263 lines
12 KiB
Python
Executable File
263 lines
12 KiB
Python
Executable File
#!/usr/bin/env python
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# -*- coding: UTF-8 no BOM -*-
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import os,sys
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import numpy as np
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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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def volTetrahedron(coords):
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"""
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Return the volume of the tetrahedron with given vertices or sides. If
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vertices 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 mismatch between volume of reconstructed (compatible) cube and
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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)
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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 xrange(grid[2]):
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for j in xrange(grid[1]):
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for i in xrange(grid[0]):
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coords[0,0:3] = nodes[0:3,i, j, k ]
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coords[1,0:3] = nodes[0:3,i+1,j, k ]
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coords[2,0:3] = nodes[0:3,i+1,j+1,k ]
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coords[3,0:3] = nodes[0:3,i, j+1,k ]
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coords[4,0:3] = nodes[0:3,i, j, k+1]
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coords[5,0:3] = nodes[0:3,i+1,j, k+1]
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coords[6,0:3] = nodes[0:3,i+1,j+1,k+1]
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coords[7,0:3] = nodes[0:3,i, j+1,k+1]
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vMismatch[i,j,k] = \
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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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vMismatch[i,j,k] = vMismatch[i,j,k]/np.linalg.det(F[0:3,0:3,i,j,k])
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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 mismatch 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)
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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 xrange(grid[2]):
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for j in xrange(grid[1]):
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for i in xrange(grid[0]):
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sMismatch[i,j,k] = \
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np.linalg.norm(nodes[0:3,i, j, k] - centres[0:3,i,j,k] - np.dot(F[:,:,i,j,k], coordsInitial[0,0:3]))\
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+ np.linalg.norm(nodes[0:3,i+1,j, k] - centres[0:3,i,j,k] - np.dot(F[:,:,i,j,k], coordsInitial[1,0:3]))\
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+ np.linalg.norm(nodes[0:3,i+1,j+1,k ] - centres[0:3,i,j,k] - np.dot(F[:,:,i,j,k], coordsInitial[2,0:3]))\
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+ np.linalg.norm(nodes[0:3,i, j+1,k ] - centres[0:3,i,j,k] - np.dot(F[:,:,i,j,k], coordsInitial[3,0:3]))\
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+ np.linalg.norm(nodes[0:3,i, j, k+1] - centres[0:3,i,j,k] - np.dot(F[:,:,i,j,k], coordsInitial[4,0:3]))\
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+ np.linalg.norm(nodes[0:3,i+1,j, k+1] - centres[0:3,i,j,k] - np.dot(F[:,:,i,j,k], coordsInitial[5,0:3]))\
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+ np.linalg.norm(nodes[0:3,i+1,j+1,k+1] - centres[0:3,i,j,k] - np.dot(F[:,:,i,j,k], coordsInitial[6,0:3]))\
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+ np.linalg.norm(nodes[0:3,i, j+1,k+1] - centres[0:3,i,j,k] - np.dot(F[:,:,i,j,k], 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 = 'coords',
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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(coords = 'ipinitialcoord',
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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.coords) != 3: errors.append('coordinates {} are not a vector.'.format(options.coords))
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else: colCoord = table.label_index(options.coords)
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if table.label_dimension(options.defgrad) != 9: errors.append('deformation gradient {} is not a tensor.'.format(options.defgrad))
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else: colF = table.label_index(options.defgrad)
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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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# ------------------------------------------ assemble header --------------------------------------
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table.info_append(scriptID + '\t' + ' '.join(sys.argv[1:]))
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if options.shape: table.labels_append('shapeMismatch({})'.format(options.defgrad))
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if options.volume: table.labels_append('volMismatch({})'.format(options.defgrad))
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# --------------- figure out size and grid ---------------------------------------------------------
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table.data_readArray()
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coords = [np.unique(table.data[:,colCoord+i]) for i in xrange(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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# --------------- figure out columns to process ---------------------------------------------------
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key = '1_%s'%options.defgrad
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if key not in table.labels:
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file['croak'].write('column %s not found...\n'%key)
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continue
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else:
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column = table.labels.index(key) # remember columns of requested data
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# ------------------------------------------ assemble header ---------------------------------------
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if options.shape: table.labels_append(['shapeMismatch(%s)' %options.defgrad])
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if options.volume: table.labels_append(['volMismatch(%s)'%options.defgrad])
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table.head_write()
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# ------------------------------------------ read deformation gradient field -----------------------
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table.data_rewind()
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F = np.zeros(N*9,'d').reshape([3,3]+list(grid))
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idx = 0
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while table.data_read():
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(x,y,z) = damask.util.gridLocation(idx,grid) # figure out (x,y,z) position from line count
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idx += 1
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F[0:3,0:3,x,y,z] = np.array(map(float,table.data[column:column+9]),'d').reshape(3,3)
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Favg = damask.core.math.tensorAvg(F)
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centres = damask.core.mesh.deformedCoordsFFT(size,F,Favg,[1.0,1.0,1.0])
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nodes = damask.core.mesh.nodesAroundCentres(size,Favg,centres)
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if options.shape: shapeMismatch = shapeMismatch( size,F,nodes,centres)
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if options.volume: volumeMismatch = volumeMismatch(size,F,nodes)
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# ------------------------------------------ process data ------------------------------------------
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table.data_rewind()
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idx = 0
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outputAlive = True
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while outputAlive and table.data_read(): # read next data line of ASCII table
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(x,y,z) = damask.util.gridLocation(idx,grid) # figure out (x,y,z) position from line count
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idx += 1
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if options.shape: table.data_append( shapeMismatch[x,y,z])
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if options.volume: table.data_append(volumeMismatch[x,y,z])
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outputAlive = table.data_write()
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# ------------------------------------------ output finalization -----------------------------------
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table.close() # close ASCII tables
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