int FMMGetEpsilon_PolBasisNV(const Simulation *S, const Layer *L, const int n, std::complex<double> *Epsilon2, std::complex<double> *Epsilon_inv){
double mp1 = 0;
int pwr = S->options.lanczos_smoothing_power;
if(S->options.use_Lanczos_smoothing){
mp1 = GetLanczosSmoothingOrder(S);
S4_TRACE("I Lanczos smoothing order = %f\n", mp1);
mp1 *= S->options.lanczos_smoothing_width;
}
if(Epsilon_inv){} // prevent unused parameter warning
const int n2 = 2*n;
const int nn = n*n;
const double unit_cell_size = Simulation_GetUnitCellSize(S);
const int *G = S->solution->G;
const int ndim = (0 == S->Lr[2] && 0 == S->Lr[3]) ? 1 : 2;
double *ivalues = (double*)S4_malloc(sizeof(double)*(2+10)*(L->pattern.nshapes+1));
double *values = ivalues + 2*(L->pattern.nshapes+1);
// Get all the dielectric tensors
//bool have_tensor = false;
for(int i = -1; i < L->pattern.nshapes; ++i){
const Material *M;
if(-1 == i){
M = Simulation_GetMaterialByName(S, L->material, NULL);
}else{
M = Simulation_GetMaterialByIndex(S, L->pattern.shapes[i].tag);
}
if(0 == M->type){
std::complex<double> eps_temp(M->eps.s[0], M->eps.s[1]);
//eps_temp = Simulation_GetEpsilonByIndex(S, L->pattern.shapes[i].tag);
values[2*(i+1)+0] = eps_temp.real();
values[2*(i+1)+1] = eps_temp.imag();
eps_temp = 1./eps_temp;
ivalues[2*(i+1)+0] = eps_temp.real();
ivalues[2*(i+1)+1] = eps_temp.imag();
}else{
//have_tensor = true;
}
}
// Epsilon2 is
// [ Epsilon - Delta*Pxx -Delta*Pxy ]
// [ -Delta*Pyx Epsilon - Delta*Pyy ]
// Pxy = Fourier transform of par_x^* par_y
//
// Need temp storage for Delta and P__
std::complex<double> *P = Simulation_GetCachedField(S, L);
std::complex<double> *work = NULL;
std::complex<double> *mDelta = NULL;
std::complex<double> *Eta = NULL;
if(NULL == P){
// We need to compute the vector field
// Make vector fields
// Determine size of the vector field grid
int ngrid[2] = {1,1};
for(int i = 0; i < 2; ++i){ // choose grid size
for(int j = 0; j < n; ++j){
if(abs(G[2*j+i]) > ngrid[i]){ ngrid[i] = abs(G[2*j+i]); }
}
if(ngrid[i] < 1){ ngrid[i] = 1; }
ngrid[i] *= S->options.resolution;
ngrid[i] = fft_next_fast_size(ngrid[i]);
}
const int ng2 = ngrid[0]*ngrid[1];
work = (std::complex<double>*)S4_malloc(sizeof(std::complex<double>)*(6*nn + 4*ng2));
mDelta = work;
Eta = mDelta + nn;
P = Eta + nn;
std::complex<double> *Ffrom = P + 4*nn; // Fourier source
std::complex<double> *Fto = Ffrom + ng2; // Fourier dest
std::complex<double> *par = Fto + ng2; // real space parallel vector
// Generate the vector field
const double ing2 = 1./(double)ng2;
int ii[2];
double *vfield = (double*)S4_malloc(sizeof(double)*2*ng2);
if(0 == S->Lr[2] && 0 == S->Lr[3]){ // 1D, generate the trivial field
double nv[2] = {-S->Lr[1], S->Lr[0]};
double nva = hypot(nv[0],nv[1]);
nv[0] /= nva; nv[1] /= nva;
for(ii[1] = 0; ii[1] < ngrid[1]; ++ii[1]){
for(ii[0] = 0; ii[0] < ngrid[0]; ++ii[0]){
vfield[2*(ii[0]+ii[1]*ngrid[0])+0] = nv[0];
vfield[2*(ii[0]+ii[1]*ngrid[0])+1] = nv[1];
}
}
}else{
int error = 0;
S4_VERB(1, "Generating polarization vector field of size %d x %d\n", ngrid[0], ngrid[1]);
error = Pattern_GenerateFlowField(&L->pattern, 0, S->Lr, ngrid[0], ngrid[1], vfield);
// Normalize the field
for(ii[1] = 0; ii[1] < ngrid[1]; ++ii[1]){
for(ii[0] = 0; ii[0] < ngrid[0]; ++ii[0]){
double a = hypot(
vfield[2*(ii[0]+ii[1]*ngrid[0])+0],
vfield[2*(ii[0]+ii[1]*ngrid[0])+1]);
if(a > 0){
vfield[2*(ii[0]+ii[1]*ngrid[0])+0] /= a;
vfield[2*(ii[0]+ii[1]*ngrid[0])+1] /= a;
}else{
vfield[2*(ii[0]+ii[1]*ngrid[0])+0] = 1;
vfield[2*(ii[0]+ii[1]*ngrid[0])+1] = 0;
}
}
}
if(0 != error){
S4_TRACE("< Simulation_ComputeLayerBands (failed; Pattern_GenerateFlowField returned %d) [omega=%f]\n", error, S->omega[0]);
if(NULL != vfield){ S4_free(vfield); }
if(NULL != work){ S4_free(work); }
if(NULL != ivalues){ S4_free(ivalues); }
return error;
}
}
if(NULL != S->options.vector_field_dump_filename_prefix){
const char *layer_name = NULL != L->name ? L->name : "";
const size_t prefix_len = strlen(S->options.vector_field_dump_filename_prefix);
char *filename = (char*)malloc(sizeof(char) * (prefix_len + strlen(layer_name) + 1));
strcpy(filename, S->options.vector_field_dump_filename_prefix);
strcpy(filename+prefix_len, layer_name);
FILE *fp = fopen(filename, "wb");
if(NULL != fp){
for(ii[1] = 0; ii[1] < ngrid[1]; ++ii[1]){
for(ii[0] = 0; ii[0] < ngrid[0]; ++ii[0]){
fprintf(fp, "%d\t%d\t%f\t%f\n", ii[0], ii[1], vfield[2*(ii[0]+ii[1]*ngrid[0])+0], vfield[2*(ii[0]+ii[1]*ngrid[0])+1]);
} fprintf(fp, "\n");
}
fclose(fp);
}
free(filename);
}
for(ii[1] = 0; ii[1] < ngrid[1]; ++ii[1]){
for(ii[0] = 0; ii[0] < ngrid[0]; ++ii[0]){
par[2*(ii[0]+ii[1]*ngrid[0])+0] = vfield[2*(ii[0]+ii[1]*ngrid[0])+0];
par[2*(ii[0]+ii[1]*ngrid[0])+1] = vfield[2*(ii[0]+ii[1]*ngrid[0])+1];
}
}
fft_plan plan = fft_plan_dft_2d(ngrid, Ffrom, Fto, 1);
// We fill in the quarter blocks of F in Fortran order
for(int w = 0; w < 4; ++w){
int Erow = (w&1 ? n : 0);
int Ecol = (w&2 ? n : 0);
int _1 = (w&1);
int _2 = ((w&2)>>1);
for(ii[1] = 0; ii[1] < ngrid[1]; ++ii[1]){
const int si1 = ii[1] >= ngrid[1]/2 ? ii[1]-ngrid[1]/2 : ii[1]+ngrid[1]/2;
for(ii[0] = 0; ii[0] < ngrid[0]; ++ii[0]){
const int si0 = ii[0] >= ngrid[0]/2 ? ii[0]-ngrid[0]/2 : ii[0]+ngrid[0]/2;
Ffrom[si1+si0*ngrid[1]] = par[2*(ii[0]+ii[1]*ngrid[0])+_1]*par[2*(ii[0]+ii[1]*ngrid[0])+_2];
}
}
fft_plan_exec(plan);
for(int j = 0; j < n; ++j){
for(int i = 0; i < n; ++i){
int f[2] = {G[2*i+0]-G[2*j+0],G[2*i+1]-G[2*j+1]};
if(f[0] < 0){ f[0] += ngrid[0]; }
if(f[1] < 0){ f[1] += ngrid[1]; }
P[Erow+i+(Ecol+j)*n2] = ing2 * Fto[f[1]+f[0]*ngrid[1]];
}
}
}
fft_plan_destroy(plan);
//free(fftcfg);
if(NULL != vfield){ S4_free(vfield); }
// Add to cache
Simulation_AddFieldToCache((Simulation*)S, L, S->n_G, P, 4*nn);
}else{
int FMMGetEpsilon_Experimental(const S4_Simulation *S, const S4_Layer *L, const int n, std::complex<double> *Epsilon2, std::complex<double> *Epsilon_inv){
const int n2 = 2*n;
const int *G = S->G;
const int ndim = (0 == S->Lr[2] && 0 == S->Lr[3]) ? 1 : 2;
double *ivalues = (double*)S4_malloc(sizeof(double)*(2+10)*(L->pattern.nshapes+1));
double *values = ivalues + 2*(L->pattern.nshapes+1);
S4_TRACE("I Experimental epsilon\n");
// Get all the dielectric tensors
bool have_tensor = false;
for(int i = -1; i < L->pattern.nshapes; ++i){
const S4_Material *M;
if(-1 == i){
M = &S->material[L->material];
}else{
M = &S->material[L->pattern.shapes[i].tag];
}
if(0 == M->type){
std::complex<double> eps_temp(M->eps.s[0], M->eps.s[1]);
//eps_temp = Simulation_GetEpsilonByIndex(S, L->pattern.shapes[i].tag);
values[2*(i+1)+0] = eps_temp.real();
values[2*(i+1)+1] = eps_temp.imag();
eps_temp = 1./eps_temp;
ivalues[2*(i+1)+0] = eps_temp.real();
ivalues[2*(i+1)+1] = eps_temp.imag();
}else{
have_tensor = true;
}
}
const double unit_cell_size = Simulation_GetUnitCellSize(S);
if(!have_tensor){
// Make Epsilon
for(int j = 0; j < n; ++j){
for(int i = 0; i < n; ++i){
int dG[2] = {G[2*i+0]-G[2*j+0],G[2*i+1]-G[2*j+1]};
double f[2] = {
dG[0] * S->Lk[0] + dG[1] * S->Lk[2],
dG[0] * S->Lk[1] + dG[1] * S->Lk[3]
};
double ft[2];
Pattern_GetFourierTransform(&L->pattern, values, f, ndim, unit_cell_size, ft);
Epsilon2[i+j*n2] = std::complex<double>(ft[0],ft[1]);
}
}
// Make Epsilon_inv
for(int j = 0; j < n; ++j){
for(int i = 0; i < n; ++i){
int dG[2] = {G[2*i+0]-G[2*j+0],G[2*i+1]-G[2*j+1]};
double f[2] = {
dG[0] * S->Lk[0] + dG[1] * S->Lk[2],
dG[0] * S->Lk[1] + dG[1] * S->Lk[3]
};
double ft[2];
Pattern_GetFourierTransform(&L->pattern, ivalues, f, ndim, unit_cell_size, ft);
Epsilon_inv[i+j*n] = std::complex<double>(ft[0],ft[1]);
}
}
S4_TRACE("I Epsilon(0,0) = %f,%f [omega=%f]\n", Epsilon2[0].real(), Epsilon2[0].imag(), S->omega[0]);
// Upper block of diagonal of Epsilon2 is already Epsilon
RNP::TBLAS::CopyMatrix<'A'>(n,n,&Epsilon2[0+0*n2],n2, &Epsilon2[n+n*n2],n2);
RNP::TBLAS::SetMatrix<'A'>(n,n, 0.,0., &Epsilon2[n+0*n2],n2);
RNP::TBLAS::SetMatrix<'A'>(n,n, 0.,0., &Epsilon2[0+n*n2],n2);
// Epsilon2 has Epsilon's on its diagonal
}else{ // have tensor dielectric
const int ldv = 2*(1+L->pattern.nshapes);
for(int i = -1; i < L->pattern.nshapes; ++i){
const S4_Material *M;
if(-1 == i){
M = &S->material[L->material];
}else{
M = &S->material[L->pattern.shapes[i].tag];
}
if(0 == M->type){
const std::complex<double> eps_temp(M->eps.s[0], M->eps.s[1]);
const std::complex<double> inveps_temp = 1./eps_temp;
values[0*ldv+2*(i+1)+0] = eps_temp.real();
values[0*ldv+2*(i+1)+1] = eps_temp.imag();
values[1*ldv+2*(i+1)+0] = 0;
values[1*ldv+2*(i+1)+1] = 0;
values[2*ldv+2*(i+1)+0] = 0;
values[2*ldv+2*(i+1)+1] = 0;
values[3*ldv+2*(i+1)+0] = eps_temp.real();
values[3*ldv+2*(i+1)+1] = eps_temp.imag();
values[4*ldv+2*(i+1)+0] = eps_temp.real();
values[4*ldv+2*(i+1)+1] = eps_temp.imag();
ivalues[0*ldv+2*(i+1)+0] = inveps_temp.real();
ivalues[0*ldv+2*(i+1)+1] = inveps_temp.imag();
}else{
std::complex<double> eps_temp(M->eps.abcde[8], M->eps.abcde[9]);
const std::complex<double> inveps_temp = 1./eps_temp;
// We must transpose the values array here, as well as transpose the tensor
values[0*ldv+2*(i+1)+0] = M->eps.abcde[0];
values[0*ldv+2*(i+1)+1] = M->eps.abcde[1];
values[1*ldv+2*(i+1)+0] = M->eps.abcde[4];
values[1*ldv+2*(i+1)+1] = M->eps.abcde[5];
values[2*ldv+2*(i+1)+0] = M->eps.abcde[2];
values[2*ldv+2*(i+1)+1] = M->eps.abcde[3];
values[3*ldv+2*(i+1)+0] = M->eps.abcde[6];
values[3*ldv+2*(i+1)+1] = M->eps.abcde[7];
values[4*ldv+2*(i+1)+0] = M->eps.abcde[8];
values[4*ldv+2*(i+1)+1] = M->eps.abcde[9];
ivalues[0*ldv+2*(i+1)+0] = inveps_temp.real();
ivalues[0*ldv+2*(i+1)+1] = inveps_temp.imag();
}
}
for(int k = -1; k < 4; ++k){
if(-1 == k){
for(int j = 0; j < n; ++j){
for(int i = 0; i < n; ++i){
int dG[2] = {G[2*i+0]-G[2*j+0],G[2*i+1]-G[2*j+1]};
double f[2] = {
dG[0] * S->Lk[0] + dG[1] * S->Lk[2],
dG[0] * S->Lk[1] + dG[1] * S->Lk[3]
};
double ft[2];
Pattern_GetFourierTransform(&L->pattern, ivalues, f, ndim, unit_cell_size, ft);
Epsilon_inv[i+j*n] = std::complex<double>(ft[0],ft[1]);
}
}
}else{
const int ib = k&1 ? n : 0;
const int jb = k&2 ? n : 0;
for(int j = 0; j < n; ++j){
for(int i = 0; i < n; ++i){
int dG[2] = {G[2*i+0]-G[2*j+0],G[2*i+1]-G[2*j+1]};
double f[2] = {
dG[0] * S->Lk[0] + dG[1] * S->Lk[2],
dG[0] * S->Lk[1] + dG[1] * S->Lk[3]
};
double ft[2];
Pattern_GetFourierTransform(&L->pattern, &values[k*ldv], f, ndim, unit_cell_size, ft);
Epsilon2[ib+i+(jb+j)*n2] = std::complex<double>(ft[0],ft[1]);
}
}
}
}
}
S4_free(ivalues);
return 0;
}