more sensible interface
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@ -1,9 +1,8 @@
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from scipy import spatial
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import numpy as np
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def __ks(size,field,first_order=False):
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def __ks(size,grid,first_order=False):
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"""Get wave numbers operator."""
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grid = np.array(np.shape(field)[:3])
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k_sk = np.where(np.arange(grid[0])>grid[0]//2,np.arange(grid[0])-grid[0],np.arange(grid[0]))/size[0]
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if grid[0]%2 == 0 and first_order: k_sk[grid[0]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011)
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@ -20,7 +19,7 @@ def __ks(size,field,first_order=False):
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def curl(size,field):
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"""Calculate curl of a vector or tensor field in Fourier space."""
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n = np.prod(field.shape[3:])
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k_s = __ks(size,field,True)
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k_s = __ks(size,field.shape[:3],True)
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e = np.zeros((3, 3, 3))
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e[0, 1, 2] = e[1, 2, 0] = e[2, 0, 1] = +1.0 # Levi-Civita symbol
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@ -36,7 +35,7 @@ def curl(size,field):
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def divergence(size,field):
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"""Calculate divergence of a vector or tensor field in Fourier space."""
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n = np.prod(field.shape[3:])
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k_s = __ks(size,field,True)
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k_s = __ks(size,field.shape[:3],True)
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field_fourier = np.fft.rfftn(field,axes=(0,1,2))
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divergence = (np.einsum('ijkl,ijkl ->ijk', k_s,field_fourier)*2.0j*np.pi if n == 3 else # vector, 3 -> 1
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@ -48,7 +47,7 @@ def divergence(size,field):
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def gradient(size,field):
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"""Calculate gradient of a vector or scalar field in Fourier space."""
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n = np.prod(field.shape[3:])
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k_s = __ks(size,field,True)
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k_s = __ks(size,field.shape[:3],True)
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field_fourier = np.fft.rfftn(field,axes=(0,1,2))
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gradient = (np.einsum('ijkl,ijkm->ijkm', field_fourier,k_s)*2.0j*np.pi if n == 1 else # scalar, 1 -> 3
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@ -72,7 +71,7 @@ def cell_displacement_fluct(size,F):
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"""Cell center displacement field from fluctuation part of the deformation gradient field."""
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integrator = 0.5j*size/np.pi
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k_s = __ks(size,F,False)
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k_s = __ks(size,F.shape[:3],False)
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k_s_squared = np.einsum('...l,...l',k_s,k_s)
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k_s_squared[0,0,0] = 1.0
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