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#ifndef STIM_MIE_H
#define STIM_MIE_H
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#include <boost/math/special_functions/bessel.hpp>
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#include "scalarwave.h"
#include "../math/bessel.h"
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#include "../cuda/cudatools/devices.h"
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#include <cmath>
namespace stim{
/// Calculate the scattering coefficients for a spherical scatterer
template<typename T>
void B_coefficients(stim::complex<T>* B, T a, T k, stim::complex<T> n, int Nl){
//temporary variables
double vm; //allocate space to store the return values for the bessel function calculation
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double* j_ka = (double*) malloc( (Nl + 2) * sizeof(double) );
double* y_ka = (double*) malloc( (Nl + 2) * sizeof(double) );
double* dj_ka= (double*) malloc( (Nl + 2) * sizeof(double) );
double* dy_ka= (double*) malloc( (Nl + 2) * sizeof(double) );
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stim::complex<double>* j_kna = (stim::complex<double>*) malloc( (Nl + 2) * sizeof(stim::complex<double>) );
stim::complex<double>* y_kna = (stim::complex<double>*) malloc( (Nl + 2) * sizeof(stim::complex<double>) );
stim::complex<double>* dj_kna= (stim::complex<double>*) malloc( (Nl + 2) * sizeof(stim::complex<double>) );
stim::complex<double>* dy_kna= (stim::complex<double>*) malloc( (Nl + 2) * sizeof(stim::complex<double>) );
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double ka = k * a; //store k*a (argument for spherical bessel and Hankel functions)
stim::complex<double> kna = k * n * a; //store k*n*a (argument for spherical bessel functions and derivatives)
stim::bessjyv_sph<double>(Nl, ka, vm, j_ka, y_ka, dj_ka, dy_ka); //calculate bessel functions and derivatives for k*a
stim::cbessjyva_sph<double>(Nl, kna, vm, j_kna, y_kna, dj_kna, dy_kna); //calculate complex bessel functions for k*n*a
stim::complex<double> h_ka, dh_ka;
stim::complex<double> numerator, denominator;
stim::complex<double> i(0, 1);
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for(int l = 0; l <= Nl; l++){
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h_ka.r = j_ka[l];
h_ka.i = y_ka[l];
dh_ka.r = dj_ka[l];
dh_ka.i = dy_ka[l];
numerator = j_ka[l] * dj_kna[l] * (stim::complex<double>)n - j_kna[l] * dj_ka[l];
denominator = j_kna[l] * dh_ka - h_ka * dj_kna[l] * (stim::complex<double>)n;
B[l] = (2 * l + 1) * pow(i, l) * numerator / denominator;
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}
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//free memory
free(j_ka); free(y_ka); free(dj_ka); free(dy_ka); free(j_kna); free(y_kna); free(dj_kna); free(dy_kna);
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}
template<typename T>
void A_coefficients(stim::complex<T>* A, T a, T k, stim::complex<T> n, int Nl){
//temporary variables
double vm; //allocate space to store the return values for the bessel function calculation
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double* j_ka = (double*) malloc( (Nl + 2) * sizeof(double) );
double* y_ka = (double*) malloc( (Nl + 2) * sizeof(double) );
double* dj_ka= (double*) malloc( (Nl + 2) * sizeof(double) );
double* dy_ka= (double*) malloc( (Nl + 2) * sizeof(double) );
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stim::complex<double>* j_kna = (stim::complex<double>*) malloc( (Nl + 2) * sizeof(stim::complex<double>) );
stim::complex<double>* y_kna = (stim::complex<double>*) malloc( (Nl + 2) * sizeof(stim::complex<double>) );
stim::complex<double>* dj_kna= (stim::complex<double>*) malloc( (Nl + 2) * sizeof(stim::complex<double>) );
stim::complex<double>* dy_kna= (stim::complex<double>*) malloc( (Nl + 2) * sizeof(stim::complex<double>) );
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double ka = k * a; //store k*a (argument for spherical bessel and Hankel functions)
stim::complex<double> kna = k * n * a; //store k*n*a (argument for spherical bessel functions and derivatives)
stim::bessjyv_sph<double>(Nl, ka, vm, j_ka, y_ka, dj_ka, dy_ka); //calculate bessel functions and derivatives for k*a
stim::cbessjyva_sph<double>(Nl, kna, vm, j_kna, y_kna, dj_kna, dy_kna); //calculate complex bessel functions for k*n*a
stim::complex<double> h_ka, dh_ka;
stim::complex<double> numerator, denominator;
stim::complex<double> i(0, 1);
for(size_t l = 0; l <= Nl; l++){
h_ka.r = j_ka[l];
h_ka.i = y_ka[l];
dh_ka.r = dj_ka[l];
dh_ka.i = dy_ka[l];
numerator = j_ka[l] * dh_ka - dj_ka[l] * h_ka;
denominator = j_kna[l] * dh_ka - h_ka * dj_kna[l] * (stim::complex<double>)n;
A[l] = (2 * l + 1) * pow(i, l) * numerator / denominator;
}
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//free memory
free(j_ka); free(y_ka); free(dj_ka); free(dy_ka); free(j_kna); free(y_kna); free(dj_kna); free(dy_kna);
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}
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#define LOCAL_NL 16
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template<typename T>
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__global__ void cuda_scalar_mie_scatter(stim::complex<T>* E, size_t N, T* x, T* y, T* z, stim::scalarwave<T>* W, size_t nW, T a, stim::complex<T> n, stim::vec3<T> c, stim::complex<T>* hB, T r_min, T dr, size_t N_hB, int Nl){
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extern __shared__ stim::complex<T> shared_hB[]; //declare the list of waves in shared memory
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size_t i = blockIdx.x * blockDim.x + threadIdx.x; //get the index into the array
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if(i >= N) return; //exit if this thread is outside the array
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stim::vec3<T> p;
(x == NULL) ? p[0] = 0 : p[0] = x[i]; // test for NULL values and set positions
(y == NULL) ? p[1] = 0 : p[1] = y[i];
(z == NULL) ? p[2] = 0 : p[2] = z[i];
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p = p - c;
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T r = p.len(); //calculate the distance from the sphere
if(r < a) return; //exit if the point is inside the sphere (we only calculate the internal field)
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T fij = (r - r_min)/dr; //FP index into the spherical bessel LUT
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size_t ij = (size_t) fij; //convert to an integral index
T alpha = fij - ij; //calculate the fractional portion of the index
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size_t n0j = ij * (Nl + 1); //start of the first entry in the LUT
size_t n1j = (ij+1) * (Nl + 1); //start of the second entry in the LUT
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T cos_phi;
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T Pl_2, Pl_1, Pl; //declare registers to store the previous two Legendre polynomials
stim::complex<T> hBl;
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stim::complex<T> Ei = 0; //create a register to store the result
int l;
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stim::complex<T> hlBl[LOCAL_NL+1]; //the first LOCAL_NL components are stored in registers for speed
int shared_start = threadIdx.x * (Nl - LOCAL_NL); //wrap up some operations so that they aren't done in the main loops
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//unroll LOCAL_NL + 1
#pragma unroll 17 //copy the first LOCAL_NL+1 h_l * B_l components to registers
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for(l = 0; l <= LOCAL_NL; l++)
hlBl[l] = clerp<T>( hB[n0j + l], hB[n1j + l], alpha );
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for(l = LOCAL_NL+1; l <= Nl; l++) //copy any additional h_l * B_l components to shared memory
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shared_hB[shared_start + (l - (LOCAL_NL+1))] = clerp<T>( hB[n0j + l], hB[n1j + l], alpha );
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complex<T> e, Ew;
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for(size_t w = 0; w < nW; w++){ //for each plane wave
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cos_phi = p.norm().dot(W[w].kvec().norm()); //calculate the cosine of the angle between the k vector and the direction from the sphere
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Pl_2 = 1; //the Legendre polynomials will be calculated recursively, initialize the first two steps of the recursive relation
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Pl_1 = cos_phi;
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e = exp(complex<T>(0, W[w].kvec().dot(c)));
Ew = W[w].E() * e;
Ei += Ew * hlBl[0] * Pl_2; //unroll the first two orders using the initial steps of the Legendre recursive relation
Ei += Ew * hlBl[1] * Pl_1;
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//LOCAL_NL - 1
#pragma unroll 15 //unroll the next LOCAL_NL-1 loops for speed (iterating through the components in the register file)
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for(l = 2; l <= LOCAL_NL; l++){
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Pl = ( (2 * (l-1) + 1) * cos_phi * Pl_1 - (l-1) * Pl_2 ) / (l); //calculate the next step in the Legendre polynomial recursive relation (this is where most of the computation occurs)
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Ei += Ew * hlBl[l] * Pl; //calculate and sum the current field order
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Pl_2 = Pl_1; //shift Pl_1 -> Pl_2 and Pl -> Pl_1
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Pl_1 = Pl;
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}
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for(l = LOCAL_NL+1; l <= Nl; l++){ //do the same as above, except for any additional orders that are stored in shared memory (not registers)
Pl = ( (2 * (l-1) + 1) * cos_phi * Pl_1 - (l-1) * Pl_2 ) / (l); //again, this is where most computation in the kernel occurs
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Ei += Ew * shared_hB[shared_start + l - LOCAL_NL - 1] * Pl;
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Pl_2 = Pl_1; //shift Pl_1 -> Pl_2 and Pl -> Pl_1
Pl_1 = Pl;
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}
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}
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E[i] += Ei; //copy the result to device memory
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}
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///Calculate the scalar Mie scattered field on the GPU
/// @param E (GPU) is the N x N destination scalar field
/// @param N is the number fo elements of the scalar field in each direction
/// @param x (GPU) is the grid of X coordinates for each point in E
/// @param y (GPU) is the grid of Y coordinates for each point in E
/// @param z (GPU) is the grid of Z coordinates for each point in E
/// @param W (CPU) is an array of coherent scalar plane waves incident on the Mie scatterer
/// @param a is the radius of the Mie scatterer
/// @param n is the complex refractive index of the Mie scatterer
/// @param r_spacing is the minimum distance between r values of the sample points in E (used to calculate look-up tables)
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template<typename T>
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void gpu_scalar_mie_scatter(stim::complex<T>* E, size_t N, T* x, T* y, T* z, stim::scalarwave<T>* W, size_t nW, T a, stim::complex<T> n, stim::vec3<T> c, stim::complex<T>* hB, T kr_min, T dkr, size_t N_hB, size_t Nl){
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size_t max_shared_mem = stim::sharedMemPerBlock();
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size_t hBl_array = sizeof(stim::complex<T>) * (Nl + 1);
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//std::cout<<"hl*Bl array size: "<<hBl_array<<std::endl;
//std::cout<<"shared memory: "<<max_shared_mem<<std::endl;
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int threads = (int)((max_shared_mem / hBl_array) / 32 * 32);
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//std::cout<<"threads per block: "<<threads<<std::endl;
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dim3 blocks((unsigned)(N / threads + 1)); //calculate the optimal number of blocks
size_t shared_mem;
if(Nl <= LOCAL_NL) shared_mem = 0;
else shared_mem = threads * sizeof(stim::complex<T>) * (Nl - LOCAL_NL); //amount of shared memory to allocate
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//std::cout<<"shared memory allocated: "<<shared_mem<<std::endl;
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cuda_scalar_mie_scatter<T><<< blocks, threads, shared_mem >>>(E, N, x, y, z, W, nW, a, n, c, hB, kr_min, dkr, N_hB, (int)Nl); //call the kernel
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}
template<typename T>
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__global__ void cuda_dist(T* r, T* x, T* y, T* z, size_t N, stim::vec3<T> c = stim::vec3<T>(0, 0, 0)){
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size_t i = blockIdx.x * blockDim.x + threadIdx.x; //get the index into the array
if(i >= N) return; //exit if this thread is outside the array
stim::vec3<T> p;
(x == NULL) ? p[0] = 0 : p[0] = x[i]; // test for NULL values and set positions
(y == NULL) ? p[1] = 0 : p[1] = y[i];
(z == NULL) ? p[2] = 0 : p[2] = z[i];
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r[i] = (p - c).len();
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}
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///Calculate the scalar Mie scattered field on the GPU
/// @param E (GPU) is the N x N destination scalar field
/// @param N is the number fo elements of the scalar field in each direction
/// @param x (GPU) is the grid of X coordinates for each point in E
/// @param y (GPU) is the grid of Y coordinates for each point in E
/// @param z (GPU) is the grid of Z coordinates for each point in E
/// @param W (CPU) is an array of coherent scalar plane waves incident on the Mie scatterer
/// @param a is the radius of the Mie scatterer
/// @param n is the complex refractive index of the Mie scatterer
/// @param r_spacing is the minimum distance between r values of the sample points in E (used to calculate look-up tables)
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template<typename T>
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void gpu_scalar_mie_scatter(stim::complex<T>* E, size_t N, T* x, T* y, T* z, std::vector<stim::scalarwave<T>> W, T a, stim::complex<T> n, stim::vec3<T> c = stim::vec3<T>(0, 0, 0), T r_spacing = 0.1){
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//calculate the necessary number of orders required to represent the scattered field
T k = W[0].kmag();
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int Nl = (int)ceil(k*a + 4 * cbrt( k * a ) + 2);
if(Nl < LOCAL_NL) Nl = LOCAL_NL; //always do at least the minimum number of local operations (kernel optimization)
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//std::cout<<"Nl: "<<Nl<<std::endl;
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//calculate the scattering coefficients for the sphere
stim::complex<T>* B = (stim::complex<T>*) malloc( sizeof(stim::complex<T>) * (Nl + 1) ); //allocate space for the scattering coefficients
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B_coefficients(B, a, k, n, Nl);
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// PLANE WAVES
stim::scalarwave<T>* dev_W; //allocate space and copy plane waves
HANDLE_ERROR( cudaMalloc(&dev_W, sizeof(stim::scalarwave<T>) * W.size()) );
HANDLE_ERROR( cudaMemcpy(dev_W, &W[0], sizeof(stim::scalarwave<T>) * W.size(), cudaMemcpyHostToDevice) );
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// BESSEL FUNCTION LOOK-UP TABLE
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//calculate the distance from the sphere center
T* dev_r;
HANDLE_ERROR( cudaMalloc(&dev_r, sizeof(T) * N) );
int threads = stim::maxThreadsPerBlock();
dim3 blocks((unsigned)(N / threads + 1));
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cuda_dist<T> <<< blocks, threads >>>(dev_r, x, y, z, N, c);
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//Find the minimum and maximum values of r
cublasStatus_t stat;
cublasHandle_t handle;
stat = cublasCreate(&handle); //create a cuBLAS handle
if (stat != CUBLAS_STATUS_SUCCESS){ //test for failure
printf ("CUBLAS initialization failed\n");
exit(1);
}
int i_min, i_max;
stat = cublasIsamin(handle, (int)N, dev_r, 1, &i_min);
if (stat != CUBLAS_STATUS_SUCCESS){ //test for failure
printf ("CUBLAS Error: failed to calculate minimum r value.\n");
exit(1);
}
stat = cublasIsamax(handle, (int)N, dev_r, 1, &i_max);
if (stat != CUBLAS_STATUS_SUCCESS){ //test for failure
printf ("CUBLAS Error: failed to calculate maximum r value.\n");
exit(1);
}
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i_min--; //cuBLAS uses 1-based indexing for Fortran compatibility
i_max--;
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T r_min, r_max; //allocate space to store the minimum and maximum values
HANDLE_ERROR( cudaMemcpy(&r_min, dev_r + i_min, sizeof(T), cudaMemcpyDeviceToHost) ); //copy the min and max values from the device to the CPU
HANDLE_ERROR( cudaMemcpy(&r_max, dev_r + i_max, sizeof(T), cudaMemcpyDeviceToHost) );
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r_min = max(r_min, a); //if the radius of the sphere is larger than r_min, change r_min to a (the scattered field doesn't exist inside the sphere)
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//size_t Nlut_j = (size_t)((r_max - r_min) / r_spacing + 1); //number of values in the look-up table based on the user-specified spacing along r
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size_t N_hB_lut = (size_t)((r_max - r_min) / r_spacing + 1);
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//T kr_min = k * r_min;
//T kr_max = k * r_max;
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//temporary variables
double vm; //allocate space to store the return values for the bessel function calculation
double* jv = (double*) malloc( (Nl + 1) * sizeof(double) );
double* yv = (double*) malloc( (Nl + 1) * sizeof(double) );
double* djv= (double*) malloc( (Nl + 1) * sizeof(double) );
double* dyv= (double*) malloc( (Nl + 1) * sizeof(double) );
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size_t hB_bytes = sizeof(stim::complex<T>) * (Nl+1) * N_hB_lut;
stim::complex<T>* hB_lut = (stim::complex<T>*) malloc(hB_bytes); //pointer to the look-up table
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T dr = (r_max - r_min) / (N_hB_lut-1); //distance between values in the LUT
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//std::cout<<"LUT jl bytes: "<<hB_bytes<<std::endl;
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stim::complex<T> hl;
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for(size_t ri = 0; ri < N_hB_lut; ri++){ //for each value in the LUT
stim::bessjyv_sph<double>(Nl, k * (r_min + ri * dr), vm, jv, yv, djv, dyv); //compute the list of spherical bessel functions from [0 Nl]
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for(size_t l = 0; l <= Nl; l++){ //for each order
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hl.r = (T)jv[l];
hl.i = (T)yv[l];
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hB_lut[ri * (Nl + 1) + l] = hl * B[l]; //store the bessel function result
//std::cout<<hB_lut[ri * (Nl + 1) + l]<<std::endl;
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}
}
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//T* real_lut = (T*) malloc(hB_bytes/2);
//stim::real(real_lut, hB_lut, N_hB_lut);
//stim::cpu2image<T>(real_lut, "hankel_B.bmp", Nl+1, N_hB_lut, stim::cmBrewer);
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//Allocate device memory and copy everything to the GPU
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stim::complex<T>* dev_hB_lut;
HANDLE_ERROR( cudaMalloc(&dev_hB_lut, hB_bytes) );
HANDLE_ERROR( cudaMemcpy(dev_hB_lut, hB_lut, hB_bytes, cudaMemcpyHostToDevice) );
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//std::cout << "r_min: " << r_min << std::endl;
//std::cout << "dr: " << dr << std::endl;
gpu_scalar_mie_scatter<T>(E, N, x, y, z, dev_W, W.size(), a, n, c, dev_hB_lut, r_min, dr, N_hB_lut, Nl);
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HANDLE_ERROR(cudaMemcpy(E, E, N * sizeof(stim::complex<T>), cudaMemcpyDeviceToHost)); //copy the field from device memory
HANDLE_ERROR(cudaFree(dev_hB_lut));
HANDLE_ERROR(cudaFree(dev_r));
HANDLE_ERROR(cudaFree(dev_W));
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}
/// Calculate the scalar Mie solution for the scattered field produced by a single plane wave
/// @param E is a pointer to the destination field values
/// @param N is the number of points used to calculate the field
/// @param x is an array of x coordinates for each point, specified relative to the sphere (x = NULL assumes all zeros)
/// @param y is an array of y coordinates for each point, specified relative to the sphere (y = NULL assumes all zeros)
/// @param z is an array of z coordinates for each point, specified relative to the sphere (z = NULL assumes all zeros)
/// @param W is an array of planewaves that will be scattered
/// @param a is the radius of the sphere
/// @param n is the complex refractive index of the sphere
template<typename T>
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void cpu_scalar_mie_scatter(stim::complex<T>* E, size_t N, T* x, T* y, T* z, std::vector<stim::scalarwave<T>> W, T a, stim::complex<T> n, stim::vec3<T> c = stim::vec3<T>(0, 0, 0)){
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/*#ifdef CUDA_FOUND
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stim::complex<T>* dev_E; //allocate space for the field
cudaMalloc(&dev_E, N * sizeof(stim::complex<T>));
cudaMemcpy(dev_E, E, N * sizeof(stim::complex<T>), cudaMemcpyHostToDevice);
//cudaMemset(dev_F, 0, N * sizeof(stim::complex<T>)); //set the field to zero (necessary because a sum is used)
// COORDINATES
T* dev_x = NULL; //allocate space and copy the X coordinate (if specified)
if(x != NULL){
HANDLE_ERROR(cudaMalloc(&dev_x, N * sizeof(T)));
HANDLE_ERROR(cudaMemcpy(dev_x, x, N * sizeof(T), cudaMemcpyHostToDevice));
}
T* dev_y = NULL; //allocate space and copy the Y coordinate (if specified)
if(y != NULL){
HANDLE_ERROR(cudaMalloc(&dev_y, N * sizeof(T)));
HANDLE_ERROR(cudaMemcpy(dev_y, y, N * sizeof(T), cudaMemcpyHostToDevice));
}
T* dev_z = NULL; //allocate space and copy the Z coordinate (if specified)
if(z != NULL){
HANDLE_ERROR(cudaMalloc(&dev_z, N * sizeof(T)));
HANDLE_ERROR(cudaMemcpy(dev_z, z, N * sizeof(T), cudaMemcpyHostToDevice));
}
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gpu_scalar_mie_scatter(dev_E, N, dev_x, dev_y, dev_z, W, a, n, c, r_spacing);
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if(x != NULL) cudaFree(dev_x); //free everything
if(y != NULL) cudaFree(dev_y);
if(z != NULL) cudaFree(dev_z);
cudaFree(dev_E);
#else
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*/
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//calculate the necessary number of orders required to represent the scattered field
T k = W[0].kmag();
int Nl = (int)ceil(k*a + 4 * cbrt( k * a ) + 2);
if(Nl < LOCAL_NL) Nl = LOCAL_NL; //always do at least the minimum number of local operations (kernel optimization)
//std::cout<<"Nl: "<<Nl<<std::endl;
//calculate the scattering coefficients for the sphere
stim::complex<T>* B = (stim::complex<T>*) malloc( sizeof(stim::complex<T>) * (Nl + 1) ); //allocate space for the scattering coefficients
B_coefficients(B, a, k, n, Nl);
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//allocate space to store the bessel function call results
double vm;
double* j_kr = (double*) malloc( (Nl + 1) * sizeof(double) );
double* y_kr = (double*) malloc( (Nl + 1) * sizeof(double) );
double* dj_kr= (double*) malloc( (Nl + 1) * sizeof(double) );
double* dy_kr= (double*) malloc( (Nl + 1) * sizeof(double) );
T* P = (T*) malloc( (Nl + 1) * sizeof(T) );
T r, kr, cos_phi;
stim::complex<T> h;
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stim::complex<T> Ew;
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for(size_t i = 0; i < N; i++){
stim::vec3<T> p; //declare a 3D point
(x == NULL) ? p[0] = 0 : p[0] = x[i]; // test for NULL values and set positions
(y == NULL) ? p[1] = 0 : p[1] = y[i];
(z == NULL) ? p[2] = 0 : p[2] = z[i];
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p = p - c;
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r = p.len();
if(r >= a){
for(size_t w = 0; w < W.size(); w++){
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Ew = W[w].E() * exp(stim::complex<float>(0, W[w].kvec().dot(c)));
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kr = p.len() * W[w].kmag(); //calculate k*r
stim::bessjyv_sph<double>(Nl, kr, vm, j_kr, y_kr, dj_kr, dy_kr);
cos_phi = p.norm().dot(W[w].kvec().norm()); //calculate the cosine of the angle from the propagating direction
stim::legendre<T>(Nl, cos_phi, P);
for(size_t l = 0; l <= Nl; l++){
h.r = j_kr[l];
h.i = y_kr[l];
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E[i] += Ew * B[l] * h * P[l];
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}
}
}
}
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//#endif
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}
template<typename T>
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void cpu_scalar_mie_scatter(stim::complex<T>* E, size_t N, T* x, T* y, T* z, stim::scalarwave<T> w, T a, stim::complex<T> n, stim::vec3<T> c = stim::vec3<T>(0, 0, 0), T r_spacing = 0.1){
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std::vector< stim::scalarwave<T> > W(1, w);
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cpu_scalar_mie_scatter(E, N, x, y, z, W, a, n, c, r_spacing);
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}
template<typename T>
__global__ void cuda_scalar_mie_internal(stim::complex<T>* E, size_t N, T* x, T* y, T* z, stim::scalarwave<T>* W, size_t nW, T a, stim::complex<T> n, stim::complex<T>* jA, T r_min, T dr, size_t N_jA, int Nl){
extern __shared__ stim::complex<T> shared_jA[]; //declare the list of waves in shared memory
size_t i = blockIdx.x * blockDim.x + threadIdx.x; //get the index into the array
if(i >= N) return; //exit if this thread is outside the array
stim::vec3<T> p;
(x == NULL) ? p[0] = 0 : p[0] = x[i]; // test for NULL values and set positions
(y == NULL) ? p[1] = 0 : p[1] = y[i];
(z == NULL) ? p[2] = 0 : p[2] = z[i];
T r = p.len(); //calculate the distance from the sphere
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if(r >= a) return; //exit if the point is inside the sphere (we only calculate the internal field)
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T fij = (r - r_min)/dr; //FP index into the spherical bessel LUT
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size_t ij = (size_t) fij; //convert to an integral index
T alpha = fij - ij; //calculate the fractional portion of the index
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size_t n0j = ij * (Nl + 1); //start of the first entry in the LUT
size_t n1j = (ij+1) * (Nl + 1); //start of the second entry in the LUT
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T cos_phi;
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T Pl_2, Pl_1, Pl; //declare registers to store the previous two Legendre polynomials
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stim::complex<T> jAl;
stim::complex<T> Ei = 0; //create a register to store the result
int l;
stim::complex<T> jlAl[LOCAL_NL+1]; //the first LOCAL_NL components are stored in registers for speed
int shared_start = threadIdx.x * (Nl - LOCAL_NL); //wrap up some operations so that they aren't done in the main loops
#pragma unroll LOCAL_NL+1 //copy the first LOCAL_NL+1 h_l * B_l components to registers
for(l = 0; l <= LOCAL_NL; l++)
jlAl[l] = clerp<T>( jA[n0j + l], jA[n1j + l], alpha );
for(l = LOCAL_NL+1; l <= Nl; l++) //copy any additional h_l * B_l components to shared memory
shared_jA[shared_start + (l - (LOCAL_NL+1))] = clerp<T>( jA[n0j + l], jA[n1j + l], alpha );
for(size_t w = 0; w < nW; w++){ //for each plane wave
if(r == 0) cos_phi = 0;
else
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cos_phi = p.norm().dot(W[w].kvec().norm()); //calculate the cosine of the angle between the k vector and the direction from the sphere
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Pl_2 = 1; //the Legendre polynomials will be calculated recursively, initialize the first two steps of the recursive relation
Pl_1 = cos_phi;
Ei += W[w].E() * jlAl[0] * Pl_2; //unroll the first two orders using the initial steps of the Legendre recursive relation
Ei += W[w].E() * jlAl[1] * Pl_1;
#pragma unroll LOCAL_NL-1 //unroll the next LOCAL_NL-1 loops for speed (iterating through the components in the register file)
for(l = 2; l <= LOCAL_NL; l++){
Pl = ( (2 * (l-1) + 1) * cos_phi * Pl_1 - (l-1) * Pl_2 ) / (l); //calculate the next step in the Legendre polynomial recursive relation (this is where most of the computation occurs)
Ei += W[w].E() * jlAl[l] * Pl; //calculate and sum the current field order
Pl_2 = Pl_1; //shift Pl_1 -> Pl_2 and Pl -> Pl_1
Pl_1 = Pl;
}
for(l = LOCAL_NL+1; l <= Nl; l++){ //do the same as above, except for any additional orders that are stored in shared memory (not registers)
Pl = ( (2 * (l-1) + 1) * cos_phi * Pl_1 - (l-1) * Pl_2 ) / (l); //again, this is where most computation in the kernel occurs
Ei += W[w].E() * shared_jA[shared_start + l - LOCAL_NL - 1] * Pl;
Pl_2 = Pl_1; //shift Pl_1 -> Pl_2 and Pl -> Pl_1
Pl_1 = Pl;
}
}
E[i] = Ei; //copy the result to device memory
}
template<typename T>
void gpu_scalar_mie_internal(stim::complex<T>* E, size_t N, T* x, T* y, T* z, stim::scalarwave<T>* W, size_t nW, T a, stim::complex<T> n, stim::complex<T>* jA, T r_min, T dr, size_t N_jA, size_t Nl){
size_t max_shared_mem = stim::sharedMemPerBlock();
size_t hBl_array = sizeof(stim::complex<T>) * (Nl + 1);
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//std::cout<<"hl*Bl array size: "<<hBl_array<<std::endl;
//std::cout<<"shared memory: "<<max_shared_mem<<std::endl;
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int threads = (int)((max_shared_mem / hBl_array) / 32 * 32);
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//std::cout<<"threads per block: "<<threads<<std::endl;
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dim3 blocks((unsigned)(N / threads + 1)); //calculate the optimal number of blocks
size_t shared_mem;
if(Nl <= LOCAL_NL) shared_mem = 0;
else shared_mem = threads * sizeof(stim::complex<T>) * (Nl - LOCAL_NL); //amount of shared memory to allocate
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//std::cout<<"shared memory allocated: "<<shared_mem<<std::endl;
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cuda_scalar_mie_internal<T><<< blocks, threads, shared_mem >>>(E, N, x, y, z, W, nW, a, n, jA, r_min, dr, N_jA, (int)Nl); //call the kernel
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}
/// Calculate the scalar Mie solution for the internal field produced by a single plane wave scattered by a sphere
/// @param E is a pointer to the destination field values
/// @param N is the number of points used to calculate the field
/// @param x is an array of x coordinates for each point, specified relative to the sphere (x = NULL assumes all zeros)
/// @param y is an array of y coordinates for each point, specified relative to the sphere (y = NULL assumes all zeros)
/// @param z is an array of z coordinates for each point, specified relative to the sphere (z = NULL assumes all zeros)
/// @param w is a planewave that will be scattered
/// @param a is the radius of the sphere
/// @param n is the complex refractive index of the sphere
template<typename T>
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void cpu_scalar_mie_internal(stim::complex<T>* E, size_t N, T* x, T* y, T* z, std::vector< stim::scalarwave<T> > W, T a, stim::complex<T> n, stim::vec3<T> c = stim::vec3<T>(0, 0, 0)){
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//calculate the necessary number of orders required to represent the scattered field
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T k = W[0].kmag();
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int Nl = (int)ceil(k*a + 4 * cbrt( k * a ) + 2);
if(Nl < LOCAL_NL) Nl = LOCAL_NL; //always do at least the minimum number of local operations (kernel optimization)
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//std::cout<<"Nl: "<<Nl<<std::endl;
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//calculate the scattering coefficients for the sphere
stim::complex<T>* A = (stim::complex<T>*) malloc( sizeof(stim::complex<T>) * (Nl + 1) ); //allocate space for the scattering coefficients
A_coefficients(A, a, k, n, Nl);
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/*#ifdef CUDA_FOUND
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stim::complex<T>* dev_E; //allocate space for the field
cudaMalloc(&dev_E, N * sizeof(stim::complex<T>));
cudaMemcpy(dev_E, E, N * sizeof(stim::complex<T>), cudaMemcpyHostToDevice);
//cudaMemset(dev_F, 0, N * sizeof(stim::complex<T>)); //set the field to zero (necessary because a sum is used)
// COORDINATES
T* dev_x = NULL; //allocate space and copy the X coordinate (if specified)
if(x != NULL){
HANDLE_ERROR(cudaMalloc(&dev_x, N * sizeof(T)));
HANDLE_ERROR(cudaMemcpy(dev_x, x, N * sizeof(T), cudaMemcpyHostToDevice));
}
T* dev_y = NULL; //allocate space and copy the Y coordinate (if specified)
if(y != NULL){
HANDLE_ERROR(cudaMalloc(&dev_y, N * sizeof(T)));
HANDLE_ERROR(cudaMemcpy(dev_y, y, N * sizeof(T), cudaMemcpyHostToDevice));
}
T* dev_z = NULL; //allocate space and copy the Z coordinate (if specified)
if(z != NULL){
HANDLE_ERROR(cudaMalloc(&dev_z, N * sizeof(T)));
HANDLE_ERROR(cudaMemcpy(dev_z, z, N * sizeof(T), cudaMemcpyHostToDevice));
}
// PLANE WAVES
stim::scalarwave<T>* dev_W; //allocate space and copy plane waves
HANDLE_ERROR( cudaMalloc(&dev_W, sizeof(stim::scalarwave<T>) * W.size()) );
HANDLE_ERROR( cudaMemcpy(dev_W, &W[0], sizeof(stim::scalarwave<T>) * W.size(), cudaMemcpyHostToDevice) );
// BESSEL FUNCTION LOOK-UP TABLE
//calculate the distance from the sphere center
T* dev_r;
HANDLE_ERROR( cudaMalloc(&dev_r, sizeof(T) * N) );
int threads = stim::maxThreadsPerBlock();
dim3 blocks((unsigned)(N / threads + 1));
cuda_dist<T> <<< blocks, threads >>>(dev_r, dev_x, dev_y, dev_z, N);
//Find the minimum and maximum values of r
cublasStatus_t stat;
cublasHandle_t handle;
stat = cublasCreate(&handle); //create a cuBLAS handle
if (stat != CUBLAS_STATUS_SUCCESS){ //test for failure
printf ("CUBLAS initialization failed\n");
exit(1);
}
int i_min, i_max;
stat = cublasIsamin(handle, (int)N, dev_r, 1, &i_min);
if (stat != CUBLAS_STATUS_SUCCESS){ //test for failure
printf ("CUBLAS Error: failed to calculate minimum r value.\n");
exit(1);
}
stat = cublasIsamax(handle, (int)N, dev_r, 1, &i_max);
if (stat != CUBLAS_STATUS_SUCCESS){ //test for failure
printf ("CUBLAS Error: failed to calculate maximum r value.\n");
exit(1);
}
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cublasDestroy(handle); //destroy the CUBLAS handle
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i_min--; //cuBLAS uses 1-based indexing for Fortran compatibility
i_max--;
T r_min, r_max; //allocate space to store the minimum and maximum values
HANDLE_ERROR( cudaMemcpy(&r_min, dev_r + i_min, sizeof(T), cudaMemcpyDeviceToHost) ); //copy the min and max values from the device to the CPU
HANDLE_ERROR( cudaMemcpy(&r_max, dev_r + i_max, sizeof(T), cudaMemcpyDeviceToHost) );
r_max = min(r_max, a); //the internal field doesn't exist outside of the sphere
size_t N_jA_lut = (size_t)((r_max - r_min) / r_spacing + 1);
//temporary variables
double vm; //allocate space to store the return values for the bessel function calculation
stim::complex<double>* jv = (stim::complex<double>*) malloc( (Nl + 1) * sizeof(stim::complex<double>) );
stim::complex<double>* yv = (stim::complex<double>*) malloc( (Nl + 1) * sizeof(stim::complex<double>) );
stim::complex<double>* djv= (stim::complex<double>*) malloc( (Nl + 1) * sizeof(stim::complex<double>) );
stim::complex<double>* dyv= (stim::complex<double>*) malloc( (Nl + 1) * sizeof(stim::complex<double>) );
size_t jA_bytes = sizeof(stim::complex<T>) * (Nl+1) * N_jA_lut;
stim::complex<T>* jA_lut = (stim::complex<T>*) malloc(jA_bytes); //pointer to the look-up table
T dr = (r_max - r_min) / (N_jA_lut-1); //distance between values in the LUT
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//std::cout<<"LUT jl bytes: "<<jA_bytes<<std::endl;
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stim::complex<T> hl;
stim::complex<double> nd = (stim::complex<double>)n;
for(size_t ri = 0; ri < N_jA_lut; ri++){ //for each value in the LUT
stim::cbessjyva_sph<double>(Nl, nd * k * (r_min + ri * dr), vm, jv, yv, djv, dyv); //compute the list of spherical bessel functions from [0 Nl]
for(size_t l = 0; l <= Nl; l++){ //for each order
jA_lut[ri * (Nl + 1) + l] = (stim::complex<T>)(jv[l] * (stim::complex<double>)A[l]); //store the bessel function result
}
}
//Allocate device memory and copy everything to the GPU
stim::complex<T>* dev_jA_lut;
HANDLE_ERROR( cudaMalloc(&dev_jA_lut, jA_bytes) );
HANDLE_ERROR( cudaMemcpy(dev_jA_lut, jA_lut, jA_bytes, cudaMemcpyHostToDevice) );
gpu_scalar_mie_internal<T>(dev_E, N, dev_x, dev_y, dev_z, dev_W, W.size(), a, n, dev_jA_lut, r_min, dr, N_jA_lut, Nl);
cudaMemcpy(E, dev_E, N * sizeof(stim::complex<T>), cudaMemcpyDeviceToHost); //copy the field from device memory
if(x != NULL) cudaFree(dev_x); //free everything
if(y != NULL) cudaFree(dev_y);
if(z != NULL) cudaFree(dev_z);
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HANDLE_ERROR( cudaFree(dev_jA_lut) );
HANDLE_ERROR( cudaFree(dev_E) );
HANDLE_ERROR( cudaFree(dev_W) );
HANDLE_ERROR( cudaFree(dev_r) );
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HANDLE_ERROR( cudaFree(dev_E) );
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#else
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*/
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//allocate space to store the bessel function call results
double vm;
stim::complex<double>* j_knr = (stim::complex<double>*) malloc( (Nl + 1) * sizeof(stim::complex<double>) );
stim::complex<double>* y_knr = (stim::complex<double>*) malloc( (Nl + 1) * sizeof(stim::complex<double>) );
stim::complex<double>* dj_knr= (stim::complex<double>*) malloc( (Nl + 1) * sizeof(stim::complex<double>) );
stim::complex<double>* dy_knr= (stim::complex<double>*) malloc( (Nl + 1) * sizeof(stim::complex<double>) );
T* P = (T*) malloc( (Nl + 1) * sizeof(T) );
T r, cos_phi;
stim::complex<double> knr;
stim::complex<T> h;
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stim::complex<T> Ew;
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for(size_t i = 0; i < N; i++){
stim::vec3<T> p; //declare a 3D point
(x == NULL) ? p[0] = 0 : p[0] = x[i]; // test for NULL values and set positions
(y == NULL) ? p[1] = 0 : p[1] = y[i];
(z == NULL) ? p[2] = 0 : p[2] = z[i];
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p = p - c;
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r = p.len();
if(r < a){
E[i] = 0;
for(size_t w = 0; w < W.size(); w++){
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Ew = W[w].E() * exp(stim::complex<float>(0, W[w].kvec().dot(c)));
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knr = (stim::complex<double>)n * p.len() * W[w].kmag(); //calculate k*n*r
stim::cbessjyva_sph<double>(Nl, knr, vm, j_knr, y_knr, dj_knr, dy_knr);
if(r == 0)
cos_phi = 0;
else
cos_phi = p.norm().dot(W[w].kvec().norm()); //calculate the cosine of the angle from the propagating direction
stim::legendre<T>(Nl, cos_phi, P);
for(size_t l = 0; l <= Nl; l++){
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E[i] += Ew * A[l] * (stim::complex<T>)j_knr[l] * P[l];
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}
}
}
}
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//#endif
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}
template<typename T>
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void cpu_scalar_mie_internal(stim::complex<T>* E, size_t N, T* x, T* y, T* z, stim::scalarwave<T> w, T a, stim::complex<T> n, stim::vec3<T> c = stim::vec3<T>(0, 0, 0)){
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std::vector< stim::scalarwave<T> > W(1, w);
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cpu_scalar_mie_internal(E, N, x, y, z, W, a, n, c);
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}
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/// Class stim::scalarmie represents a scalar Mie scattering model that can be used to calculate the fields produced by a scattering sphere.
template<typename T>
class scalarmie
{
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T radius; //radius of the scattering sphere
stim::complex<T> n; //refractive index of the scattering sphere
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vec3<T> c; //position of the sphere in space
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public:
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scalarmie() { //default constructor
radius = 0.5;
n = stim::complex<T>(1.4, 0.0);
c = stim::vec3<T>(0, 0, 0);
}
scalarmie(T r, stim::complex<T> ri, stim::vec3<T> center = stim::vec3<T>(0, 0, 0)){
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radius = r;
n = ri;
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c = center;
//c = stim::vec3<T>(2, 1, 0);
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}
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//void sum_scat(stim::scalarfield<T>& E, T* X, T* Y, T* Z, stim::scalarbeam<T> b, int samples = 1000){
// std::vector< stim::scalarwave<float> > wave_array = b.mc(samples); //decompose the beam into an array of plane waves
// stim::cpu_scalar_mie_scatter<float>(E.ptr(), E.size(), X, Y, Z, wave_array, radius, n, E.spacing());
//}
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//void sum_intern(stim::scalarfield<T>& E, T* X, T* Y, T* Z, stim::scalarbeam<T> b, int samples = 1000){
// std::vector< stim::scalarwave<float> > wave_array = b.mc(samples); //decompose the beam into an array of plane waves
// stim::cpu_scalar_mie_internal<float>(E.ptr(), E.size(), X, Y, Z, wave_array, radius, n, E.spacing());
//}
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//void eval(stim::scalarfield<T>& E, T* X, T* Y, T* Z, stim::scalarbeam<T> b, int order = 500, int samples = 1000){
// b.eval(E, X, Y, Z, order); //evaluate the incident field using a plane wave expansion
// std::vector< stim::scalarwave<float> > wave_array = b.mc(samples); //decompose the beam into an array of plane waves
// sum_scat(E, X, Y, Z, b, samples);
// sum_intern(E, X, Y, Z, b, samples);
//}
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void eval(stim::scalarfield<T>& E, stim::scalarbeam<T> b, int order = 500, int samples = 1000){
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E.meshgrid();
b.eval(E, order);
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std::vector< stim::scalarwave<float> > wave_array = b.mc(samples); //decompose the beam into an array of plane waves
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if(E.gpu()){
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stim::gpu_scalar_mie_scatter<float>(E.ptr(), E.size(), E.x(), E.y(), E.z(), wave_array, radius, n, c, E.spacing());
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}
else{
stim::cpu_scalar_mie_scatter<float>(E.ptr(), E.size(), E.x(), E.y(), E.z(), wave_array, radius, n, E.spacing());
stim::cpu_scalar_mie_internal<float>(E.ptr(), E.size(), E.x(), E.y(), E.z(), wave_array, radius, n, E.spacing());
}
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}
}; //end stim::scalarmie
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template<typename T>
class scalarcluster : public std::vector< scalarmie<T> > {
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public:
void eval(stim::scalarfield<T>& E, stim::scalarbeam<T> b, int order = 500, int samples = 1000) {
E.meshgrid();
b.eval(E, order);
std::vector< stim::scalarwave<float> > wave_array = b.mc(samples); //decompose the beam into an array of plane waves
T radius;
stim::complex<T> n;
stim::vec3<T> c;
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for (size_t si = 0; si < std::vector< scalarmie<T> >::size(); si++) { //for each sphere in the cluster
radius = std::vector< scalarmie<T> >::at(si).radius;
n = std::vector< scalarmie<T> >::at(si).n;
c = std::vector< scalarmie<T> >::at(si).c;
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if (E.gpu()) {
stim::gpu_scalar_mie_scatter<float>(E.ptr(), E.size(), E.x(), E.y(), E.z(), wave_array, radius, n, c, E.spacing());
}
else {
stim::cpu_scalar_mie_scatter<float>(E.ptr(), E.size(), E.x(), E.y(), E.z(), wave_array, radius, n, c);
stim::cpu_scalar_mie_internal<float>(E.ptr(), E.size(), E.x(), E.y(), E.z(), wave_array, radius, n, c);
}
}
}
};
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} //end namespace stim
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#endif
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