// mul1N pointwise multiplies a scalar (1-component) with an N-component vector,
// yielding an N-component vector stored in dst.
func mul1N(dst, a, b *data.Slice) {
util.Assert(a.NComp() == 1)
util.Assert(dst.NComp() == b.NComp())
for c := 0; c < dst.NComp(); c++ {
cuda.Mul(dst.Comp(c), a, b.Comp(c))
}
}
func divN1(dst, a, b *data.Slice) {
util.Assert(dst.NComp() == a.NComp())
util.Assert(b.NComp() == 1)
for c := 0; c < dst.NComp(); c++ {
cuda.Div(dst.Comp(c), a.Comp(c), b)
}
}
// multiply-add: dst[i] = src1[i] * factor1 + src2[i] * factor2 + src3 * factor3
func Madd3(dst, src1, src2, src3 *data.Slice, factor1, factor2, factor3 float32) {
N := dst.Len()
nComp := dst.NComp()
util.Assert(src1.Len() == N && src2.Len() == N && src3.Len() == N)
util.Assert(src1.NComp() == nComp && src2.NComp() == nComp && src3.NComp() == nComp)
cfg := make1DConf(N)
for c := 0; c < nComp; c++ {
k_madd3_async(dst.DevPtr(c), src1.DevPtr(c), factor1,
src2.DevPtr(c), factor2, src3.DevPtr(c), factor3, N, cfg)
}
}
// Select and resize one layer for interactive output
func Resize(dst, src *data.Slice, layer int) {
dstsize := dst.Size()
srcsize := src.Size()
util.Assert(dstsize[Z] == 1)
util.Assert(dst.NComp() == 1 && src.NComp() == 1)
scalex := srcsize[X] / dstsize[X]
scaley := srcsize[Y] / dstsize[Y]
util.Assert(scalex > 0 && scaley > 0)
cfg := make3DConf(dstsize)
k_resize_async(dst.DevPtr(0), dstsize[X], dstsize[Y], dstsize[Z],
src.DevPtr(0), srcsize[X], srcsize[Y], srcsize[Z], layer, scalex, scaley, cfg)
}
// shift dst by shx cells (positive or negative) along X-axis.
// new edge value is clampL at left edge or clampR at right edge.
func ShiftX(dst, src *data.Slice, shiftX int, clampL, clampR float32) {
util.Argument(dst.NComp() == 1 && src.NComp() == 1)
util.Assert(dst.Len() == src.Len())
N := dst.Size()
cfg := make3DConf(N)
k_shiftx_async(dst.DevPtr(0), src.DevPtr(0), N[X], N[Y], N[Z], shiftX, clampL, clampR, cfg)
}
// multiply: dst[i] = a[i] * b[i]
// a and b must have the same number of components
func Mul(dst, a, b *data.Slice) {
N := dst.Len()
nComp := dst.NComp()
util.Assert(a.Len() == N && a.NComp() == nComp && b.Len() == N && b.NComp() == nComp)
cfg := make1DConf(N)
for c := 0; c < nComp; c++ {
k_mul_async(dst.DevPtr(c), a.DevPtr(c), b.DevPtr(c), N, cfg)
}
}
// Copies src into dst, which is larger, and multiplies by vol*Bsat.
// The remainder of dst is not filled with zeros.
// Used to zero-pad magnetization before convolution and in the meanwhile multiply m by its length.
func copyPadMul(dst, src, vol *data.Slice, dstsize, srcsize [3]int, Msat MSlice) {
util.Argument(dst.NComp() == 1 && src.NComp() == 1)
util.Assert(dst.Len() == prod(dstsize) && src.Len() == prod(srcsize))
cfg := make3DConf(srcsize)
k_copypadmul2_async(dst.DevPtr(0), dstsize[X], dstsize[Y], dstsize[Z],
src.DevPtr(0), srcsize[X], srcsize[Y], srcsize[Z],
Msat.DevPtr(0), Msat.Mul(0), vol.DevPtr(0), cfg)
}
// Copies src into dst, which is larger, and multiplies by vol*Bsat.
// The remainder of dst is not filled with zeros.
// Used to zero-pad magnetization before convolution and in the meanwhile multiply m by its length.
func copyPadMul(dst, src, vol *data.Slice, dstsize, srcsize [3]int, Bsat LUTPtr, regions *Bytes) {
util.Argument(dst.NComp() == 1 && src.NComp() == 1)
util.Assert(dst.Len() == prod(dstsize) && src.Len() == prod(srcsize))
cfg := make3DConf(srcsize)
k_copypadmul_async(dst.DevPtr(0), dstsize[X], dstsize[Y], dstsize[Z],
src.DevPtr(0), vol.DevPtr(0), srcsize[X], srcsize[Y], srcsize[Z],
unsafe.Pointer(Bsat), regions.Ptr, cfg)
}
// Adaptive Heun method, can be used as solver.Step
func (_ *Heun) Step() {
y := M.Buffer()
dy0 := cuda.Buffer(VECTOR, y.Size())
defer cuda.Recycle(dy0)
if FixDt != 0 {
Dt_si = FixDt
}
dt := float32(Dt_si * GammaLL)
util.Assert(dt > 0)
// stage 1
torqueFn(dy0)
cuda.Madd2(y, y, dy0, 1, dt) // y = y + dt * dy
// stage 2
dy := cuda.Buffer(3, y.Size())
defer cuda.Recycle(dy)
Time += Dt_si
torqueFn(dy)
err := cuda.MaxVecDiff(dy0, dy) * float64(dt)
// adjust next time step
if err < MaxErr || Dt_si <= MinDt || FixDt != 0 { // mindt check to avoid infinite loop
// step OK
cuda.Madd3(y, y, dy, dy0, 1, 0.5*dt, -0.5*dt)
M.normalize()
NSteps++
adaptDt(math.Pow(MaxErr/err, 1./2.))
setLastErr(err)
setMaxTorque(dy)
} else {
// undo bad step
util.Assert(FixDt == 0)
Time -= Dt_si
cuda.Madd2(y, y, dy0, 1, -dt)
NUndone++
adaptDt(math.Pow(MaxErr/err, 1./3.))
}
}
// Downsample returns a slice of new size N, smaller than in.Size().
// Averaging interpolation over the input slice.
// in is returned untouched if the sizes are equal.
func Downsample(In [][][][]float32, N [3]int) [][][][]float32 {
if SizeOf(In[0]) == N {
return In // nothing to do
}
nComp := len(In)
out := NewSlice(nComp, N)
Out := out.Tensors()
srcsize := SizeOf(In[0])
dstsize := SizeOf(Out[0])
Dx := dstsize[X]
Dy := dstsize[Y]
Dz := dstsize[Z]
Sx := srcsize[X]
Sy := srcsize[Y]
Sz := srcsize[Z]
scalex := Sx / Dx
scaley := Sy / Dy
scalez := Sz / Dz
util.Assert(scalex > 0 && scaley > 0)
for c := range Out {
for iz := 0; iz < Dz; iz++ {
for iy := 0; iy < Dy; iy++ {
for ix := 0; ix < Dx; ix++ {
sum, n := 0.0, 0.0
for I := 0; I < scalez; I++ {
i2 := iz*scalez + I
for J := 0; J < scaley; J++ {
j2 := iy*scaley + J
for K := 0; K < scalex; K++ {
k2 := ix*scalex + K
if i2 < Sz && j2 < Sy && k2 < Sx {
sum += float64(In[c][i2][j2][k2])
n++
}
}
}
}
Out[c][iz][iy][ix] = float32(sum / n)
}
}
}
}
return Out
}
// Calculates the magnetostatic kernel by brute-force integration
// of magnetic charges over the faces and averages over cell volumes.
func CalcDemagKernel(inputSize, pbc [3]int, cellsize [3]float64, accuracy float64) (kernel [3][3]*data.Slice) {
// Add zero-padding in non-PBC directions
size := padSize(inputSize, pbc)
// Sanity check
{
util.Assert(size[Z] > 0 && size[Y] > 0 && size[X] > 0)
util.Assert(cellsize[X] > 0 && cellsize[Y] > 0 && cellsize[Z] > 0)
util.Assert(pbc[X] >= 0 && pbc[Y] >= 0 && pbc[Z] >= 0)
util.Assert(accuracy > 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, size)
array[i][j] = kernel[i][j].Scalars()
}
}
// Field (destination) loop ranges
r1, r2 := kernelRanges(size, pbc)
// 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]
}
}
progress, progmax := 0, (1+(r2[Y]-r1[Y]))*(1+(r2[Z]-r1[Z])) // progress bar
done := make(chan struct{}, 3) // parallel calculation of one component done?
// Start brute integration
// 9 nested loops, does that stress you out?
// Fortunately, the 5 inner ones usually loop over just one element.
for s := 0; s < 3; s++ { // source index Ksdxyz (parallelized over)
go func(s int) {
u, v, w := s, (s+1)%3, (s+2)%3 // u = direction of source (s), v & w are the orthogonal directions
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 z := r1[Z]; z <= r2[Z]; z++ {
zw := wrap(z, size[Z])
// skip one half, reconstruct from symmetry later
// check on wrapped index instead of loop range so it also works for PBC
if zw > size[Z]/2 {
if s == 0 {
progress += (1 + (r2[Y] - r1[Y]))
}
continue
}
R[Z] = float64(z) * cellsize[Z]
for y := r1[Y]; y <= r2[Y]; y++ {
if s == 0 { // show progress of only one component
progress++
util.Progress(progress, progmax, "Calculating demag kernel")
}
yw := wrap(y, size[Y])
if yw > size[Y]/2 {
continue
}
R[Y] = float64(y) * cellsize[Y]
for x := r1[X]; x <= r2[X]; x++ {
xw := wrap(x, size[X])
if xw > size[X]/2 {
continue
}
R[X] = float64(x) * cellsize[X]
// 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, 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
array[s][d][zw][yw][xw] += float32(B[d]) // += needed in case of PBC
}
}
}
}
done <- struct{}{} // notify parallel computation of this component is done
}(s)
}
// wait for all 3 components to finish
<-done
<-done
<-done
// Reconstruct skipped parts from symmetry (X)
for z := 0; z < size[Z]; z++ {
for y := 0; y < size[Y]; y++ {
for x := size[X]/2 + 1; x < size[X]; x++ {
x2 := size[X] - x
array[X][X][z][y][x] = array[X][X][z][y][x2]
array[X][Y][z][y][x] = -array[X][Y][z][y][x2]
array[X][Z][z][y][x] = -array[X][Z][z][y][x2]
array[Y][Y][z][y][x] = array[Y][Y][z][y][x2]
array[Y][Z][z][y][x] = array[Y][Z][z][y][x2]
array[Z][Z][z][y][x] = array[Z][Z][z][y][x2]
}
}
}
// Reconstruct skipped parts from symmetry (Y)
for z := 0; z < size[Z]; z++ {
for y := size[Y]/2 + 1; y < size[Y]; y++ {
y2 := size[Y] - y
for x := 0; x < size[X]; x++ {
array[X][X][z][y][x] = array[X][X][z][y2][x]
array[X][Y][z][y][x] = -array[X][Y][z][y2][x]
array[X][Z][z][y][x] = array[X][Z][z][y2][x]
array[Y][Y][z][y][x] = array[Y][Y][z][y2][x]
array[Y][Z][z][y][x] = -array[Y][Z][z][y2][x]
array[Z][Z][z][y][x] = array[Z][Z][z][y2][x]
}
}
}
// Reconstruct skipped parts from symmetry (Z)
for z := size[Z]/2 + 1; z < size[Z]; z++ {
z2 := size[Z] - z
for y := 0; y < size[Y]; y++ {
for x := 0; x < size[X]; x++ {
array[X][X][z][y][x] = array[X][X][z2][y][x]
array[X][Y][z][y][x] = array[X][Y][z2][y][x]
array[X][Z][z][y][x] = -array[X][Z][z2][y][x]
array[Y][Y][z][y][x] = array[Y][Y][z2][y][x]
array[Y][Z][z][y][x] = -array[Y][Z][z2][y][x]
array[Z][Z][z][y][x] = array[Z][Z][z2][y][x]
}
}
}
// for 2D these elements are zero:
if size[Z] == 1 {
kernel[X][Z] = nil
kernel[Y][Z] = nil
}
// make result symmetric for tools that expect it so.
kernel[Y][X] = kernel[X][Y]
kernel[Z][X] = kernel[X][Z]
kernel[Z][Y] = kernel[Y][Z]
return kernel
}
func (c *DemagConvolution) init(realKern [3][3]*data.Slice) {
// init device buffers
// 2D re-uses fftBuf[X] as fftBuf[Z], 3D needs all 3 fftBufs.
nc := fftR2COutputSizeFloats(c.realKernSize)
c.fftCBuf[X] = NewSlice(1, nc)
c.fftCBuf[Y] = NewSlice(1, nc)
if c.is2D() {
c.fftCBuf[Z] = c.fftCBuf[X]
} else {
c.fftCBuf[Z] = NewSlice(1, nc)
}
// Real buffer shares storage with Complex buffer
for i := 0; i < 3; i++ {
c.fftRBuf[i] = data.SliceFromPtrs(c.realKernSize, data.GPUMemory, []unsafe.Pointer{c.fftCBuf[i].DevPtr(0)})
}
// init FFT plans
c.fwPlan = newFFT3DR2C(c.realKernSize[X], c.realKernSize[Y], c.realKernSize[Z])
c.bwPlan = newFFT3DC2R(c.realKernSize[X], c.realKernSize[Y], c.realKernSize[Z])
// init FFT kernel
// logic size of FFT(kernel): store real parts only
c.fftKernLogicSize = fftR2COutputSizeFloats(c.realKernSize)
util.Assert(c.fftKernLogicSize[X]%2 == 0)
c.fftKernLogicSize[X] /= 2
// physical size of FFT(kernel): store only non-redundant part exploiting Y, Z mirror symmetry
// X mirror symmetry already exploited: FFT(kernel) is purely real.
physKSize := [3]int{c.fftKernLogicSize[X], c.fftKernLogicSize[Y]/2 + 1, c.fftKernLogicSize[Z]/2 + 1}
output := c.fftCBuf[0]
input := c.fftRBuf[0]
fftKern := data.NewSlice(1, physKSize)
kfull := data.NewSlice(1, output.Size()) // not yet exploiting symmetry
kfulls := kfull.Scalars()
kCSize := physKSize
kCSize[X] *= 2 // size of kernel after removing Y,Z redundant parts, but still complex
kCmplx := data.NewSlice(1, kCSize) // not yet exploiting X symmetry
kc := kCmplx.Scalars()
for i := 0; i < 3; i++ {
for j := i; j < 3; j++ { // upper triangular part
if realKern[i][j] != nil { // ignore 0's
// FW FFT
data.Copy(input, realKern[i][j])
c.fwPlan.ExecAsync(input, output)
data.Copy(kfull, output)
// extract non-redundant part (Y,Z symmetry)
for iz := 0; iz < kCSize[Z]; iz++ {
for iy := 0; iy < kCSize[Y]; iy++ {
for ix := 0; ix < kCSize[X]; ix++ {
kc[iz][iy][ix] = kfulls[iz][iy][ix]
}
}
}
// extract real parts (X symmetry)
scaleRealParts(fftKern, kCmplx, 1/float32(c.fwPlan.InputLen()))
c.kern[i][j] = GPUCopy(fftKern)
}
}
}
}
func (rk *RK4) Step() {
m := M.Buffer()
size := m.Size()
if FixDt != 0 {
Dt_si = FixDt
}
t0 := Time
// backup magnetization
m0 := cuda.Buffer(3, size)
defer cuda.Recycle(m0)
data.Copy(m0, m)
k1, k2, k3, k4 := cuda.Buffer(3, size), cuda.Buffer(3, size), cuda.Buffer(3, size), cuda.Buffer(3, size)
defer cuda.Recycle(k1)
defer cuda.Recycle(k2)
defer cuda.Recycle(k3)
defer cuda.Recycle(k4)
h := float32(Dt_si * GammaLL) // internal time step = Dt * gammaLL
// stage 1
torqueFn(k1)
// stage 2
Time = t0 + (1./2.)*Dt_si
cuda.Madd2(m, m, k1, 1, (1./2.)*h) // m = m*1 + k1*h/2
M.normalize()
torqueFn(k2)
// stage 3
cuda.Madd2(m, m0, k2, 1, (1./2.)*h) // m = m0*1 + k2*1/2
M.normalize()
torqueFn(k3)
// stage 4
Time = t0 + Dt_si
cuda.Madd2(m, m0, k3, 1, 1.*h) // m = m0*1 + k3*1
M.normalize()
torqueFn(k4)
err := cuda.MaxVecDiff(k1, k4) * float64(h)
// adjust next time step
if err < MaxErr || Dt_si <= MinDt || FixDt != 0 { // mindt check to avoid infinite loop
// step OK
// 4th order solution
madd5(m, m0, k1, k2, k3, k4, 1, (1./6.)*h, (1./3.)*h, (1./3.)*h, (1./6.)*h)
M.normalize()
NSteps++
adaptDt(math.Pow(MaxErr/err, 1./4.))
setLastErr(err)
setMaxTorque(k4)
} else {
// undo bad step
//util.Println("Bad step at t=", t0, ", err=", err)
util.Assert(FixDt == 0)
Time = t0
data.Copy(m, m0)
NUndone++
adaptDt(math.Pow(MaxErr/err, 1./5.))
}
}
func (rk *RK45DP) Step() {
m := M.Buffer()
size := m.Size()
if FixDt != 0 {
Dt_si = FixDt
}
// upon resize: remove wrongly sized k1
if rk.k1.Size() != m.Size() {
rk.Free()
}
// first step ever: one-time k1 init and eval
if rk.k1 == nil {
rk.k1 = cuda.NewSlice(3, size)
torqueFn(rk.k1)
}
// FSAL cannot be used with finite temperature
if !Temp.isZero() {
torqueFn(rk.k1)
}
t0 := Time
// backup magnetization
m0 := cuda.Buffer(3, size)
defer cuda.Recycle(m0)
data.Copy(m0, m)
k2, k3, k4, k5, k6 := cuda.Buffer(3, size), cuda.Buffer(3, size), cuda.Buffer(3, size), cuda.Buffer(3, size), cuda.Buffer(3, size)
defer cuda.Recycle(k2)
defer cuda.Recycle(k3)
defer cuda.Recycle(k4)
defer cuda.Recycle(k5)
defer cuda.Recycle(k6)
// k2 will be re-used as k7
h := float32(Dt_si * GammaLL) // internal time step = Dt * gammaLL
// there is no explicit stage 1: k1 from previous step
// stage 2
Time = t0 + (1./5.)*Dt_si
cuda.Madd2(m, m, rk.k1, 1, (1./5.)*h) // m = m*1 + k1*h/5
M.normalize()
torqueFn(k2)
// stage 3
Time = t0 + (3./10.)*Dt_si
cuda.Madd3(m, m0, rk.k1, k2, 1, (3./40.)*h, (9./40.)*h)
M.normalize()
torqueFn(k3)
// stage 4
Time = t0 + (4./5.)*Dt_si
madd4(m, m0, rk.k1, k2, k3, 1, (44./45.)*h, (-56./15.)*h, (32./9.)*h)
M.normalize()
torqueFn(k4)
// stage 5
Time = t0 + (8./9.)*Dt_si
madd5(m, m0, rk.k1, k2, k3, k4, 1, (19372./6561.)*h, (-25360./2187.)*h, (64448./6561.)*h, (-212./729.)*h)
M.normalize()
torqueFn(k5)
// stage 6
Time = t0 + (1.)*Dt_si
madd6(m, m0, rk.k1, k2, k3, k4, k5, 1, (9017./3168.)*h, (-355./33.)*h, (46732./5247.)*h, (49./176.)*h, (-5103./18656.)*h)
M.normalize()
torqueFn(k6)
// stage 7: 5th order solution
Time = t0 + (1.)*Dt_si
// no k2
madd6(m, m0, rk.k1, k3, k4, k5, k6, 1, (35./384.)*h, (500./1113.)*h, (125./192.)*h, (-2187./6784.)*h, (11./84.)*h) // 5th
M.normalize()
k7 := k2 // re-use k2
torqueFn(k7) // next torque if OK
// error estimate
Err := cuda.Buffer(3, size) //k3 // re-use k3 as error estimate
defer cuda.Recycle(Err)
madd6(Err, rk.k1, k3, k4, k5, k6, k7, (35./384.)-(5179./57600.), (500./1113.)-(7571./16695.), (125./192.)-(393./640.), (-2187./6784.)-(-92097./339200.), (11./84.)-(187./2100.), (0.)-(1./40.))
// determine error
err := cuda.MaxVecNorm(Err) * float64(h)
// adjust next time step
if err < MaxErr || Dt_si <= MinDt || FixDt != 0 { // mindt check to avoid infinite loop
// step OK
setLastErr(err)
setMaxTorque(k7)
NSteps++
Time = t0 + Dt_si
adaptDt(math.Pow(MaxErr/err, 1./5.))
data.Copy(rk.k1, k7) // FSAL
} else {
// undo bad step
//util.Println("Bad step at t=", t0, ", err=", err)
util.Assert(FixDt == 0)
Time = t0
data.Copy(m, m0)
NUndone++
adaptDt(math.Pow(MaxErr/err, 1./6.))
}
}
func unslice(v []float64) [3]float64 {
util.Assert(len(v) == 3)
return [3]float64{v[0], v[1], v[2]}
}
// dst = a/b, unless b == 0
func paramDiv(dst, a, b [][NREGION]float32) {
util.Assert(len(dst) == 1 && len(a) == 1 && len(b) == 1)
for i := 0; i < NREGION; i++ { // not regions.maxreg
dst[0][i] = safediv(a[0][i], b[0][i])
}
}
func (rk *RK23) Step() {
m := M.Buffer()
size := m.Size()
if FixDt != 0 {
Dt_si = FixDt
}
// upon resize: remove wrongly sized k1
if rk.k1.Size() != m.Size() {
rk.Free()
}
// first step ever: one-time k1 init and eval
if rk.k1 == nil {
rk.k1 = cuda.NewSlice(3, size)
torqueFn(rk.k1)
}
// FSAL cannot be used with temperature
if !Temp.isZero() {
torqueFn(rk.k1)
}
t0 := Time
// backup magnetization
m0 := cuda.Buffer(3, size)
defer cuda.Recycle(m0)
data.Copy(m0, m)
k2, k3, k4 := cuda.Buffer(3, size), cuda.Buffer(3, size), cuda.Buffer(3, size)
defer cuda.Recycle(k2)
defer cuda.Recycle(k3)
defer cuda.Recycle(k4)
h := float32(Dt_si * GammaLL) // internal time step = Dt * gammaLL
// there is no explicit stage 1: k1 from previous step
// stage 2
Time = t0 + (1./2.)*Dt_si
cuda.Madd2(m, m, rk.k1, 1, (1./2.)*h) // m = m*1 + k1*h/2
M.normalize()
torqueFn(k2)
// stage 3
Time = t0 + (3./4.)*Dt_si
cuda.Madd2(m, m0, k2, 1, (3./4.)*h) // m = m0*1 + k2*3/4
M.normalize()
torqueFn(k3)
// 3rd order solution
madd4(m, m0, rk.k1, k2, k3, 1, (2./9.)*h, (1./3.)*h, (4./9.)*h)
M.normalize()
// error estimate
Time = t0 + Dt_si
torqueFn(k4)
Err := k2 // re-use k2 as error
// difference of 3rd and 2nd order torque without explicitly storing them first
madd4(Err, rk.k1, k2, k3, k4, (7./24.)-(2./9.), (1./4.)-(1./3.), (1./3.)-(4./9.), (1. / 8.))
// determine error
err := cuda.MaxVecNorm(Err) * float64(h)
// adjust next time step
if err < MaxErr || Dt_si <= MinDt || FixDt != 0 { // mindt check to avoid infinite loop
// step OK
setLastErr(err)
setMaxTorque(k4)
NSteps++
Time = t0 + Dt_si
adaptDt(math.Pow(MaxErr/err, 1./3.))
data.Copy(rk.k1, k4) // FSAL
} else {
// undo bad step
//util.Println("Bad step at t=", t0, ", err=", err)
util.Assert(FixDt == 0)
Time = t0
data.Copy(m, m0)
NUndone++
adaptDt(math.Pow(MaxErr/err, 1./4.))
}
}
func (p *Excitation) MSlice() cuda.MSlice {
buf, r := p.Slice()
util.Assert(r == true)
return cuda.ToMSlice(buf)
}
// Kernel for the vertical derivative of the force on an MFM tip due to mx, my, mz.
// This is the 2nd derivative of the energy w.r.t. z.
func MFMKernel(mesh *d.Mesh, lift, tipsize float64) (kernel [3]*d.Slice) {
const TipCharge = 1 / Mu0 // tip charge
const Δ = 1e-9 // tip oscillation, take 2nd derivative over this distance
util.AssertMsg(lift > 0, "MFM tip crashed into sample, please lift the new one higher")
{ // Kernel mesh is 2x larger than input, instead in case of PBC
pbc := mesh.PBC()
sz := padSize(mesh.Size(), pbc)
cs := mesh.CellSize()
mesh = d.NewMesh(sz[X], sz[Y], sz[Z], cs[X], cs[Y], cs[Z], pbc[:]...)
}
// Shorthand
size := mesh.Size()
pbc := mesh.PBC()
cellsize := mesh.CellSize()
volume := cellsize[X] * cellsize[Y] * cellsize[Z]
fmt.Println("calculating MFM kernel")
// Sanity check
{
util.Assert(size[Z] >= 1 && size[Y] >= 2 && size[X] >= 2)
util.Assert(cellsize[X] > 0 && cellsize[Y] > 0 && cellsize[Z] > 0)
util.AssertMsg(size[X]%2 == 0 && size[Y]%2 == 0, "Even kernel size needed")
if size[Z] > 1 {
util.AssertMsg(size[Z]%2 == 0, "Even kernel size needed")
}
}
// Allocate only upper diagonal part. The rest is symmetric due to reciprocity.
var K [3][][][]float32
for i := 0; i < 3; i++ {
kernel[i] = d.NewSlice(1, mesh.Size())
K[i] = kernel[i].Scalars()
}
r1, r2 := kernelRanges(size, pbc)
progress, progmax := 0, (1+r2[Y]-r1[Y])*(1+r2[Z]-r1[Z])
for iz := r1[Z]; iz <= r2[Z]; iz++ {
zw := wrap(iz, size[Z])
z := float64(iz) * cellsize[Z]
for iy := r1[Y]; iy <= r2[Y]; iy++ {
yw := wrap(iy, size[Y])
y := float64(iy) * cellsize[Y]
progress++
util.Progress(progress, progmax, "Calculating MFM kernel")
for ix := r1[X]; ix <= r2[X]; ix++ {
x := float64(ix) * cellsize[X]
xw := wrap(ix, size[X])
for s := 0; s < 3; s++ { // source index Ksxyz
m := d.Vector{0, 0, 0}
m[s] = 1
var E [3]float64 // 3 energies for 2nd derivative
for i := -1; i <= 1; i++ {
I := float64(i)
R := d.Vector{-x, -y, z - (lift + (I * Δ))}
r := R.Len()
B := R.Mul(TipCharge / (4 * math.Pi * r * r * r))
R = d.Vector{-x, -y, z - (lift + tipsize + (I * Δ))}
r = R.Len()
B = B.Add(R.Mul(-TipCharge / (4 * math.Pi * r * r * r)))
E[i+1] = B.Dot(m) * volume // i=-1 stored in E[0]
}
dFdz_tip := ((E[0] - E[1]) + (E[2] - E[1])) / (Δ * Δ) // dFz/dz = d2E/dz2
K[s][zw][yw][xw] += float32(dFdz_tip) // += needed in case of PBC
}
}
}
}
return kernel
}
// utility for LUT of single-component data
func (p *lut) gpuLUT1() cuda.LUTPtr {
util.Assert(len(p.gpu_buf) == 1)
return cuda.LUTPtr(p.gpuLUT()[0])
}
