func testConvolution(c *DemagConvolution, mesh *data.Mesh) {
inhost := data.NewSlice(3, mesh)
initConvTestInput(inhost.Vectors())
gpu := NewSlice(3, mesh)
defer gpu.Free()
data.Copy(gpu, inhost)
c.Exec(gpu, gpu, data.NilSlice(1, mesh), 1)
output := gpu.HostCopy()
//data.MustWriteFile("gpu.dump", output, 0) // rm!
brute := data.NewSlice(3, mesh)
bruteConv(inhost.Vectors(), brute.Vectors(), c.kern)
//data.MustWriteFile("brute.dump", brute, 0) // rm!
a, b := output.Host(), brute.Host()
err := float32(0)
for c := range a {
for i := range a[c] {
if abs(a[c][i]-b[c][i]) > err {
err = abs(a[c][i] - b[c][i])
}
}
}
if err > CONV_TOLERANCE {
log.Fatal("convolution self-test error: ", err)
} else {
log.Println("convolution self-test error:", err)
}
}
func TestCpy(t *testing.T) {
N0, N1, N2 := 2, 4, 32
N := N0 * N1 * N2
mesh := data.NewMesh(N0, N1, N2, 1, 1, 1)
h1 := make([]float32, N)
for i := range h1 {
h1[i] = float32(i)
}
hs := data.SliceFromList([][]float32{h1}, mesh)
d := NewSlice(1, mesh)
data.Copy(d, hs)
d2 := NewSlice(1, mesh)
data.Copy(d2, d)
h2 := data.NewSlice(1, mesh)
data.Copy(h2, d2)
res := h2.Host()[0]
for i := range res {
if res[i] != h1[i] {
t.Fail()
}
}
}
// Initialize GPU FFT kernel for 2D.
// Only the non-redundant parts are stored on the GPU.
func (c *DemagConvolution) initFFTKern2D() {
padded := c.kernSize
ffted := fftR2COutputSizeFloats(padded)
realsize := ffted
realsize[2] /= 2
c.fftKernSize = realsize
halfkern := realsize
halfkern[1] = halfkern[1]/2 + 1
fwPlan := c.fwPlan
output := c.fftCBuf[0]
input := c.fftRBuf[0]
// upper triangular part
fftKern := data.NewSlice(1, data.NewMesh(halfkern[0], halfkern[1], halfkern[2], 1, 1, 1))
for i := 0; i < 3; i++ {
for j := i; j < 3; j++ {
if c.kern[i][j] != nil { // ignore 0's
data.Copy(input, c.kern[i][j])
fwPlan.Exec(input, output)
scaleRealParts(fftKern, output.Slice(0, prod(halfkern)*2), 1/float32(fwPlan.InputLen()))
c.gpuFFTKern[i][j] = GPUCopy(fftKern)
}
}
}
}
// 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
}
// 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
}