void VectorVectorConvolution_Simple::execute(const VectorMatrix &rhs, Matrix &res)
{
VectorMatrix::const_accessor S_acc(lhs);
VectorMatrix::const_accessor M_acc(rhs);
Matrix:: accessor phi_acc(res);
// phi(r) = int S(r-r')*M(r') dr'
// phi = Sx*Mx + Sy*My + Sz*Mz
for (int z=0; z<dim_z; ++z)
for (int y=0; y<dim_y; ++y)
for (int x=0; x<dim_x; ++x)
{
double sum = 0.0;
for (int o=0; o<dim_z; ++o)
for (int n=0; n<dim_y; ++n)
for (int m=0; m<dim_x; ++m)
{
// (X,Y,Z): position in demag tensor field matrix
const int X = (x-m+exp_x) % exp_x;
const int Y = (y-n+exp_y) % exp_y;
const int Z = (z-o+exp_z) % exp_z;
const Vector3d &S = S_acc.get(X, Y, Z);
const Vector3d &M = M_acc.get(m, n, o);
sum = S.x*M.x + S.y*M.y + S.z*M.z;
}
phi_acc.at(x, y, z) = sum;
}
}
void fdm_zhangli_cpu(
int dim_x, int dim_y, int dim_z,
double delta_x, double delta_y, double delta_z,
bool do_precess,
const Matrix &P, const Matrix &xi,
const Matrix &Ms, const Matrix &alpha,
const VectorMatrix &j, const VectorMatrix &M,
VectorMatrix &dM)
{
VectorMatrix::const_accessor M_acc(M), j_acc(j);
Matrix::ro_accessor Ms_acc(Ms), alpha_acc(alpha), P_acc(P), xi_acc(xi);
VectorMatrix::accessor dM_acc(dM);
for (int z=0; z<dim_z; ++z)
for (int y=0; y<dim_y; ++y)
for (int x=0; x<dim_x; ++x) {
const int k = z*dim_x*dim_y + y*dim_x + x;
const double Ms = Ms_acc.at(k);
const double alpha = alpha_acc.at(k);
const double P = P_acc.at(k);
const double xi = xi_acc.at(k);
const Vector3d j = j_acc.get(k);
dM_acc.set(k, zhangli_dMdt(x, y, z, dim_x, dim_y, dim_z, delta_x, delta_y, delta_z, do_precess, P, xi, Ms, alpha, j, M_acc));
}
}
void Transposer_CUDA::copy_pad(const VectorMatrix &M, float *out_x, float *out_y, float *out_z)
{
// Ifdef HAVE_CUDA_64, we directly support input matrices that
// are stored with 64 bit precision on the GPU.
#ifdef HAVE_CUDA_64
const bool M_is_cuda64_bit = M.isCached(2); // 0 = CPU device, 2 = CUDA_64 device
if (M_is_cuda64_bit) {
VectorMatrix::const_cu64_accessor M_acc(M);
// xyz, M -> s1
cuda_copy_pad_r2r(dim_x, dim_y, dim_z, exp_x, M_acc.ptr_x(), M_acc.ptr_y(), M_acc.ptr_z(), out_x, out_y, out_z);
}
else
#endif
{
VectorMatrix::const_cu32_accessor M_acc(M);
// xyz, M -> s1
cuda_copy_pad_r2r(dim_x, dim_y, dim_z, exp_x, M_acc.ptr_x(), M_acc.ptr_y(), M_acc.ptr_z(), out_x, out_y, out_z);
}
}
Vector3d findExtremum_cpu(VectorMatrix &M, int z_slice, int component)
{
if (M.getShape().getRank() != 3) {
throw std::runtime_error("findExtremum: Fixme: Need matrix of rank 3");
}
if (component < 0 || component > 2) {
throw std::runtime_error("findExtremum: Invalid 'component' value, must be 0, 1 or 2.");
}
const int dim_x = M.getShape().getDim(0);
const int dim_y = M.getShape().getDim(1);
VectorMatrix::const_accessor M_acc(M);
// Find cell with maximum absolute value
double max_val = -1.0;
int max_x = -1, max_y = -1;
for (int y=1; y<dim_y-1; ++y)
for (int x=1; x<dim_x-1; ++x) {
const int val = std::fabs(M_acc.get(x, y, z_slice)[component]);
if (val > max_val) {
max_val = val;
max_x = x;
max_y = y;
}
}
assert(max_x > 0);
assert(max_y > 0);
// Refine maximum by fitting to sub-cell precision
const double xdir_vals[3] = {
M_acc.get(max_x-1, max_y+0, z_slice)[component],
M_acc.get(max_x+0, max_y+0, z_slice)[component],
M_acc.get(max_x+1, max_y+0, z_slice)[component]
};
const double ydir_vals[3] = {
M_acc.get(max_x+0, max_y-1, z_slice)[component],
M_acc.get(max_x+0, max_y+0, z_slice)[component],
M_acc.get(max_x+0, max_y+1, z_slice)[component]
};
return Vector3d(
fit(max_x-1, max_x+0, max_x+1, xdir_vals[0], xdir_vals[1], xdir_vals[2]),
fit(max_y-1, max_y+0, max_y+1, ydir_vals[0], ydir_vals[1], ydir_vals[2]),
static_cast<double>(z_slice)
);
}
void fdm_slonchewski(
int dim_x, int dim_y, int dim_z,
double delta_x, double delta_y, double delta_z,
double a_j,
const VectorMatrix &p, // spin polarization
const Matrix &Ms,
const Matrix &alpha,
const VectorMatrix &M,
VectorMatrix &dM)
{
// Calculate:
// c1*(M x (M x p)) + c2*(M x p)
//
// c1(theta): damping factor
// c2(theta): precession factor
// Ms*cos(theta) = M*p
Matrix::ro_accessor Ms_acc(Ms), alpha_acc(alpha);
VectorMatrix::const_accessor p_acc(p);
VectorMatrix::const_accessor M_acc(M);
VectorMatrix::accessor dM_acc(dM);
const int N = dim_x * dim_y * dim_z;
for (int n=0; n<N; ++n) {
const double alpha = alpha_acc.at(n);
const double Ms = Ms_acc.at(n);
const Vector3d p = p_acc.get(n);
const Vector3d M = M_acc.get(n);
if (p == Vector3d(0.0, 0.0, 0.0)) continue;
if (Ms == 0.0) continue;
// Calculate precession and damping terms
const Vector3d Mxp = cross(M, p); // precession: u=mxp
const Vector3d MxMxp = cross(M, Mxp); // damping: t=mxu=mx(mxp)
// add both terms to dm/dt in LLGE
const double gamma_pr = GYROMAGNETIC_RATIO / (1.0 + alpha*alpha);
Vector3d dM_n;
dM_n.x = gamma_pr * a_j * (-MxMxp.x/Ms + Mxp.x*alpha);
dM_n.y = gamma_pr * a_j * (-MxMxp.y/Ms + Mxp.y*alpha);
dM_n.z = gamma_pr * a_j * (-MxMxp.z/Ms + Mxp.z*alpha);
dM_acc.set(n, dM_n);
}
}
void SymmetricMatrixVectorConvolution_Simple::execute(const VectorMatrix &rhs, VectorMatrix &res)
{
Matrix::ro_accessor N_acc(lhs);
VectorMatrix::const_accessor M_acc(rhs);
VectorMatrix:: accessor H_acc(res);
// H(r) = int N(r-r')*M(r') dr'
// Hx = Nxx*Mx + Nxy*My + Nxz*Mz
// Hy = Nyx*Mx + Nyy*My + Nyz*Mz
// Hz = Nxz*Mx + Nyz*My + Nzz*Mz
for (int z=0; z<dim_z; ++z)
for (int y=0; y<dim_y; ++y)
for (int x=0; x<dim_x; ++x)
{
Vector3d H(0.0, 0.0, 0.0);
for (int o=0; o<dim_z; ++o)
for (int n=0; n<dim_y; ++n)
for (int m=0; m<dim_x; ++m)
{
// (X,Y,Z): position in demag tensor field matrix
const int X = (x-m+exp_x) % exp_x;
const int Y = (y-n+exp_y) % exp_y;
const int Z = (z-o+exp_z) % exp_z;
const double Nxx = N_acc.at(0,X,Y,Z);
const double Nxy = N_acc.at(1,X,Y,Z);
const double Nxz = N_acc.at(2,X,Y,Z);
const double Nyy = N_acc.at(3,X,Y,Z);
const double Nyz = N_acc.at(4,X,Y,Z);
const double Nzz = N_acc.at(5,X,Y,Z);
const Vector3d &M = M_acc.get(m, n, o);
H.x += Nxx*M.x + Nxy*M.y + Nxz*M.z;
H.y += Nxy*M.x + Nyy*M.y + Nyz*M.z;
H.z += Nxz*M.x + Nyz*M.y + Nzz*M.z;
}
H_acc.set(x,y,z,H);
}
}
static double fdm_exchange_cpu_nonperiodic(
int dim_x, int dim_y, int dim_z,
double delta_x, double delta_y, double delta_z,
const Matrix &Ms,
const Matrix &A,
const VectorMatrix &M,
VectorMatrix &H)
{
const int dim_xy = dim_x * dim_y;
const double wx = 1.0 / (delta_x * delta_x);
const double wy = 1.0 / (delta_y * delta_y);
const double wz = 1.0 / (delta_z * delta_z);
VectorMatrix::const_accessor M_acc(M);
VectorMatrix::accessor H_acc(H);
Matrix::ro_accessor Ms_acc(Ms), A_acc(A);
double energy = 0.0;
for (int z=0; z<dim_z; ++z) {
for (int y=0; y<dim_y; ++y) {
for (int x=0; x<dim_x; ++x) {
const int i = z*dim_xy + y*dim_x + x; // linear index of (x,y,z)
const double Ms = Ms_acc.at(i);
if (Ms == 0.0) {
H_acc.set(i, Vector3d(0.0, 0.0, 0.0));
continue;
}
const int idx_l = i- 1;
const int idx_r = i+ 1;
const int idx_u = i- dim_x;
const int idx_d = i+ dim_x;
const int idx_f = i-dim_xy;
const int idx_b = i+dim_xy;
const Vector3d M_i = M_acc.get(i) / Ms; // magnetization at (x,y,z)
Vector3d sum(0.0, 0.0, 0.0);
// left / right (X)
if (x > 0) {
const double Ms_l = Ms_acc.at(idx_l);
if (Ms_l != 0.0) sum += ((M_acc.get(idx_l) / Ms_l) - M_i) * wx;
}
if (x < dim_x-1) {
const double Ms_r = Ms_acc.at(idx_r);
if (Ms_r != 0.0) sum += ((M_acc.get(idx_r) / Ms_r) - M_i) * wx;
}
// up / down (Y)
if (y > 0) {
const double Ms_u = Ms_acc.at(idx_u);
if (Ms_u != 0.0) sum += ((M_acc.get(idx_u) / Ms_u) - M_i) * wy;
}
if (y < dim_y-1) {
const double Ms_d = Ms_acc.at(idx_d);
if (Ms_d != 0.0) sum += ((M_acc.get(idx_d) / Ms_d) - M_i) * wy;
}
// forward / backward (Z)
if (z > 0) {
const double Ms_f = Ms_acc.at(idx_f);
if (Ms_f != 0.0) sum += ((M_acc.get(idx_f) / Ms_f) - M_i) * wz;
}
if (z < dim_z-1) {
const double Ms_b = Ms_acc.at(idx_b);
if (Ms_b != 0.0) sum += ((M_acc.get(idx_b) / Ms_b) - M_i) * wz;
}
// Exchange field at (x,y,z)
const Vector3d H_i = (2/MU0) * A_acc.at(i) * sum / Ms;
H_acc.set(i, H_i);
// Exchange energy sum
energy += dot(M_i, H_i);
}
}
}
energy *= -MU0/2.0 * delta_x * delta_y * delta_z;
return energy;
}