MatrixXd tanh(const MatrixXd& x) {
const int n(x.rows());
const int p(x.cols());
MatrixXd expmat(MatrixXd(n, p));
expmat = (2 * x.array()).array().exp();
expmat = (expmat.array() - 1) / (expmat.array() + 1);
return (expmat);
}
void resp2nd (const double w1_max, const double w2_max,
const int nt1, const int nt2, const double dt,
const double staticErr, const int nk,
const cx_mat& dipo0, const cx_mat& dipo1, cx_mat& dipo2,
const char sch_hei, const syst& s, const bath &b, const hidx& h) {
const double dw1 = w1_max/nt1;
const double dw2 = w2_max/nt2;
const double dt1 = 2.0*deom_pi/w1_max;
const double dt2 = 2.0*deom_pi/w2_max;
const int mt1 = floor(dt1/dt);
const int mt2 = floor(dt2/dt);
const double dt1_res = dt1-dt*mt1;
const double dt2_res = dt2-dt*mt2;
deom d1(s,b,h);
const mat& exph = expmat(-real(d1.ham1)/d1.temperature);
cx_cube rho_t1 = zeros<cx_cube>(size(d1.ddos1));
rho_t1.slice(0).set_real(exph/trace(exph));
d1.equilibrium (rho_t1,dt,staticErr,nk);
for (int iado=0; iado<d1.nddo; ++iado) {
rho_t1.slice(iado) = dipo0*rho_t1.slice(iado)-rho_t1.slice(iado)*dipo0;
}
cx_mat ft = zeros<cx_mat>(nt2,nt1);
if (sch_hei == 's') { // sch-pic
for (int it1=0; it1<nt1; ++it1) {
deom d2(d1);
cx_cube rho_t2 = zeros<cx_cube>(size(d2.ddos1));
for (int iado=0; iado<d1.nddo; ++iado) {
rho_t2.slice(iado) = dipo1*rho_t1.slice(iado)-rho_t1.slice(iado)*dipo1;
}
for (int it2=0; it2<nt2; ++it2) {
double t2 = it2*dt2;
ft(it2,it1) = trace(dipo2*rho_t2.slice(0));
printf("In sch-pic: it2=%d, nddo=%d, lddo=%d\n", it2, d2.nddo, d2.lddo);
for (int jt2=0; jt2<mt2; ++jt2) {
d2.rk4 (rho_t2,t2,dt);
t2 += dt;
}
d2.rk4 (rho_t2,t2,dt2_res);
t2 += dt2_res;
}
printf("In sch-pic: it1=%d, nddo=%d, lddo=%d\n", it1, d1.nddo, d1.lddo);
double t1 = it1*dt1;
for (int jt1=0; jt1<mt1; ++jt1) {
d1.rk4 (rho_t1,t1,dt);
t1 += dt;
}
d1.rk4 (rho_t1,t1,dt1_res);
t1 += dt1_res;
}
} else if (sch_hei == 'h') { // hei-pic
deom d2(s,b,h);
cx_cube opr_t2 = zeros<cx_cube>(size(d2.ddos1));
opr_t2.slice(0) = dipo2;
for (int it2=0; it2<nt2; ++it2) {
const hkey& keys = d2.keys.rows(0,d2.nddo-1);
const cx_cube& oprs = opr_t2.slices(0,d2.nddo-1);
stringstream ss1, ss2;
ss1 << "key_t2_" << it2 << ".tmp";
ss2 << "opr_t2_" << it2 << ".tmp";
keys.save(ss1.str(),arma_binary);
oprs.save(ss2.str(),arma_binary);
printf("In hei-pic: it2=%d, nddo=%d, lddo=%d\n", it2, d2.nddo, d2.lddo);
double t2 = it2*dt2;
for (int jt2=0; jt2<mt2; ++jt2) {
d2.rk4 (opr_t2,t2,dt,'h');
t2 += dt;
}
d2.rk4 (opr_t2,t2,dt2_res,'h');
}
for (int it1=0; it1<nt1; ++it1) {
cx_cube rho_t2 = zeros<cx_cube>(d1.nsys,d1.nsys,d1.nddo);
for (int iado=0; iado<d1.nddo; ++iado) {
rho_t2.slice(iado) = dipo1*rho_t1.slice(iado)-rho_t1.slice(iado)*dipo1;
}
for (int it2=0; it2<nt2; ++it2) {
stringstream ss1, ss2;
hkey keys;
cx_cube oprs;
ss1 << "key_t2_" << it2 << ".tmp";
ss2 << "opr_t2_" << it2 << ".tmp";
keys.load(ss1.str(),arma_binary);
oprs.load(ss2.str(),arma_binary);
const int nddo_t2 = keys.n_rows;
cx_double ctmp = 0.0;
for (int iado=0; iado<nddo_t2; ++iado) {
auto iter = d1.maps.find(keys(iado));
if (iter != d1.maps.end()) {
const int jado = iter->second.rank;
ctmp += trace(oprs.slice(iado)*rho_t2.slice(jado));
}
}
ft(it2,it1) = ctmp;
}
printf("In sch-pic: it1=%d, nddo=%d, lddo=%d\n", it1, d1.nddo, d1.lddo);
double t1 = it1*dt1;
for (int jt1=0; jt1<mt1; ++jt1) {
d1.rk4 (rho_t1,t1,dt);
t1 += dt;
}
d1.rk4 (rho_t1,t1,dt1_res);
}
// clean tmp files
for (int it2=0; it2<nt2; ++it2) {
stringstream ss1, ss2;
ss1 << "key_t2_" << it2 << ".tmp";
ss2 << "opr_t2_" << it2 << ".tmp";
const string& s1 = ss1.str();
const string& s2 = ss2.str();
remove (s1.c_str());
remove (s2.c_str());
}
}
// write time-domain signal
const vec& ft_t1 = linspace(0.0,dt1*(nt1-1)/deom_fs2unit,nt1);
const vec& ft_t2 = linspace(0.0,dt2*(nt2-1)/deom_fs2unit,nt2);
const mat& ft_re = real(ft);
const mat& ft_im = imag(ft);
ft_t1.save("resp2nd.t1",raw_ascii);
ft_t2.save("resp2nd.t2",raw_ascii);
ft_re.save("resp2nd_re.t",raw_ascii);
ft_im.save("resp2nd_im.t",raw_ascii);
// 2D FFT
ft = real(ft)*deom_c1;
ft.row(0) *= 0.5;
ft.col(0) *= 0.5;
const cx_mat& fw2 = imag(ifft(ft))*nt2*dt2*deom_c1;
const cx_mat& fw1 = ifft(fw2.st())*nt1*dt1;
const cx_mat& fw = fw1.st();
// const cx_mat& fw = ifft2(ft)*nt1*nt2*dt1*dt2;
// write freq-domain signal
const vec& fw_w1 = linspace(0.0,dw1*(nt1/2-1)/deom_cm2unit,nt1/2);
const vec& fw_w2 = linspace(0.0,dw2*(nt2/2-1)/deom_cm2unit,nt2/2);
const mat& fw_re = real(fw.submat(0,0,nt2/2-1,nt1/2-1));
const mat& fw_im = imag(fw.submat(0,0,nt2/2-1,nt1/2-1));
fw_w1.save("resp2nd.w1",raw_ascii);
fw_w2.save("resp2nd.w2",raw_ascii);
fw_re.save("resp2nd_re.w",raw_ascii);
fw_im.save("resp2nd_im.w",raw_ascii);
}