void IsingModel2d::mcstep_dry( const unsigned int& k_max )
{
for ( unsigned int k = 0; k < k_max; k++ ) {
mcstep();
}
time -= k_max;
if ( fsize_correction_mode == 2 ) {
// try do determine if the system is in the ordered phase
unsigned int msmall_count = 0, mlarge_count = 0;
for ( unsigned int k = 0; k < k_max; k++ ) {
mcstep();
if ( abs( M() ) < N / 2 ) {
msmall_count++;
} else {
mlarge_count++;
}
}
if ( mlarge_count > msmall_count ) {
fsize_ordered_phase = true;
cout << "assuming ordered phase @ T = " << T << endl;
} else {
cout << "assuming disordered phase @ T = " << T << endl;
}
time -= k_max;
}
}
int main(int argc, char **argv)
{
double T=0;;
double mag=0.0;
int N;
int i;
Ising **S;
double tot_Erg=0;
double capacity=0.0;
double kai=0.0;
init_rnd(gus());
N=atoi(argv[1]);
S=(Ising **)malloc(sizeof(Ising *) * N);
for(i=0; i<N; i++)
S[i]=(Ising *)malloc(sizeof(Ising) * N);
initialize(N, S);
for(T=3.01; T>=0.01; T-=0.01)
{
mag=0.0;
tot_Erg=0.0;
kai=0.0;
capacity=0.0;
for(i=0; i<200000; i++)
mcstep(N, T, S);
for(i=0; i<200000; i++)
{
mcstep(N, T, S);
mag+=magnetization(N, S);
tot_Erg+=energy(N, S);
kai+=pow(magnetization(N, S), 2);
capacity+=pow(energy(N,S), 2);
}
mag=mag/200000;
tot_Erg=tot_Erg/200000;
kai=kai/200000;
capacity=capacity/200000;
kai=(kai-mag*mag)/T;
capacity=(capacity - tot_Erg*tot_Erg)/(T*T);
kai=kai*N*N;
capacity=capacity*N*N;
printf("%lf\t%lf\t%lf\t%lf\t%lf\n", T, mag, tot_Erg, kai, capacity);
}
free(S);
return 0;
}
void mcsrch(int size,
double *x,
double f, const double *g, double *s,
double *stp,
int *info, int *nfev, double *wa, bool orthant, double C) {
static const double p5 = 0.5;
static const double p66 = 0.66;
static const double xtrapf = 4.0;
static const int maxfev = 20;
/* Parameter adjustments */
--wa;
--s;
--g;
--x;
if (*info == -1) goto L45;
infoc = 1;
if (size <= 0 || *stp <= 0.0) return;
dginit = ddot_(size, &g[1], &s[1]);
if (dginit >= 0.0) return;
brackt = false;
stage1 = true;
*nfev = 0;
finit = f;
dgtest = ftol * dginit;
width = lb3_1_stpmax - lb3_1_stpmin;
width1 = width / p5;
for (int j = 1; j <= size; ++j) {
wa[j] = x[j];
}
stx = 0.0;
fx = finit;
dgx = dginit;
sty = 0.0;
fy = finit;
dgy = dginit;
while (true) {
if (brackt) {
stmin = min(stx, sty);
stmax = max(stx, sty);
} else {
stmin = stx;
stmax = *stp + xtrapf * (*stp - stx);
}
*stp = max(*stp, lb3_1_stpmin);
*stp = min(*stp, lb3_1_stpmax);
if ((brackt && ((*stp <= stmin || *stp >= stmax) ||
*nfev >= maxfev - 1 || infoc == 0)) ||
(brackt && (stmax - stmin <= xtol * stmax))) {
*stp = stx;
}
if (orthant) {
for (int j = 1; j <= size; ++j) {
double grad_neg = 0.0;
double grad_pos = 0.0;
double grad = 0.0;
if (wa[j] == 0.0) {
grad_neg = g[j] - 1.0 / C;
grad_pos = g[j] + 1.0 / C;
} else {
grad_pos = grad_neg = g[j] + 1.0 * sigma(wa[j]) / C;
}
if (grad_neg > 0.0) {
grad = grad_neg;
} else if (grad_pos < 0.0) {
grad = grad_pos;
} else {
grad = 0.0;
}
const double p = pi(s[j], -grad);
const double xi = wa[j] == 0.0 ? sigma(-grad) : sigma(wa[j]);
x[j] = pi(wa[j] + *stp * p, xi);
}
} else {
for (int j = 1; j <= size; ++j) {
x[j] = wa[j] + *stp * s[j];
}
}
*info = -1;
return;
L45:
*info = 0;
++(*nfev);
double dg = ddot_(size, &g[1], &s[1]);
double ftest1 = finit + *stp * dgtest;
if (brackt && ((*stp <= stmin || *stp >= stmax) || infoc == 0)) {
*info = 6;
}
if (*stp == lb3_1_stpmax && f <= ftest1 && dg <= dgtest) {
*info = 5;
}
if (*stp == lb3_1_stpmin && (f > ftest1 || dg >= dgtest)) {
*info = 4;
}
if (*nfev >= maxfev) {
*info = 3;
}
if (brackt && stmax - stmin <= xtol * stmax) {
*info = 2;
}
if (f <= ftest1 && std::abs(dg) <= lb3_1_gtol * (-dginit)) {
*info = 1;
}
if (*info != 0) {
return;
}
if (stage1 && f <= ftest1 && dg >= min(ftol, lb3_1_gtol) * dginit) {
stage1 = false;
}
if (stage1 && f <= fx && f > ftest1) {
double fm = f - *stp * dgtest;
double fxm = fx - stx * dgtest;
double fym = fy - sty * dgtest;
double dgm = dg - dgtest;
double dgxm = dgx - dgtest;
double dgym = dgy - dgtest;
mcstep(&stx, &fxm, &dgxm, &sty, &fym, &dgym, stp, fm, dgm, &brackt,
stmin, stmax, &infoc);
fx = fxm + stx * dgtest;
fy = fym + sty * dgtest;
dgx = dgxm + dgtest;
dgy = dgym + dgtest;
} else {
mcstep(&stx, &fx, &dgx, &sty, &fy, &dgy, stp, f, dg, &brackt,
stmin, stmax, &infoc);
}
if (brackt) {
double d1 = 0.0;
if ((d1 = sty - stx, std::abs(d1)) >= p66 * width1) {
*stp = stx + p5 * (sty - stx);
}
width1 = width;
width = (d1 = sty - stx, std::abs(d1));
}
}
return;
}
std::tuple<ook::message, T, T, T>
operator()(F phi, T finit, T dginit, T stp, const Options& opts) const
{
const T ftol = opts.ftol;
const T xtol = std::numeric_limits<T>::epsilon();
const T p5 = .5;
const T p66 = .66;
const T xtrapf = 4.;
const T stpmin = 1e-20;
const T stpmax = 1e20;
int infoc = 1;
int nfev = 0;
bool brackt = false;
bool stage1 = true;
const T dgtest = ftol * dginit;
T width = stpmax - stpmin;
T width1 = width / p5;
// The values stx, fx, dgx are step, function and derivative at the best
// step.
// The values sty, fy, dgy are the step, function and derivative at the
// other endpoint of the interval of uncertainty.
// The values stp, f, dg are the step, function and derivative at the
// current step.
T stx = 0.0;
T fx = finit;
T dgx = dginit;
T sty = 0.0;
T fy = finit;
T dgy = dginit;
while (true)
{
T stmin = stx;
T stmax = stp + xtrapf * (stp - stx);
if (brackt)
{
// Set max and min step to the present interval of uncertainty.
stmin = std::min(stx, sty);
stmax = std::max(stx, sty);
}
// Clamp the step to be between maximum and minimum values.
stp = std::max(stp, stpmin);
stp = std::min(stp, stpmax);
// If an unusual termination occues, set stp to be the lowest point
// obtained so far.
if ((brackt && (stp <= stmin || stp >= stmax)) || infoc == 0 ||
(brackt && stmax - stmin <= xtol * stmax))
{
stp = stx;
}
// Evaluate the function and derivative.
T f, dg;
std::tie(f, dg) = phi(stp);
const T ftest1 = finit + stp * dgtest;
// Test for convergence.
ook::message msg = ook::message::null;
if ((brackt && (stp <= stmin || stp >= stmax)) || infoc == 0)
{
msg = ook::message::warning_rounding_error_prevents_progress;
}
if (stp == stpmax && f <= ftest1 && dg <= dgtest)
{
msg = ook::message::warning_stp_eq_stpmax;
}
if (stp == stpmin && (f > ftest1 || dg >= dgtest))
{
msg = ook::message::warning_stp_eq_stpmin;
}
if (nfev >= opts.maxfev)
{
msg = ook::message::warning_max_line_search_attempts_reached;
}
if (brackt && stmax - stmin <= xtol * stmax)
{
msg = ook::message::warning_xtol_satisfied;
}
if (f <= ftest1 && fabs(dg) <= opts.gtol * (-dginit))
{
msg = ook::message::convergence;
}
// Check for termination.
if (msg != ook::message::null)
{
return std::make_tuple(msg, stp, f, dg);
}
// In the first state, seek a step for which the modified function
// has
// a non-positive value and non-negative derivative.
if (stage1 && f <= ftest1 &&
dg >= std::min(ftol, opts.gtol) * dginit)
{
stage1 = false;
}
// A modified function is used to predict the step only if we have
// not
// obtained a step for which the modified function has a
// non-positive
// function value and non-negative derivative, and if a lower
// function
// value has been obtained but the decrease is not sufficient.
if (stage1 && f <= fx && f > ftest1)
{
/// Define the modified function and derivative values.
T fm = f - stp * dgtest;
T fxm = fx - stx * dgtest;
T fym = fy - sty * dgtest;
T dgm = dg - dgtest;
T dgxm = dgx - dgtest;
T dgym = dgy - dgtest;
// Compute new step and update the interval of uncertainty.
infoc = mcstep(stx,
fxm,
dgxm,
sty,
fym,
dgym,
stp,
fm,
dgm,
brackt,
stmin,
stmax);
// Reset function and gradient values.
fx = fxm + stx * dgtest;
fy = fym + sty * dgtest;
dgx = dgxm + dgtest;
dgy = dgym + dgtest;
}
else
{
// Compute new step and update the interval of uncertainty.
infoc = mcstep(stx,
fx,
dgx,
sty,
fy,
dgy,
stp,
f,
dg,
brackt,
stmin,
stmax);
}
// Force a sufficient decrease in the size od the interval of
// uncertainty.
if (brackt)
{
if (fabs(sty - stx) >= p66 * width1)
{
stp = stx + p5 * (sty - stx);
}
width1 = width;
width = fabs(sty - stx);
}
}
}
void CMcsrch::mcsrch ( int n , double x[] , double f , double g[] , double s[] ,
int is0 , double stp[] , double ftol , double xtol , int maxfev ,
int info[] , int nfev[] , double wa[] )
{
p5 = 0.5;
p66 = 0.66;
xtrapf = 4;
if ( info[0] != - 1 )
{
infoc[0] = 1;
if ( n <= 0 || stp[0] <= 0 || ftol < 0 || CLBFGSCPP::gtol < 0 || xtol < 0 || CLBFGSCPP::stpmin < 0 || CLBFGSCPP::stpmax < CLBFGSCPP::stpmin || maxfev <= 0 )
return;
// Compute the initial gradient in the search direction
// and check that s is a descent direction.
dginit = 0;
for ( j = 1 ; j <= n ; j += 1 ) {
dginit = dginit + g [ j -1] * s [ is0+j -1];
}
if ( dginit >= 0 ) {
return;
}
brackt[0] = false;
stage1 = true;
nfev[0] = 0;
finit = f;
dgtest = ftol*dginit;
width = CLBFGSCPP::stpmax - CLBFGSCPP::stpmin;
width1 = width/p5;
for ( j = 1 ; j <= n ; j += 1 ) {
wa [ j -1] = x [ j -1];
}
// The variables stx, fx, dgx contain the values of the step,
// function, and directional derivative at the best step.
// The variables sty, fy, dgy contain the value of the step,
// function, and derivative at the other endpoint of
// the interval of uncertainty.
// The variables stp, f, dg contain the values of the step,
// function, and derivative at the current step.
stx[0] = 0;
fx[0] = finit;
dgx[0] = dginit;
sty[0] = 0;
fy[0] = finit;
dgy[0] = dginit;
}
while ( true )
{
if ( info[0] != -1 )
{
// Set the minimum and maximum steps to correspond
// to the present interval of uncertainty.
if ( brackt[0] ) {
stmin = min ( stx[0] , sty[0] );
stmax = max ( stx[0] , sty[0] );
} else {
stmin = stx[0];
stmax = stp[0] + xtrapf * ( stp[0] - stx[0] );
}
// Force the step to be within the bounds stpmax and stpmin.
stp[0] = max ( stp[0] , CLBFGSCPP::stpmin );
stp[0] = min ( stp[0] , CLBFGSCPP::stpmax );
// If an unusual termination is to occur then let
// stp be the lowest point obtained so far.
if ( ( brackt[0] && ( stp[0] <= stmin || stp[0] >= stmax ) ) || nfev[0] >= maxfev - 1 || infoc[0] == 0 || ( brackt[0] && stmax - stmin <= xtol * stmax ) ) stp[0] = stx[0];
// Evaluate the function and gradient at stp
// and compute the directional derivative.
// We return to main program to obtain F and G.
for ( j = 1 ; j <= n ; j += 1 ) {
x [ j -1] = wa [ j -1] + stp[0] * s [ is0+j -1];
}
info[0]=-1;
return;
}
info[0]=0;
nfev[0] = nfev[0] + 1;
dg = 0;
for ( j = 1 ; j <= n ; j += 1 ) {
dg = dg + g [ j -1] * s [ is0+j -1];
}
ftest1 = finit + stp[0]*dgtest;
// Test for convergence.
if ( ( brackt[0] && ( stp[0] <= stmin || stp[0] >= stmax ) ) || infoc[0] == 0 )
info[0] = 6;
//stp[0] == CLBFGSCPP::stpmax
if ( fabs(stp[0] - CLBFGSCPP::stpmax)<1e-55 && f <= ftest1 && dg <= dgtest )
info[0] = 5;
//stp[0] == CLBFGSCPP::stpmin
if ( fabs(stp[0] - CLBFGSCPP::stpmin)<1e-55 && ( f > ftest1 || dg >= dgtest ) )
info[0] = 4;
if ( nfev[0] >= maxfev )
info[0] = 3;
if ( brackt[0] && stmax - stmin <= xtol * stmax )
info[0] = 2;
if ( f <= ftest1 && fabs ( dg ) <= CLBFGSCPP::gtol * ( - dginit ) )
info[0] = 1;
// Check for termination.
if ( info[0] != 0 ) return;
// In the first stage we seek a step for which the modified
// function has a nonpositive value and nonnegative derivative.
if ( stage1 && f <= ftest1 && dg >= min ( ftol , CLBFGSCPP::gtol ) * dginit )
stage1 = false;
// A modified function is used to predict the step only if
// we have not obtained a step for which the modified
// function has a nonpositive function value and nonnegative
// derivative, and if a lower function value has been
// obtained but the decrease is not sufficient.
//wprintf(L">>L-BFGS.mscrch (Step Search): %d\n", ++nIter);
if ( stage1 && f <= fx[0] && f > ftest1 )
{
// Define the modified function and derivative values.
fm = f - stp[0]*dgtest;
fxm[0] = fx[0] - stx[0]*dgtest;
fym[0] = fy[0] - sty[0]*dgtest;
dgm = dg - dgtest;
dgxm[0] = dgx[0] - dgtest;
dgym[0] = dgy[0] - dgtest;
// Call cstep to update the interval of uncertainty
// and to compute the new step.
mcstep ( stx , fxm , dgxm , sty , fym , dgym , stp , fm , dgm , brackt , stmin , stmax , infoc );
// Reset the function and gradient values for f.
fx[0] = fxm[0] + stx[0]*dgtest;
fy[0] = fym[0] + sty[0]*dgtest;
dgx[0] = dgxm[0] + dgtest;
dgy[0] = dgym[0] + dgtest;
} else {
// Call mcstep to update the interval of uncertainty
// and to compute the new step.
mcstep ( stx , fx , dgx , sty , fy , dgy , stp , f , dg , brackt , stmin , stmax , infoc );
}
// Force a sufficient decrease in the size of the
// interval of uncertainty.
if ( brackt[0] )
{
if ( fabs ( sty[0] - stx[0] ) >= p66 * width1 )
stp[0] = stx[0] + p5 * ( sty[0] - stx[0] );
width1 = width;
width = fabs( sty[0] - stx[0] );
}
}
}