diff --git a/python/damask/grid_filters.py b/python/damask/grid_filters.py index db9f243c9..1375b4408 100644 --- a/python/damask/grid_filters.py +++ b/python/damask/grid_filters.py @@ -1,14 +1,14 @@ from scipy import spatial import numpy as np -def __ks(size,grid,first_order=False): +def _ks(size,grid,first_order=False): """ Get wave numbers operator. Parameters ---------- size : numpy.ndarray - physical size of the periodic field. + physical size of the periodic field. """ k_sk = np.where(np.arange(grid[0])>grid[0]//2,np.arange(grid[0])-grid[0],np.arange(grid[0]))/size[0] @@ -30,14 +30,14 @@ def curl(size,field): Parameters ---------- size : numpy.ndarray - physical size of the periodic field. + physical size of the periodic field. """ n = np.prod(field.shape[3:]) - k_s = __ks(size,field.shape[:3],True) + k_s = _ks(size,field.shape[:3],True) 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, 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 field_fourier = np.fft.rfftn(field,axes=(0,1,2)) @@ -54,11 +54,11 @@ def divergence(size,field): Parameters ---------- size : numpy.ndarray - physical size of the periodic field. + physical size of the periodic field. """ n = np.prod(field.shape[3:]) - k_s = __ks(size,field.shape[:3],True) + k_s = _ks(size,field.shape[:3],True) field_fourier = np.fft.rfftn(field,axes=(0,1,2)) divergence = (np.einsum('ijkl,ijkl ->ijk', k_s,field_fourier)*2.0j*np.pi if n == 3 else # vector, 3 -> 1 @@ -74,11 +74,11 @@ def gradient(size,field): Parameters ---------- size : numpy.ndarray - physical size of the periodic field. + physical size of the periodic field. """ n = np.prod(field.shape[3:]) - k_s = __ks(size,field.shape[:3],True) + k_s = _ks(size,field.shape[:3],True) field_fourier = np.fft.rfftn(field,axes=(0,1,2)) gradient = (np.einsum('ijkl,ijkm->ijkm', field_fourier,k_s)*2.0j*np.pi if n == 1 else # scalar, 1 -> 3 @@ -96,7 +96,7 @@ def cell_coord0(grid,size,origin=np.zeros(3)): grid : numpy.ndarray number of grid points. size : numpy.ndarray - physical size of the periodic field. + physical size of the periodic field. origin : numpy.ndarray, optional physical origin of the periodic field. Default is [0.0,0.0,0.0]. @@ -108,7 +108,8 @@ def cell_coord0(grid,size,origin=np.zeros(3)): np.linspace(start[0],end[0],grid[0]), indexing = 'ij') - return np.concatenate((z[:,:,:,None],y[:,:,:,None],x[:,:,:,None]),axis = 3) + return np.concatenate((z[:,:,:,None],y[:,:,:,None],x[:,:,:,None]),axis = 3) + def cell_displacement_fluct(size,F): """ @@ -117,14 +118,14 @@ def cell_displacement_fluct(size,F): Parameters ---------- size : numpy.ndarray - physical size of the periodic field. + physical size of the periodic field. F : numpy.ndarray deformation gradient field. """ integrator = 0.5j*size/np.pi - k_s = __ks(size,F.shape[:3],False) + k_s = _ks(size,F.shape[:3],False) k_s_squared = np.einsum('...l,...l',k_s,k_s) k_s_squared[0,0,0] = 1.0 @@ -136,6 +137,7 @@ def cell_displacement_fluct(size,F): return np.fft.irfftn(displacement,axes=(0,1,2),s=F.shape[:3]) + def cell_displacement_avg(size,F): """ Cell center displacement field from average part of the deformation gradient field. @@ -143,7 +145,7 @@ def cell_displacement_avg(size,F): Parameters ---------- size : numpy.ndarray - physical size of the periodic field. + physical size of the periodic field. F : numpy.ndarray deformation gradient field. @@ -151,6 +153,7 @@ def cell_displacement_avg(size,F): F_avg = np.average(F,axis=(0,1,2)) return np.einsum('ml,ijkl->ijkm',F_avg-np.eye(3),cell_coord0(F.shape[:3][::-1],size)) + def cell_displacement(size,F): """ Cell center displacement field from deformation gradient field. @@ -158,13 +161,14 @@ def cell_displacement(size,F): Parameters ---------- size : numpy.ndarray - physical size of the periodic field. + physical size of the periodic field. F : numpy.ndarray deformation gradient field. """ return cell_displacement_avg(size,F) + cell_displacement_fluct(size,F) + def cell_coord(size,F,origin=np.zeros(3)): """ Cell center positions. @@ -172,7 +176,7 @@ def cell_coord(size,F,origin=np.zeros(3)): Parameters ---------- size : numpy.ndarray - physical size of the periodic field. + physical size of the periodic field. F : numpy.ndarray deformation gradient field. origin : numpy.ndarray, optional @@ -181,6 +185,7 @@ def cell_coord(size,F,origin=np.zeros(3)): """ return cell_coord0(F.shape[:3][::-1],size,origin) + cell_displacement(size,F) + def cell_coord0_gridSizeOrigin(coord0,ordered=True): """ Return grid 'DNA', i.e. grid, size, and origin from array of cell positions. @@ -200,11 +205,11 @@ def cell_coord0_gridSizeOrigin(coord0,ordered=True): size = grid/np.maximum(grid-1,1) * (maxcorner-mincorner) delta = size/grid origin = mincorner - delta*.5 - + # 1D/2D: size/origin combination undefined, set origin to 0.0 size [np.where(grid==1)] = origin[np.where(grid==1)]*2. origin[np.where(grid==1)] = 0.0 - + if grid.prod() != len(coord0): raise ValueError('Data count {} does not match grid {}.'.format(len(coord0),grid)) @@ -221,6 +226,7 @@ def cell_coord0_gridSizeOrigin(coord0,ordered=True): return (grid,size,origin) + def coord0_check(coord0): """ Check whether coordinates lie on a regular grid. @@ -234,7 +240,6 @@ def coord0_check(coord0): cell_coord0_gridSizeOrigin(coord0,ordered=True) - def node_coord0(grid,size,origin=np.zeros(3)): """ Nodal positions (undeformed). @@ -244,7 +249,7 @@ def node_coord0(grid,size,origin=np.zeros(3)): grid : numpy.ndarray number of grid points. size : numpy.ndarray - physical size of the periodic field. + physical size of the periodic field. origin : numpy.ndarray, optional physical origin of the periodic field. Default is [0.0,0.0,0.0]. @@ -253,8 +258,9 @@ def node_coord0(grid,size,origin=np.zeros(3)): np.linspace(origin[1],size[1]+origin[1],1+grid[1]), np.linspace(origin[0],size[0]+origin[0],1+grid[0]), indexing = 'ij') - - return np.concatenate((z[:,:,:,None],y[:,:,:,None],x[:,:,:,None]),axis = 3) + + return np.concatenate((z[:,:,:,None],y[:,:,:,None],x[:,:,:,None]),axis = 3) + def node_displacement_fluct(size,F): """ @@ -263,13 +269,14 @@ def node_displacement_fluct(size,F): Parameters ---------- size : numpy.ndarray - physical size of the periodic field. + physical size of the periodic field. F : numpy.ndarray deformation gradient field. """ return cell_2_node(cell_displacement_fluct(size,F)) + def node_displacement_avg(size,F): """ Nodal displacement field from average part of the deformation gradient field. @@ -277,7 +284,7 @@ def node_displacement_avg(size,F): Parameters ---------- size : numpy.ndarray - physical size of the periodic field. + physical size of the periodic field. F : numpy.ndarray deformation gradient field. @@ -285,6 +292,7 @@ def node_displacement_avg(size,F): F_avg = np.average(F,axis=(0,1,2)) return np.einsum('ml,ijkl->ijkm',F_avg-np.eye(3),node_coord0(F.shape[:3][::-1],size)) + def node_displacement(size,F): """ Nodal displacement field from deformation gradient field. @@ -292,13 +300,14 @@ def node_displacement(size,F): Parameters ---------- size : numpy.ndarray - physical size of the periodic field. + physical size of the periodic field. F : numpy.ndarray deformation gradient field. """ return node_displacement_avg(size,F) + node_displacement_fluct(size,F) + def node_coord(size,F,origin=np.zeros(3)): """ Nodal positions. @@ -306,7 +315,7 @@ def node_coord(size,F,origin=np.zeros(3)): Parameters ---------- size : numpy.ndarray - physical size of the periodic field. + physical size of the periodic field. F : numpy.ndarray deformation gradient field. origin : numpy.ndarray, optional @@ -315,22 +324,25 @@ def node_coord(size,F,origin=np.zeros(3)): """ return node_coord0(F.shape[:3][::-1],size,origin) + node_displacement(size,F) + def cell_2_node(cell_data): """Interpolate periodic cell data to nodal data.""" n = ( cell_data + np.roll(cell_data,1,(0,1,2)) + np.roll(cell_data,1,(0,)) + np.roll(cell_data,1,(1,)) + np.roll(cell_data,1,(2,)) + np.roll(cell_data,1,(0,1)) + np.roll(cell_data,1,(1,2)) + np.roll(cell_data,1,(2,0)))*0.125 - + return np.pad(n,((0,1),(0,1),(0,1))+((0,0),)*len(cell_data.shape[3:]),mode='wrap') + def node_2_cell(node_data): """Interpolate periodic nodal data to cell data.""" c = ( node_data + np.roll(node_data,1,(0,1,2)) + np.roll(node_data,1,(0,)) + np.roll(node_data,1,(1,)) + np.roll(node_data,1,(2,)) + np.roll(node_data,1,(0,1)) + np.roll(node_data,1,(1,2)) + np.roll(node_data,1,(2,0)))*0.125 - + return c[:-1,:-1,:-1] + def node_coord0_gridSizeOrigin(coord0,ordered=False): """ Return grid 'DNA', i.e. grid, size, and origin from array of nodal positions. @@ -349,7 +361,7 @@ def node_coord0_gridSizeOrigin(coord0,ordered=False): grid = np.array(list(map(len,coords)),'i') - 1 size = maxcorner-mincorner origin = mincorner - + if (grid+1).prod() != len(coord0): raise ValueError('Data count {} does not match grid {}.'.format(len(coord0),grid))