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_Kottke(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;
// Make grid
// Determine size of the 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]);
}
S4_TRACE("I Subpixel smoothing on %d x %d grid\n", ngrid[0], ngrid[1]);
const int ng2 = ngrid[0]*ngrid[1];
const double ing2 = 1./(double)ng2;
// The grid needs to hold 5 matrix elements: xx,xy,yx,yy,zz
// We actually make 5 different grids to facilitate the fft routines
//std::complex<double> *work = (std::complex<double>*)S4_malloc(sizeof(std::complex<double>)*(6*ng2));
std::complex<double> *work = fft_alloc_complex(6*ng2);
std::complex<double>*fxx = work;
std::complex<double>*fxy = fxx + ng2;
std::complex<double>*fyx = fxy + ng2;
std::complex<double>*fyy = fyx + ng2;
std::complex<double>*fzz = fyy + ng2;
std::complex<double>*Fto = fzz + ng2;
//memset(work, 0, sizeof(std::complex<double>) * 6*ng2);
double *discval = (double*)S4_malloc(sizeof(double)*(L->pattern.nshapes+1));
fft_plan plans[5];
for(int i = 0; i <= 4; ++i){
plans[i] = fft_plan_dft_2d(ngrid, fxx+i*ng2, Fto, 1);
}
int ii[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;
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;
Pattern_DiscretizeCell(&L->pattern, S->Lr, ngrid[0], ngrid[1], ii[0], ii[1], discval);
int nnz = 0;
int imat[2] = {-1,-1};
for(int i = 0; i <= L->pattern.nshapes; ++i){
if(fabs(discval[i]) > 2*std::numeric_limits<double>::epsilon()){
if(0 == nnz){ imat[0] = i; }
else if(1 == nnz){ imat[1] = i; }
++nnz;
}
}
//S4_TRACE("I %d,%d nnz = %d\n", ii[0], ii[1], nnz);
if(nnz < 2){ // just one material
//fprintf(stderr, "%d\t%d\t0\t0\n", ii[0], ii[1]);
const S4_Material *M;
if(0 == imat[0]){
M = &S->material[L->material];
}else{
M = &S->material[L->pattern.shapes[imat[0]-1].tag];
}
if(0 == M->type){
std::complex<double> eps_scalar(M->eps.s[0], M->eps.s[1]);
fxx[si1+si0*ngrid[1]] = eps_scalar;
fxy[si1+si0*ngrid[1]] = 0;
fyx[si1+si0*ngrid[1]] = 0;
fyy[si1+si0*ngrid[1]] = eps_scalar;
fzz[si1+si0*ngrid[1]] = eps_scalar;
}else{
fxx[si1+si0*ngrid[1]] = std::complex<double>(M->eps.abcde[0],M->eps.abcde[1]);
fyy[si1+si0*ngrid[1]] = std::complex<double>(M->eps.abcde[6],M->eps.abcde[7]);
fxy[si1+si0*ngrid[1]] = std::complex<double>(M->eps.abcde[2],M->eps.abcde[3]);
fyx[si1+si0*ngrid[1]] = std::complex<double>(M->eps.abcde[4],M->eps.abcde[5]);
fzz[si1+si0*ngrid[1]] = std::complex<double>(M->eps.abcde[8],M->eps.abcde[9]);
}
}else{
if(imat[1] > imat[0]){
std::swap(imat[0],imat[1]);
}
// imat[0] is the more-contained shape
double nvec[2];
const double nxvec[2] = { ((double)ii[0]+0.5)/(double)ngrid[0]-0.5, ((double)ii[1]+0.5)/(double)ngrid[1]-0.5 };
const double xvec[2] = { // center of current parallelogramic pixel
S->Lr[0]*nxvec[0] + S->Lr[2]*nxvec[1],
S->Lr[1]*nxvec[0] + S->Lr[3]*nxvec[1]
};
shape_get_normal(&(L->pattern.shapes[imat[0]-1]), xvec, nvec);
if(2 == nnz && imat[1] != imat[0] && !(0 == nvec[0] && 0 == nvec[1])){ // use Kottke averaging
//fprintf(stderr, "%d\t%d\t%f\t%f\n", ii[0], ii[1], nvec[0], nvec[1]);
const double fill = discval[imat[0]];
// Get the two tensors
std::complex<double> abcde[2][5];
for(int i = 0; i < 2; ++i){
const S4_Material *M;
if(0 == imat[i]){
M = &S->material[L->material];
}else{
M = &S->material[L->pattern.shapes[imat[i]-1].tag];
}
if(0 == M->type){
std::complex<double> eps_scalar(M->eps.s[0], M->eps.s[1]);
abcde[i][0] = eps_scalar;
abcde[i][1] = 0;
abcde[i][2] = 0;
abcde[i][3] = eps_scalar;
abcde[i][4] = eps_scalar;
}else{
for(int j = 0; j < 4; ++j){
abcde[i][j] = std::complex<double>(M->eps.abcde[2*j+0],M->eps.abcde[2*j+1]);
}
abcde[i][4] = std::complex<double>(M->eps.abcde[8],M->eps.abcde[9]);
}
}
// The zz component is just directly obtained by averaging
fzz[si1+si0*ngrid[1]] = discval[imat[0]] * abcde[0][4] + discval[imat[1]] * abcde[1][4];
// Compute rotated tensors
// abcd1 = Rot^T abcd1 Rot
// Rot = [ nvec[0] -nvec[1] ]
// [ nvec[1] nvec[0] ]
std::complex<double> abcd[2][4];
//fprintf(stderr, " nvec = {%f,%f}, fill = %f\n", nvec[0], nvec[1], fill);
//fprintf(stderr, " abcde[0] = {%f,%f,%f,%f}\n", abcde[0][0].real(), abcde[0][1].real(), abcde[0][2].real(), abcde[0][3].real());
//fprintf(stderr, " abcde[1] = {%f,%f,%f,%f}\n", abcde[1][0].real(), abcde[1][1].real(), abcde[1][2].real(), abcde[1][3].real());
sym2x2rot(abcde[0], nvec, abcd[0]);
sym2x2rot(abcde[1], nvec, abcd[1]);
// Compute the average tau tensor into abcde[0][0-3]
// tau(e__) = [ -1/e11 e12/e11 ]
// [ e21/e11 e22 - e21 e12/e11 ]
abcde[0][0] = fill * (-1./abcd[0][0]) + (1.-fill) * (-1./abcd[1][0]);
abcde[0][1] = fill * (abcd[0][1]/abcd[0][0]) + (1.-fill) * (abcd[1][1]/abcd[1][0]);
abcde[0][2] = fill * (abcd[0][2]/abcd[0][0]) + (1.-fill) * (abcd[1][2]/abcd[1][0]);
abcde[0][3] = fill * (abcd[0][3]-abcd[0][1]*abcd[0][2]/abcd[0][0]) + (1.-fill) * (abcd[1][3]-abcd[1][1]*abcd[1][2]/abcd[1][0]);
// Invert the tau transform into abcd[1]
// invtau(t__) = [ -1/t11 -t12/t11 ]
// [ -t21/t11 t22 - t21 t12/t11 ]
abcd[1][0] = -1./abcde[0][0];
abcd[1][1] = -abcde[0][1]/abcde[0][0];
abcd[1][2] = -abcde[0][2]/abcde[0][0];
abcd[1][3] = abcde[0][3] - abcde[0][1]*abcde[0][2]/abcde[0][0];
//fprintf(stderr, " abcd[1] = {%f,%f,%f,%f}\n", abcd[1][0].real(), abcd[1][1].real(), abcd[1][2].real(), abcd[1][3].real());
// Unrotate abcd[1] into abcd[0]
nvec[1] = -nvec[1];
sym2x2rot(abcd[1], nvec, abcd[0]);
//fprintf(stderr, " abcd[0] = {%f,%f,%f,%f}\n\n", abcd[0][0].real(), abcd[0][1].real(), abcd[0][2].real(), abcd[0][3].real());
fxx[si1+si0*ngrid[1]] = abcd[0][0];
fxy[si1+si0*ngrid[1]] = abcd[0][1];
fyx[si1+si0*ngrid[1]] = abcd[0][2];
fyy[si1+si0*ngrid[1]] = abcd[0][3];
}else{ // too many, just use the area weighting
//fprintf(stderr, "%d\t%d\t3\n", ii[0], ii[1]);
fxx[si1+si0*ngrid[1]] = 0;
fxy[si1+si0*ngrid[1]] = 0;
fyx[si1+si0*ngrid[1]] = 0;
fyy[si1+si0*ngrid[1]] = 0;
fzz[si1+si0*ngrid[1]] = 0;
for(int i = 0; i <= L->pattern.nshapes; ++i){
if(0 == discval[i]){ continue; }
int j = i-1;
const S4_Material *M;
if(-1 == j){
M = &S->material[L->material];
}else{
M = &S->material[L->pattern.shapes[j].tag];
}
if(0 == M->type){
std::complex<double> eps_scalar(M->eps.s[0], M->eps.s[1]);
fxx[si1+si0*ngrid[0]] += discval[i]*eps_scalar;
fyy[si1+si0*ngrid[0]] += discval[i]*eps_scalar;
fzz[si1+si0*ngrid[0]] += discval[i]*eps_scalar;
}else{
std::complex<double> ea(M->eps.abcde[0],M->eps.abcde[1]);
std::complex<double> eb(M->eps.abcde[2],M->eps.abcde[3]);
std::complex<double> ec(M->eps.abcde[4],M->eps.abcde[5]);
std::complex<double> ed(M->eps.abcde[6],M->eps.abcde[7]);
fxx[si1+si0*ngrid[1]] += discval[i]*ea;
fxy[si1+si0*ngrid[1]] += discval[i]*eb;
fyx[si1+si0*ngrid[1]] += discval[i]*ec;
fyy[si1+si0*ngrid[1]] += discval[i]*ed;
fzz[si1+si0*ngrid[1]] += discval[i]*std::complex<double>(M->eps.abcde[8],M->eps.abcde[9]);
}
}
}
}
/*
fprintf(stderr, "%d\t%d\t%f\t%f\t%f\t%f\t%f\t%f\t%f\t%f\t%f\t%f\n", ii[0], ii[1],
fxx[si1+si0*ngrid[1]].real(), fxx[si1+si0*ngrid[1]].imag(),
fxy[si1+si0*ngrid[1]].real(), fxy[si1+si0*ngrid[1]].imag(),
fyx[si1+si0*ngrid[1]].real(), fyx[si1+si0*ngrid[1]].imag(),
fyy[si1+si0*ngrid[1]].real(), fyy[si1+si0*ngrid[1]].imag(),
fzz[si1+si0*ngrid[1]].real(), fzz[si1+si0*ngrid[1]].imag()
);//*/
}
//fprintf(stderr, "\n");
}
// Make Epsilon_inv first
{
//fprintf(stderr, "fzz1[0] = %f+I %f\n", fzz[0].real(), fzz[0].imag());
//memset(Fto, 0, sizeof(std::complex<double>)*ng2);
fft_plan_exec(plans[4]);
//fprintf(stderr, "fzz2[0] = %f+I %f\n", fzz[0].real(), fzz[0].imag());
//fprintf(stderr, "Fto[0] = %f+I %f\n", Fto[0].real(), Fto[0].imag());
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]; }
Epsilon2[i+j*n] = ing2 * Fto[f[1]+f[0]*ngrid[1]];
}
}
}
//fprintf(stderr, "Epsilon2[0] = %f+I %f\n", Epsilon2[0].real(), Epsilon2[0].imag());
// Epsilon_inv needs inverting
RNP::TBLAS::SetMatrix<'A'>(n,n, 0.,1., Epsilon_inv,n);
int solve_info;
RNP::LinearSolve<'N'>(n,n, Epsilon2,n, Epsilon_inv,n, &solve_info, NULL);
//fprintf(stderr, "Epsilon_inv[0] = %f+I %f\n", Epsilon_inv[0].real(), Epsilon_inv[0].imag());
// We fill in the quarter blocks of F in Fortran order
for(int w = 0; w < 4; ++w){
int Ecol = (w&1 ? n : 0);
int Erow = (w&2 ? n : 0);
//memset(Fto, 0, sizeof(std::complex<double>)*ng2);
fft_plan_exec(plans[w]);
//fprintf(stderr, "Fto(%d)[0] = %f+I %f\n", w, Fto[0].real(), Fto[0].imag());
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]; }
Epsilon2[Erow+i+(Ecol+j)*n2] = ing2 * Fto[f[1]+f[0]*ngrid[1]];
}
}
}
//fprintf(stderr, "Epsilon2[0] = %f+I %f\n", Epsilon2[0].real(), Epsilon2[0].imag());
for(int i = 0; i <= 4; ++i){
fft_plan_destroy(plans[i]);
}
S4_free(discval);
//S4_free(work);
fft_free(work);
return 0;
}