xi[j][n-1];
xi[j][n-1] = xit[j];
}
}
}
}
}