// Extract real parts, copy them from src to dst.
// In the meanwhile, check if imaginary parts are nearly zero
// and scale the kernel to compensate for unnormalized FFTs.
func scaleRealParts(dst, src *data.Slice, scale float32) {
util.Argument(2*dst.Len() == src.Len())
util.Argument(dst.NComp() == 1 && src.NComp() == 1)
srcList := src.HostCopy().Host()[0]
dstList := dst.Host()[0]
// Normally, the FFT'ed kernel is purely real because of symmetry,
// so we only store the real parts...
maximg := float32(0.)
maxreal := float32(0.)
for i := 0; i < src.Len()/2; i++ {
dstList[i] = srcList[2*i] * scale
if fabs(srcList[2*i+0]) > maxreal {
maxreal = fabs(srcList[2*i+0])
}
if fabs(srcList[2*i+1]) > maximg {
maximg = fabs(srcList[2*i+1])
}
}
// ...however, we check that the imaginary parts are nearly zero,
// just to be sure we did not make a mistake during kernel creation.
if maximg/maxreal > FFT_IMAG_TOLERANCE {
log.Fatalf("Too large FFT kernel imaginary/real part: %v", maximg/maxreal)
}
}
func kernMulRSymm2Dx(fftMx, K00 *data.Slice, N1, N2 int, str cu.Stream) {
util.Argument(K00.Len() == (N1/2+1)*N2)
util.Argument(fftMx.NComp() == 1 && K00.NComp() == 1)
cfg := make2DConf(N1, N2)
k_kernmulRSymm2Dx_async(fftMx.DevPtr(0), K00.DevPtr(0), N1, N2, cfg, str)
}
// Does not yet use Y mirror symmetry!!
// Even though it is implemented partially in kernel
func kernMulRSymm3D(fftM [3]*data.Slice, K00, K11, K22, K12, K02, K01 *data.Slice, N0, N1, N2 int, str cu.Stream) {
util.Argument(K00.Len() == N0*(N1)*N2) // no symmetry yet
util.Argument(fftM[0].NComp() == 1 && K00.NComp() == 1)
cfg := make2DConf(N1, N2)
k_kernmulRSymm3D_async(fftM[0].DevPtr(0), fftM[1].DevPtr(0), fftM[2].DevPtr(0),
K00.DevPtr(0), K11.DevPtr(0), K22.DevPtr(0), K12.DevPtr(0), K02.DevPtr(0), K01.DevPtr(0),
N0, N1, N2, cfg, str)
}
func kernMulRSymm2Dyz(fftMy, fftMz, K11, K22, K12 *data.Slice, N1, N2 int, str cu.Stream) {
util.Argument(K11.Len() == (N1/2+1)*N2)
util.Argument(fftMy.NComp() == 1 && K11.NComp() == 1)
cfg := make2DConf(N1, N2)
k_kernmulRSymm2Dyz_async(fftMy.DevPtr(0), fftMz.DevPtr(0),
K11.DevPtr(0), K22.DevPtr(0), K12.DevPtr(0),
N1, N2, cfg, str)
}
// Copies src into dst, which is larger or smaller, and multiplies by vol*Bsat.
// The remainder of dst is not filled with zeros.
func copyPadMul(dst, src *data.Slice, dstsize, srcsize [3]int, vol *data.Slice, Bsat float64, str cu.Stream) {
util.Argument(dst.NComp() == 1)
util.Argument(src.NComp() == 1)
util.Argument(vol.NComp() == 1)
util.Assert(dst.Len() == prod(dstsize) && src.Len() == prod(srcsize))
util.Assert(vol.Mesh().Size() == srcsize)
N0 := iMin(dstsize[1], srcsize[1])
N1 := iMin(dstsize[2], srcsize[2])
cfg := make2DConf(N0, N1)
k_copypadmul_async(dst.DevPtr(0), dstsize[0], dstsize[1], dstsize[2],
src.DevPtr(0), srcsize[0], srcsize[1], srcsize[2],
vol.DevPtr(0), float32(Bsat), cfg, str)
}
//// Maximum of the norms of the difference between all vectors (x1,y1,z1) and (x2,y2,z2)
//// (dx, dy, dz) = (x1, y1, z1) - (x2, y2, z2)
//// max_i sqrt( dx[i]*dx[i] + dy[i]*dy[i] + dz[i]*dz[i] )
func MaxVecDiff(x, y *data.Slice) float64 {
util.Argument(x.Len() == y.Len())
out := reduceBuf(0)
k_reducemaxvecdiff2(x.DevPtr(0), x.DevPtr(1), x.DevPtr(2),
y.DevPtr(0), y.DevPtr(1), y.DevPtr(2),
out, 0, x.Len(), reducecfg)
return math.Sqrt(float64(copyback(out)))
}
// Memset sets the Slice's components to the specified values.
func Memset(s *data.Slice, val ...float32) {
util.Argument(len(val) == s.NComp())
str := stream()
for c, v := range val {
cu.MemsetD32Async(cu.DevicePtr(s.DevPtr(c)), math.Float32bits(v), int64(s.Len()), str)
}
syncAndRecycle(str)
}
// Adds a constant to each element of the slice.
// dst[comp][index] += cnst[comp]
func AddConst(dst *data.Slice, cnst ...float32) {
util.Argument(len(cnst) == dst.NComp())
N := dst.Len()
cfg := make1DConf(N)
str := stream()
for c := 0; c < dst.NComp(); c++ {
if cnst[c] != 0 {
k_madd2_async(dst.DevPtr(c), dst.DevPtr(c), 1, nil, cnst[c], N, cfg, str)
}
}
syncAndRecycle(str)
}
// Execute the FFT plan, asynchronous.
// src and dst are 3D arrays stored 1D arrays.
func (p *fft3DR2CPlan) ExecAsync(src, dst *data.Slice) {
util.Argument(src.NComp() == 1 && dst.NComp() == 1)
oksrclen := p.InputLen()
if src.Len() != oksrclen {
log.Panicf("fft size mismatch: expecting src len %v, got %v", oksrclen, src.Len())
}
okdstlen := p.OutputLen()
if dst.Len() != okdstlen {
log.Panicf("fft size mismatch: expecting dst len %v, got %v", okdstlen, dst.Len())
}
p.handle.ExecR2C(cu.DevicePtr(src.DevPtr(0)), cu.DevicePtr(dst.DevPtr(0)))
}
// Copies src into dst, which is larger or smaller.
// The remainder of dst is not filled with zeros.
func copyPad(dst, src *data.Slice, dstsize, srcsize [3]int, str cu.Stream) {
util.Argument(dst.NComp() == 1 && src.NComp() == 1)
util.Assert(dst.Len() == prod(dstsize))
util.Assert(src.Len() == prod(srcsize))
N0 := iMin(dstsize[1], srcsize[1])
N1 := iMin(dstsize[2], srcsize[2])
cfg := make2DConf(N0, N1)
k_copypad_async(dst.DevPtr(0), dstsize[0], dstsize[1], dstsize[2],
src.DevPtr(0), srcsize[0], srcsize[1], srcsize[2], cfg, str)
}
// Make a vortex magnetization with given circulation and core polarization (+1 or -1)
// Example:
// M.Upload(Vortex(1, 1))
func Vortex(circ, pol int) *data.Slice {
util.Argument(circ == 1 || circ == -1)
util.Argument(pol == 1 || pol == -1)
mh := data.NewSlice(3, Mesh())
v := mh.Vectors()
cy, cz := len(v[0][0])/2, len(v[0][0][0])/2
for i := range v[0] {
for j := range v[0][i] {
for k := range v[0][0][j] {
y := j - cy
x := k - cz
v[X][i][j][k] = 0
v[Y][i][j][k] = float32(x * circ)
v[Z][i][j][k] = float32(-y * circ)
}
}
v[Z][i][cy][cz] = 0.
v[Y][i][cy][cz] = 0.
v[X][i][cy][cz] = float32(pol)
}
return mh
}
func AddZhangLiTorque(torque, m *data.Slice, j [3]float64, Msat float64, j_MsMap *data.Slice, alpha, xi float64) {
// TODO: assert...
util.Argument(j_MsMap == nil) // not yet supported
c := torque.Mesh().CellSize()
N := torque.Mesh().Size()
cfg := make2DConfSize(N[2], N[1], STENCIL_BLOCKSIZE)
b := MuB / (Qe * Msat * (1 + xi*xi))
ux := float32((j[0] * b) / (Gamma0 * 2 * c[0]))
uy := float32((j[1] * b) / (Gamma0 * 2 * c[1]))
uz := float32((j[2] * b) / (Gamma0 * 2 * c[2]))
k_addzhanglitorque(torque.DevPtr(0), torque.DevPtr(1), torque.DevPtr(2),
m.DevPtr(0), m.DevPtr(1), m.DevPtr(2),
ux, uy, uz,
j_MsMap.DevPtr(0), j_MsMap.DevPtr(1), j_MsMap.DevPtr(2),
float32(alpha), float32(xi),
N[0], N[1], N[2], cfg)
}
// Calculates the magnetostatic kernel by brute-force integration
// of magnetic charges over the faces and averages over cell volumes.
// Mesh should NOT yet be zero-padded.
func BruteKernel(mesh *data.Mesh, accuracy float64) (kernel [3][3]*data.Slice) {
{ // Kernel mesh is 2x larger than input, instead in case of PBC
pbc := mesh.PBC()
util.Argument(pbc == [3]int{0, 0, 0}) // PBC not supported yet
sz := padSize(mesh.Size(), pbc)
cs := mesh.CellSize()
mesh = data.NewMesh(sz[0], sz[1], sz[2], cs[0], cs[1], cs[2], pbc[:]...)
}
// Shorthand
size := mesh.Size()
cellsize := mesh.CellSize()
periodic := mesh.PBC()
log.Println("calculating demag kernel:", "accuracy:", accuracy, ", size:", size[0], "x", size[1], "x", size[2])
// Sanity check
{
util.Assert(size[0] > 0 && size[1] > 1 && size[2] > 1)
util.Assert(cellsize[0] > 0 && cellsize[1] > 0 && cellsize[2] > 0)
util.Assert(periodic[0] >= 0 && periodic[1] >= 0 && periodic[2] >= 0)
util.Assert(accuracy > 0)
// TODO: in case of PBC, this will not be met:
util.Assert(size[1]%2 == 0 && size[2]%2 == 0)
if size[0] > 1 {
util.Assert(size[0]%2 == 0)
}
}
// Allocate only upper diagonal part. The rest is symmetric due to reciprocity.
var array [3][3][][][]float32
for i := 0; i < 3; i++ {
for j := i; j < 3; j++ {
kernel[i][j] = data.NewSlice(1, mesh)
array[i][j] = kernel[i][j].Scalars()
}
}
// Field (destination) loop ranges
x1, x2 := -(size[X]-1)/2, size[X]/2-1
y1, y2 := -(size[Y]-1)/2, size[Y]/2-1
z1, z2 := -(size[Z]-1)/2, size[Z]/2-1
// support for 2D simulations (thickness 1)
if size[X] == 1 && periodic[X] == 0 {
x2 = 0
}
{ // Repeat for PBC:
x1 *= (periodic[X] + 1)
x2 *= (periodic[X] + 1)
y1 *= (periodic[Y] + 1)
y2 *= (periodic[Y] + 1)
z1 *= (periodic[Z] + 1)
z2 *= (periodic[Z] + 1)
}
// smallest cell dimension is our typical length scale
L := cellsize[X]
if cellsize[Y] < L {
L = cellsize[Y]
}
if cellsize[Z] < L {
L = cellsize[Z]
}
// Start brute integration
// 9 nested loops, does that stress you out?
// Fortunately, the 5 inner ones usually loop over just one element.
// It might be nice to get rid of that branching though.
var (
R, R2 [3]float64 // field and source cell center positions
pole [3]float64 // position of point charge on the surface
points int // counts used integration points
)
for s := 0; s < 3; s++ { // source index Ksdxyz
u, v, w := s, (s+1)%3, (s+2)%3 // u = direction of source (s), v & w are the orthogonal directions
for x := x1; x <= x2; x++ { // in each dimension, go from -(size-1)/2 to size/2 -1, wrapped.
xw := wrap(x, size[X])
R[X] = float64(x) * cellsize[X]
for y := y1; y <= y2; y++ {
yw := wrap(y, size[Y])
R[Y] = float64(y) * cellsize[Y]
for z := z1; z <= z2; z++ {
zw := wrap(z, size[Z])
R[Z] = float64(z) * cellsize[Z]
// choose number of integration points depending on how far we are from source.
dx, dy, dz := delta(x)*cellsize[X], delta(y)*cellsize[Y], delta(z)*cellsize[Z]
d := math.Sqrt(dx*dx + dy*dy + dz*dz)
if d == 0 {
d = L
}
maxSize := d / accuracy // maximum acceptable integration size
nv := int(math.Max(cellsize[v]/maxSize, 1) + 0.5)
nw := int(math.Max(cellsize[w]/maxSize, 1) + 0.5)
nx := int(math.Max(cellsize[X]/maxSize, 1) + 0.5)
ny := int(math.Max(cellsize[Y]/maxSize, 1) + 0.5)
nz := int(math.Max(cellsize[Z]/maxSize, 1) + 0.5)
// Stagger source and destination grids.
// Massively improves accuracy. Could play with variations.
// See note.
nv *= 2
nw *= 2
util.Assert(nv > 0 && nw > 0 && nx > 0 && ny > 0 && nz > 0)
scale := 1 / float64(nv*nw*nx*ny*nz)
surface := cellsize[v] * cellsize[w] // the two directions perpendicular to direction s
charge := surface * scale
pu1 := cellsize[u] / 2. // positive pole center
pu2 := -pu1 // negative pole center
// Do surface integral over source cell, accumulate in B
var B [3]float64
for i := 0; i < nv; i++ {
pv := -(cellsize[v] / 2.) + cellsize[v]/float64(2*nv) + float64(i)*(cellsize[v]/float64(nv))
pole[v] = pv
for j := 0; j < nw; j++ {
pw := -(cellsize[w] / 2.) + cellsize[w]/float64(2*nw) + float64(j)*(cellsize[w]/float64(nw))
pole[w] = pw
// Do volume integral over destination cell
for α := 0; α < nx; α++ {
rx := R[X] - cellsize[X]/2 + cellsize[X]/float64(2*nx) + (cellsize[X]/float64(nx))*float64(α)
for β := 0; β < ny; β++ {
ry := R[Y] - cellsize[Y]/2 + cellsize[Y]/float64(2*ny) + (cellsize[Y]/float64(ny))*float64(β)
for γ := 0; γ < nz; γ++ {
rz := R[Z] - cellsize[Z]/2 + cellsize[Z]/float64(2*nz) + (cellsize[Z]/float64(nz))*float64(γ)
points++
pole[u] = pu1
R2[X], R2[Y], R2[Z] = rx-pole[X], ry-pole[Y], rz-pole[Z]
r := math.Sqrt(R2[X]*R2[X] + R2[Y]*R2[Y] + R2[Z]*R2[Z])
qr := charge / (4 * math.Pi * r * r * r)
bx := R2[X] * qr
by := R2[Y] * qr
bz := R2[Z] * qr
pole[u] = pu2
R2[X], R2[Y], R2[Z] = rx-pole[X], ry-pole[Y], rz-pole[Z]
r = math.Sqrt(R2[X]*R2[X] + R2[Y]*R2[Y] + R2[Z]*R2[Z])
qr = -charge / (4 * math.Pi * r * r * r)
B[X] += (bx + R2[X]*qr) // addition ordered for accuracy
B[Y] += (by + R2[Y]*qr)
B[Z] += (bz + R2[Z]*qr)
}
}
}
}
}
for d := s; d < 3; d++ { // destination index Ksdxyz
// TODO: for PBC, need to add here
array[s][d][xw][yw][zw] = float32(B[d])
}
}
}
}
}
log.Println("kernel used", points, "integration points")
// for 2D these elements are zero:
if size[0] == 1 {
kernel[0][1] = nil
kernel[0][2] = nil
}
// make result symmetric for tools that expect it so.
kernel[1][0] = kernel[0][1]
kernel[2][0] = kernel[0][2]
kernel[2][1] = kernel[1][2]
return kernel
}
// Maximum of absolute values of all elements.
func MaxAbs(in *data.Slice) float32 {
util.Argument(in.NComp() == 1)
out := reduceBuf(0)
k_reducemaxabs(in.DevPtr(0), out, 0, in.Len(), reducecfg)
return copyback(out)
}
func NewHeun(y *data.Synced, torqueFn func(bool) *data.Synced, postStep func(*data.Slice), dt, multiplier float64, time *float64) *Heun {
util.Argument(dt > 0 && multiplier > 0)
m := y.Mesh()
dy0 := NewSlice(3, m)
return &Heun{newSolverCommon(dt, multiplier, time), y, dy0, torqueFn, postStep}
}