/*
* FUNCTION
* Name: entropy_of_state
* Description: Calculate the Von Neumann entropy of state 'rho'
*
*/
double entropy_of_state ( const gsl_vector* rho )
{
double entr = 0 ;
/* Finding the eigenvalues */
gsl_eigen_herm_workspace* rho_ei = gsl_eigen_herm_alloc(2);
gsl_matrix_complex* dens = gsl_matrix_complex_calloc (2,2);
gsl_matrix_complex_set (dens, 0, 0, gsl_complex_rect(1+VECTOR(rho, 3),0));
gsl_matrix_complex_set (dens,0,1,gsl_complex_rect(VECTOR(rho,1),-VECTOR(rho,2)));
gsl_matrix_complex_set (dens,1,0,gsl_complex_rect(VECTOR(rho,1),VECTOR(rho,2)));
gsl_matrix_complex_set (dens,1,1,gsl_complex_rect(1-VECTOR(rho,3),0));
gsl_matrix_complex_scale (dens, gsl_complex_rect(0.5,0));
gsl_vector* eigenvalues = gsl_vector_calloc(2) ;
gsl_eigen_herm (dens, eigenvalues, rho_ei) ;
/* Calculating entropy */
double norm = gsl_hypot3( VECTOR(rho,1), VECTOR(rho,2), VECTOR(rho,3) ) ;
if ( gsl_fcmp(norm, 1, 1e-9) > 0 )
entr = 0 ;
else
entr = - (VECTOR(eigenvalues,0)*gsl_sf_log(VECTOR(eigenvalues,0)) +
VECTOR(eigenvalues,1)*gsl_sf_log(VECTOR(eigenvalues,1))) ;
return (entr);
} /* ----- end of function entropy_of_state ----- */
lls_complex_workspace *
lls_complex_alloc(const size_t max_block, const size_t p)
{
const gsl_multifit_robust_type *robust_t = gsl_multifit_robust_huber;
const size_t nblock = GSL_MAX(max_block, p);
lls_complex_workspace *w;
w = calloc(1, sizeof(lls_complex_workspace));
if (!w)
return 0;
w->AHA = gsl_matrix_complex_alloc(p, p);
w->work_A = gsl_matrix_complex_alloc(p, p);
if (!w->AHA || !w->work_A)
{
lls_complex_free(w);
return 0;
}
w->AHb = gsl_vector_complex_alloc(p);
w->work_b = gsl_vector_complex_alloc(p);
w->AF = gsl_matrix_complex_alloc(p, p);
w->S = gsl_vector_alloc(p);
if (!w->AHb || !w->work_b)
{
lls_complex_free(w);
return 0;
}
w->r_complex = gsl_vector_complex_alloc(nblock);
w->c = gsl_vector_complex_alloc(p);
w->r = gsl_vector_alloc(nblock);
w->w_robust = gsl_vector_alloc(nblock);
w->robust_workspace_p = gsl_multifit_robust_alloc(robust_t, nblock, p);
if (!w->r_complex || !w->w_robust || !w->c)
{
lls_complex_free(w);
return 0;
}
w->eigen_p = gsl_eigen_herm_alloc(p);
w->eval = gsl_vector_alloc(p);
w->p = p;
w->max_block = nblock;
w->residual = 0.0;
w->chisq = 0.0;
w->cond = -1.0;
w->niter = 0;
w->bHb = 0.0;
/* initialize matrices/vectors to 0 */
lls_complex_reset(w);
return w;
} /* lls_complex_alloc() */
void
test_eigen_herm_matrix(const gsl_matrix_complex * m, size_t count,
const char * desc)
{
const size_t N = m->size1;
gsl_matrix_complex * A = gsl_matrix_complex_alloc(N, N);
gsl_vector * eval = gsl_vector_alloc(N);
gsl_vector * evalv = gsl_vector_alloc(N);
gsl_vector * x = gsl_vector_alloc(N);
gsl_vector * y = gsl_vector_alloc(N);
gsl_matrix_complex * evec = gsl_matrix_complex_alloc(N, N);
gsl_eigen_herm_workspace * w = gsl_eigen_herm_alloc(N);
gsl_eigen_hermv_workspace * wv = gsl_eigen_hermv_alloc(N);
gsl_matrix_complex_memcpy(A, m);
gsl_eigen_hermv(A, evalv, evec, wv);
test_eigen_herm_results(m, evalv, evec, count, desc, "unsorted");
gsl_matrix_complex_memcpy(A, m);
gsl_eigen_herm(A, eval, w);
/* sort eval and evalv */
gsl_vector_memcpy(x, eval);
gsl_vector_memcpy(y, evalv);
gsl_sort_vector(x);
gsl_sort_vector(y);
test_eigenvalues_real(y, x, desc, "unsorted");
gsl_eigen_hermv_sort(evalv, evec, GSL_EIGEN_SORT_VAL_ASC);
test_eigen_herm_results(m, evalv, evec, count, desc, "val/asc");
gsl_eigen_hermv_sort(evalv, evec, GSL_EIGEN_SORT_VAL_DESC);
test_eigen_herm_results(m, evalv, evec, count, desc, "val/desc");
gsl_eigen_hermv_sort(evalv, evec, GSL_EIGEN_SORT_ABS_ASC);
test_eigen_herm_results(m, evalv, evec, count, desc, "abs/asc");
gsl_eigen_hermv_sort(evalv, evec, GSL_EIGEN_SORT_ABS_DESC);
test_eigen_herm_results(m, evalv, evec, count, desc, "abs/desc");
gsl_matrix_complex_free(A);
gsl_vector_free(eval);
gsl_vector_free(evalv);
gsl_vector_free(x);
gsl_vector_free(y);
gsl_matrix_complex_free(evec);
gsl_eigen_herm_free(w);
gsl_eigen_hermv_free(wv);
} /* test_eigen_herm_matrix() */
PetscErrorCode cHamiltonianMatrix::measurement(){
double *ALLdepart = new double[Nt];
double *ALLentropy = new double[Nt];
gsl_matrix* density1 = gsl_matrix_alloc(L,Nt);//background fermion density
gsl_matrix* density2 = gsl_matrix_alloc(L,Nt);//background fermion density
gsl_vector* corr12 = gsl_vector_alloc(Nt);//correlation betwen fermion up and down.
// The density correlation is in fact proportional to the interacting energy.
double var_rank;
PetscScalar var_tmp, var_tmp2;
gsl_complex var_tmp_gsl;
Vec vectort;
VecScatter ctx;
ofstream output;
VecScatterCreateToZero(WFt[0],&ctx,&vectort);
if(rank==0) cout << size << endl;
gsl_matrix_complex* RDM = gsl_matrix_complex_alloc(dim2,dim2);
gsl_vector *eval_RDM = gsl_vector_alloc(dim2);
gsl_eigen_herm_workspace* w_RDM = gsl_eigen_herm_alloc(dim2);
for (int itime = 0; itime < Nt; ++itime) {
if (rank==0&&itime%10==0) cout << "this is time " << itime << endl;
// % ## departure ##
var_rank = 0.0;
for (int ivar = rstart; ivar < rend; ++ivar) {
ierr = VecGetValues(WFt[itime],1,&ivar,&var_tmp);CHKERRQ(ierr);
var_rank += pow(gsl_vector_get(rr,ivar)*PetscAbsComplex(var_tmp),2);
}
MPI_Reduce(&var_rank, &(ALLdepart[itime]), 1, MPI_DOUBLE, MPI_SUM, 0, PETSC_COMM_WORLD);
ALLdepart[itime] = sqrt(ALLdepart[itime]);
// % ## entropy ##
VecScatterBegin(ctx,WFt[itime],vectort,INSERT_VALUES,SCATTER_FORWARD);
VecScatterEnd(ctx,WFt[itime],vectort,INSERT_VALUES,SCATTER_FORWARD);
if(rank==0) {
int ivar;double eigen_RDM;
gsl_matrix_complex_set_zero(RDM);
for (int row2 = 0; row2 < dim2; ++row2) {
for (int col2 = row2; col2 < dim2; ++col2) {
var_tmp_gsl.dat[0] = 0.0; var_tmp_gsl.dat[1] = 0.0;
for (int jjj = 0; jjj < dim; ++jjj) {
ivar = row2*dim+jjj;
ierr = VecGetValues(vectort,1,&ivar,&var_tmp);CHKERRQ(ierr);
ivar = col2*dim+jjj;
ierr = VecGetValues(vectort,1,&ivar,&var_tmp2);CHKERRQ(ierr);
var_tmp_gsl.dat[0] += PetscRealPart(var_tmp*PetscConj(var_tmp2));
var_tmp_gsl.dat[1] += PetscImaginaryPart(var_tmp*PetscConj(var_tmp2));
}
gsl_matrix_complex_set(RDM,row2,col2,var_tmp_gsl);
if (col2 != row2) {
gsl_matrix_complex_set(RDM,col2,row2,gsl_matrix_complex_get(RDM,row2,col2));
}
}
}
gsl_eigen_herm(RDM,eval_RDM,w_RDM);
ALLentropy[itime] = 0;
for (ivar = 0; ivar < dim2; ++ivar) {
eigen_RDM = gsl_vector_get(eval_RDM, ivar);
// cout << eigen_RDM << endl;
ALLentropy[itime] += -eigen_RDM*log(eigen_RDM);
}
}
// % ## density distribution of impurity fermion
if(rank==0) {
int ivar;
for (int row2 = 0; row2 < dim2; ++row2) {
for (int jpar = 0; jpar < N2; ++jpar) {
double density_tmp=0;
for (int jjj = 0; jjj < dim; ++jjj) {
ivar = row2*dim+jjj;
ierr = VecGetValues(vectort,1,&ivar,&var_tmp);CHKERRQ(ierr);
density_tmp +=pow(PetscAbsComplex(var_tmp),2);
}
/*if (itime==0) {
if (rank==0) cout << "density_tmp=" << density_tmp << endl;
}*/
gsl_matrix_set(density2,gsl_matrix_get(basis2,jpar,row2)-1,itime,gsl_matrix_get(density2,gsl_matrix_get(basis2,jpar,row2)-1,itime)+density_tmp);
}
}
}
/*if (rank==0) {
cout << "density of impurity:" << endl;
for (int jpar =0; jpar < L; ++jpar) {
cout << gsl_matrix_get(density2,jpar,itime) << "\t";
}
cout << endl;
}*/
// % ## density distribution of majority fermions
if(rank==0) {
int ivar;
for (int jjj = 0; jjj < dim; ++jjj) {
for (int jpar = 0; jpar < N; ++jpar) {
double density_tmp=0;
for (int row2 = 0; row2 < dim2; ++row2) {
ivar = row2*dim+jjj;
ierr = VecGetValues(vectort,1,&ivar,&var_tmp);CHKERRQ(ierr);
density_tmp +=pow(PetscAbsComplex(var_tmp),2);
}
gsl_matrix_set(density1,gsl_matrix_get(basis1,jpar,jjj)-1,itime,gsl_matrix_get(density1,gsl_matrix_get(basis1,jpar,jjj)-1,itime)+density_tmp);
}
}
}
// correlation between impurity and majority fermion
if(rank==0) {
int ivar;
double corr_tmp=0;
for (int jimp=0; jimp<dim2; ++jimp) {
for (int jmaj=0; jmaj<dim; ++jmaj) {
for (int jpar=0; jpar<N; ++jpar) {
if (gsl_matrix_get(basis1,jpar,jmaj)==jimp+1){
ivar = jimp*dim+jmaj;
ierr = VecGetValues(vectort,1,&ivar,&var_tmp);CHKERRQ(ierr);
corr_tmp+=pow(PetscAbsComplex(var_tmp),2);
}
}
}
}
gsl_vector_set(corr12,itime,corr_tmp);
}// end of correlation
}
if (rank == 0) {
char filename[50];
sprintf(filename,"measurement.data");
output.open(filename);
output.is_open();
output.precision(16);
for (int itime = 0; itime < Nt; ++itime) {
if (itime==0) {
// cout << "time t[1] " << '\t' << "departure[2] " << '\t' << "entropy[3]" << '\t' << "density of majority [L]" <<'\t' << "density of impurity [L]" << endl;
}
output << dt*itime-3 << '\t' << ALLdepart[itime] << '\t' << ALLentropy[itime] << '\t';
for (int jpar = 0; jpar < L; ++jpar) {
output << gsl_matrix_get(density1,jpar,itime) << '\t';
}
for (int jpar = 0; jpar < L; ++jpar) {
output << gsl_matrix_get(density2,jpar,itime) << '\t';
}
output << gsl_vector_get(corr12,itime) << '\t';
output << endl;
}
output.close();
}
// CopyFile(source,destination,FALSE);
delete[] ALLdepart;
VecScatterDestroy(&ctx);
VecDestroy(&vectort);
gsl_matrix_complex_free(RDM);
gsl_vector_free(eval_RDM);
gsl_eigen_herm_free(w_RDM);
gsl_matrix_free(density1);
gsl_matrix_free(density2);
gsl_vector_free(corr12);
// CopyFile(source,destination,FALSE);
return ierr;
}
