bool IASIAM::Run(IAResult* r) //output
{
this->r = r;
N = r->iagrid->get_N();
iagrid = r->iagrid;
printf(" -------IASIAM: mu=%.3f, U=%.3f, T=%.3f, epsilon=%.3f -------\n", r->mu, U, T, epsilon);
complex<double>* V = new complex<double>[1];
//----- initial guess ------//
V[0] = r->mu0;
//---------------------------//
//------ SOLVE IASIAM ---------//
double mu0inits [] = {0.0, 1.0, -1.0, -0.8, 2.0, 1.5, -1.5, 2.5, -2.5,
-2.0, 0.05, 0.8, 0.1, -0.1, 0.3, -0.3, 0.5, -0.5, -0.05,
0.4, -0.4, 0.6, -0.6, 2.3, -2.3, 2.8, -2.8, 1.8, -1.8 };
bool failed = !UseBroydenFormu0;
int c = 0;
//printf("IASIAM: about to do mu0 search\n");
while ( UseBroydenFormu0 and ( UseBroyden<IASIAM>(1, MAX_ITS, Accr, &IASIAM::SolveSiam, this, V) != 1 ) )
{ c++; //printf("IASIAM: passed the first broyden use\n");
if ( (c >= max_tries) or (c >= sizeof(mu0inits)/sizeof(double) - 1 ) )
{
printf("\n\n\n\n==== IASIAM ERROR ====: Broyden mu0 search failed to converge. Now switching to amoeba ...\n\n\n\n");
failed = true;
break;
}
V[0] = mu0inits[c];
printf("==================== ====================== ========== TRYING new mu0 int!!! c = %d, mu0init = %f\n\n\n",c, mu0inits[c]);
};
if ( (failed) or (abs(V[0])>5.0) )
{ V[0] = mu0inits[0];
Amoeba(Accr, V, &IASIAM::SolveSiam);
}
delete [] V;
//----------------------------//
r->mu0 = mu0;
printf(" IASIAM: mu0 = %f, n = %f\n",r->mu0, r->n);
return false;
}
double AmoebaMinimizer::Minimize(double ftol)
{
int i, ilo, ihi, inhi, m, nvertex = point.dim + 1;
double rtol, ysave, ytry;
if (point.dim == 0)
return fmin = f(point);
// Setup the simplex, and evaluate f at each vortex
for (i=0; i < point.dim; i++)
{
simplex[i] = point;
simplex[i].Add (directions[i]);
y[i] = f(simplex[i]);
if (y[i] < fmin) fmin = y[i];
}
simplex[nvertex - 1] = point;
y[nvertex - 1] = f(simplex[nvertex - 1]);
if (y[nvertex - 1] < fmin) fmin = y[nvertex - 1];
cycleCount = nvertex;
// Calculate psum
for (psum = simplex[0], m = 1; m < nvertex; m++)
psum.Add(simplex[m]);
while (true)
{
// First we must determine which is the highest, next
// highest and lowest point in the simplex
ihi = y[0] > y[1] ? (ilo = inhi = 1, 0) : (ilo = inhi = 0, 1);
for (i = 2; i < nvertex; i++)
{
if (y[i] <= y[ilo])
ilo = i;
else if (y[i] > y[ihi])
{
inhi = ihi;
ihi = i;
}
else if (y[i] > y[inhi])
inhi = i;
}
// Compute the range from highest to lowest, return if satisfactory
rtol = 2 * fabs(y[ihi] - y[ilo])/(fabs(y[ihi])+fabs(y[ilo])+ZEPS);
if (rtol < ftol)
{
point = simplex[ilo];
return fmin = y[ilo];
}
if (cycleCount > cycleMax)
error("Amoeba.Minimize - Couldn't converge in %d cycles", cycleMax);
// begin a new iteration...
// first extrapolate by a factor of -1 through the face of the simplex
// (reflection)
cycleCount += 2;
ytry = Amoeba(ihi, -1.0);
if (ytry <= y[ilo])
// Better than previous best, keep going
Amoeba(ihi, 2.0);
else if (ytry >= y[inhi])
{
// still worse than next highest point, so do a one-
// dimensional contraction to find an intermediate
// lower point
ysave = y[ihi];
ytry = Amoeba(ihi, 0.5);
if (ytry >= ysave)
{
// Can't get rid of that high point
// Better to contract around lowest point
for (i = 0; i < nvertex; i++)
if (i != ilo)
{
simplex[i].Add(simplex[ilo]);
simplex[i].Multiply(0.5);
y[i] = f(simplex[i]);
}
cycleCount += point.dim; // keep track of function evaluations
for (psum = simplex[0], m = 1; m < nvertex; m++)
psum.Add(simplex[m]);
}
}
else
cycleCount --;
}
}
double SAMinimizer::MinimizeLoop(double )
{
int i, ihi, ilo, m, nvertex = point.dim + 1;
double ylo, ynhi, ysave, yt, ytry;
// Calculate psum
for (psum = simplex[0], m = 1; m < nvertex; m++)
psum.Add(simplex[m]);
while (true)
{
// Determine which point is highest (worst),
// next highest, and lowest (best)
//
ilo = 0;
ihi = 1;
// whenever we look at a vertex it gets a
// random 'thermal' fluctuation
ynhi = ylo = y[0] - T * log(rand->Next());
yhi = y[1] - T * log(rand->Next());
if (ylo > yhi)
{
ihi = 1;
ilo = 0;
ynhi = yhi;
yhi = ylo;
ylo = ynhi;
}
for (i = 2; i < nvertex; i++)
{
yt = y[i] - T * log(rand->Next());
if (yt <= ylo)
{
ilo = i;
ylo = yt;
}
else if (yt > yhi)
{
ynhi = yhi;
ihi = i;
yhi = yt;
}
else if (yt > ynhi)
ynhi = yt;
}
// Compute the fractional range from highest to lowest
// and return if satisfactory
// rtol = 2.0 * (yhi - ylo) / (fabs(yhi) + fabs(ylo));
// if ((rtol < ftol) || (iter < 0))
if (iter < 0)
{
// put best point and value in slot 1 before return
y.Swap(0, ilo);
simplex.SwapRows(0, ilo);
return fmin;
}
// Begin a new iteration:
// First. Extrapolate by a factor -1 through the face of the simplex
// across from the high point (ie. reflect from the high point)
iter -= 2;
ytry = Amoeba(ihi, -1.0);
if (ytry < ylo)
// gives a better result than the best point, so go even further
Amoeba(ihi, 2.0);
else if (ytry >= ynhi)
{
// the reflected point is worse than the second highest so
// look for an intermediate (do a one-dimensional contration)
ysave = yhi;
ytry = Amoeba(ihi, 0.5);
if (ytry >= ysave)
{
// Can't get rid of worst point, so contract around
// lowest point
for (i = 0; i < nvertex; i++)
if ( i != ilo )
{
simplex[i].Add(simplex[ilo]);
simplex[i].Multiply(0.5);
y[i] = f(simplex[i]);
if (y[i] <= fmin)
{
point = simplex[i];
fmin = y[i];
}
}
// Calculate psum
for (psum = simplex[0], m = 1; m < nvertex; m++)
psum.Add(simplex[m]);
iter -= point.dim;
}
}
else
iter++; // correct evaluation count
}
}
bool IASIAM::Run_CHM(IAResult* r) //output
{
this->r = r;
N = r->iagrid->get_N();
iagrid = r->iagrid;
epsilon = 0;
printf(" ------- IASIAM for CHM: n=%.3f, U=%.3f, T=%.3f, epsilon=%.3f -------\n", r->n, U, T, epsilon);
//----------------- CALCULATION ----------------------//
if (PHSymmetricCase)
{
mu0 = 0.0;
get_G0();
}
else
{
complex<double>* V = new complex<double>[1];
//------initial guess---------//
V[0] = r->mu0; //initial guess is always the last mu0. in first DMFT iteration it is 0
//---------------------------//
printf(" IASIAM: about to calc mu0. at the moment: mu0 = %.3f mu=%.3f\n",r->mu0, r->mu);
double initGuesses [] = {-1.0, 1.0, 0.3, -0.3, 0.1, -0.1,
-0.8, 0.8, -0.6, 0.6, -0.7, 0.7,
-3.0, 3.0, 0.9, -0.9, 0.05, -0.05,
0.5, -0.5, 0.2, -0.2, 2.0, -2.0};
bool converged = false;
int i;
for (i=0; ( (i<sizeof(initGuesses)/sizeof(double)) and (i<max_tries) ); i++)
{ printf("------ IASIAM: trying with init guess: %f\n",real(V[0]));
converged = UseBroyden<IASIAM>(1, 50, 1e-8, &IASIAM::get_G0, this, V);
if (converged) break;
else V[0] = initGuesses[i];
}
if ((i==max_tries)and(!converged))
{ V[0] = initGuesses[0];
Amoeba(Accr, V, &IASIAM::get_G0);
}
delete [] V;
}
r->mu0 = mu0;
//PrintFunc("G0", N, r->G0, r->omega);
printf(" mu0 = %f\n", mu0);
fft->FtoT(r->G0, r->G0_tau);
get_SOCSigma_tau();
fft->TtoF(r->SOCSigma_tau, r->SOCSigma);
if (PHSymmetricCase)
{ r->mu = 0.5*U;
r->n=0.5;
get_G();
}
else
{
complex<double>* V = new complex<double>[1];
V[0] = r->mu;
double initGuesses [] = {-1.0, 1.0, -0.8, 0.8, -0.6, 0.6, 0.2, -0.2, 2.0, -2.0};
bool converged = false;
int i;
for (i=0; ( (i<sizeof(initGuesses)/sizeof(double)) and (i<max_tries) ); i++)
{ printf("------ IASIAM: trying with init guess: %f\n",real(V[0]));
converged = UseBroyden<IASIAM>(1, MAX_ITS, 1e-8, &IASIAM::get_G, this, V);
if (converged){ break; }
else V[0] = initGuesses[i];
}
if ((i==max_tries)and(!converged))
{ V[0] = initGuesses[0];
Amoeba(Accr, V, &IASIAM::get_G);
}
delete [] V;
}
printf(" mu = %f\n", r->mu);
//-----------------------------------------------------//
return false;
}