bool PreconditionedDownhillType::improve_energy(bool verbose) {
iter++;
const double old_energy = energy();
const VectorXd g = pgrad();
// Let's immediately free the cached gradient stored internally!
invalidate_cache();
// We waste some memory storing newx (besides *x itself), but this
// avoids roundoff weirdness of trying to add nu*g back to *x, which
// won't always get us back to the same value.
Grid newx(gd, *x - nu*g);
double newE = f.integral(kT, newx);
int num_tries = 0;
while (better(old_energy,newE)) {
nu *= 0.5;
newx = *x - nu*g;
newE = f.integral(kT, newx);
if (num_tries++ > 40) {
printf("PreconditionedDownhill giving up after %d tries...\n", num_tries);
return false; // It looks like we can't do any better with this algorithm.
}
}
*x = newx;
invalidate_cache();
nu *= 1.1;
if (verbose) {
//lm->print_info();
print_info();
}
return true;
}
boost::tuple< fit_tuple_t, fit_tuple_t >
find_grad( const fitness_f &f, const fit_tuple_t ¤t,
const double x2, const double delta ) {
// Declare our first and 2nd derivatives
int psize = current.get<0>().size();
int nsize = current.get<1>().size();
vector_t pgrad( psize );
vector_t ngrad( nsize );
vector_t plapl( psize );
vector_t nlapl( nsize );
// Protons
for ( int i = 0; i < psize; ++i ) {
fit_tuple_t plus( current );
fit_tuple_t minus( current );
plus.get<0>()[i] += delta;
minus.get<0>()[i] -= delta;
double x2plus = f( plus );
double x2minus = f( minus );
pgrad[i] = ( x2plus - x2minus ) / ( 2 * delta );
plapl[i] = ( x2plus + x2minus - 2 * x2 ) / bm::pow<2>(delta); }
// Neutrons
for ( int i = 0; i < nsize; ++i ) {
fit_tuple_t plus( current );
fit_tuple_t minus( current );
plus.get<1>()[i] += delta;
minus.get<1>()[i] -= delta;
double x2plus = f( plus );
double x2minus = f( minus );
ngrad[i] = ( x2plus - x2minus ) / ( 2 * delta );
nlapl[i] = ( x2plus + x2minus - 2 * x2 ) / bm::pow<2>(delta); }
return boost::make_tuple( fit_tuple_t( pgrad, ngrad ),
fit_tuple_t( plapl, nlapl ) ); }
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);
}