VectorXd GLMObjective::coordinate_descent(RegFunction *regfunc, int idx) {
VectorXd gr = X[idx].transpose() * -R / n;
VectorXd tmp;
MatrixXd wXX(p, p);
wXX.setZero();
for (int i = 0; i < n; i++)
wXX += W[i] * X[idx].row(i).transpose() * X[idx].row(i);
wXX /= n;
VectorXcd eigenvalues = wXX.eigenvalues();
double step_size = 0;
for (int i = 0; i < eigenvalues.size(); i++) {
step_size = std::max(step_size, eigenvalues[i].real());
}
assert(step_size >= 0);
tmp = regfunc->threshold_p((model_param.beta[idx] - gr / step_size), step_size);
VectorXd delta_beta = tmp - model_param.beta[idx];
tmp = (wXX*model_param.beta[idx] - gr);
VectorXd old_beta = model_param.beta[idx];
model_param.beta[idx] = regfunc->threshold(tmp)/step_size;
delta_beta = model_param.beta[idx] - old_beta;
if (calc_norm(delta_beta) > 1e-8) {
Xb += X[idx] * delta_beta;
R -= W.cwiseProduct(X[idx] * delta_beta);
}
return model_param.beta[idx];
}
void eigs_gen_Cpp(MatrixXd &M, VectorXd &init_resid, int k, int m,
double &time_used, double &prec_err)
{
double start, end;
start = get_wall_time();
DenseGenMatProd<double> op(M);
GenEigsSolver< double, LARGEST_MAGN, DenseGenMatProd<double> > eigs(&op, k, m);
eigs.init(init_resid.data());
int nconv = eigs.compute();
int niter = eigs.num_iterations();
int nops = eigs.num_operations();
// std::cout << "nops = " << nops << std::endl;
VectorXcd evals = eigs.eigenvalues();
MatrixXcd evecs = eigs.eigenvectors();
/*
std::cout << "computed eigenvalues D = \n" << evals.transpose() << std::endl;
std::cout << "first 5 rows of computed eigenvectors U = \n" << evecs.topRows<5>() << std::endl;
std::cout << "nconv = " << nconv << std::endl;
std::cout << "niter = " << niter << std::endl;
std::cout << "nops = " << nops << std::endl;
MatrixXcd err = M * evecs - evecs * evals.asDiagonal();
std::cout << "||AU - UD||_inf = " << err.array().abs().maxCoeff() << std::endl;
*/
end = get_wall_time();
time_used = (end - start) * 1000;
MatrixXcd err = M * evecs - evecs * evals.asDiagonal();
prec_err = err.cwiseAbs().maxCoeff();
}
Proector::Proector(HilbertSpace space)
{
for (int i = 0; i < space.totalDimension(); ++i) {
VectorXi toLabel = space.getVector(i);
VectorXcd op = space.getBasisVector(toLabel);
addOperator(op * op.transpose(), _vecToLabel(toLabel));
}
}
Vector<Pointf> DataSource::FFT(Getdatafun getdata, double tSample, bool frequency, int type, bool window) {
int numData = int(GetCount());
VectorXd timebuf(numData);
int num = 0;
for (int i = 0; i < numData; ++i) {
double data = Membercall(getdata)(i);
if (!IsNull(data)) {
timebuf[i] = Membercall(getdata)(i);
num++;
}
}
Vector<Pointf> res;
if (num < 3)
return res;
timebuf.resize(num);
double windowSum = 0;
if (window) {
for (int i = 0; i < numData; ++i) {
double windowDat = 0.54 - 0.46*cos(2*M_PI*i/numData);
windowSum += windowDat;
timebuf[i] *= windowDat; // Hamming window
}
} else
windowSum = numData;
VectorXcd freqbuf;
try {
Eigen::FFT<double> fft;
fft.SetFlag(fft.HalfSpectrum);
fft.fwd(freqbuf, timebuf);
} catch(...) {
return res;
}
if (frequency) {
for (int i = 0; i < int(freqbuf.size()); ++i) {
double xdata = i/(tSample*numData);
switch (type) {
case T_PHASE: res << Pointf(xdata, std::arg(freqbuf[i])); break;
case T_FFT: res << Pointf(xdata, 2*std::abs(freqbuf[i])/windowSum); break;
case T_PSD: res << Pointf(xdata, 2*sqr(std::abs(freqbuf[i]))/(windowSum/tSample));
}
}
} else {
for (int i = int(freqbuf.size()) - 1; i > 0; --i) {
double xdata = (tSample*numData)/i;
switch (type) {
case T_PHASE: res << Pointf(xdata, std::arg(freqbuf[i])); break;
case T_FFT: res << Pointf(xdata, 2*std::abs(freqbuf[i])/windowSum); break;
case T_PSD: res << Pointf(xdata, 2*sqr(std::abs(freqbuf[i]))/(windowSum/tSample));
}
}
}
return res;
}
void HIntegrand::CalculateOriginalIntegrand(const VectorXd &x,
VectorXcd &y) const {
complex_t Hband, Hpow = 1.;
y.resize(dim_out());
y.setZero();
getHband(x, Hband, SK, Hf);
for (int n = 0; n < N_order; ++n) {
Hpow *= Hband;
for (int i = 0; i < MSIZE; ++i)
y(MSIZE*n+i) = Hpow;
}
}
double GLMObjective::get_local_change(const VectorXd &old, int idx) {
VectorXd delta_beta = old - model_param.beta[idx];
VectorXd delta_Xb = X[idx] * delta_beta;
MatrixXd wXX(p, p);
for (int i = 0; i < p; i++)
for (int j = 0; j < p; j++)
wXX(i, j) = 0;
for (int i = 0; i < n; i++)
wXX += W[i] * X[idx].row(i).transpose() * X[idx].row(i);
VectorXcd eigenvalues = wXX.eigenvalues();
double max_eigen = 0;
for (int i = 0; i < eigenvalues.size(); i++) {
max_eigen = std::max(max_eigen, eigenvalues[i].real());
}
return max_eigen * (delta_beta.dot(delta_beta)) / (2 * n);
}
void EigsGen::eigenvalueSchur(const MatrixXd &Rm, VectorXcd &result)
{
int m = Rm.cols();
if(result.size() != m)
result.resize(m);
for(int i = 0; i < m; i++)
{
if(i == m - 1 || fabs(Rm(i + 1, i)) < 1e-16)
{
result[i] = std::complex<double>(Rm(i, i), 0);
} else {
result[i] = eigenvalue2x2(Rm(i, i), Rm(i, i + 1),
Rm(i + 1, i), Rm(i + 1, i + 1));
i++;
result[i] = conj(result[i - 1]);
}
}
}
VectorTypeHost eigenToCusp(const VectorXcd& psiEigen)
{
int length = psiEigen.size();
VectorTypeHost psiCusp(length, 0.0);
for (int i = 0; i < length; ++i)
psiCusp[i] = eigenToCusp(psiEigen[i]);
return psiCusp;
}
void GreenIntegrand::CalculateOriginalIntegrand(const VectorXd &x,
VectorXcd &y) const {
y.resize(dim_out());
complex_t Hband;
getHband(x, Hband, SK, H);
for (int L = 0; L < MSIZE; ++L) {
y(L) = 1. / (w + mu - Hband - SE(L));
}
}
void EigsGen::sortDesc(VectorXcd &values)
{
if(values.imag().isZero())
std::sort(values.data(), values.data() + values.size(),
compare_complex_real);
else
std::sort(values.data(), values.data() + values.size(),
compare_complex_mod);
}
PyObject* calc_Gavg(PyObject *pyw, const double &delta, const double &mu,
PyObject *pySE, PyObject *pyTB, const double &Hf, PyObject *py_bp,
PyObject *py_wf, const int nthreads) {
try {
if (nthreads > 0) omp_set_num_threads(nthreads);
MatrixXcd SE;
VectorXcd w;
VectorXd bp, wf;
VectorXd SlaterKosterCoeffs;
numpy::from_numpy(pySE, SE);
numpy::from_numpy(pyTB, SlaterKosterCoeffs);
numpy::from_numpy(py_bp, bp);
numpy::from_numpy(py_wf, wf);
numpy::from_numpy(pyw, w);
assert(w.size() == SE.rows());
double t = SlaterKosterCoeffs(0);
VectorXd xl(DIM), xh(DIM);
xl << -2*t;
xh << 2*t;
double BZ1 = 1.;
MatrixXcd result(SE.rows(), MSIZE*MSIZE);
VectorXcd tmp(MSIZE);
GreenIntegrand green_integrand(w, mu, SE, SlaterKosterCoeffs, Hf);
result.setZero();
for (int n = 0; n < w.size(); ++n) {
green_integrand.set_data(n);
tmp = md_int::Integrate(xl, xh, green_integrand, bp, wf);
for (int i = 0; i < MSIZE; ++i)
result(n, MSIZE*i + i) = tmp(i);
}
result /= BZ1;
return numpy::to_numpy(result);
} catch (const char *str) {
std::cerr << str << std::endl;
return Py_None;
}
}
void EigsGen::sortDescPair(VectorXcd &values, VectorXi &index)
{
int len = values.size();
if(len != index.size())
return;
std::vector<SortPair> v(len);
for(int i = 0; i < len; i++)
{
v[i].first = values[i];
v[i].second = index[i];
}
if(values.imag().isZero())
std::sort(v.begin(), v.end(), compare_pair<COMPREAL>);
else
std::sort(v.begin(), v.end(), compare_pair<COMPMOD>);
for(int i = 0; i < len; i++)
{
values[i] = v[i].first;
index[i] = v[i].second;
}
}
void getRealValues(std::vector<double> &realValues,
VectorXcd &complexValues,
double &a, double &b)
{
double threshold = 10;
threshold = pow(10, -20);
for (int i = 0; i < complexValues.size(); ++i)
{
double imagValue = fabs(complexValues(i).imag());
if(imagValue < threshold) {
if(a <= complexValues(i).real() && b >= complexValues(i).real()) {
realValues.push_back(complexValues(i).real());
}
}
}
std::sort(realValues.begin(), realValues.end());
}
VectorXcd _LC_EXPs<M>::DAtR(const VectorXcd& rs) const {
int num_rs(rs.size());
VectorXcd ys = VectorXcd::Zero(num_rs);
for(int i_r = 0; i_r < num_rs; i_r++) {
dcomplex r(rs[i_r]);
dcomplex y(0);
for(int j_b = 0; j_b < this->size(); j_b++) {
dcomplex c(this->cs[j_b]);
int n(this->ns[j_b]);
dcomplex z(this->zs[j_b]);
y += Exp_DAtR<M>(r, c, n, z);
}
ys[i_r] = y;
}
return ys;
}
VectorXcd _LC_EXPs<M>::AtR(const VectorXcd& rs) const {
int num_rs(rs.size());
VectorXcd ys = VectorXcd::Zero(num_rs);
for(int i_r = 0; i_r < num_rs; i_r++) {
dcomplex r(rs[i_r]);
dcomplex rr(pow(r, M));
dcomplex y(0);
for(int j_b = 0; j_b < this->size(); j_b++) {
dcomplex c(this->cs[j_b]);
int n(this->ns[j_b]);
dcomplex z(this->zs[j_b]);
y += c * pow(r, n) * exp(-z * rr);
}
ys[i_r] = y;
}
return ys;
}
int main() {
// The eigen approach
ArrayXd n = ArrayXd::LinSpaced(N+1,0,N);
double multiplier = M_PI/N;
Array<double, 1, N+1> nT = n.transpose();
ArrayXd x = - cos(multiplier*n);
ArrayXd xsub = x.middleRows(1, N-1);
ArrayXd ysub = (x1-x0)/2*xsub + (x1+x0)/2;
ArrayXXd T = cos((acos(x).matrix()*nT.matrix()).array());
ArrayXXd Tsub = cos((acos(xsub).matrix()*nT.matrix()).array());
ArrayXd sqinx = 1/sqrt(1-xsub*xsub);
MatrixXd inv1x2 = (sqinx).matrix().asDiagonal();
// Can't use the following to test elements of inv1x2
// std::cout << inv1x2(0,0) << "\n";
MatrixXd Usub = inv1x2 * sin(((acos(xsub).matrix())*nT.matrix()).array()).matrix();
MatrixXd dTsub = Usub*(n.matrix().asDiagonal());
MatrixXd d2Tsub = ((sqinx*sqinx).matrix().asDiagonal())*((xsub.matrix().asDiagonal()) * (dTsub.matrix()) - (Tsub.matrix()) * ((n*n).matrix().asDiagonal()));
MatrixXd d2T(N+1, N+1);
RowVectorXd a = (pow((-1),nT))*(nT*nT+1)*(nT*nT)/3;
RowVectorXd b = (nT*nT+1)*(nT*nT)/3;
d2T.middleRows(1,N-1) = d2Tsub;
d2T.row(0) = a;
d2T.row(N) = b;
MatrixXd D2 = d2T.matrix() * ((T.matrix()).inverse());
MatrixXd E2 = D2.middleRows(1,N-1).middleCols(1,N-1);
MatrixXd Y = ysub.matrix().asDiagonal();
MatrixXd H = - (4 / ((x1-x0)*(x1-x0))) * E2 + k*Y;
Eigen::EigenSolver<Eigen::MatrixXd> HE(H);
VectorXcd D = HE.eigenvalues();
MatrixXcd V = HE.eigenvectors();
std::cout << HE.info() << std::endl;
// Open ofstream
ofstream Dfile;
Dfile.open("D-output.txt");
ofstream Vfile;
Vfile.open("V-output.txt");
ofstream V544file;
V544file.open("V544-output.txt");
Dfile.precision(15);
Dfile << D.real() << "\n";
Vfile.precision(15);
Vfile << V.real() << "\n";
V544file.precision(15);
for(int i = 1; i<N-1; i++)
{
V544file << ysub[i-1];
V544file << " " << V.col(544).row(i-1).real() << "\n";
}
Dfile.close();
Vfile.close();
V544file.close();
system("gnuplot -p plot.gp");
system("rsvg-convert -w 2000 -o V544-plot.png V544-plot.svg");
}
void EigsGen::transformEigenvalues(VectorXcd &evals)
{
// Only transform eigenvalues when using real sigma
if(workmode == 3 && fabs(op->getsigmai()) < 1e-16)
evals = 1.0 / evals.array() + op->getsigmar();
}
void calc_pseudogap_selfenergy(double kx,double ky, VectorXcd &Epg, double &norm){
MPI_Comm_rank(MPI_COMM_WORLD,&myrank);
int namelen;
char processor_name[MPI_MAX_PROCESSOR_NAME];
MPI_Get_processor_name(processor_name, &namelen);
cout << "hello rank " << myrank << " " << processor_name << endl;
VectorXcd one = VectorXcd::Ones(2*Nf-1);
VectorXd wd = VectorXd::LinSpaced(2*Nf-1,wLower,wUpper);
VectorXcd w = VectorXcd::Zero(2*Nf-1);
for(int i=0; i<2*Nf-1; i++)
w[i]=wd[i];
int Nk = Nkpoints;
double totalN = pow(2*Nk,2)*(2*Nkz);
if (Nkz==1)
totalN = pow(2*Nk,2);
double pgap = PseudoGap(kx,ky);
complex<double> i1(0.0,1.0);
double qx,qy,qz,px,py,pofq,Energy;
for (int q1=-Nk+myrank; q1<Nk; q1+=numprocs){ //BZ momentum loop
qx = M_PI*q1/Nk;
for(int q2=-Nk; q2<Nk; q2++){
qy = M_PI*q2/Nk;
if (Nkz==1){
px = kx - qx;
py = ky - qy;
Energy = E(px,py);
pofq = 1.0/M_PI*gammacdw/(pow(gammacdw,2)+pow(qx-Q,2)+pow(qy,2)) + 1.0/M_PI*gammacdw/(pow(gammacdw,2)+pow(qx+Q,2)+pow(qy,2)) + 1.0/M_PI*gammacdw/(pow(gammacdw,2)+pow(qx,2)+pow(qy-Q,2)) + 1.0/M_PI*gammacdw/(pow(gammacdw,2)+pow(qx,2)+pow(qy+Q,2));
//pofq = 1.0/M_PI*gammacdw/(pow(gammacdw,2)+pow(qx-Q,2)+pow(qy,2)) + 1.0/M_PI*gammacdw/(pow(gammacdw,2)+pow(qx+Q,2)+pow(qy,2));
Epg += pgap*pofq*one.cwiseQuotient(w-one*E(px,py)+i1*gammae*one)/totalN;
norm += pofq/totalN;
}
else{
for(int q3=-Nkz; q3<Nkz; q3++){
qz = M_PI*q3/Nkz;
px = kx - qx;
py = ky - qy;
pofq = 1.0/M_PI*gammacdw/(pow(gammacdw,2)+pow(qx-Q,2)+pow(qy,2)) + 1.0/M_PI*gammacdw/(pow(gammacdw,2)+pow(qx+Q,2)+pow(qy,2)) + 1.0/M_PI*gammacdw/(pow(gammacdw,2)+pow(qx,2)+pow(qy-Q,2)) + 1.0/M_PI*gammacdw/(pow(gammacdw,2)+pow(qx,2)+pow(qy+Q,2));
//pofq = 1.0/M_PI*gammacdw/(pow(gammacdw,2)+pow(qx-Q,2)+pow(qy,2)) + 1.0/M_PI*gammacdw/(pow(gammacdw,2)+pow(qx+Q,2)+pow(qy,2));
Epg += pgap*pofq*one.cwiseQuotient(w-one*(E(px,py)-2*tz*cos(qz))+i1*gammae*one)/totalN;
norm += pofq/totalN;
}
}
}
} // end BZ loop
}
int main(int argc, char* argv[]){
MPI_Init(&argc, &argv);
MPI_Comm_size(MPI_COMM_WORLD,&numprocs);
MPI_Comm_rank(MPI_COMM_WORLD,&myrank);
if(myrank==0){
cout << "starting program" << endl;
cout << "numprocs" << numprocs << endl;
}
time_t tStart = time(NULL);
kx = Q/2;
ky = 1.94643;
Nkpoints = 300;
wLower = E(0,M_PI);
wUpper = 0;
Nf = 50;
VectorXcd Epg = VectorXcd::Zero(2*Nf-1);
double norm;
double norm_private;
VectorXcd one = VectorXcd::Ones(2*Nf-1);
VectorXd wd = VectorXd::LinSpaced(2*Nf-1,wLower,wUpper);
VectorXcd w = VectorXcd::Zero(2*Nf-1);
for(int i=0; i<2*Nf-1; i++)
w[i]=wd[i];
while(true){
if (myrank==0){
cout << "Enter new D0_pg \n" << endl;
cin >> D0_pg;
D0_pg /= tval;
}
MPI_Bcast(&D0_pg, 1, MPI_DOUBLE, 0, MPI_COMM_WORLD);
if (D0_pg == 0){
MPI_Finalize();
return 0;
}
MPI_Barrier(MPI_COMM_WORLD);
if (1==1){ //pseudogap
Epg = VectorXcd::Zero(2*Nf-1);
norm = 0;
norm_private = 0;
if(myrank==0)
cout << endl << "Calculating pseudogap selfenergies..." << endl;
MPI_Barrier(MPI_COMM_WORLD);
//calc_phonon_selfenergy(kx, ky, Eph_private, Ephm_private);
calc_pseudogap_selfenergy(kx,ky,Epg,norm_private);
//set up double[] for reduction
complex<double> Epg_private_array[2*Nf-1];
complex<double> Epg_array[2*Nf-1];
for(int i=0;i<2*Nf-1;i++){
Epg_private_array[i] = Epg[i];
}
MPI_Reduce(&Epg_private_array, &Epg_array, 2*Nf-1, MPI_DOUBLE_COMPLEX, MPI_SUM, 0, MPI_COMM_WORLD);
MPI_Reduce(&norm_private, &norm, 1, MPI_DOUBLE, MPI_SUM, 0, MPI_COMM_WORLD);
if(myrank==0)
cout << "the norm is: " << norm << endl;
if (myrank==0){
for(int i=0;i<2*Nf-1;i++){
Epg[i] = Epg_array[i];
}
Epg /= norm;
cout<<"Time taken "<< time(NULL)-tStart<<endl;
ofstream myfile;
myfile.open("Epg.dat");
for (int i=0; i<2*Nf-1; i++){
myfile << real(Epg[i]) << " " << imag(Epg[i]) << endl;
}
myfile.close();
VectorXcd G = VectorXcd::Zero(2*Nf-1);
//VectorXd A = VectorXd::Zero(2*Nf-1);
double A[2*Nf-1];
G = one.cwiseQuotient(w + (1j*gammae + E(kx,ky))*one - Epg);
///A = -imag(G);
for (int i=0;i<2*Nf-1;i++){
A[i] = -imag(G[i]);
cout << A[i] << endl;
}
double* biggest;
double* first = A;
double* last = first + 2*Nf-1;
biggest = max_element(first,last);
cout << "freq at max " << w[distance(first,biggest)]*tval << endl;
//double maxIndex;
//G.maxCoeff(&maxIndex);
//cout << maxIndex << endl;
cout << endl << "Done With Program" << endl;
}
}
}