proper spacing
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Martin Diehl
parent
ab88ffd28e
commit
a670ab269f
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@ -1,14 +1,14 @@
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from scipy import spatial
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import numpy as np
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def __ks(size,grid,first_order=False):
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def _ks(size,grid,first_order=False):
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"""
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Get wave numbers operator.
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Parameters
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----------
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size : numpy.ndarray
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physical size of the periodic field.
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physical size of the periodic field.
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"""
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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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@ -30,14 +30,14 @@ def curl(size,field):
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Parameters
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----------
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size : numpy.ndarray
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physical size of the periodic field.
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physical size of the periodic field.
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"""
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n = np.prod(field.shape[3:])
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k_s = __ks(size,field.shape[:3],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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e[0, 1, 2] = e[1, 2, 0] = e[2, 0, 1] = +1.0 # Levi-Civita symbol
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e[0, 2, 1] = e[2, 1, 0] = e[1, 0, 2] = -1.0
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field_fourier = np.fft.rfftn(field,axes=(0,1,2))
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@ -54,11 +54,11 @@ def divergence(size,field):
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Parameters
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----------
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size : numpy.ndarray
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physical size of the periodic field.
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physical size of the periodic field.
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"""
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n = np.prod(field.shape[3:])
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k_s = __ks(size,field.shape[:3],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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@ -74,11 +74,11 @@ def gradient(size,field):
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Parameters
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----------
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size : numpy.ndarray
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physical size of the periodic field.
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physical size of the periodic field.
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"""
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n = np.prod(field.shape[3:])
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k_s = __ks(size,field.shape[:3],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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@ -96,7 +96,7 @@ def cell_coord0(grid,size,origin=np.zeros(3)):
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grid : numpy.ndarray
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number of grid points.
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size : numpy.ndarray
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physical size of the periodic field.
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physical size of the periodic field.
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origin : numpy.ndarray, optional
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physical origin of the periodic field. Default is [0.0,0.0,0.0].
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@ -108,7 +108,8 @@ def cell_coord0(grid,size,origin=np.zeros(3)):
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np.linspace(start[0],end[0],grid[0]),
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indexing = 'ij')
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return np.concatenate((z[:,:,:,None],y[:,:,:,None],x[:,:,:,None]),axis = 3)
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return np.concatenate((z[:,:,:,None],y[:,:,:,None],x[:,:,:,None]),axis = 3)
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def cell_displacement_fluct(size,F):
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"""
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@ -117,14 +118,14 @@ def cell_displacement_fluct(size,F):
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Parameters
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----------
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size : numpy.ndarray
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physical size of the periodic field.
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physical size of the periodic field.
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F : numpy.ndarray
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deformation gradient field.
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"""
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integrator = 0.5j*size/np.pi
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k_s = __ks(size,F.shape[:3],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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@ -136,6 +137,7 @@ def cell_displacement_fluct(size,F):
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return np.fft.irfftn(displacement,axes=(0,1,2),s=F.shape[:3])
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def cell_displacement_avg(size,F):
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"""
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Cell center displacement field from average part of the deformation gradient field.
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@ -143,7 +145,7 @@ def cell_displacement_avg(size,F):
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Parameters
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----------
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size : numpy.ndarray
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physical size of the periodic field.
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physical size of the periodic field.
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F : numpy.ndarray
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deformation gradient field.
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@ -151,6 +153,7 @@ def cell_displacement_avg(size,F):
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F_avg = np.average(F,axis=(0,1,2))
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return np.einsum('ml,ijkl->ijkm',F_avg-np.eye(3),cell_coord0(F.shape[:3][::-1],size))
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def cell_displacement(size,F):
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"""
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Cell center displacement field from deformation gradient field.
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@ -158,13 +161,14 @@ def cell_displacement(size,F):
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Parameters
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----------
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size : numpy.ndarray
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physical size of the periodic field.
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physical size of the periodic field.
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F : numpy.ndarray
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deformation gradient field.
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"""
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return cell_displacement_avg(size,F) + cell_displacement_fluct(size,F)
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def cell_coord(size,F,origin=np.zeros(3)):
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"""
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Cell center positions.
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@ -172,7 +176,7 @@ def cell_coord(size,F,origin=np.zeros(3)):
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Parameters
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----------
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size : numpy.ndarray
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physical size of the periodic field.
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physical size of the periodic field.
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F : numpy.ndarray
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deformation gradient field.
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origin : numpy.ndarray, optional
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@ -181,6 +185,7 @@ def cell_coord(size,F,origin=np.zeros(3)):
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"""
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return cell_coord0(F.shape[:3][::-1],size,origin) + cell_displacement(size,F)
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def cell_coord0_gridSizeOrigin(coord0,ordered=True):
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"""
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Return grid 'DNA', i.e. grid, size, and origin from array of cell positions.
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@ -200,11 +205,11 @@ def cell_coord0_gridSizeOrigin(coord0,ordered=True):
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size = grid/np.maximum(grid-1,1) * (maxcorner-mincorner)
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delta = size/grid
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origin = mincorner - delta*.5
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# 1D/2D: size/origin combination undefined, set origin to 0.0
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size [np.where(grid==1)] = origin[np.where(grid==1)]*2.
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origin[np.where(grid==1)] = 0.0
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if grid.prod() != len(coord0):
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raise ValueError('Data count {} does not match grid {}.'.format(len(coord0),grid))
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@ -221,6 +226,7 @@ def cell_coord0_gridSizeOrigin(coord0,ordered=True):
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return (grid,size,origin)
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def coord0_check(coord0):
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"""
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Check whether coordinates lie on a regular grid.
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@ -234,7 +240,6 @@ def coord0_check(coord0):
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cell_coord0_gridSizeOrigin(coord0,ordered=True)
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def node_coord0(grid,size,origin=np.zeros(3)):
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"""
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Nodal positions (undeformed).
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@ -244,7 +249,7 @@ def node_coord0(grid,size,origin=np.zeros(3)):
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grid : numpy.ndarray
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number of grid points.
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size : numpy.ndarray
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physical size of the periodic field.
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physical size of the periodic field.
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origin : numpy.ndarray, optional
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physical origin of the periodic field. Default is [0.0,0.0,0.0].
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@ -253,8 +258,9 @@ def node_coord0(grid,size,origin=np.zeros(3)):
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np.linspace(origin[1],size[1]+origin[1],1+grid[1]),
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np.linspace(origin[0],size[0]+origin[0],1+grid[0]),
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indexing = 'ij')
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return np.concatenate((z[:,:,:,None],y[:,:,:,None],x[:,:,:,None]),axis = 3)
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return np.concatenate((z[:,:,:,None],y[:,:,:,None],x[:,:,:,None]),axis = 3)
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def node_displacement_fluct(size,F):
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"""
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@ -263,13 +269,14 @@ def node_displacement_fluct(size,F):
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Parameters
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----------
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size : numpy.ndarray
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physical size of the periodic field.
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physical size of the periodic field.
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F : numpy.ndarray
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deformation gradient field.
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"""
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return cell_2_node(cell_displacement_fluct(size,F))
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def node_displacement_avg(size,F):
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"""
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Nodal displacement field from average part of the deformation gradient field.
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@ -277,7 +284,7 @@ def node_displacement_avg(size,F):
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Parameters
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----------
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size : numpy.ndarray
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physical size of the periodic field.
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physical size of the periodic field.
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F : numpy.ndarray
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deformation gradient field.
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@ -285,6 +292,7 @@ def node_displacement_avg(size,F):
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F_avg = np.average(F,axis=(0,1,2))
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return np.einsum('ml,ijkl->ijkm',F_avg-np.eye(3),node_coord0(F.shape[:3][::-1],size))
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def node_displacement(size,F):
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"""
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Nodal displacement field from deformation gradient field.
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@ -292,13 +300,14 @@ def node_displacement(size,F):
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Parameters
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----------
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size : numpy.ndarray
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physical size of the periodic field.
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physical size of the periodic field.
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F : numpy.ndarray
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deformation gradient field.
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"""
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return node_displacement_avg(size,F) + node_displacement_fluct(size,F)
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def node_coord(size,F,origin=np.zeros(3)):
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"""
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Nodal positions.
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@ -306,7 +315,7 @@ def node_coord(size,F,origin=np.zeros(3)):
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Parameters
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----------
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size : numpy.ndarray
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physical size of the periodic field.
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physical size of the periodic field.
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F : numpy.ndarray
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deformation gradient field.
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origin : numpy.ndarray, optional
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@ -315,22 +324,25 @@ def node_coord(size,F,origin=np.zeros(3)):
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"""
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return node_coord0(F.shape[:3][::-1],size,origin) + node_displacement(size,F)
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def cell_2_node(cell_data):
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"""Interpolate periodic cell data to nodal data."""
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n = ( cell_data + np.roll(cell_data,1,(0,1,2))
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+ np.roll(cell_data,1,(0,)) + np.roll(cell_data,1,(1,)) + np.roll(cell_data,1,(2,))
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+ np.roll(cell_data,1,(0,1)) + np.roll(cell_data,1,(1,2)) + np.roll(cell_data,1,(2,0)))*0.125
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return np.pad(n,((0,1),(0,1),(0,1))+((0,0),)*len(cell_data.shape[3:]),mode='wrap')
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def node_2_cell(node_data):
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"""Interpolate periodic nodal data to cell data."""
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c = ( node_data + np.roll(node_data,1,(0,1,2))
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+ np.roll(node_data,1,(0,)) + np.roll(node_data,1,(1,)) + np.roll(node_data,1,(2,))
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+ np.roll(node_data,1,(0,1)) + np.roll(node_data,1,(1,2)) + np.roll(node_data,1,(2,0)))*0.125
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return c[:-1,:-1,:-1]
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def node_coord0_gridSizeOrigin(coord0,ordered=False):
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"""
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Return grid 'DNA', i.e. grid, size, and origin from array of nodal positions.
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@ -349,7 +361,7 @@ def node_coord0_gridSizeOrigin(coord0,ordered=False):
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grid = np.array(list(map(len,coords)),'i') - 1
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size = maxcorner-mincorner
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origin = mincorner
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if (grid+1).prod() != len(coord0):
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raise ValueError('Data count {} does not match grid {}.'.format(len(coord0),grid))
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