void SIAM::get_Ps()
{
double** p1 = new double*[N];
double** p2 = new double*[N];
#pragma omp parallel for
for (int i=0; i<N; i++)
{
p1[i] = new double[N];
p2[i] = new double[N];
for (int j=0; j<N; j++)
{
p1[i][j] = r->Am[j] * grid->interpl(r->Ap, r->omega[j] - r->omega[i]);
p2[i][j] = r->Ap[j] * grid->interpl(r->Am, r->omega[j] - r->omega[i]);
}
//get Ps by integrating
r->P1[i] = pi * TrapezIntegral(N, p1[i], r->omega);
r->P2[i] = pi * TrapezIntegral(N, p2[i], r->omega);
delete [] p1[i];
delete [] p2[i];
}
delete [] p1;
delete [] p2;
}
bool SIAM::Run(double mu, complex<double>* Delta, //input
complex<double>* G_out, complex<double>* Sigma_out, double &n_out) //output
{
if (!Initialized) exit(1);
Clipped = false;
this->mu = mu;
this->Delta = Delta;
if ((mu==0)&&(epsilon==-U/2.0))
SymmetricCase = true;
else
SymmetricCase = false;
printf(" -------%s SIAM: mu=%.3f, U=%.3f, T=%.3f, epsilon=%.3f -------\n", (SymmetricCase) ? "Symmetric" : "",mu, U, T, epsilon);
//----- initial guess ------//
n = 0.5;
mu0 = 0.0;
if ((!SymmetricCase)and(UseMPT_Bs))
MPT_B = epsilon;
else
MPT_B = 0.0;
complex<double>* V = new complex<double>[2];
V[0] = mu0;
V[1] = MPT_B;
//---------------------------//
//------ SOLVE SIAM ---------//
if (SymmetricCase)
//mu0 and n are known => there's no solving of system of equations
SolveSiam(V);
else
//use broyden to solve system of two equations
UseBroyden<SIAM>(2, MAX_ITS, Accr, &SIAM::SolveSiam, this, V);
delete [] V;
//----------------------------//
//output spectral weight if optioned
if (CheckSpectralWeight)
{
printf(" Spectral weight G: %fe\n", -imag(TrapezIntegral(N,G,omega))/pi);
printf(" Spectral weight G0: %fe\n", -imag(TrapezIntegral(N,G0,omega))/pi);
}
//-------- OUTPUT ---------//
for (int i=0; i<N; i++)
{
G_out[i] = G[i];
Sigma_out[i] = Sigma[i];
}
n_out = n;
//-------------------------//
return Clipped;
}
int main()
{
int N=1000;
GRID grid(N, 1.5, false);
//GRID grid("params");
//int N=grid.get_N();
double* omega = new double[N];
double* dos = new double[N];
grid.assign_omega(omega);
printf("-----grid ready\n");
int Nx = 4000;
int Ny = 4000;
IBZ ibz(IBZtypes::TriangularLattice, Nx, Ny);
printf("-----ibz ready\n");
for(int n=0; n<N; n++)
{ for(int i=0; i<Nx; i++)
for(int j=0; j<Ny; j++)
ibz.summand[i][j] = 1.0/(omega[n]-ibz.epsilon[i][j]+ii*1e-3);
printf("-----summand ready, n=%d \n",n);
dos[n] = -(1.0/pi)*imag(ibz.sum());
}
PrintFunc("triangular_dos",N,dos,omega);
printf("Spectral weight: %.6f\n",TrapezIntegral(N, dos, omega));
delete [] dos;
delete [] omega;
return 0;
}
void SIAM::get_SOCSigma()
{
double** s = new double*[N];
#pragma omp parallel for
for (int i=0; i<N; i++)
{ //printf("tid: %d i: %d\n",omp_get_thread_num(),i);
s[i] = new double[N];
for (int j=0; j<N; j++)
{ //printf("tid: %d j: %d\n",omp_get_thread_num());
s[i][j] = grid->interpl(r->Ap, r->omega[i] - r->omega[j]) * r->P2[j]
+ grid->interpl(r->Am, r->omega[i] - r->omega[j]) * r->P1[j];
}
//integrate
r->SOCSigma[i] = complex<double>(0.0, - U*U * TrapezIntegral(N, s[i], r->omega) );
if (ClipOff( r->SOCSigma[i] )) Clipped = true ;
delete [] s[i];
}
delete [] s;
//int i;
//cin >> i;
if (Clipped) printf(" !!!Clipping SOCSigma!!!!\n");
grid->KramarsKronig( r->SOCSigma );
}
double SIAM::get_n(complex<double> X[])
{
double* g = new double[N];
for (int i=0; i<N; i++)
g[i]=-(1/pi)*imag(X[i])*fermi[i];
double n = TrapezIntegral(N, g,omega);
delete [] g;
return n;
}
void SIAM::get_Ps()
{
for (int i=0; i<N; i++)
{
//get integrand arrays
double* p1 = new double[N];
double* p2 = new double[N];
for (int j=0; j<N; j++)
{
p1[j] = Am[j]*grid->interpl(Ap, omega[j]-omega[i]);
p2[j] = Ap[j]*grid->interpl(Am, omega[j]-omega[i]);
}
//get Ps by integrating
P1[i] = pi*TrapezIntegral(N, p1, omega);
P2[i] = pi*TrapezIntegral(N, p2, omega);
delete [] p1;
delete [] p2;
}
}
double SIAM::get_MPT_B()
{
if (!UseMPT_Bs) return 0.0;
complex<double>* b = new complex<double>[N];
for(int i=0; i<N; i++)
b[i] = complex<double>(fermi[i]) * Delta[i] * G[i]
* ( complex<double>(2.0 / U) * Sigma[i] - (double)1.0 );
double mpt_b = epsilon - 1.0/(pi*n*(1.0-n)) * imag(TrapezIntegral(N, b,omega));
delete [] b;
return mpt_b;
}
double SIAM::get_MPT_B0()
{
if (!UseMPT_Bs) return 0.0;
complex<double>* b0 = new complex<double>[N]; //integrand function
for(int i=0; i<N; i++)
b0[i] = complex<double>(fermi[i]) * Delta[i] * G0[i];
double mpt_b0 = epsilon - 1.0 * (2*n-1) * imag(TrapezIntegral(N, b0,omega))
/ ( pi * n * (1-n) ) ;
delete [] b0;
return mpt_b0;
}
void SIAM::get_G_CHM()
{
get_Sigma();
if (UseLatticeSpecificG)
#pragma omp parallel for
for (int i=0; i<N; i++)
{ complex<double> com = r->omega[i] + r->mu - r->Sigma[i];
r->G[i] = LS_get_G(LatticeType, t, com);
}
else
{
complex<double>** g = new complex<double>*[N];
#pragma omp parallel for
for (int i=0; i<N; i++)
{
//treat integrand carefully
double D = 0.0;
complex<double> LogTerm = 0.0;
if (abs(imag(r->Sigma[i]))<0.1)
{
D = grid->interpl(r->NIDOS, r->mu + r->omega[i] - real(r->Sigma[i]));
LogTerm = complex<double>(D, 0.0) * log( (r->mu + r->omega[i] - r->Sigma[i] + r->omega[N-1])
/(r->mu + r->omega[i] - r->Sigma[i] - r->omega[N-1]) );
}
//create integrand array
g[i] = new complex<double>[N];
for (int j=0; j<N; j++)
g[i][j] = complex<double>(r->NIDOS[j] - D, 0.0)
/ ( r->mu + r->omega[i] - r->omega[j] - r->Sigma[i] );
//integrate to get G
r->G[i] = TrapezIntegral(N, g[i], r->omega) + LogTerm ;
if (ClipOff(r->G[i])) Clipped = true;
delete [] g[i];
}
delete [] g;
if (Clipped) printf(" !!!!Clipping G!!!!\n");
}
}
void SIAM::GetGfOnImagAxis(int M, complex<double> * G_out)
{
complex<double>* g = new complex<double>[N];
double* mf = new double[M];
for(int m=0; m<M; m++)
{
mf[m]=MatsFreq(m);
for(int i=0; i<N; i++)
g[i] = imag(G[i]) / complex<double>( -omega[i], mf[m] );
G_out[m] = -1/(pi)*TrapezIntegral(N, g,omega);
}
delete [] g;
delete [] mf;
}
void SIAM::get_G_CHM()
{
get_Sigma();
for (int i=0; i<N; i++)
{
//treat integrand carefully
double D = 0.0;
complex<double> LogTerm = 0.0;
if (abs(imag(Sigma[i]))<0.1)
{
D = grid->interpl(Dos,mu + omega[i]-real(Sigma[i]));/*DOS(DOStype_CHM, t_CHM, mu + omega[i]-real(Sigma[i]));*/
LogTerm = complex<double>(D, 0.0) * log( (mu + omega[i] - Sigma[i] + omega[N-1])
/(mu + omega[i] - Sigma[i] - omega[N-1]) );
}
//create integrand array
complex<double>* g = new complex<double>[N];
for (int j=0; j<N; j++)
g[j] = complex<double>(/*DOS( DOStype_CHM, t_CHM, omega[j] )*/Dos[j] - D, 0.0)
/ ( mu + omega[i] - omega[j] - Sigma[i] );
/* //treat integrand less carefully
complex<double>* g = new complex<double>[N];
for (int j=0; j<N; j++)
g[j] = complex<double>(DOS( DOStype_CHM, t_CHM, omega[j] ))
/ ( complex<double>(mu,eta) + omega[i] - omega[j] - Sigma[i] );
*/
//integrate to get G
G[i] = TrapezIntegral(N, g,omega) + LogTerm ;
if (ClipOff(G[i])) Clipped = true;
delete [] g;
}
if (Clipped) printf(" !!!!Clipping G!!!!\n");
}
void SIAM::get_SOCSigma()
{
int i,j;
for (i=0; i<N; i++)
{
//get integrand array
double* s = new double[N];
for (j=0; j<N; j++)
s[j] = grid->interpl(Ap,omega[i]-omega[j])*P2[j]
+ grid->interpl(Am,omega[i]-omega[j])*P1[j];
//integrate
SOCSigma[i] = complex<double>(0.0, - U*U * TrapezIntegral(N, s,omega) );
if (ClipOff(SOCSigma[i])) Clipped = true ;
delete [] s;
}
if (Clipped) printf(" !!!Clipping SOCSigma!!!!\n");
grid->KramarsKronig(SOCSigma);
}
bool SIAM::Run_CHM(double n, complex<double>* Delta, //input
complex<double>* G_out, complex<double>* Sigma_out, double &mu_out) //output
{
if (!Initialized) exit(1);
Clipped = false;
for (int i=0; i<N; i++) if (ClipOff(Delta[i])) Clipped = true;
if (Clipped) printf(" !!! Clipping Delta !!!\n");
this->n = n;
this->Delta = Delta;
//PrintFunc("DeltaSiam",N,Delta,omega);
this->epsilon = 0;
if (n==0.5) HalfFilling = true;
else HalfFilling = false;
printf(" ------- SIAM for CHM: n=%.3f, U=%.3f, T=%.3f, epsilon=%.3f -------\n", n, U, T, epsilon);
if (HalfFilling)
{
mu = 0.5*U;
mu0 = 0.0;
MPT_B = 0.0;
MPT_B0 = 0.0;
SymmetricCase = true;
}
//------initial guess---------//
complex<double>* V = new complex<double>[1];
V[0] = mu0; //initial guess is always the last mu0. in first DMFT iteration it is 0
//---------------------------//
printf(" MPT: B = %fe, B0 = %fe\n", MPT_B, MPT_B0);
//----------------- CALCULATION ----------------------//
if (HalfFilling)//and (SymmetricCase))
get_G0();
else
UseBroyden<SIAM>(1, MAX_ITS, Accr, &SIAM::get_G0, this, V);
printf(" mu0 = %f\n", mu0);
printf("Integral G0: %.6f\n",imag(TrapezIntegral(N,G0,omega)));
get_As();
get_Ps();
get_SOCSigma();
V[0] = mu;
if (HalfFilling)//and (SymmetricCase))
{ if (IsBethe)
{ get_Sigma();
get_G(); //get_G() !!!! samo proba
// printf(" Integral G = %.6f\n",imag(TrapezIntegral(N,G,omega)));
}
else
get_G_CHM();
}
else
{ if (IsBethe)
UseBroyden<SIAM>(1, MAX_ITS, Accr, &SIAM::get_G, this, V);
else
UseBroyden<SIAM>(1, MAX_ITS, Accr, &SIAM::get_G_CHM, this, V);
}
MPT_B = get_MPT_B();
MPT_B0 = get_MPT_B0();
printf(" mu = %f\n", mu);
delete [] V;
//-----------------------------------------------------//
//output spectral weight if optioned
if (CheckSpectralWeight)
{
printf(" Spectral weight G: %fe\n", -imag(TrapezIntegral(N,G,omega))/pi);
printf(" Spectral weight G0: %fe\n", -imag(TrapezIntegral(N,G0,omega))/pi);
}
//-------- OUTPUT ---------//
for (int i=0; i<N; i++)
{
G_out[i] = G[i];
Sigma_out[i] = Sigma[i];
}
mu_out = mu;
//-------------------------//
// printf(" PROVERA: n = %f, U = %f \n",n, U);
return Clipped;
}
