// Detects matrix symmetry.
// returns NOSYMMETRY, SYMMETRIC, ANTISYMMETRIC
func MatrixSymmetry(matrix *host.Array) int {
AssertMsg(matrix.NComp() == 9, "MatrixSymmetry NComp")
symm := true
asymm := true
max := 1e-100
for i := 0; i < 3; i++ {
for j := 0; j < 3; j++ {
scount := 0
acount := 0
total := 0
idx1 := FullTensorIdx[i][j]
idx2 := FullTensorIdx[j][i]
comp1 := matrix.Comp[idx1]
comp2 := matrix.Comp[idx2]
for x := range comp1 {
if math.Abs(float64(comp1[x])) > max {
max = math.Abs(float64(comp1[x]))
}
total++
if comp1[x] == comp2[x] {
scount++
}
if comp1[x] != comp2[x] {
//Debug(comp1[x], "!=", comp2[x])
symm = false
//if !asymm {
//break
//}
}
if comp1[x] == -comp2[x] {
acount++
}
if comp1[x] != -comp2[x] {
//Debug(comp1[x] ,"!= -", comp2[x])
asymm = false
//if !symm {
//break
//}
}
}
Debug("max", max)
Debug(i, j, "symm", scount, "asymm", acount, "(of", total, ")")
}
}
if symm {
return SYMMETRIC // also covers all zeros
}
if asymm {
return ANTISYMMETRIC
}
return NOSYMMETRY
}
// Convert mumax's internal ZYX convention to userspace XYZ.
func convertXYZ(arr *host.Array) *host.Array {
s := arr.Size3D
n := arr.NComp()
a := arr.Array
transp := host.NewArray(n, []int{s[Z], s[Y], s[X]})
t := transp.Array
for c := 0; c < n; c++ {
for i := 0; i < s[X]; i++ {
for j := 0; j < s[Y]; j++ {
for k := 0; k < s[Z]; k++ {
t[(n-1)-c][k][j][i] = a[c][i][j][k]
}
}
}
}
runtime.GC() // a LOT of garbage has been made
return transp
}
// Returns a new host array of size size2, re-sized from the input array by nearest-neighbor interpolation.
func Resample(in *host.Array, size2 []int) *host.Array {
Assert(len(size2) == 3)
out := host.NewArray(in.NComp(), size2)
out_a := out.Array
in_a := in.Array
size1 := in.Size3D
for c := range out_a {
for i := range out_a[c] {
i1 := (i * size1[X]) / size2[X]
for j := range out_a[0][i] {
j1 := (j * size1[Y]) / size2[Y]
for k := range out_a[0][i][j] {
k1 := (k * size1[Z]) / size2[Z]
out_a[c][i][j][k] = in_a[c][i1][j1][k1]
}
}
}
}
return out
}
// Extract real or imaginary parts, copy them from src to dst.
// In the meanwhile, check if the other parts are nearly zero
// and scale the kernel to compensate for unnormalized FFTs.
// real_imag = 0: real parts
// real_imag = 1: imag parts
func extract(src *host.Array) *host.Array {
sx := src.Size3D[X]/2 + 1 // antisymmetric
sy := src.Size3D[Y]/2 + 1 // antisymmetric
sz := src.Size3D[Z] / 2 // only real parts should be stored, the value of the imaginary part should stay below the zero threshould
dst := host.NewArray(src.NComp(), []int{sx, sy, sz})
dstArray := dst.Array
srcArray := src.Array
// Normally, the FFT'ed kernel is purely real because of symmetry,
// so we only store the real parts...
maxImg := float64(0.)
maxReal := float64(0.)
for c := range dstArray {
for k := range dstArray[c] {
for j := range dstArray[c][k] {
for i := range dstArray[c][k][j] {
dstArray[c][k][j][i] = srcArray[c][k][j][2*i]
if Abs32(srcArray[c][k][j][2*i+1]) > maxImg {
maxImg = Abs32(srcArray[c][k][j][2*i+1])
}
if Abs32(srcArray[c][k][j][2*i+0]) > maxReal {
maxReal = Abs32(srcArray[c][k][j][2*i+0])
}
}
}
}
}
// ...however, we check that the imaginary parts are nearly zero,
// just to be sure we did not make a mistake during kernel creation.
Debug("FFT Kernel max real part", 0, ":", maxReal)
Debug("FFT Kernel max imag part", 1, ":", maxImg)
Debug("FFT Kernel max imag/real part=", maxImg/maxReal)
if maxImg/maxReal > 1e-12 { // TODO: is this reasonable?
panic(BugF("FFT Kernel max bad/good part=", maxImg/maxReal))
}
return dst
}
//// Loads a sub-kernel at position pos in the 3x3 global kernel matrix.
//// The symmetry and real/imaginary/complex properties are taken into account to reduce storage.
func (plan *MaxwellPlan) LoadKernel(kernel *host.Array, matsymm int, realness int) {
// for i := range kernel.Array {
// Debug("kernel", TensorIndexStr[i], ":", kernel.Array[i], "\n\n\n")
// }
//Assert(kernel.NComp() == 9) // full tensor
if kernel.NComp() > 3 {
testedsymm := MatrixSymmetry(kernel)
Debug("matsymm", testedsymm)
// TODO: re-enable!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
//Assert(matsymm == testedsymm)
}
Assert(matsymm == SYMMETRIC || matsymm == ANTISYMMETRIC || matsymm == NOSYMMETRY || matsymm == DIAGONAL)
//if FFT'd kernel is pure real or imag,
//store only relevant part and multiply by scaling later
scaling := [3]complex128{complex(1, 0), complex(0, 1), complex(0, 0)}[realness]
Debug("scaling=", scaling)
// FFT input on GPU
logic := plan.logicSize[:]
devIn := gpu.NewArray(1, logic)
defer devIn.Free()
// FFT output on GPU
devOut := gpu.NewArray(1, gpu.FFTOutputSize(logic))
defer devOut.Free()
fullFFTPlan := gpu.NewDefaultFFT(logic, logic)
defer fullFFTPlan.Free()
// Maximum of all elements gives idea of scale.
max := maxAbs(kernel.List)
// FFT all components
for k := 0; k < 9; k++ {
i, j := IdxToIJ(k) // fills diagonal first, then upper, then lower
// ignore off-diagonals of vector (would go out of bounds)
if k > ZZ && matsymm == DIAGONAL {
Debug("break", TensorIndexStr[k], "(off-diagonal)")
break
}
// elements of diagonal kernel are stored in one column
if matsymm == DIAGONAL {
i = 0
}
// clear data first
AssertMsg(plan.fftKern[i][j] == nil, "I'm afraid I can't let you overwrite that")
AssertMsg(plan.fftMul[i][j] == 0, "Likewise")
// auto-fill lower triangle if possible
if k > XY {
if matsymm == SYMMETRIC {
plan.fftKern[i][j] = plan.fftKern[j][i]
plan.fftMul[i][j] = plan.fftMul[j][i]
continue
}
if matsymm == ANTISYMMETRIC {
plan.fftKern[i][j] = plan.fftKern[j][i]
plan.fftMul[i][j] = -plan.fftMul[j][i]
continue
}
}
// ignore zeros
if k < kernel.NComp() && IsZero(kernel.Comp[k], max) {
Debug("kernel", TensorIndexStr[k], " == 0")
plan.fftKern[i][j] = gpu.NilArray(1, []int{plan.fftKernSize[X], plan.fftKernSize[Y], plan.fftKernSize[Z]})
continue
}
// calculate FFT of kernel elementx
Debug("use", TensorIndexStr[k])
devIn.CopyFromHost(kernel.Component(k))
fullFFTPlan.Forward(devIn, devOut)
hostOut := devOut.LocalCopy()
// extract real part of the kernel from the first quadrant (other parts are redundunt due to the symmetry properties)
hostFFTKern := extract(hostOut)
rescale(hostFFTKern, 1/float64(gpu.FFTNormLogic(logic)))
plan.fftKern[i][j] = gpu.NewArray(1, hostFFTKern.Size3D)
plan.fftKern[i][j].CopyFromHost(hostFFTKern)
plan.fftMul[i][j] = scaling
}
}