338 lines
16 KiB
Python
Executable File
338 lines
16 KiB
Python
Executable File
#!/usr/bin/env python2.7
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# -*- coding: UTF-8 no BOM -*-
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import os
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import math
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import numpy as np
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import scipy.ndimage
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from optparse import OptionParser
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import damask
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scriptName = os.path.splitext(os.path.basename(__file__))[0]
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scriptID = ' '.join([scriptName,damask.version])
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#--------------------------------------------------------------------------------------------------
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def cell2node(cellData,grid):
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nodeData = 0.0
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datalen = np.array(cellData.shape[3:]).prod()
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for i in range(datalen):
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node = scipy.ndimage.convolve(cellData.reshape(tuple(grid[::-1])+(datalen,))[...,i],
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np.ones((2,2,2))/8., # 2x2x2 neighborhood of cells
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mode = 'wrap',
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origin = -1, # offset to have cell origin as center
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) # now averaged at cell origins
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node = np.append(node,node[np.newaxis,0,:,:,...],axis=0) # wrap along z
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node = np.append(node,node[:,0,np.newaxis,:,...],axis=1) # wrap along y
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node = np.append(node,node[:,:,0,np.newaxis,...],axis=2) # wrap along x
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nodeData = node[...,np.newaxis] if i==0 else np.concatenate((nodeData,node[...,np.newaxis]),axis=-1)
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return nodeData
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#--------------------------------------------------------------------------------------------------
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def deformationAvgFFT(F,grid,size,nodal=False,transformed=False):
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"""Calculate average cell center (or nodal) deformation for deformation gradient field specified in each grid cell"""
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if nodal:
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x, y, z = np.meshgrid(np.linspace(0,size[2],1+grid[2]),
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np.linspace(0,size[1],1+grid[1]),
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np.linspace(0,size[0],1+grid[0]),
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indexing = 'ij')
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else:
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x, y, z = np.meshgrid(np.linspace(size[2]/grid[2]/2.,size[2]-size[2]/grid[2]/2.,grid[2]),
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np.linspace(size[1]/grid[1]/2.,size[1]-size[1]/grid[1]/2.,grid[1]),
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np.linspace(size[0]/grid[0]/2.,size[0]-size[0]/grid[0]/2.,grid[0]),
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indexing = 'ij')
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origCoords = np.concatenate((z[:,:,:,None],y[:,:,:,None],x[:,:,:,None]),axis = 3)
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F_fourier = F if transformed else np.fft.rfftn(F,axes=(0,1,2)) # transform or use provided data
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Favg = np.real(F_fourier[0,0,0,:,:])/grid.prod() # take zero freq for average
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avgDeformation = np.einsum('ml,ijkl->ijkm',Favg,origCoords) # dX = Favg.X
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return avgDeformation
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#--------------------------------------------------------------------------------------------------
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def displacementFluctFFT(F,grid,size,nodal=False,transformed=False):
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"""Calculate cell center (or nodal) displacement for deformation gradient field specified in each grid cell"""
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integrator = 0.5j * size / math.pi
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kk, kj, ki = np.meshgrid(np.where(np.arange(grid[2])>grid[2]//2,np.arange(grid[2])-grid[2],np.arange(grid[2])),
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np.where(np.arange(grid[1])>grid[1]//2,np.arange(grid[1])-grid[1],np.arange(grid[1])),
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np.arange(grid[0]//2+1),
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indexing = 'ij')
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k_s = np.concatenate((ki[:,:,:,None],kj[:,:,:,None],kk[:,:,:,None]),axis = 3)
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k_sSquared = np.einsum('...l,...l',k_s,k_s)
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k_sSquared[0,0,0] = 1.0 # ignore global average frequency
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#--------------------------------------------------------------------------------------------------
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# integration in Fourier space
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displacement_fourier = -np.einsum('ijkml,ijkl,l->ijkm',
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F if transformed else np.fft.rfftn(F,axes=(0,1,2)),
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k_s,
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integrator,
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) / k_sSquared[...,np.newaxis]
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#--------------------------------------------------------------------------------------------------
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# backtransformation to real space
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displacement = np.fft.irfftn(displacement_fourier,grid[::-1],axes=(0,1,2))
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return cell2node(displacement,grid) if nodal else displacement
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def volTetrahedron(coords):
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"""
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Return the volume of the tetrahedron with given vertices or sides.
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Ifvertices are given they must be in a NumPy array with shape (4,3): the
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position vectors of the 4 vertices in 3 dimensions; if the six sides are
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given, they must be an array of length 6. If both are given, the sides
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will be used in the calculation.
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This method implements
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Tartaglia's formula using the Cayley-Menger determinant:
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|0 1 1 1 1 |
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|1 0 s1^2 s2^2 s3^2|
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288 V^2 = |1 s1^2 0 s4^2 s5^2|
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|1 s2^2 s4^2 0 s6^2|
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|1 s3^2 s5^2 s6^2 0 |
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where s1, s2, ..., s6 are the tetrahedron side lengths.
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from http://codereview.stackexchange.com/questions/77593/calculating-the-volume-of-a-tetrahedron
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"""
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# The indexes of rows in the vertices array corresponding to all
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# possible pairs of vertices
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vertex_pair_indexes = np.array(((0, 1), (0, 2), (0, 3),
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(1, 2), (1, 3), (2, 3)))
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# Get all the squares of all side lengths from the differences between
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# the 6 different pairs of vertex positions
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vertices = np.concatenate((coords[0],coords[1],coords[2],coords[3])).reshape([4,3])
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vertex1, vertex2 = vertex_pair_indexes[:,0], vertex_pair_indexes[:,1]
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sides_squared = np.sum((vertices[vertex1] - vertices[vertex2])**2,axis=-1)
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# Set up the Cayley-Menger determinant
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M = np.zeros((5,5))
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# Fill in the upper triangle of the matrix
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M[0,1:] = 1
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# The squared-side length elements can be indexed using the vertex
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# pair indices (compare with the determinant illustrated above)
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M[tuple(zip(*(vertex_pair_indexes + 1)))] = sides_squared
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# The matrix is symmetric, so we can fill in the lower triangle by
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# adding the transpose
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M = M + M.T
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return np.sqrt(np.linalg.det(M) / 288)
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def volumeMismatch(size,F,nodes):
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"""
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Calculates the volume mismatch
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volume mismatch is defined as the difference between volume of reconstructed
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(compatible) cube and determinant of defgrad at the FP
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"""
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coords = np.empty([8,3])
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vMismatch = np.empty(grid[::-1])
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volInitial = size.prod()/grid.prod()
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#--------------------------------------------------------------------------------------------------
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# calculate actual volume and volume resulting from deformation gradient
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for k in range(grid[2]):
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for j in range(grid[1]):
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for i in range(grid[0]):
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coords[0,0:3] = nodes[k, j, i ,0:3]
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coords[1,0:3] = nodes[k ,j, i+1,0:3]
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coords[2,0:3] = nodes[k ,j+1,i+1,0:3]
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coords[3,0:3] = nodes[k, j+1,i ,0:3]
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coords[4,0:3] = nodes[k+1,j, i ,0:3]
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coords[5,0:3] = nodes[k+1,j, i+1,0:3]
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coords[6,0:3] = nodes[k+1,j+1,i+1,0:3]
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coords[7,0:3] = nodes[k+1,j+1,i ,0:3]
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vMismatch[k,j,i] = \
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( abs(volTetrahedron([coords[6,0:3],coords[0,0:3],coords[7,0:3],coords[3,0:3]])) \
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+ abs(volTetrahedron([coords[6,0:3],coords[0,0:3],coords[7,0:3],coords[4,0:3]])) \
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+ abs(volTetrahedron([coords[6,0:3],coords[0,0:3],coords[2,0:3],coords[3,0:3]])) \
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+ abs(volTetrahedron([coords[6,0:3],coords[0,0:3],coords[2,0:3],coords[1,0:3]])) \
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+ abs(volTetrahedron([coords[6,0:3],coords[4,0:3],coords[1,0:3],coords[5,0:3]])) \
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+ abs(volTetrahedron([coords[6,0:3],coords[4,0:3],coords[1,0:3],coords[0,0:3]]))) \
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/np.linalg.det(F[k,j,i,0:3,0:3])
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return vMismatch/volInitial
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def shapeMismatch(size,F,nodes,centres):
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"""
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Routine to calculate the shape mismatch
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shape mismatch is defined as difference between the vectors from the central point to
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the corners of reconstructed (combatible) volume element and the vectors calculated by deforming
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the initial volume element with the current deformation gradient
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"""
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coordsInitial = np.empty([8,3])
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sMismatch = np.empty(grid[::-1])
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#--------------------------------------------------------------------------------------------------
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# initial positions
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coordsInitial[0,0:3] = [-size[0]/grid[0],-size[1]/grid[1],-size[2]/grid[2]]
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coordsInitial[1,0:3] = [+size[0]/grid[0],-size[1]/grid[1],-size[2]/grid[2]]
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coordsInitial[2,0:3] = [+size[0]/grid[0],+size[1]/grid[1],-size[2]/grid[2]]
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coordsInitial[3,0:3] = [-size[0]/grid[0],+size[1]/grid[1],-size[2]/grid[2]]
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coordsInitial[4,0:3] = [-size[0]/grid[0],-size[1]/grid[1],+size[2]/grid[2]]
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coordsInitial[5,0:3] = [+size[0]/grid[0],-size[1]/grid[1],+size[2]/grid[2]]
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coordsInitial[6,0:3] = [+size[0]/grid[0],+size[1]/grid[1],+size[2]/grid[2]]
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coordsInitial[7,0:3] = [-size[0]/grid[0],+size[1]/grid[1],+size[2]/grid[2]]
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coordsInitial = coordsInitial/2.0
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#--------------------------------------------------------------------------------------------------
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# compare deformed original and deformed positions to actual positions
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for k in range(grid[2]):
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for j in range(grid[1]):
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for i in range(grid[0]):
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sMismatch[k,j,i] = \
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+ np.linalg.norm(nodes[k, j, i ,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[0,0:3]))\
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+ np.linalg.norm(nodes[k, j, i+1,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[1,0:3]))\
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+ np.linalg.norm(nodes[k, j+1,i+1,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[2,0:3]))\
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+ np.linalg.norm(nodes[k, j+1,i ,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[3,0:3]))\
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+ np.linalg.norm(nodes[k+1,j, i ,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[4,0:3]))\
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+ np.linalg.norm(nodes[k+1,j, i+1,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[5,0:3]))\
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+ np.linalg.norm(nodes[k+1,j+1,i+1,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[6,0:3]))\
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+ np.linalg.norm(nodes[k+1,j+1,i ,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[7,0:3]))
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return sMismatch
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# --------------------------------------------------------------------
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# MAIN
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# --------------------------------------------------------------------
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parser = OptionParser(option_class=damask.extendableOption, usage='%prog options file[s]', description = """
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Add column(s) containing the shape and volume mismatch resulting from given deformation gradient.
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Operates on periodic three-dimensional x,y,z-ordered data sets.
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""", version = scriptID)
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parser.add_option('-c','--coordinates',
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dest = 'pos',
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type = 'string', metavar = 'string',
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help = 'column heading of coordinates [%default]')
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parser.add_option('-f','--defgrad',
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dest = 'defgrad',
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type = 'string', metavar = 'string ',
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help = 'column heading of deformation gradient [%default]')
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parser.add_option('--no-shape','-s',
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dest = 'shape',
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action = 'store_false',
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help = 'omit shape mismatch')
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parser.add_option('--no-volume','-v',
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dest = 'volume',
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action = 'store_false',
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help = 'omit volume mismatch')
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parser.set_defaults(pos = 'pos',
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defgrad = 'f',
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shape = True,
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volume = True,
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)
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(options,filenames) = parser.parse_args()
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# --- loop over input files -------------------------------------------------------------------------
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if filenames == []: filenames = [None]
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for name in filenames:
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try:
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table = damask.ASCIItable(name = name,
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buffered = False)
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except: continue
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damask.util.report(scriptName,name)
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# ------------------------------------------ read header ------------------------------------------
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table.head_read()
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# ------------------------------------------ sanity checks ----------------------------------------
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errors = []
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remarks = []
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if table.label_dimension(options.defgrad) != 9:
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errors.append('deformation gradient "{}" is not a 3x3 tensor.'.format(options.defgrad))
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coordDim = table.label_dimension(options.pos)
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if not 3 >= coordDim >= 1:
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errors.append('coordinates "{}" need to have one, two, or three dimensions.'.format(options.pos))
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elif coordDim < 3:
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remarks.append('appending {} dimension{} to coordinates "{}"...'.format(3-coordDim,
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's' if coordDim < 2 else '',
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options.pos))
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if remarks != []: damask.util.croak(remarks)
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if errors != []:
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damask.util.croak(errors)
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table.close(dismiss=True)
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continue
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# --------------- figure out size and grid ---------------------------------------------------------
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table.data_readArray([options.defgrad,options.pos])
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table.data_rewind()
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if len(table.data.shape) < 2: table.data.shape += (1,) # expand to 2D shape
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if table.data[:,9:].shape[1] < 3:
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table.data = np.hstack((table.data,
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np.zeros((table.data.shape[0],
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3-table.data[:,9:].shape[1]),dtype='f'))) # fill coords up to 3D with zeros
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coords = [np.unique(table.data[:,9+i]) for i in range(3)]
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mincorner = np.array(map(min,coords))
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maxcorner = np.array(map(max,coords))
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grid = np.array(map(len,coords),'i')
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size = grid/np.maximum(np.ones(3,'d'), grid-1.0) * (maxcorner-mincorner) # size from edge to edge = dim * n/(n-1)
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size = np.where(grid > 1, size, min(size[grid > 1]/grid[grid > 1])) # spacing for grid==1 set to smallest among other spacings
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N = grid.prod()
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if N != len(table.data): errors.append('data count {} does not match grid {}x{}x{}.'.format(N,*grid))
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if errors != []:
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damask.util.croak(errors)
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table.close(dismiss = True)
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continue
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# -----------------------------process data and assemble header -------------------------------------
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F_fourier = np.fft.rfftn(table.data[:,:9].reshape(grid[2],grid[1],grid[0],3,3),axes=(0,1,2)) # perform transform only once...
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nodes = displacementFluctFFT(F_fourier,grid,size,True,transformed=True)\
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+ deformationAvgFFT (F_fourier,grid,size,True,transformed=True)
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if options.shape:
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table.labels_append(['shapeMismatch({})'.format(options.defgrad)])
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centres = displacementFluctFFT(F_fourier,grid,size,False,transformed=True)\
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+ deformationAvgFFT (F_fourier,grid,size,False,transformed=True)
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if options.volume:
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table.labels_append(['volMismatch({})'.format(options.defgrad)])
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table.head_write()
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if options.shape:
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shapeMismatch = shapeMismatch( size,table.data[:,:9].reshape(grid[2],grid[1],grid[0],3,3),nodes,centres)
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if options.volume:
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volumeMismatch = volumeMismatch(size,table.data[:,:9].reshape(grid[2],grid[1],grid[0],3,3),nodes)
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# ------------------------------------------ output data -------------------------------------------
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for i in range(grid[2]):
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for j in range(grid[1]):
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for k in range(grid[0]):
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table.data_read()
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if options.shape: table.data_append(shapeMismatch[i,j,k])
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if options.volume: table.data_append(volumeMismatch[i,j,k])
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table.data_write()
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# ------------------------------------------ output finalization -----------------------------------
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table.close() # close ASCII tables
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