inline double Grape::Phi4TraceCav() const{
//the measure implemented, phi (PHI_4_sub) is phi = |sum_{i=0,1} <i|U_desired* UN-1....U_0|i>|^2/2^2
std::complex<double> temp1=0.0;
matrix<std::complex<double> > Rtemp=MOs::TraceOutB(rho_[num_time_-1],5);///5=dimCav
for(size_t q=0; q< 2; ++q){
for(size_t p=0; p<dimQ_; ++p){
temp1 += std::conj(rho_desired_(p,q))*Rtemp(p,q);
}
}
return std::real(temp1*std::conj(temp1))*0.25;
}
inline double RobustGrape::GradPhi3(const size_t point, const size_t j, const size_t k) const{
//phi_3
std::complex<double> temp1=0;
matrix<std::complex<double> > Rtemp;
Rtemp=H_controls_tdep_[point][k]*rho_[point][j];
for(size_t q=0; q< dim_; ++q){
for(size_t p=0; p<dim_; ++p){
temp1 +=std::conj(lambda_[point][j](p,q))*Rtemp(p,q);
}
}
return epsilon_*std::imag(temp1);
}
inline double RobustGrape::GradPhi0(const size_t point, const size_t j, const size_t k) const{
//phi_0
std::complex<double> temp1=0;
matrix<std::complex<double> > Rtemp;
Rtemp=QOs::SuperHami(H_controls_tdep_[point][k],rho_[point][j]);
//Fill in the upper triangle
for (size_t p=0; p< dim_; ++p){
for(size_t q=p+1; q < dim_; ++q){
Rtemp(p,q)=std::conj(Rtemp(q,p));
}
}
for(size_t q=0; q< dim_; ++q){
for(size_t p=0; p<dim_; ++p){
temp1 +=std::conj(lambda_[point][j](p,q))*Rtemp(p,q);
}
}
// std::cout << h_*QOs::Expectation(L,-i*H*R+i*R*H)- h_*temp1 << std::endl;
// std::cout << temp1 << std::endl;
// Rtemp.SetOutputStyle(Matrix);
// std::cout << Rtemp << std::endl;
return epsilon_*real(temp1);
}
inline double RobustGrape::GradPhi4Sub2(const size_t point, const size_t j, const size_t k) const{
//Phi_4_subsystem
//2.0*h_*imag(QOs::Expectation( MOs::Dagger(L),H*R)*QOs::Expectation(MOs::Dagger(R),L));
std::complex<double> temp1=0, temp2=0;
matrix<std::complex<double> > Rtemp;
Rtemp=H_controls_tdep_[point][k]*rho_[point][j];
for(size_t q=0; q< 2; ++q){
for(size_t p=0; p<dim_; ++p){
temp1 +=std::conj(lambda_[point][j](p,q))*Rtemp(p,q);
temp2 += std::conj(rho_[point][j](p,q))*lambda_[point][j](p,q);
}
}
return 2.0*epsilon_*std::imag(temp1*temp2);//*one_on_dim_*one_on_dim_;
}
inline double Grape::GradPhi4Sub2Filter(const size_t j, const size_t k) const{
double gradient=0.0;
if(j<nsubpixels_[k] || j>num_time_-nsubpixels_[k]) return gradient;
std::complex<double> temp1=0, temp2=0;
matrix<std::complex<double> > Rtemp;
int endtime = j + 100;
if(j>num_time_-100) endtime = num_time_;
for(size_t l = (j>100)*(j-100); l <endtime; ++l){
Rtemp=cos(((double)l)*drive_freq_*h_ - (k%2)*M_PI/2)*H_controls_tdep_[k]*rho_[l]*exp(-abs((int)j-(int)l)*h_/filter_rate_)*(h_/filter_rate_/2.0 /filter_norm_);
for(size_t q=0; q< 2; ++q){
for(size_t p=0; p<dim_; ++p){
temp1 +=std::conj(lambda_[l](p,q))*Rtemp(p,q);
temp2 += std::conj(rho_[l](p,q))*lambda_[l](p,q);
}
}
gradient +=2.0*epsilon_*std::imag(temp1*temp2);
}
return gradient;
}
inline double Grape::GradPhi4Sub2RWFilter(const size_t j, const size_t k) const{
double gradient=0.0;
double prefac;
if(j<nsubpixels_[k]*12 || j>num_time_-12*nsubpixels_[k]) return gradient;
int span=100;
int endtime = j + span;
if(j>num_time_-span) endtime = num_time_;
double phase = config_*2*M_PI/nconfigs_;
for(size_t l = (j>span)*(j-span); l <endtime; ++l)
//int l=j;
{
prefac = cos(phase + ((double)j)*(drive_freq_)*h_ - (k%2)*M_PI/2)*exp(-abs((int)j-(int)l)*h_/filter_rate_)*(h_/filter_rate_/2.0 /filter_norm_);
Udiag_[k][0][0]=Udiag_[k][1][0]=1;
Udiag_[k][0][1]=exp(-std::complex<double>(0.0,phase +(double)j*drive_freq_*h_));
Udiag_[k][0][2]=exp(-std::complex<double>(0.0,2.0*(phase + (double)j*drive_freq_*h_)));
Udiag_[k][0][3]=exp(-std::complex<double>(0.0,3.0*(phase + (double)j*drive_freq_*h_)));
Udiag_[k][1][1]=exp(std::complex<double>(0.0,(phase + (double)j*drive_freq_*h_)));
Udiag_[k][1][2]=exp(std::complex<double>(0.0,2.0*(phase + (double)j*drive_freq_*h_)));
Udiag_[k][1][3]=exp(std::complex<double>(0.0,3.0*(phase + (double)j*drive_freq_*h_)));
for(size_t q=0; q< dim_; ++q){
for(size_t p=0; p<dim_; ++p){
H_controls_tdep_[k](p,q)= Udiag_[k][0][q]*H_controls_[k](p,q)*Udiag_[k][1][p]*prefac;
}
} std::complex<double> temp1=0, temp2=0;
matrix<std::complex<double> > Rtemp;
Rtemp=H_controls_tdep_[k]*rho_[j];
for(size_t q=0; q< 2; ++q){
for(size_t p=0; p<dim_; ++p){
temp1 +=std::conj(lambda_[j](p,q))*Rtemp(p,q);
temp2 += std::conj(rho_[j](p,q))*lambda_[j](p,q);
}
}
gradient+= 2.0*epsilon_*std::imag(temp1*temp2);//*one_on_dim_*one_on_dim_;
}
return gradient;
}
void updateQR(Matrix & Q, Matrix & R, int NUM_TX, int NUM_RX,int i)
{
int ni = NUM_RX - i;
int ti = NUM_TX - i;
Matrix Rtemp(ni,ti);
Matrix Qtemp(ni,ni);
Matrix Atemp(ni,ti);
Matrix Itemp(ni,ni);
int k,l;
for(k = i; k < NUM_RX; k++)
{
for(l = i ; l < NUM_TX; l++)
{
Atemp(k-i , l-i) = R(k,l);
}
}
for(k = 0; k < ni; k++)
{
for(l = 0; l < ni; l++)
{
if(k == l) Itemp(k,l) = 1;
else Itemp(k,l) = 0;
}
}
Matrix x(ni,1);
for(k = 0; k < ni; k++)
x(k,0) = Atemp(k,0);
double xSize = eSize(x,ni);
int sign;
if ( x(0,0) >= 0 ) sign = 1;
else sign = -1;
Matrix g(ni,1);
g(0,0) = x(0,0) + sign * xSize;
for(k = 1; k < ni; k++)
g(k,0) = x(k,0);
double gSize = eSize(g,ni);
double Qscale = 2/(gSize * gSize);
Matrix ggT(ni,ni);
ggT = g * (~g);
for(k = 0; k < ni; k++)
for(l = 0; l < ni; l++)
ggT(k,l) = Qscale * ggT(k,l);
Qtemp = Itemp - ggT;
Rtemp = Qtemp * Atemp;
Matrix Qeff(NUM_RX,NUM_RX);
for(k = 0; k < NUM_RX; k++)
for(l = 0; l < NUM_RX; l++)
Qeff(k,l) = 0;
for(k = 0; k < i; k++) Qeff(k,k) = 1;
for(k = i; k < NUM_RX; k++)
{
for(l = i; l < NUM_TX; l++)
R(k,l) = Rtemp(k-i,l-i);
for(l = i; l < NUM_RX; l++)
Qeff(k,l) = Qtemp(k-i,l-i);
}
Q = Q * Qeff;
}