diff --git a/processing/post/addCurl.py b/processing/post/addCurl.py index fd358703f..ba310750b 100755 --- a/processing/post/addCurl.py +++ b/processing/post/addCurl.py @@ -22,39 +22,26 @@ def curlFFT(geomdim,field): curl_fourier = np.empty(field_fourier.shape,'c16') # differentiation in Fourier space - k_s = np.zeros([3],'i') TWOPIIMG = 2.0j*math.pi - for i in range(grid[2]): - k_s[0] = i - if grid[2]%2 == 0 and i == grid[2]//2: k_s[0] = 0 # for even grid, set Nyquist freq to 0 (Johnson, MIT, 2011) - elif i > grid[2]//2: k_s[0] -= grid[2] - - for j in range(grid[1]): - k_s[1] = j - if grid[1]%2 == 0 and j == grid[1]//2: k_s[1] = 0 # for even grid, set Nyquist freq to 0 (Johnson, MIT, 2011) - elif j > grid[1]//2: k_s[1] -= grid[1] - - for k in range(grid[0]//2+1): - k_s[2] = k - if grid[0]%2 == 0 and k == grid[0]//2: k_s[2] = 0 # for even grid, set Nyquist freq to 0 (Johnson, MIT, 2011) - - xi = (k_s/geomdim)[2::-1].astype('c16') # reversing the field input order - - if dataType == 'tensor': - for l in range(3): - curl_fourier[i,j,k,0,l] = ( field_fourier[i,j,k,l,2]*xi[1]\ - -field_fourier[i,j,k,l,1]*xi[2]) *TWOPIIMG - curl_fourier[i,j,k,1,l] = (-field_fourier[i,j,k,l,2]*xi[0]\ - +field_fourier[i,j,k,l,0]*xi[2]) *TWOPIIMG - curl_fourier[i,j,k,2,l] = ( field_fourier[i,j,k,l,1]*xi[0]\ - -field_fourier[i,j,k,l,0]*xi[1]) *TWOPIIMG - elif dataType == 'vector': - curl_fourier[i,j,k,0] = ( field_fourier[i,j,k,2]*xi[1]\ - -field_fourier[i,j,k,1]*xi[2]) *TWOPIIMG - curl_fourier[i,j,k,1] = (-field_fourier[i,j,k,2]*xi[0]\ - +field_fourier[i,j,k,0]*xi[2]) *TWOPIIMG - curl_fourier[i,j,k,2] = ( field_fourier[i,j,k,1]*xi[0]\ - -field_fourier[i,j,k,0]*xi[1]) *TWOPIIMG + k_sk = np.where(np.arange(grid[2])>grid[2]//2,np.arange(grid[2])-grid[2],np.arange(grid[2]))/geomdim[0] + if grid[2]%2 == 0: k_sk[grid[2]//2] = 0 # for even grid, set Nyquist freq to 0 (Johnson, MIT, 2011) + + k_sj = np.where(np.arange(grid[1])>grid[1]//2,np.arange(grid[1])-grid[1],np.arange(grid[1]))/geomdim[1] + if grid[1]%2 == 0: k_sj[grid[1]//2] = 0 # for even grid, set Nyquist freq to 0 (Johnson, MIT, 2011) + + k_si = np.arange(grid[0]//2+1)/geomdim[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 symbols + e[0, 2, 1] = e[2, 1, 0] = e[1, 0, 2] = -1.0 + + if dataType == 'tensor': + curl_fourier = np.einsum('slm,ijkl,ijknm->ijksn',e,k_s,field_fourier)*TWOPIIMG + elif dataType == 'vector': + curl_fourier = np.einsum('slm,ijkl,ijkm->ijks',e,k_s,field_fourier)*TWOPIIMG return np.fft.irfftn(curl_fourier,axes=(0,1,2),s=shapeFFT).reshape([N,n]) diff --git a/processing/post/addDivergence.py b/processing/post/addDivergence.py index bbb7ac8d4..3ce35d275 100755 --- a/processing/post/addDivergence.py +++ b/processing/post/addDivergence.py @@ -19,29 +19,22 @@ def divFFT(geomdim,field): div_fourier = np.empty(field_fourier.shape[0:len(np.shape(field))-1],'c16') # size depents on whether tensor or vector # differentiation in Fourier space - k_s = np.zeros([3],'i') TWOPIIMG = 2.0j*math.pi - for i in range(grid[2]): - k_s[0] = i - if grid[2]%2 == 0 and i == grid[2]//2: k_s[0] = 0 # for even grid, set Nyquist freq to 0 (Johnson, MIT, 2011) - elif i > grid[2]//2: k_s[0] -= grid[2] - - for j in range(grid[1]): - k_s[1] = j - if grid[1]%2 == 0 and j == grid[1]//2: k_s[1] = 0 # for even grid, set Nyquist freq to 0 (Johnson, MIT, 2011) - elif j > grid[1]//2: k_s[1] -= grid[1] - - for k in range(grid[0]//2+1): - k_s[2] = k - if grid[0]%2 == 0 and k == grid[0]//2: k_s[2] = 0 # for even grid, set Nyquist freq to 0 (Johnson, MIT, 2011) - - xi = (k_s/geomdim)[2::-1].astype('c16') # reversing the field input order - if n == 9: # tensor, 3x3 -> 3 - for l in range(3): - div_fourier[i,j,k,l] = sum(field_fourier[i,j,k,l,0:3]*xi) *TWOPIIMG - elif n == 3: # vector, 3 -> 1 - div_fourier[i,j,k] = sum(field_fourier[i,j,k,0:3]*xi) *TWOPIIMG + k_sk = np.where(np.arange(grid[2])>grid[2]//2,np.arange(grid[2])-grid[2],np.arange(grid[2]))/geomdim[0] + if grid[2]%2 == 0: k_sk[grid[2]//2] = 0 # for even grid, set Nyquist freq to 0 (Johnson, MIT, 2011) + + k_sj = np.where(np.arange(grid[1])>grid[1]//2,np.arange(grid[1])-grid[1],np.arange(grid[1]))/geomdim[1] + if grid[1]%2 == 0: k_sj[grid[1]//2] = 0 # for even grid, set Nyquist freq to 0 (Johnson, MIT, 2011) + k_si = np.arange(grid[0]//2+1)/geomdim[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') + if n == 9: # tensor, 3x3 -> 3 + div_fourier = np.einsum('ijklm,ijkm->ijkl',field_fourier,k_s)*TWOPIIMG + elif n == 3: # vector, 3 -> 1 + div_fourier = np.einsum('ijkl,ijkl->ijk',field_fourier,k_s)*TWOPIIMG + return np.fft.irfftn(div_fourier,axes=(0,1,2),s=shapeFFT).reshape([N,n/3]) diff --git a/processing/post/addGradient.py b/processing/post/addGradient.py index da6852ac2..d28a6f813 100755 --- a/processing/post/addGradient.py +++ b/processing/post/addGradient.py @@ -22,29 +22,21 @@ def gradFFT(geomdim,field): grad_fourier = np.empty(field_fourier.shape+(3,),'c16') # differentiation in Fourier space - k_s = np.zeros([3],'i') TWOPIIMG = 2.0j*math.pi - for i in range(grid[2]): - k_s[0] = i - if grid[2]%2 == 0 and i == grid[2]//2: k_s[0] = 0 # for even grid, set Nyquist freq to 0 (Johnson, MIT, 2011) - elif i > grid[2]//2: k_s[0] -= grid[2] - - for j in range(grid[1]): - k_s[1] = j - if grid[1]%2 == 0 and j == grid[1]//2: k_s[1] = 0 # for even grid, set Nyquist freq to 0 (Johnson, MIT, 2011) - elif j > grid[1]//2: k_s[1] -= grid[1] - - for k in range(grid[0]//2+1): - k_s[2] = k - if grid[0]%2 == 0 and k == grid[0]//2: k_s[2] = 0 # for even grid, set Nyquist freq to 0 (Johnson, MIT, 2011) - - xi = (k_s/geomdim)[2::-1].astype('c16') # reversing the field order - - grad_fourier[i,j,k,0,:] = field_fourier[i,j,k,0]*xi *TWOPIIMG # vector field from scalar data - - if dataType == 'vector': - grad_fourier[i,j,k,1,:] = field_fourier[i,j,k,1]*xi *TWOPIIMG # tensor field from vector data - grad_fourier[i,j,k,2,:] = field_fourier[i,j,k,2]*xi *TWOPIIMG + k_sk = np.where(np.arange(grid[2])>grid[2]//2,np.arange(grid[2])-grid[2],np.arange(grid[2]))/geomdim[0] + if grid[2]%2 == 0: k_sk[grid[2]//2] = 0 # for even grid, set Nyquist freq to 0 (Johnson, MIT, 2011) + + k_sj = np.where(np.arange(grid[1])>grid[1]//2,np.arange(grid[1])-grid[1],np.arange(grid[1]))/geomdim[1] + if grid[1]%2 == 0: k_sj[grid[1]//2] = 0 # for even grid, set Nyquist freq to 0 (Johnson, MIT, 2011) + + k_si = np.arange(grid[0]//2+1)/geomdim[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') + if n == 3: # vector, 3 -> 3x3 + grad_fourier = np.einsum('ijkl,ijkm->ijklm',field_fourier,k_s)*TWOPIIMG + elif n == 1: # scalar, 1 -> 3 + grad_fourier = np.einsum('ijkl,ijkl->ijkl',field_fourier,k_s)*TWOPIIMG return np.fft.irfftn(grad_fourier,axes=(0,1,2),s=shapeFFT).reshape([N,3*n])