From 23f5e0fa58e8ca0137236bd8499a53534f11a2cb Mon Sep 17 00:00:00 2001 From: Martin Diehl Date: Tue, 26 Nov 2019 10:25:39 +0100 Subject: [PATCH] filters for operations on regular grids (in fourier space) --- python/damask/grid_filters.py | 113 ++++++++++++++++++++++++++++++++++ 1 file changed, 113 insertions(+) create mode 100644 python/damask/grid_filters.py diff --git a/python/damask/grid_filters.py b/python/damask/grid_filters.py new file mode 100644 index 000000000..6588e59bc --- /dev/null +++ b/python/damask/grid_filters.py @@ -0,0 +1,113 @@ +import numpy as np + + +def curl(size,field): + """Calculate curl of a vector or tensor field in Fourier space.""" + shapeFFT = np.array(np.shape(field))[0:3] + grid = np.array(np.shape(field)[2::-1]) + N = grid.prod() # field size + n = np.array(np.shape(field)[3:]).prod() # data size + + field_fourier = np.fft.rfftn(field,axes=(0,1,2),s=shapeFFT) + curl_fourier = np.empty(field_fourier.shape,'c16') + + k_sk = np.where(np.arange(grid[2])>grid[2]//2,np.arange(grid[2])-grid[2],np.arange(grid[2]))/size[0] + if grid[2]%2 == 0: k_sk[grid[2]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011) + + k_sj = np.where(np.arange(grid[1])>grid[1]//2,np.arange(grid[1])-grid[1],np.arange(grid[1]))/size[1] + if grid[1]%2 == 0: k_sj[grid[1]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011) + + k_si = np.arange(grid[0]//2+1)/size[2] + + kk, kj, ki = np.meshgrid(k_sk,k_sj,k_si,indexing = 'ij') + k_s = np.concatenate((ki[:,:,:,None],kj[:,:,:,None],kk[:,:,:,None]),axis = 3).astype('c16') + + e = np.zeros((3, 3, 3)) + e[0, 1, 2] = e[1, 2, 0] = e[2, 0, 1] = +1.0 # Levi-Civita symbol + e[0, 2, 1] = e[2, 1, 0] = e[1, 0, 2] = -1.0 + + curl_fourier = np.einsum('slm,ijkl,ijkm, ->ijks', e,k_s,field_fourier)*2.0j*np.pi if n == 3 else# vector, 3 -> 3 + np.einsum('slm,ijkl,ijknm,->ijksn',e,k_s,field_fourier)*2.0j*np.pi # tensor, 3x3 -> 3x3 + + return np.fft.irfftn(curl_fourier,axes=(0,1,2),s=shapeFFT).reshape([N,n]) + + +def divergence(size,field): + """Calculate divergence of a vector or tensor field in Fourier space.""" + shapeFFT = np.array(np.shape(field))[0:3] + grid = np.array(np.shape(field)[2::-1]) + N = grid.prod() # field size + n = np.array(np.shape(field)[3:]).prod() # data size + + field_fourier = np.fft.rfftn(field,axes=(0,1,2),s=shapeFFT) + div_fourier = np.empty(field_fourier.shape[0:len(np.shape(field))-1],'c16') + + k_sk = np.where(np.arange(grid[2])>grid[2]//2,np.arange(grid[2])-grid[2],np.arange(grid[2]))/size[0] + if grid[2]%2 == 0: k_sk[grid[2]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011) + + k_sj = np.where(np.arange(grid[1])>grid[1]//2,np.arange(grid[1])-grid[1],np.arange(grid[1]))/size[1] + if grid[1]%2 == 0: k_sj[grid[1]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011) + + k_si = np.arange(grid[0]//2+1)/size[2] + + kk, kj, ki = np.meshgrid(k_sk,k_sj,k_si,indexing = 'ij') + k_s = np.concatenate((ki[:,:,:,None],kj[:,:,:,None],kk[:,:,:,None]),axis = 3).astype('c16') + + div_fourier = np.einsum('ijkl,ijkl ->ijk', k_s,field_fourier)*2.0j*np.pi if n == 3 else # vector, 3 -> 1 + np.einsum('ijkm,ijklm->ijkl',k_s,field_fourier)*2.0j*np.pi # tensor, 3x3 -> 3 + + return np.fft.irfftn(div_fourier,axes=(0,1,2),s=shapeFFT).reshape([N,n//3]) + + +def gradient(size,field): + """Calculate gradient of a vector or scalar field in Fourier space.""" + shapeFFT = np.array(np.shape(field))[0:3] + grid = np.array(np.shape(field)[2::-1]) + N = grid.prod() # field size + n = np.array(np.shape(field)[3:]).prod() # data size + + field_fourier = np.fft.rfftn(field,axes=(0,1,2),s=shapeFFT) + grad_fourier = np.empty(field_fourier.shape+(3,),'c16') + + k_sk = np.where(np.arange(grid[2])>grid[2]//2,np.arange(grid[2])-grid[2],np.arange(grid[2]))/size[0] + if grid[2]%2 == 0: k_sk[grid[2]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011) + + k_sj = np.where(np.arange(grid[1])>grid[1]//2,np.arange(grid[1])-grid[1],np.arange(grid[1]))/size[1] + if grid[1]%2 == 0: k_sj[grid[1]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011) + + k_si = np.arange(grid[0]//2+1)/size[2] + + kk, kj, ki = np.meshgrid(k_sk,k_sj,k_si,indexing = 'ij') + k_s = np.concatenate((ki[:,:,:,None],kj[:,:,:,None],kk[:,:,:,None]),axis = 3).astype('c16') + grad_fourier = np.einsum('ijkl,ijkm->ijkm', field_fourier,k_s)*2.0j*np.pi if n == 1 else # scalar, 1 -> 3 + np.einsum('ijkl,ijkm->ijklm',field_fourier,k_s)*2.0j*np.pi # vector, 3 -> 3x3 + + return np.fft.irfftn(grad_fourier,axes=(0,1,2),s=shapeFFT).reshape([N,3*n]) + + +#-------------------------------------------------------------------------------------------------- +def displacementFluctFFT(F,size): + """Calculate displacement field from deformation gradient field.""" + integrator = 0.5j * size / np.pi + + kk, kj, ki = np.meshgrid(np.where(np.arange(grid[2])>grid[2]//2,np.arange(grid[2])-grid[2],np.arange(grid[2])), + np.where(np.arange(grid[1])>grid[1]//2,np.arange(grid[1])-grid[1],np.arange(grid[1])), + np.arange(grid[0]//2+1), + indexing = 'ij') + k_s = np.concatenate((ki[:,:,:,None],kj[:,:,:,None],kk[:,:,:,None]),axis = 3) + k_sSquared = np.einsum('...l,...l',k_s,k_s) + k_sSquared[0,0,0] = 1.0 # ignore global average frequency + +#-------------------------------------------------------------------------------------------------- +# integration in Fourier space + + displacement_fourier = -np.einsum('ijkml,ijkl,l->ijkm', + np.fft.rfftn(F,axes=(0,1,2)), + k_s, + integrator, + ) / k_sSquared[...,np.newaxis] + +#-------------------------------------------------------------------------------------------------- +# backtransformation to real space + + return np.fft.irfftn(displacement_fourier,grid[::-1],axes=(0,1,2))