void EigsGen::findMatchedIndex(const Eigen::VectorXcd &target,
const Eigen::VectorXcd &collection,
Eigen::VectorXi &result)
{
int nfound = 0;
int maxn = target.size();
if(result.size() < maxn)
result.resize(maxn);
for(int i = 0; i < collection.size(); i++)
{
int j;
for(j = 0; j < maxn; j++)
{
if(abs(collection[i] - target[j]) < 1e-8 * abs(target[j]))
break;
}
if(j < maxn)
{
result[nfound] = i;
nfound++;
if(collection[i].imag() != 0)
{
i++;
result[nfound] = i;
nfound++;
}
}
if(nfound >= maxn) break;
}
if(result.size() > nfound)
result.conservativeResize(nfound);
}
//Main-Function
int main () {
double xiMax = 10;
double xiMin = -10;
double deltaXi = 0.1;
double deltaT = 0.05;
double mittelWert = 0, mittelWert2 = 0;
double impuls = 0, impuls2 = 0;
int cn = floor(10./deltaT+0.5);
int iN = 0;
std::complex<double> c_i = (0,1);
Eigen::MatrixXcd Sh = S_H(deltaT, &H, deltaXi, xiMax, xiMin);
Eigen::VectorXcd xi = init(xiMax, xiMin, deltaXi);
Eigen::VectorXcd xi_n = xi;
Eigen::VectorXcd xi_temp;
//Dateistreams für geforderte Ausgabe-Plots
std::ofstream datei("A1d_Normierung.dat");
std::ofstream datei2("A1f.dat");
//Anwenden des Zeitentwicklungsoperators bis t=10
for (int i = 0; i < cn; i++) {
xi_n = Sh*xi_n;
datei << i*deltaT << " " << Norm(xi_n) << std::endl;
//Animationssequenz
//if (i%2 == 0) {
// SchreibeZustand(xi_n, "A1d_Animation_"+convertInt(i/2));
//}
//Mittelwert des Ortes und des Impulses
for (int j = 0; j < xi.size(); j++) {
iN = j - floor(xi.size()/2);
mittelWert += iN*deltaXi*abs(xi_n(j))*abs(xi_n(j));
mittelWert2 += (iN*deltaXi)*(iN*deltaXi)*abs(xi_n(j))*abs(xi_n(j));
impuls += abs(xi_n(j)*(-c_i)*Ableitung(xi_n, j, deltaXi));
impuls2 += abs(xi_n(j)*(-1.)*Ableitung2(xi_n, j, deltaXi));
}
datei2 << i*deltaT << " " << mittelWert << " " << (mittelWert2 - mittelWert*mittelWert) << " " << impuls << " " << impuls2 << std::endl;
mittelWert = 0;
mittelWert2 = 0;
impuls = 0;
impuls2 = 0;
}
datei.close();
datei2.close();
SchreibeZustand(xi_n, "A1d_Zustand");
return 0;
}
// -----------------------------------------------------------------------------
// -----------------------------------------------------------------------------
void LapH::OperatorsForMesons::build_vdaggerv(const std::string& filename) {
clock_t t2 = clock();
const size_t dim_row = 3*Lx*Ly*Lz;
const size_t id_unity = operator_lookuptable.index_of_unity;
// resizing each matrix in vdaggerv
// TODO: check if it is better to use for_each and resize instead of std::fill
std::fill(vdaggerv.origin(), vdaggerv.origin() + vdaggerv.num_elements(),
Eigen::MatrixXcd::Zero(nb_ev, nb_ev));
#pragma omp parallel
{
Eigen::VectorXcd mom = Eigen::VectorXcd::Zero(dim_row);
LapH::EigenVector V_t(1, dim_row, nb_ev);// each thread needs its own copy
#pragma omp for schedule(dynamic)
for(size_t t = 0; t < Lt; ++t){
// creating full filename for eigenvectors and reading them in
char inter_name[200];
sprintf(inter_name, "%s%03d", filename.c_str(), (int) t);
//avoid reading eigenvectors for now, since no displacement or momentum is
//used
//V_t.read_eigen_vector(inter_name, 0, 0); // reading eigenvectors
// VdaggerV is independent of the gamma structure and momenta connected by
// sign flip are related by adjoining VdaggerV. Thus the expensive
// calculation must only be performed for a subset of quantum numbers given
// in op_VdaggerV.
for(const auto& op : operator_lookuptable.vdaggerv_lookup){
// For zero momentum and displacement VdaggerV is the unit matrix, thus
// the calculation is not performed
if(op.id != id_unity){
// momentum vector contains exp(-i p x). Divisor 3 for colour index.
// All three colours on same lattice site get the same momentum.
for(size_t x = 0; x < dim_row; ++x) {
mom(x) = momentum[op.id][x/3];
}
vdaggerv[op.id][t] = V_t[0].adjoint() * mom.asDiagonal() * V_t[0];
}
else // zero momentum
vdaggerv[op.id][t] = Eigen::MatrixXcd::Identity(nb_ev, nb_ev);
}
} // loop over time
}// pragma omp parallel ends here
t2 = clock() - t2;
std::cout << std::setprecision(1) << "\t\t\tSUCCESS - " << std::fixed
<< ((float) t2)/CLOCKS_PER_SEC << " seconds" << std::endl;
is_vdaggerv_set = true;
}
//Norm eines Zustands
double Norm(Eigen::VectorXcd xi) {
double summe = 0;
int n_max = xi.size();
for (int i = 0; i < n_max; i++) {
summe += abs(xi(i))*abs(xi(i));
}
return summe;
}
//Zustandsvektor in Datei schreiben
void SchreibeZustand(Eigen::VectorXcd xi, std::string name) {
int n_max = xi.size();
std::ofstream datei(name + ".dat");
for (int i = 0; i < n_max; i++) {
datei << (i - floor(n_max/2)) << " " << abs(xi(i))*abs(xi(i)) << std::endl;
}
datei.close();
}
// Calculates U_mu^dagger(x-\hat{mu})V(x-\hat{\mu})
Eigen::MatrixXcd GaugeField::backward_uv(const Eigen::VectorXcd &v,
const ssize_t t,
const int spatial_ind,
const int direction) const {
int down_ind = idown[spatial_ind][direction];
return (tslices.at(t))[down_ind][direction].adjoint() * v.segment(3 * down_ind, 3);
}
// Calculates U_mu(x)V(x+\hat{\mu})
Eigen::MatrixXcd GaugeField::forward_uv(const Eigen::VectorXcd &v,
const ssize_t t,
const int spatial_ind,
const int direction) const {
int up_ind = iup[spatial_ind][direction];
return (tslices.at(t))[spatial_ind][direction] * v.segment(3 * up_ind, 3);
}
//Ableitung der Wellenfunktion an der Stelle n
std::complex<double> Ableitung(Eigen::VectorXcd xi, int n, double deltaXi) {
int laenge = xi.size();
if (n == 0) {
return (xi(1)-xi(0))/(deltaXi);
} else if (n == (laenge-1)) {
return (xi(laenge-1) - xi(laenge-2))/(deltaXi);
} else {
return (xi(n+1)-xi(n-1))/(2.*deltaXi);
}
}
unsigned int Model::check_feedback_matrix(Eigen::MatrixXd &S) {
Eigen::VectorXcd eigenvalues = S.eigenvalues();
Eigen::VectorXd real = eigenvalues.real();
Eigen::VectorXd imag = eigenvalues.imag();
double magnitude, max_magnitude = 0;
for (unsigned int i = 0; i < n_alternatives; i++) {
magnitude = sqrt(real(i) * real(i) + imag(i) * imag(i));
if (magnitude > max_magnitude) {
max_magnitude = magnitude;
}
}
// unsigned int res = 1;
unsigned int res = 0;
if (max_magnitude < 1) {
res = 0;
}
return res;
}
// partial reorthogonalization
double EigenTriangle::solve(int maxIter, double tol)
{
int n = graph -> VertexCount();
srand(time(0));
if (maxIter > n)
maxIter = n;
double na = adjMatrix.norm();
double phi = tol * na;
double delta = tol * sqrt(na);
vector<Triplet<double> > omega_vector;
//MatrixXd omega = MatrixXd::Zero(n + 2, n + 2);
for (int i = 0; i < n + 2; i ++)
{
//omega(i, i - 1) = phi;
if (i > 0)
omega_vector.push_back(Triplet<double>(i, i - 1, phi));
omega_vector.push_back(Triplet<double>(i, i, 1));
}
omega.resize(n + 2, n + 2);
omega.setFromTriplets(omega_vector.begin(), omega_vector.end());
//std::cout << omega << std::endl;
vector<SparseVector<double> > v;
//v.push_back(SparseVector::Random(n));
SparseVector<double> firstV(n);
for (int i = 0; i < 100; i ++)
firstV.coeffRef(i % n) = i;
v.push_back(firstV);
v[0] /= v[0].norm();
VectorXd alpha(n);
VectorXd beta(n + 1);
beta[0] = 0;
SparseVector<double> w;
bool flag = false;
int num = 0; // reorthogonalization times
int last = -1;
for (int i = 0; i < maxIter; i ++)
{
if ((i + 1) * 100 / maxIter > last)
{
last = (i + 1) * 100 / maxIter;
std::cout << "\r" << "[EigenTriangle] Processing " << last << "% ..." << std::flush;
}
//printf("== Iter %d ===\n", i);
w = adjMatrix * v[i];
alpha.coeffRef(i) = w.dot(v[i]);
if (i == maxIter - 1)
break;
w -= alpha[i] * v[i];
if (i > 0)
w -= beta[i] * v[i - 1];
beta[i + 1] = w.norm();
v.push_back(w / beta[i + 1]);
if (flag)
{
flag = false;
for (int j = 0; j <= i; j ++)
v[i + 1] -= v[j].dot(v[i + 1]) * v[j];
for (int j = 0; j <= i; j ++)
omega.coeffRef(i + 1, j) = phi;
//for (int j = 0; j <= i; j ++)
// printf("%.5lf\n", v[i + 1].dot(v[j]));
}
else
{
omega.coeffRef(i + 1, 0) = 0.0;
if (i > 0)
{
omega.coeffRef(i + 1, 0) = 1.0 / beta(i) * ((alpha(0) - alpha(i)) * omega.coeffRef(i, 0) - beta(i - 1) * omega.coeffRef(i - 1, 0)) + delta;
}
for (int j = 1; j <= i; j ++)
{
omega.coeffRef(i + 1, j) = 1.0 / beta(i) * (beta(j) * omega.coeffRef(i, j + 1) + (alpha(j) - alpha(i)) * omega.coeffRef(i, j) - beta(j - 1) * omega.coeffRef(i, j - 1) - beta(i - 1) * omega.coeffRef(i - 1, j)) + delta;
}
}
double mx = 0.0;
for (int j = 0; j <= i; j ++)
if (mx < fabs(omega.coeffRef(i + 1, j)))
mx = fabs(omega.coeffRef(i + 1, j));
if (mx > sqrt(tol))
{
for (int j = 0; j <= i; j ++)
omega.coeffRef(i + 1, j) = phi;
num ++;
for (int j = 0; j <= i; j ++)
v[i + 1] -= v[i + 1].dot(v[j]) * v[j];
flag = true;
}
}
printf("\n");
int k = maxIter;
MatrixXd T = MatrixXd::Zero(k, k);
for (int i = 0; i < k; i ++)
{
T(i, i) = alpha[i];
if (i < k - 1)
T(i, i + 1) = beta[i + 1];
if (i > 0)
T(i, i - 1) = beta[i];
}
//std::cout << T << std::endl;
Eigen::EigenSolver<MatrixXd> eigenSolver;
eigenSolver.compute(T, false);
Eigen::VectorXcd eigens = eigenSolver.eigenvalues();
double res = 0;
for (int i = 0; i < eigens.size(); i ++)
{
std::complex<double> tmp = eigens[i];
res += pow(tmp.real(), 3) / 6;
std::cout << i << ": " << tmp << std::endl;
}
//res /= 6;
return res;
}
// full reorthogonalization
double EigenTriangle::solve(int maxIter)
{
int n = graph -> VertexCount();
srand(time(0));
// check if rows == cols()
if (maxIter > n)
maxIter = n;
vector<VectorXd> v;
v.push_back(VectorXd::Random(n));
v[0] = v[0] / v[0].norm();
VectorXd alpha(n);
VectorXd beta(n + 1);
beta[0] = 0;
VectorXd w;
int last = 0;
printf("%d\n", maxIter);
for (int i = 0; i < maxIter; i ++)
{
if (i * 100 / maxIter > last + 10 || i == maxIter - 1)
{
last = (i + 1) * 100 / maxIter;
std::cout << "\r" << "[EigenTriangle] Processing " << last << "% ..." << std::flush;
}
w = adjMatrix * v[i];
alpha[i] = w.dot(v[i]);
if (i == maxIter - 1)
break;
w -= alpha[i] * v[i];
if (i > 0)
w -= beta[i] * v[i - 1];
beta[i + 1] = w.norm();
v.push_back(w / beta[i + 1]);
for (int j = 0; j <= i; j ++)
{
v[i + 1] = v[i + 1] - v[i + 1].dot(v[j]) * v[j];
}
}
printf("\n");
int k = maxIter;
MatrixXd T = MatrixXd::Zero(k, k);
for (int i = 0; i < k; i ++)
{
T(i, i) = alpha[i];
if (i < k - 1)
T(i, i + 1) = beta[i + 1];
if (i > 0)
T(i, i - 1) = beta[i];
}
//std::cout << T << std::endl;
Eigen::EigenSolver<MatrixXd> eigenSolver;
eigenSolver.compute(T, /* computeEigenvectors = */ false);
Eigen::VectorXcd eigens = eigenSolver.eigenvalues();
double res = 0;
for (int i = 0; i < eigens.size(); i ++)
{
std::complex<double> tmp = eigens[i];
res += pow(tmp.real(), 3);
printf("%.5lf\n", tmp.real());
}
res /= 6;
return res;
}
inline int size_zeta() const { return zeta_iz.rows(); }
void propa_2d()
{
trace.beginBlock("2d propagation");
typedef DiscreteExteriorCalculus<2, 2, EigenLinearAlgebraBackend> Calculus;
typedef DiscreteExteriorCalculusFactory<EigenLinearAlgebraBackend> CalculusFactory;
{
trace.beginBlock("solving time dependent equation");
const Calculus::Scalar cc = 8; // px/s
trace.info() << "cc = " << cc << endl;
const Z2i::Domain domain(Z2i::Point(0,0), Z2i::Point(29,29));
const Calculus calculus = CalculusFactory::createFromDigitalSet(generateDiskSet(domain), false);
//! [time_laplace]
const Calculus::DualIdentity0 laplace = calculus.laplace<DUAL>() + 1e-8 * calculus.identity<0, DUAL>();
//! [time_laplace]
trace.info() << "laplace = " << laplace << endl;
trace.beginBlock("finding eigen pairs");
//! [time_eigen]
typedef Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> EigenSolverMatrix;
const EigenSolverMatrix eigen_solver(laplace.myContainer);
const Eigen::VectorXd eigen_values = eigen_solver.eigenvalues();
const Eigen::MatrixXd eigen_vectors = eigen_solver.eigenvectors();
//! [time_eigen]
trace.info() << "eigen_values_range = " << eigen_values.minCoeff() << "/" << eigen_values.maxCoeff() << endl;
trace.endBlock();
//! [time_omega]
const Eigen::VectorXd angular_frequencies = cc * eigen_values.array().sqrt();
//! [time_omega]
Eigen::VectorXcd initial_wave = Eigen::VectorXcd::Zero(calculus.kFormLength(0, DUAL));
//set_initial_phase_null(calculus, initial_wave);
set_initial_phase_dir_yy(calculus, initial_wave);
{
Board2D board;
board << domain;
board << CustomStyle("KForm", new KFormStyle2D(-1, 1));
board << Calculus::DualForm0(calculus, initial_wave.real());
board.saveSVG("propagation_time_wave_initial_coarse.svg");
}
//! [time_init_proj]
Eigen::VectorXcd initial_projections = eigen_vectors.transpose() * initial_wave;
//! [time_init_proj]
// low pass
//! [time_low_pass]
const Calculus::Scalar lambda_cutoff = 4.5;
const Calculus::Scalar angular_frequency_cutoff = 2*M_PI * cc / lambda_cutoff;
int cutted = 0;
for (int kk=0; kk<initial_projections.rows(); kk++)
{
const Calculus::Scalar angular_frequency = angular_frequencies(kk);
if (angular_frequency < angular_frequency_cutoff) continue;
initial_projections(kk) = 0;
cutted ++;
}
//! [time_low_pass]
trace.info() << "cutted = " << cutted << "/" << initial_projections.rows() << endl;
{
const Eigen::VectorXcd wave = eigen_vectors * initial_projections;
Board2D board;
board << domain;
board << CustomStyle("KForm", new KFormStyle2D(-1, 1));
board << Calculus::DualForm0(calculus, wave.real());
board.saveSVG("propagation_time_wave_initial_smoothed.svg");
}
const int kk_max = 60;
trace.progressBar(0,kk_max);
for (int kk=0; kk<kk_max; kk++)
{
//! [time_solve_time]
const Calculus::Scalar time = kk/20.;
const Eigen::VectorXcd current_projections = (angular_frequencies * std::complex<double>(0,time)).array().exp() * initial_projections.array();
const Eigen::VectorXcd current_wave = eigen_vectors * current_projections;
//! [time_solve_time]
std::stringstream ss;
ss << "propagation_time_wave_solution_" << std::setfill('0') << std::setw(3) << kk << ".svg";
Board2D board;
board << domain;
board << CustomStyle("KForm", new KFormStyle2D(-1, 1));
board << Calculus::DualForm0(calculus, current_wave.real());
board.saveSVG(ss.str().c_str());
trace.progressBar(kk+1,kk_max);
}
trace.info() << endl;
trace.endBlock();
}
{
trace.beginBlock("forced oscillations");
const Z2i::Domain domain(Z2i::Point(0,0), Z2i::Point(50,50));
const Calculus calculus = CalculusFactory::createFromDigitalSet(generateDiskSet(domain), false);
const Calculus::DualIdentity0 laplace = calculus.laplace<DUAL>();
trace.info() << "laplace = " << laplace << endl;
trace.beginBlock("finding eigen pairs");
typedef Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> EigenSolverMatrix;
const EigenSolverMatrix eigen_solver(laplace.myContainer);
const Eigen::VectorXd laplace_eigen_values = eigen_solver.eigenvalues();
const Eigen::MatrixXd laplace_eigen_vectors = eigen_solver.eigenvectors();
trace.info() << "eigen_values_range = " << laplace_eigen_values.minCoeff() << "/" << laplace_eigen_values.maxCoeff() << endl;
trace.endBlock();
Calculus::DualForm0 concentration(calculus);
{
const Z2i::Point point(25,25);
const Calculus::Cell cell = calculus.myKSpace.uSpel(point);
const Calculus::Index index = calculus.getCellIndex(cell);
concentration.myContainer(index) = 1;
}
{
Board2D board;
board << domain;
board << concentration;
board.saveSVG("propagation_forced_concentration.svg");
}
for (int ll=0; ll<6; ll++)
{
//! [forced_lambda]
const Calculus::Scalar lambda = 4*20.75/(1+2*ll);
//! [forced_lambda]
trace.info() << "lambda = " << lambda << endl;
//! [forced_dalembert_eigen]
const Eigen::VectorXd dalembert_eigen_values = (laplace_eigen_values.array() - (2*M_PI/lambda)*(2*M_PI/lambda)).array().inverse();
const Eigen::MatrixXd concentration_to_wave = laplace_eigen_vectors * dalembert_eigen_values.asDiagonal() * laplace_eigen_vectors.transpose();
//! [forced_dalembert_eigen]
//! [forced_wave]
Calculus::DualForm0 wave(calculus, concentration_to_wave * concentration.myContainer);
//! [forced_wave]
wave.myContainer /= wave.myContainer(calculus.getCellIndex(calculus.myKSpace.uSpel(Z2i::Point(25,25))));
{
trace.info() << "saving samples" << endl;
const Calculus::Properties properties = calculus.getProperties();
{
std::stringstream ss;
ss << "propagation_forced_samples_hv_" << ll << ".dat";
std::ofstream handle(ss.str().c_str());
for (int kk=0; kk<=50; kk++)
{
const Z2i::Point point_horizontal(kk,25);
const Z2i::Point point_vertical(25,kk);
const Calculus::Scalar xx = 2 * (kk/50. - .5);
handle << xx << " ";
handle << sample_dual_0_form<Calculus>(properties, wave, point_horizontal) << " ";
handle << sample_dual_0_form<Calculus>(properties, wave, point_vertical) << endl;
}
}
{
std::stringstream ss;
ss << "propagation_forced_samples_diag_" << ll << ".dat";
std::ofstream handle(ss.str().c_str());
for (int kk=0; kk<=50; kk++)
{
const Z2i::Point point_diag_pos(kk,kk);
const Z2i::Point point_diag_neg(kk,50-kk);
const Calculus::Scalar xx = 2 * sqrt(2) * (kk/50. - .5);
handle << xx << " ";
handle << sample_dual_0_form<Calculus>(properties, wave, point_diag_pos) << " ";
handle << sample_dual_0_form<Calculus>(properties, wave, point_diag_neg) << endl;
}
}
}
{
std::stringstream ss;
ss << "propagation_forced_wave_" << ll << ".svg";
Board2D board;
board << domain;
board << CustomStyle("KForm", new KFormStyle2D(-.5, 1));
board << wave;
board.saveSVG(ss.str().c_str());
}
}
trace.endBlock();
}
trace.endBlock();
}
// -----------------------------------------------------------------------------
// -----------------------------------------------------------------------------
void LapH::OperatorsForMesons::build_vdaggerv(const std::string& filename,
const int config) {
clock_t t2 = clock();
const size_t dim_row = 3*Lx*Ly*Lz;
const int id_unity = operator_lookuptable.index_of_unity;
// prepare full path for writing
char dummy_path[200];
sprintf(dummy_path, "/%s/cnfg%04d/", path_vdaggerv.c_str(), config);
const std::string full_path(dummy_path);
// check if directory exists
if(handling_vdaggerv == "write" && access(full_path.c_str(), 0 ) != 0) {
std::cout << "\tdirectory " << full_path.c_str()
<< " does not exist and will be created";
boost::filesystem::path dir(full_path.c_str());
if(!boost::filesystem::create_directories(dir))
std::cout << "\tSuccess" << std::endl;
else
std::cout << "\tFailure" << std::endl;
}
// resizing each matrix in vdaggerv
// TODO: check if it is better to use for_each and resize instead of std::fill
std::fill(vdaggerv.origin(), vdaggerv.origin() + vdaggerv.num_elements(),
Eigen::MatrixXcd::Zero(nb_ev, nb_ev));
#pragma omp parallel
{
Eigen::VectorXcd mom = Eigen::VectorXcd::Zero(dim_row);
LapH::EigenVector V_t(1, dim_row, nb_ev);// each thread needs its own copy
#pragma omp for schedule(dynamic)
for(size_t t = 0; t < Lt; ++t){
// creating full filename for eigenvectors and reading them in
if(!(operator_lookuptable.vdaggerv_lookup.size() == 1 &&
operator_lookuptable.vdaggerv_lookup[0].id == id_unity)){
char inter_name[200];
sprintf(inter_name, "%s%03d", filename.c_str(), (int) t);
V_t.read_eigen_vector(inter_name, 0, 0); // reading eigenvectors
}
// VdaggerV is independent of the gamma structure and momenta connected by
// sign flip are related by adjoining VdaggerV. Thus the expensive
// calculation must only be performed for a subset of quantum numbers given
// in op_VdaggerV.
for(const auto& op : operator_lookuptable.vdaggerv_lookup){
// For zero momentum and displacement VdaggerV is the unit matrix, thus
// the calculation is not performed
if(op.id != id_unity){
// momentum vector contains exp(-i p x). Divisor 3 for colour index.
// All three colours on same lattice site get the same momentum.
for(size_t x = 0; x < dim_row; ++x) {
mom(x) = momentum[op.id][x/3];
}
vdaggerv[op.id][t] = V_t[0].adjoint() * mom.asDiagonal() * V_t[0];
// writing vdaggerv to disk
if(handling_vdaggerv == "write"){
char dummy2[200];
sprintf(dummy2, "operators.%04d.p_", config);
std::string dummy = std::string(dummy2) +
std::to_string(op.momentum[0]) +
std::to_string(op.momentum[1]) +
std::to_string(op.momentum[2]);
char outfile[200];
sprintf(outfile, "%s_.t_%03d", dummy.c_str(), (int) t);
write_vdaggerv(full_path, std::string(outfile), vdaggerv[op.id][t]);
}
}
else // zero momentum
vdaggerv[op.id][t] = Eigen::MatrixXcd::Identity(nb_ev, nb_ev);
}
} // loop over time
}// pragma omp parallel ends here
t2 = clock() - t2;
std::cout << std::setprecision(1) << "\t\t\tSUCCESS - " << std::fixed
<< ((float) t2)/CLOCKS_PER_SEC << " seconds" << std::endl;
is_vdaggerv_set = true;
}