/* * 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 ----- */
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; }
int lls_complex_lcurve(gsl_vector *reg_param, gsl_vector *rho, gsl_vector *eta, lls_complex_workspace *w) { const size_t N = rho->size; /* number of points on L-curve */ if (N != reg_param->size) { GSL_ERROR("size of reg_param and rho do not match", GSL_EBADLEN); } else if (N != eta->size) { GSL_ERROR("size of eta and rho do not match", GSL_EBADLEN); } else { int s; const gsl_complex negtwo = gsl_complex_rect(-2.0, 0.0); /* smallest regularization parameter */ const double smin_ratio = 16.0 * GSL_DBL_EPSILON; double s1, sp, ratio, tmp; size_t i; /* compute eigenvalues of A^H A */ gsl_matrix_complex_transpose_memcpy(w->work_A, w->AHA); s = gsl_eigen_herm(w->work_A, w->eval, w->eigen_p); if (s) return s; /* find largest and smallest eigenvalues */ gsl_vector_minmax(w->eval, &sp, &s1); /* singular values are square roots of eigenvalues */ s1 = sqrt(s1); if (sp > GSL_DBL_EPSILON) sp = sqrt(fabs(sp)); tmp = GSL_MAX(sp, s1*smin_ratio); gsl_vector_set(reg_param, N - 1, tmp); /* ratio so that reg_param(1) = s(1) */ ratio = pow(s1 / tmp, 1.0 / (N - 1.0)); /* calculate the regularization parameters */ for (i = N - 1; i > 0 && i--; ) { double rp1 = gsl_vector_get(reg_param, i + 1); gsl_vector_set(reg_param, i, ratio * rp1); } for (i = 0; i < N; ++i) { double r2; double lambda = gsl_vector_get(reg_param, i); gsl_complex val; lls_complex_solve(lambda, w->c, w); /* store ||c|| */ gsl_vector_set(eta, i, gsl_blas_dznrm2(w->c)); /* compute: A^H A c - 2 A^H b */ gsl_vector_complex_memcpy(w->work_b, w->AHb); gsl_blas_zhemv(CblasUpper, GSL_COMPLEX_ONE, w->AHA, w->c, negtwo, w->work_b); /* compute: c^T A^T A c - 2 c^T A^T b */ gsl_blas_zdotc(w->c, w->work_b, &val); r2 = GSL_REAL(val) + w->bHb; gsl_vector_set(rho, i, sqrt(r2)); } return GSL_SUCCESS; } } /* lls_complex_lcurve() */