do not clutter namespace
we do not need damask.util.np etc
This commit is contained in:
Martin Diehl
parent
9c0ea13e4f
commit
9837390406
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@ -1,5 +1,5 @@
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from scipy import spatial
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import numpy as np
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from scipy import spatial as _spatial
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import numpy as _np
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def _ks(size,grid,first_order=False):
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"""
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@ -11,16 +11,16 @@ def _ks(size,grid,first_order=False):
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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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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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k_sj = np.where(np.arange(grid[1])>grid[1]//2,np.arange(grid[1])-grid[1],np.arange(grid[1]))/size[1]
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k_sj = _np.where(_np.arange(grid[1])>grid[1]//2,_np.arange(grid[1])-grid[1],_np.arange(grid[1]))/size[1]
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if grid[1]%2 == 0 and first_order: k_sj[grid[1]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011)
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k_si = np.arange(grid[2]//2+1)/size[2]
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k_si = _np.arange(grid[2]//2+1)/size[2]
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kk, kj, ki = np.meshgrid(k_sk,k_sj,k_si,indexing = 'ij')
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return np.concatenate((ki[:,:,:,None],kj[:,:,:,None],kk[:,:,:,None]),axis = 3)
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kk, kj, ki = _np.meshgrid(k_sk,k_sj,k_si,indexing = 'ij')
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return _np.concatenate((ki[:,:,:,None],kj[:,:,:,None],kk[:,:,:,None]),axis = 3)
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def curl(size,field):
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@ -33,18 +33,18 @@ def curl(size,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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n = _np.prod(field.shape[3:])
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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 = _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, 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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curl_ = (np.einsum('slm,ijkl,ijkm ->ijks', e,k_s,field_fourier)*2.0j*np.pi if n == 3 else # vector, 3 -> 3
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np.einsum('slm,ijkl,ijknm->ijksn',e,k_s,field_fourier)*2.0j*np.pi) # tensor, 3x3 -> 3x3
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field_fourier = _np.fft.rfftn(field,axes=(0,1,2))
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curl_ = (_np.einsum('slm,ijkl,ijkm ->ijks', e,k_s,field_fourier)*2.0j*_np.pi if n == 3 else # vector, 3 -> 3
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_np.einsum('slm,ijkl,ijknm->ijksn',e,k_s,field_fourier)*2.0j*_np.pi) # tensor, 3x3 -> 3x3
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return np.fft.irfftn(curl_,axes=(0,1,2),s=field.shape[:3])
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return _np.fft.irfftn(curl_,axes=(0,1,2),s=field.shape[:3])
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def divergence(size,field):
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@ -57,14 +57,14 @@ def divergence(size,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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n = _np.prod(field.shape[3:])
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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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div_ = (np.einsum('ijkl,ijkl ->ijk', k_s,field_fourier)*2.0j*np.pi if n == 3 else # vector, 3 -> 1
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np.einsum('ijkm,ijklm->ijkl',k_s,field_fourier)*2.0j*np.pi) # tensor, 3x3 -> 3
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field_fourier = _np.fft.rfftn(field,axes=(0,1,2))
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div_ = (_np.einsum('ijkl,ijkl ->ijk', k_s,field_fourier)*2.0j*_np.pi if n == 3 else # vector, 3 -> 1
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_np.einsum('ijkm,ijklm->ijkl',k_s,field_fourier)*2.0j*_np.pi) # tensor, 3x3 -> 3
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return np.fft.irfftn(div_,axes=(0,1,2),s=field.shape[:3])
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return _np.fft.irfftn(div_,axes=(0,1,2),s=field.shape[:3])
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def gradient(size,field):
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@ -77,17 +77,17 @@ def gradient(size,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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n = _np.prod(field.shape[3:])
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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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grad_ = (np.einsum('ijkl,ijkm->ijkm', field_fourier,k_s)*2.0j*np.pi if n == 1 else # scalar, 1 -> 3
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np.einsum('ijkl,ijkm->ijklm',field_fourier,k_s)*2.0j*np.pi) # vector, 3 -> 3x3
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field_fourier = _np.fft.rfftn(field,axes=(0,1,2))
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grad_ = (_np.einsum('ijkl,ijkm->ijkm', field_fourier,k_s)*2.0j*_np.pi if n == 1 else # scalar, 1 -> 3
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_np.einsum('ijkl,ijkm->ijklm',field_fourier,k_s)*2.0j*_np.pi) # vector, 3 -> 3x3
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return np.fft.irfftn(grad_,axes=(0,1,2),s=field.shape[:3])
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return _np.fft.irfftn(grad_,axes=(0,1,2),s=field.shape[:3])
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def cell_coord0(grid,size,origin=np.zeros(3)):
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def cell_coord0(grid,size,origin=_np.zeros(3)):
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"""
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Cell center positions (undeformed).
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@ -103,7 +103,7 @@ def cell_coord0(grid,size,origin=np.zeros(3)):
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"""
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start = origin + size/grid*.5
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end = origin + size - size/grid*.5
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return np.mgrid[start[0]:end[0]:grid[0]*1j,start[1]:end[1]:grid[1]*1j,start[2]:end[2]:grid[2]*1j].T
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return _np.mgrid[start[0]:end[0]:grid[0]*1j,start[1]:end[1]:grid[1]*1j,start[2]:end[2]:grid[2]*1j].T
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def cell_displacement_fluct(size,F):
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@ -118,19 +118,19 @@ def cell_displacement_fluct(size,F):
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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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integrator = 0.5j*size/_np.pi
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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 = _np.einsum('...l,...l',k_s,k_s)
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k_s_squared[0,0,0] = 1.0
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displacement = -np.einsum('ijkml,ijkl,l->ijkm',
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np.fft.rfftn(F,axes=(0,1,2)),
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displacement = -_np.einsum('ijkml,ijkl,l->ijkm',
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_np.fft.rfftn(F,axes=(0,1,2)),
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k_s,
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integrator,
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) / k_s_squared[...,np.newaxis]
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) / k_s_squared[...,_np.newaxis]
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return np.fft.irfftn(displacement,axes=(0,1,2),s=F.shape[:3])
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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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@ -145,8 +145,8 @@ def cell_displacement_avg(size,F):
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deformation gradient field.
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"""
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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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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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@ -164,7 +164,7 @@ def cell_displacement(size,F):
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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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def cell_coord(size,F,origin=_np.zeros(3)):
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"""
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Cell center positions.
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@ -193,17 +193,17 @@ def cell_coord0_gridSizeOrigin(coord0,ordered=True):
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expect coord0 data to be ordered (x fast, z slow).
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"""
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coords = [np.unique(coord0[:,i]) for i in range(3)]
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mincorner = np.array(list(map(min,coords)))
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maxcorner = np.array(list(map(max,coords)))
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grid = np.array(list(map(len,coords)),'i')
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size = grid/np.maximum(grid-1,1) * (maxcorner-mincorner)
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coords = [_np.unique(coord0[:,i]) for i in range(3)]
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mincorner = _np.array(list(map(min,coords)))
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maxcorner = _np.array(list(map(max,coords)))
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grid = _np.array(list(map(len,coords)),'i')
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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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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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@ -211,13 +211,13 @@ def cell_coord0_gridSizeOrigin(coord0,ordered=True):
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start = origin + delta*.5
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end = origin - delta*.5 + size
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if not np.allclose(coords[0],np.linspace(start[0],end[0],grid[0])) and \
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np.allclose(coords[1],np.linspace(start[1],end[1],grid[1])) and \
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np.allclose(coords[2],np.linspace(start[2],end[2],grid[2])):
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if not _np.allclose(coords[0],_np.linspace(start[0],end[0],grid[0])) and \
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_np.allclose(coords[1],_np.linspace(start[1],end[1],grid[1])) and \
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_np.allclose(coords[2],_np.linspace(start[2],end[2],grid[2])):
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raise ValueError('Regular grid spacing violated.')
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if ordered and not np.allclose(coord0.reshape(tuple(grid[::-1])+(3,)),cell_coord0(grid,size,origin)):
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raise ValueError('Input data is not a regular grid.')
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if ordered and not _np.allclose(coord0.reshape(tuple(grid[::-1])+(3,)),cell_coord0(grid,size,origin)):
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raise ValueError('I_nput data is not a regular grid.')
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return (grid,size,origin)
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@ -235,7 +235,7 @@ 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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def node_coord0(grid,size,origin=_np.zeros(3)):
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"""
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Nodal positions (undeformed).
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@ -249,7 +249,7 @@ def node_coord0(grid,size,origin=np.zeros(3)):
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physical origin of the periodic field. Defaults to [0.0,0.0,0.0].
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"""
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return np.mgrid[origin[0]:size[0]+origin[0]:(grid[0]+1)*1j,
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return _np.mgrid[origin[0]:size[0]+origin[0]:(grid[0]+1)*1j,
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origin[1]:size[1]+origin[1]:(grid[1]+1)*1j,
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origin[2]:size[2]+origin[2]:(grid[2]+1)*1j].T
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@ -281,8 +281,8 @@ def node_displacement_avg(size,F):
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deformation gradient field.
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"""
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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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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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@ -300,7 +300,7 @@ def node_displacement(size,F):
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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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def node_coord(size,F,origin=_np.zeros(3)):
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"""
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Nodal positions.
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@ -319,18 +319,18 @@ def node_coord(size,F,origin=np.zeros(3)):
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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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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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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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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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@ -347,23 +347,23 @@ def node_coord0_gridSizeOrigin(coord0,ordered=False):
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expect coord0 data to be ordered (x fast, z slow).
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"""
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coords = [np.unique(coord0[:,i]) for i in range(3)]
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mincorner = np.array(list(map(min,coords)))
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maxcorner = np.array(list(map(max,coords)))
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grid = np.array(list(map(len,coords)),'i') - 1
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coords = [_np.unique(coord0[:,i]) for i in range(3)]
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mincorner = _np.array(list(map(min,coords)))
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maxcorner = _np.array(list(map(max,coords)))
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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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if not np.allclose(coords[0],np.linspace(mincorner[0],maxcorner[0],grid[0]+1)) and \
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np.allclose(coords[1],np.linspace(mincorner[1],maxcorner[1],grid[1]+1)) and \
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np.allclose(coords[2],np.linspace(mincorner[2],maxcorner[2],grid[2]+1)):
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if not _np.allclose(coords[0],_np.linspace(mincorner[0],maxcorner[0],grid[0]+1)) and \
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_np.allclose(coords[1],_np.linspace(mincorner[1],maxcorner[1],grid[1]+1)) and \
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_np.allclose(coords[2],_np.linspace(mincorner[2],maxcorner[2],grid[2]+1)):
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raise ValueError('Regular grid spacing violated.')
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if ordered and not np.allclose(coord0.reshape(tuple((grid+1)[::-1])+(3,)),node_coord0(grid,size,origin)):
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raise ValueError('Input data is not a regular grid.')
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if ordered and not _np.allclose(coord0.reshape(tuple((grid+1)[::-1])+(3,)),node_coord0(grid,size,origin)):
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raise ValueError('I_nput data is not a regular grid.')
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return (grid,size,origin)
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@ -386,10 +386,10 @@ def regrid(size,F,new_grid):
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+ cell_displacement_avg(size,F) \
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+ cell_displacement_fluct(size,F)
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outer = np.dot(np.average(F,axis=(0,1,2)),size)
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outer = _np.dot(_np.average(F,axis=(0,1,2)),size)
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for d in range(3):
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c[np.where(c[:,:,:,d]<0)] += outer[d]
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c[np.where(c[:,:,:,d]>outer[d])] -= outer[d]
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c[_np.where(c[:,:,:,d]<0)] += outer[d]
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c[_np.where(c[:,:,:,d]>outer[d])] -= outer[d]
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tree = spatial.cKDTree(c.reshape(-1,3),boxsize=outer)
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tree = _spatial.cKDTree(c.reshape(-1,3),boxsize=outer)
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return tree.query(cell_coord0(new_grid,outer))[1].flatten()
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@ -1,4 +1,4 @@
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import numpy as np
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import numpy as _np
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def Cauchy(P,F):
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"""
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@ -14,10 +14,10 @@ def Cauchy(P,F):
|
|||
First Piola-Kirchhoff stress.
|
||||
|
||||
"""
|
||||
if np.shape(F) == np.shape(P) == (3,3):
|
||||
sigma = 1.0/np.linalg.det(F) * np.dot(P,F.T)
|
||||
if _np.shape(F) == _np.shape(P) == (3,3):
|
||||
sigma = 1.0/_np.linalg.det(F) * _np.dot(P,F.T)
|
||||
else:
|
||||
sigma = np.einsum('i,ijk,ilk->ijl',1.0/np.linalg.det(F),P,F)
|
||||
sigma = _np.einsum('i,ijk,ilk->ijl',1.0/_np.linalg.det(F),P,F)
|
||||
return symmetric(sigma)
|
||||
|
||||
|
||||
|
|
@ -31,8 +31,8 @@ def deviatoric_part(T):
|
|||
Tensor of which the deviatoric part is computed.
|
||||
|
||||
"""
|
||||
return T - np.eye(3)*spherical_part(T) if np.shape(T) == (3,3) else \
|
||||
T - np.einsum('ijk,i->ijk',np.broadcast_to(np.eye(3),[T.shape[0],3,3]),spherical_part(T))
|
||||
return T - _np.eye(3)*spherical_part(T) if _np.shape(T) == (3,3) else \
|
||||
T - _np.einsum('ijk,i->ijk',_np.broadcast_to(_np.eye(3),[T.shape[0],3,3]),spherical_part(T))
|
||||
|
||||
|
||||
def eigenvalues(T_sym):
|
||||
|
|
@ -48,7 +48,7 @@ def eigenvalues(T_sym):
|
|||
Symmetric tensor of which the eigenvalues are computed.
|
||||
|
||||
"""
|
||||
return np.linalg.eigvalsh(symmetric(T_sym))
|
||||
return _np.linalg.eigvalsh(symmetric(T_sym))
|
||||
|
||||
|
||||
def eigenvectors(T_sym,RHS=False):
|
||||
|
|
@ -65,13 +65,13 @@ def eigenvectors(T_sym,RHS=False):
|
|||
Enforce right-handed coordinate system. Default is False.
|
||||
|
||||
"""
|
||||
(u,v) = np.linalg.eigh(symmetric(T_sym))
|
||||
(u,v) = _np.linalg.eigh(symmetric(T_sym))
|
||||
|
||||
if RHS:
|
||||
if np.shape(T_sym) == (3,3):
|
||||
if np.linalg.det(v) < 0.0: v[:,2] *= -1.0
|
||||
if _np.shape(T_sym) == (3,3):
|
||||
if _np.linalg.det(v) < 0.0: v[:,2] *= -1.0
|
||||
else:
|
||||
v[np.linalg.det(v) < 0.0,:,2] *= -1.0
|
||||
v[_np.linalg.det(v) < 0.0,:,2] *= -1.0
|
||||
return v
|
||||
|
||||
|
||||
|
|
@ -99,7 +99,7 @@ def maximum_shear(T_sym):
|
|||
|
||||
"""
|
||||
w = eigenvalues(T_sym)
|
||||
return (w[0] - w[2])*0.5 if np.shape(T_sym) == (3,3) else \
|
||||
return (w[0] - w[2])*0.5 if _np.shape(T_sym) == (3,3) else \
|
||||
(w[:,0] - w[:,2])*0.5
|
||||
|
||||
|
||||
|
|
@ -141,10 +141,10 @@ def PK2(P,F):
|
|||
Deformation gradient.
|
||||
|
||||
"""
|
||||
if np.shape(F) == np.shape(P) == (3,3):
|
||||
S = np.dot(np.linalg.inv(F),P)
|
||||
if _np.shape(F) == _np.shape(P) == (3,3):
|
||||
S = _np.dot(_np.linalg.inv(F),P)
|
||||
else:
|
||||
S = np.einsum('ijk,ikl->ijl',np.linalg.inv(F),P)
|
||||
S = _np.einsum('ijk,ikl->ijl',_np.linalg.inv(F),P)
|
||||
return symmetric(S)
|
||||
|
||||
|
||||
|
|
@ -187,14 +187,14 @@ def spherical_part(T,tensor=False):
|
|||
|
||||
"""
|
||||
if T.shape == (3,3):
|
||||
sph = np.trace(T)/3.0
|
||||
return sph if not tensor else np.eye(3)*sph
|
||||
sph = _np.trace(T)/3.0
|
||||
return sph if not tensor else _np.eye(3)*sph
|
||||
else:
|
||||
sph = np.trace(T,axis1=1,axis2=2)/3.0
|
||||
sph = _np.trace(T,axis1=1,axis2=2)/3.0
|
||||
if not tensor:
|
||||
return sph
|
||||
else:
|
||||
return np.einsum('ijk,i->ijk',np.broadcast_to(np.eye(3),(T.shape[0],3,3)),sph)
|
||||
return _np.einsum('ijk,i->ijk',_np.broadcast_to(_np.eye(3),(T.shape[0],3,3)),sph)
|
||||
|
||||
|
||||
def strain_tensor(F,t,m):
|
||||
|
|
@ -216,22 +216,22 @@ def strain_tensor(F,t,m):
|
|||
"""
|
||||
F_ = F.reshape(1,3,3) if F.shape == (3,3) else F
|
||||
if t == 'V':
|
||||
B = np.matmul(F_,transpose(F_))
|
||||
w,n = np.linalg.eigh(B)
|
||||
B = _np.matmul(F_,transpose(F_))
|
||||
w,n = _np.linalg.eigh(B)
|
||||
elif t == 'U':
|
||||
C = np.matmul(transpose(F_),F_)
|
||||
w,n = np.linalg.eigh(C)
|
||||
C = _np.matmul(transpose(F_),F_)
|
||||
w,n = _np.linalg.eigh(C)
|
||||
|
||||
if m > 0.0:
|
||||
eps = 1.0/(2.0*abs(m)) * (+ np.matmul(n,np.einsum('ij,ikj->ijk',w**m,n))
|
||||
- np.broadcast_to(np.eye(3),[F_.shape[0],3,3]))
|
||||
eps = 1.0/(2.0*abs(m)) * (+ _np.matmul(n,_np.einsum('ij,ikj->ijk',w**m,n))
|
||||
- _np.broadcast_to(_np.eye(3),[F_.shape[0],3,3]))
|
||||
elif m < 0.0:
|
||||
eps = 1.0/(2.0*abs(m)) * (- np.matmul(n,np.einsum('ij,ikj->ijk',w**m,n))
|
||||
+ np.broadcast_to(np.eye(3),[F_.shape[0],3,3]))
|
||||
eps = 1.0/(2.0*abs(m)) * (- _np.matmul(n,_np.einsum('ij,ikj->ijk',w**m,n))
|
||||
+ _np.broadcast_to(_np.eye(3),[F_.shape[0],3,3]))
|
||||
else:
|
||||
eps = np.matmul(n,np.einsum('ij,ikj->ijk',0.5*np.log(w),n))
|
||||
eps = _np.matmul(n,_np.einsum('ij,ikj->ijk',0.5*_np.log(w),n))
|
||||
|
||||
return eps.reshape(3,3) if np.shape(F) == (3,3) else \
|
||||
return eps.reshape(3,3) if _np.shape(F) == (3,3) else \
|
||||
eps
|
||||
|
||||
|
||||
|
|
@ -258,8 +258,8 @@ def transpose(T):
|
|||
Tensor of which the transpose is computed.
|
||||
|
||||
"""
|
||||
return T.T if np.shape(T) == (3,3) else \
|
||||
np.transpose(T,(0,2,1))
|
||||
return T.T if _np.shape(T) == (3,3) else \
|
||||
_np.transpose(T,(0,2,1))
|
||||
|
||||
|
||||
def _polar_decomposition(T,requested):
|
||||
|
|
@ -275,17 +275,17 @@ def _polar_decomposition(T,requested):
|
|||
‘V’ for left stretch tensor and ‘U’ for right stretch tensor.
|
||||
|
||||
"""
|
||||
u, s, vh = np.linalg.svd(T)
|
||||
R = np.dot(u,vh) if np.shape(T) == (3,3) else \
|
||||
np.einsum('ijk,ikl->ijl',u,vh)
|
||||
u, s, vh = _np.linalg.svd(T)
|
||||
R = _np.dot(u,vh) if _np.shape(T) == (3,3) else \
|
||||
_np.einsum('ijk,ikl->ijl',u,vh)
|
||||
|
||||
output = []
|
||||
if 'R' in requested:
|
||||
output.append(R)
|
||||
if 'V' in requested:
|
||||
output.append(np.dot(T,R.T) if np.shape(T) == (3,3) else np.einsum('ijk,ilk->ijl',T,R))
|
||||
output.append(_np.dot(T,R.T) if _np.shape(T) == (3,3) else _np.einsum('ijk,ilk->ijl',T,R))
|
||||
if 'U' in requested:
|
||||
output.append(np.dot(R.T,T) if np.shape(T) == (3,3) else np.einsum('ikj,ikl->ijl',R,T))
|
||||
output.append(_np.dot(R.T,T) if _np.shape(T) == (3,3) else _np.einsum('ikj,ikl->ijl',R,T))
|
||||
|
||||
return tuple(output)
|
||||
|
||||
|
|
@ -303,5 +303,5 @@ def _Mises(T_sym,s):
|
|||
|
||||
"""
|
||||
d = deviatoric_part(T_sym)
|
||||
return np.sqrt(s*(np.sum(d**2.0))) if np.shape(T_sym) == (3,3) else \
|
||||
np.sqrt(s*np.einsum('ijk->i',d**2.0))
|
||||
return _np.sqrt(s*(_np.sum(d**2.0))) if _np.shape(T_sym) == (3,3) else \
|
||||
_np.sqrt(s*_np.einsum('ijk->i',d**2.0))
|
||||
|
|
|
|||
Loading…
Reference in New Issue