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