360 lines
15 KiB
Python
Executable File
360 lines
15 KiB
Python
Executable File
#!/usr/bin/env python
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from optparse import OptionParser
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import damask
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import os,sys,math,re,random,string
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import numpy as np
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scriptID = string.replace('$Id$','\n','\\n')
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scriptName = scriptID.split()[1]
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# --- helper functions ---
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def binAsBins(bin,intervals):
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""" explode compound bin into 3D bins list """
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bins = [0]*3
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bins[0] = (bin//(intervals[1] * intervals[2])) % intervals[0]
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bins[1] = (bin//intervals[2]) % intervals[1]
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bins[2] = bin % intervals[2]
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return bins
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def binsAsBin(bins,intervals):
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""" implode 3D bins into compound bin """
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return (bins[0]*intervals[1] + bins[1])*intervals[2] + bins[2]
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def EulersAsBins(Eulers,intervals,deltas,center):
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""" return list of Eulers translated into 3D bins list """
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return [int((euler+(0.5-center)*delta)//delta)%interval \
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for euler,delta,interval in zip(Eulers,deltas,intervals) \
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]
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def binAsEulers(bin,intervals,deltas,center):
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""" compound bin number translated into list of Eulers """
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Eulers = [0.0]*3
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Eulers[2] = (bin%intervals[2] + center)*deltas[2]
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Eulers[1] = (bin//intervals[2]%intervals[1] + center)*deltas[1]
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Eulers[0] = (bin//(intervals[2]*intervals[1]) + center)*deltas[0]
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return Eulers
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def directInvRepetitions(probability,scale):
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""" calculate number of samples drawn by direct inversion """
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nDirectInv = 0
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for bin in range(len(probability)): # loop over bins
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nDirectInv += int(round(probability[bin]*scale)) # calc repetition
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return nDirectInv
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# ---------------------- sampling methods -----------------------------------------------------------------------
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# ----- efficient algorithm ---------
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def directInversion (ODF,nSamples):
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""" ODF contains 'dV_V' (normalized to 1), 'center', 'intervals', 'limits' (in radians) """
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nOptSamples = max(ODF['nNonZero'],nSamples) # random subsampling if too little samples requested
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nInvSamples = 0
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repetition = [None]*ODF['nBins']
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probabilityScale = nOptSamples # guess
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scaleLower = 0.0
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nInvSamplesLower = 0
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scaleUpper = float(nOptSamples)
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incFactor = 1.0
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nIter = 0
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nInvSamplesUpper = directInvRepetitions(ODF['dV_V'],scaleUpper)
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while (\
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(scaleUpper-scaleLower > scaleUpper*1e-15 or nInvSamplesUpper < nOptSamples) and \
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nInvSamplesUpper != nOptSamples \
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): # closer match required?
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if nInvSamplesUpper < nOptSamples:
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scaleLower,scaleUpper = scaleUpper,scaleUpper+incFactor*(scaleUpper-scaleLower)/2.0
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incFactor *= 2.0
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nInvSamplesLower,nInvSamplesUpper = nInvSamplesUpper,directInvRepetitions(ODF['dV_V'],scaleUpper)
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else:
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scaleUpper = (scaleLower+scaleUpper)/2.0
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incFactor = 1.0
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nInvSamplesUpper = directInvRepetitions(ODF['dV_V'],scaleUpper)
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nIter += 1
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file['croak'].write('%i:(%12.11f,%12.11f) %i <= %i <= %i\n'\
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%(nIter,scaleLower,scaleUpper,nInvSamplesLower,nOptSamples,nInvSamplesUpper))
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nInvSamples = nInvSamplesUpper
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scale = scaleUpper
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file['croak'].write('created set of %i samples (%12.11f) with scaling %12.11f delivering %i\n'\
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%(nInvSamples,float(nInvSamples)/nOptSamples-1.0,scale,nSamples))
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repetition = [None]*ODF['nBins'] # preallocate and clear
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for bin in range(ODF['nBins']): # loop over bins
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repetition[bin] = int(round(ODF['dV_V'][bin]*scale)) # calc repetition
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# build set
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set = [None]*nInvSamples
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i = 0
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for bin in range(ODF['nBins']):
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set[i:i+repetition[bin]] = [bin]*repetition[bin] # fill set with bin, i.e. orientation
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i += repetition[bin] # advance set counter
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orientations = [None]*nSamples
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reconstructedODF = [0.0]*ODF['nBins']
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unitInc = 1.0/nSamples
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for j in range(nSamples):
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if (j == nInvSamples-1): ex = j
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else: ex = int(round(random.uniform(j+0.5,nInvSamples-0.5)))
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bin = set[ex]
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bins = binAsBins(bin,ODF['interval'])
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Eulers = binAsEulers(bin,ODF['interval'],ODF['delta'],ODF['center'])
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orientations[j] = '%g\t%g\t%g' %( math.degrees(Eulers[0]),math.degrees(Eulers[1]),math.degrees(Eulers[2]) )
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reconstructedODF[bin] += unitInc
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set[ex] = set[j] # exchange orientations
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return orientations, reconstructedODF
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# ----- trial and error algorithms ---------
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def MonteCarloEulers (ODF,nSamples):
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""" ODF contains 'dV_V' (normalized to 1), 'center', 'intervals', 'limits' (in radians) """
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countMC = 0
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maxdV_V = max(ODF['dV_V'])
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orientations = [None]*nSamples
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reconstructedODF = [0.0]*ODF['nBins']
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unitInc = 1.0/nSamples
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for j in range(nSamples):
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MC = maxdV_V*2.0
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bin = 0
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while MC > ODF['dV_V'][bin]:
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countMC += 1
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MC = maxdV_V*random.random()
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Eulers = [limit*random.random() for limit in ODF['limit']]
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bins = EulersAsBins(Eulers,ODF['interval'],ODF['delta'],ODF['center'])
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bin = binsAsBin(bins,ODF['interval'])
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orientations[j] = '%g\t%g\t%g' %( math.degrees(Eulers[0]),math.degrees(Eulers[1]),math.degrees(Eulers[2]) )
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reconstructedODF[bin] += unitInc
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return orientations, reconstructedODF, countMC
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def MonteCarloBins (ODF,nSamples):
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""" ODF contains 'dV_V' (normalized to 1), 'center', 'intervals', 'limits' (in radians) """
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countMC = 0
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maxdV_V = max(ODF['dV_V'])
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orientations = [None]*nSamples
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reconstructedODF = [0.0]*ODF['nBins']
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unitInc = 1.0/nSamples
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for j in range(nSamples):
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MC = maxdV_V*2.0
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bin = 0
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while MC > ODF['dV_V'][bin]:
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countMC += 1
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MC = maxdV_V*random.random()
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bin = int(ODF['nBins'] * random.random())
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Eulers = binAsEulers(bin,ODF['interval'],ODF['delta'],ODF['center'])
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orientations[j] = '%g\t%g\t%g' %( math.degrees(Eulers[0]),math.degrees(Eulers[1]),math.degrees(Eulers[2]) )
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reconstructedODF[bin] += unitInc
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return orientations, reconstructedODF
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def TothVanHoutteSTAT (ODF,nSamples):
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""" ODF contains 'dV_V' (normalized to 1), 'center', 'intervals', 'limits' (in radians) """
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orientations = [None]*nSamples
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reconstructedODF = [0.0]*ODF['nBins']
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unitInc = 1.0/nSamples
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selectors = [random.random() for i in range(nSamples)]
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selectors.sort()
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indexSelector = 0
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cumdV_V = 0.0
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countSamples = 0
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for bin in range(ODF['nBins']) :
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cumdV_V += ODF['dV_V'][bin]
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while indexSelector < nSamples and selectors[indexSelector] < cumdV_V:
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Eulers = binAsEulers(bin,ODF['interval'],ODF['delta'],ODF['center'])
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orientations[countSamples] = '%g\t%g\t%g' %( math.degrees(Eulers[0]),math.degrees(Eulers[1]),math.degrees(Eulers[2]) )
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reconstructedODF[bin] += unitInc
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countSamples += 1
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indexSelector += 1
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file['croak'].write('created set of %i when asked to deliver %i\n'%(countSamples,nSamples))
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return orientations, reconstructedODF
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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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Transform linear binned data into Euler angles.
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""", version = scriptID)
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parser.add_option('-n', '--nsamples', dest='number', type='int', metavar = 'int',
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help='number of orientations to be generated [%default]')
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parser.add_option('-a','--algorithm', dest='algorithm', type='string', metavar = 'string',
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help='sampling algorithm. IA: direct inversion, STAT: Van Houtte, MC: Monte Carlo. [%default].') #make choice
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parser.add_option('-p','--phase', dest='phase', type='int', metavar = 'int',
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help='phase index to be used [%default]')
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parser.add_option('--crystallite', dest='crystallite', type='int', metavar = 'int',
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help='crystallite index to be used [%default]')
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parser.add_option('-r', '--rnd', dest='randomSeed', type='int', metavar='int', \
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help='seed of random number generator [%default]')
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parser.set_defaults(randomSeed = None)
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parser.set_defaults(number = 500)
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parser.set_defaults(algorithm = 'IA')
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parser.set_defaults(phase = 1)
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parser.set_defaults(crystallite = 1)
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(options,filenames) = parser.parse_args()
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nSamples = options.number
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methods = [options.algorithm]
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#--- setup file handles ---------------------------------------------------------------------------
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files = []
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if filenames == []:
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files.append({'name':'STDIN','input':sys.stdin,'output':sys.stdout,'croak':sys.stderr})
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else:
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for name in filenames:
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if os.path.exists(name):
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files.append({'name':name,'input':open(name),'output':open(name+'_tmp','w'),'croak':sys.stdout})
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#--- loop over input files ------------------------------------------------------------------------
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for file in files:
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file['croak'].write('\033[1m' + scriptName + '\033[0m: ' + (file['name'] if file['name'] != 'STDIN' else '') + '\n')
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table = damask.ASCIItable(file['input'],file['output'],buffered = False)
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table.head_read()
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randomSeed = int(os.urandom(4).encode('hex'), 16) if options.randomSeed == None else options.randomSeed # radom seed per file for second phase
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random.seed(randomSeed)
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# --------------- figure out columns in table ----------- -----------------------------------------
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column = {}
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pos = 0
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keys = ['phi1','Phi','phi2','intensity']
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for key in keys:
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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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else:
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column[key] = pos
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pos+=1
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if pos != 4: continue
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binnedODF = table.data_readArray(keys)
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# --------------- figure out limits (left/right), delta, and interval -----------------------------
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ODF = {}
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limits = np.array([[np.min(table.data[:,column['phi1']]),\
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np.min(table.data[:,column['Phi']]),\
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np.min(table.data[:,column['phi2']])],\
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[np.max(table.data[:,column['phi1']]),\
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np.max(table.data[:,column['Phi']]),\
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np.max(table.data[:,column['phi2']])]])
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ODF['limit'] = np.radians(limits[1,:])
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if all(limits[0,:]<1e-8): # vertex centered
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ODF['center'] = 0.0
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else: # cell centered
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ODF['center'] = 0.5
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eulers = [{},{},{}]
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for i in xrange(table.data.shape[0]):
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for j in xrange(3):
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eulers[j][str(table.data[i,column[keys[j]]])] = True # remember eulers along phi1, Phi, and phi2
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ODF['interval'] = np.array([len(eulers[0]),len(eulers[1]),len(eulers[2]),],'i') # steps are number of distict values
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ODF['nBins'] = ODF['interval'].prod()
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ODF['delta'] = np.radians(np.array(limits[1,0:3]-limits[0,0:3])/(ODF['interval']-1))
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if binnedODF[0] != ODF['nBins']:
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file['croak'].write('expecting %i values but got %i'%(ODF['nBins'],len(linesBinnedODF)))
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continue
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# build binnedODF array
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sumdV_V = 0.0
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ODF['dV_V'] = [None]*ODF['nBins']
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ODF['nNonZero'] = 0
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dg = ODF['delta'][0]*2.0*math.sin(ODF['delta'][1]/2.0)*ODF['delta'][2]
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for b in range(ODF['nBins']):
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ODF['dV_V'][b] = \
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max(0.0,table.data[b,column['intensity']]) * dg * \
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math.sin(((b//ODF['interval'][2])%ODF['interval'][1]+ODF['center'])*ODF['delta'][1])
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if ODF['dV_V'][b] > 0.0:
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sumdV_V += ODF['dV_V'][b]
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ODF['nNonZero'] += 1
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for b in range(ODF['nBins']): ODF['dV_V'][b] /= sumdV_V # normalize dV/V
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file['croak'].write('non-zero fraction: %12.11f (%i/%i)\n'\
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%(float(ODF['nNonZero'])/ODF['nBins'],ODF['nNonZero'],ODF['nBins']))
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file['croak'].write('Volume integral of ODF: %12.11f\n'%sumdV_V)
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file['croak'].write('Reference Integral: %12.11f\n'\
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%(ODF['limit'][0]*ODF['limit'][2]*(1-math.cos(ODF['limit'][1]))))
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# call methods
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Functions = {'IA': 'directInversion', 'STAT': 'TothVanHoutteSTAT', 'MC': 'MonteCarloBins'}
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method = Functions[options.algorithm]
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Orientations, ReconstructedODF = (globals()[method])(ODF,nSamples)
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# calculate accuracy of sample
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squaredDiff = {'orig':0.0,method:0.0}
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squaredRelDiff = {'orig':0.0,method:0.0}
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mutualProd = {'orig':0.0,method:0.0}
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indivSum = {'orig':0.0,method:0.0}
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indivSquaredSum = {'orig':0.0,method:0.0}
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for bin in range(ODF['nBins']):
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squaredDiff[method] += (ODF['dV_V'][bin] - ReconstructedODF[bin])**2
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if ODF['dV_V'][bin] > 0.0:
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squaredRelDiff[method] += (ODF['dV_V'][bin] - ReconstructedODF[bin])**2/ODF['dV_V'][bin]**2
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mutualProd[method] += ODF['dV_V'][bin]*ReconstructedODF[bin]
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indivSum[method] += ReconstructedODF[bin]
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indivSquaredSum[method] += ReconstructedODF[bin]**2
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indivSum['orig'] += ODF['dV_V'][bin]
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indivSquaredSum['orig'] += ODF['dV_V'][bin]**2
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file['croak'].write('sqrt(N*)RMSD of ODFs:\t %12.11f\n'% math.sqrt(nSamples*squaredDiff[method]))
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file['croak'].write('RMSrD of ODFs:\t %12.11f\n'%math.sqrt(squaredRelDiff[method]))
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file['croak'].write('rMSD of ODFs:\t %12.11f\n'%(squaredDiff[method]/indivSquaredSum['orig']))
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file['croak'].write('nNonZero correlation slope:\t %12.11f\n'\
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%((ODF['nNonZero']*mutualProd[method]-indivSum['orig']*indivSum[method])/\
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(ODF['nNonZero']*indivSquaredSum['orig']-indivSum['orig']**2)))
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file['croak'].write( 'nNonZero correlation confidence:\t %12.11f\n'\
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%((mutualProd[method]-indivSum['orig']*indivSum[method]/ODF['nNonZero'])/\
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(ODF['nNonZero']*math.sqrt((indivSquaredSum['orig']/ODF['nNonZero']-(indivSum['orig']/ODF['nNonZero'])**2)*\
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(indivSquaredSum[method]/ODF['nNonZero']-(indivSum[method]/ODF['nNonZero'])**2)))))
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if method == 'IA' and nSamples < ODF['nNonZero']:
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strOpt = '(%i)'%ODF['nNonZero']
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formatwidth = 1
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file['output'].write('#' + scriptID + ' ' + ' '.join(sys.argv[1:])+'\n')
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file['output'].write('# random seed %i\n'%randomSeed)
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file['output'].write('#-------------------#')
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file['output'].write('\n<microstructure>\n')
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file['output'].write('#-------------------#\n')
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for i,ID in enumerate(xrange(nSamples)):
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file['output'].write('[Grain%s]\n'%(str(ID+1).zfill(formatwidth)) + \
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'crystallite %i\n'%options.crystallite + \
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'(constituent) phase %i texture %s fraction 1.0\n'%(options.phase,str(ID+1).rjust(formatwidth)))
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file['output'].write('\n#-------------------#')
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file['output'].write('\n<texture>\n')
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file['output'].write('#-------------------#\n')
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for ID in xrange(nSamples):
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eulers = re.split(r'[\t]', Orientations[ID].strip())
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file['output'].write('[Grain%s]\n'%(str(ID+1).zfill(formatwidth)) + \
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'(gauss) phi1 %10.5f Phi %10.5f phi2 %10.6f scatter 0.0 fraction 1.0\n'\
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%(float(eulers[0]),float(eulers[1]),float(eulers[2])))
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#--- output finalization --------------------------------------------------------------------------
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if file['name'] != 'STDIN':
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file['output'].close()
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os.rename(file['name']+'_tmp',
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os.path.splitext(file['name'])[0] +'_'+method+'%s'%('_material.config'))
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