FFT-based gradient calculation of scalar or vector field data (sibling of addCurl and addDivergence)
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Aritra Chakraborty
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#!/usr/bin/env python
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# -*- coding: UTF-8 no BOM -*-
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import os,sys,math
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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 gradFFT(geomdim,field):
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grid = np.array(np.shape(field)[2::-1])
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N = grid.prod() # field size
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n = np.array(np.shape(field)[3:]).prod() # data size
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if n == 3: dataType = 'vector'
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elif n == 1: dataType = 'scalar'
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field_fourier = np.fft.fftpack.rfftn(field,axes=(0,1,2))
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grad_fourier = np.zeros(field_fourier.shape+(3,),'c16')
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# differentiation in Fourier space
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k_s = np.zeros([3],'i')
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TWOPIIMG = 2.0j*math.pi
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for i in xrange(grid[2]):
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k_s[0] = i
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if grid[2]%2 == 0 and i == grid[2]//2: k_s[0] = 0 # for even grid, set Nyquist freq to 0 (Johnson, MIT, 2011)
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elif i > grid[2]//2: k_s[0] -= grid[2]
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for j in xrange(grid[1]):
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k_s[1] = j
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if grid[1]%2 == 0 and j == grid[1]//2: k_s[1] = 0 # for even grid, set Nyquist freq to 0 (Johnson, MIT, 2011)
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elif j > grid[1]//2: k_s[1] -= grid[1]
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for k in xrange(grid[0]//2+1):
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k_s[2] = k
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if grid[0]%2 == 0 and k == grid[0]//2: k_s[2] = 0 # for even grid, set Nyquist freq to 0 (Johnson, MIT, 2011)
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xi = (k_s/geomdim)[2::-1].astype('c16') # reversing the field order
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grad_fourier[i,j,k,0,:] = field_fourier[i,j,k,0]*xi *TWOPIIMG # vector field from scalar data
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if dataType == 'vector':
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grad_fourier[i,j,k,1,:] = field_fourier[i,j,k,1]*xi *TWOPIIMG # tensor field from vector data
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grad_fourier[i,j,k,2,:] = field_fourier[i,j,k,2]*xi *TWOPIIMG
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return np.fft.fftpack.irfftn(grad_fourier,axes=(0,1,2)).reshape([N,3*n])
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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 gradient of requested column(s).
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Operates on periodic ordered three-dimensional data sets.
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Deals with both vector- and scalar fields.
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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 for coordinates [%default]')
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parser.add_option('-v','--vector',
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dest = 'vector',
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action = 'extend', metavar = '<string LIST>',
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help = 'heading of columns containing vector field values')
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parser.add_option('-s','--scalar',
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dest = 'scalar',
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action = 'extend', metavar = '<string LIST>',
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help = 'heading of columns containing scalar field values')
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parser.set_defaults(coords = 'ipinitialcoord',
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)
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(options,filenames) = parser.parse_args()
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if options.vector is None and options.scalar is None:
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parser.error('no data column specified.')
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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: table = damask.ASCIItable(name = name,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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items = {
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'scalar': {'dim': 1, 'shape': [1], 'labels':options.scalar, 'active':[], 'column': []},
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'vector': {'dim': 3, 'shape': [3], 'labels':options.vector, 'active':[], 'column': []},
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}
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errors = []
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remarks = []
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column = {}
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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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for type, data in items.iteritems():
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for what in (data['labels'] if data['labels'] is not None else []):
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dim = table.label_dimension(what)
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if dim != data['dim']: remarks.append('column {} is not a {}.'.format(what,type))
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else:
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items[type]['active'].append(what)
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items[type]['column'].append(table.label_index(what))
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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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for type, data in items.iteritems():
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for label in data['active']:
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table.labels_append(['{}_gradFFT({})'.format(i+1,label) for i in xrange(3 * data['dim'])]) # extend ASCII header with new labels # grad increases the field dimension by one
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table.head_write()
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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]))
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# ------------------------------------------ process value field -----------------------------------
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stack = [table.data]
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for type, data in items.iteritems():
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for i,label in enumerate(data['active']):
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stack.append(gradFFT(size[::-1], # we need to reverse order here, because x is fastest,ie rightmost, but leftmost in our x,y,z notation
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table.data[:,data['column'][i]:data['column'][i]+data['dim']].
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reshape([grid[2],grid[1],grid[0]]+data['shape'])))
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# ------------------------------------------ output result -----------------------------------------
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if len(stack) > 1: table.data = np.hstack(tuple(stack))
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table.data_writeArray('%.12g')
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# ------------------------------------------ output finalization -----------------------------------
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table.close() # close input ASCII table (works for stdin)
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