332 lines
12 KiB
Python
332 lines
12 KiB
Python
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#!/usr/bin/env python
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import os,sys,math,re,random
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random.seed()
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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 [\
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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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nBins = ODF['intervals'][0]*ODF['intervals'][1]*ODF['intervals'][2]
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deltas = [limit/intervals for limit,intervals in zip(ODF['limits'],ODF['intervals'])]
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# calculate repetitions of each orientation
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if re.search(r'hybrid',sys.argv[0],re.IGNORECASE): # my script's name contains "hybrid"
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nOptSamples = max(ODF['nNonZero'],nSamples) # random subsampling if too little samples requested
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else: # blunt integer approximation
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nOptSamples = nSamples
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nInvSamples = 0
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repetition = [None]*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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print '%i:(%12.11f,%12.11f) %i <= %i <= %i'%(nIter,scaleLower,scaleUpper,nInvSamplesLower,nOptSamples,nInvSamplesUpper)
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nInvSamples = nInvSamplesUpper
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scale = scaleUpper
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print 'created set of',nInvSamples,'samples (',float(nInvSamples)/nOptSamples-1.0,') with scaling',scale,'delivering',nSamples
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repetition = [None]*nBins # preallocate and clear
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for bin in range(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(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]*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['intervals'])
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Eulers = binAsEulers(bin,ODF['intervals'],deltas,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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nBins = ODF['intervals'][0]*ODF['intervals'][1]*ODF['intervals'][2]
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deltas = [limit/intervals for limit,intervals in zip(ODF['limits'],ODF['intervals'])]
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orientations = [None]*nSamples
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reconstructedODF = [0.0]*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['limits']]
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bins = EulersAsBins(Eulers,ODF['intervals'],deltas,ODF['center'])
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bin = binsAsBin(bins,ODF['intervals'])
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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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nBins = ODF['intervals'][0]*ODF['intervals'][1]*ODF['intervals'][2]
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deltas = [limit/intervals for limit,intervals in zip(ODF['limits'],ODF['intervals'])]
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orientations = [None]*nSamples
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reconstructedODF = [0.0]*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(nBins * random.random())
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Eulers = binAsEulers(bin,ODF['intervals'],deltas,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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nBins = ODF['intervals'][0]*ODF['intervals'][1]*ODF['intervals'][2]
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deltas = [limit/intervals for limit,intervals in zip(ODF['limits'],ODF['intervals'])]
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orientations = [None]*nSamples
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reconstructedODF = [0.0]*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(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['intervals'],deltas,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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print 'created set of',countSamples,'when asked to deliver',nSamples
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return orientations, reconstructedODF
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# check usage
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try:
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nameBinnedODF = sys.argv[1]
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nSamples = int(float(sys.argv[2]))
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except:
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print "\nusage:",os.path.basename(sys.argv[0]),"nameLinearODF nSamples [nameSampledODF]\n"
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sys.exit(1);
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methods = ['IA','STAT']
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#open binned ODF
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try:
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fileBinnedODF = open(nameBinnedODF,'r')
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except:
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print 'unable to open binnedODF:', nameBinnedODF;
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sys.exit(1);
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# process header info
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ODF = {}
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ODF['limits'] = [math.radians(float(limit)) for limit in fileBinnedODF.readline().split()]
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ODF['deltas'] = [math.radians(float(delta)) for delta in fileBinnedODF.readline().split()]
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ODF['intervals'] = [int(round(limit/delta)) for limit,delta in zip(ODF['limits'],ODF['deltas'])]
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nBins = ODF['intervals'][0]*ODF['intervals'][1]*ODF['intervals'][2]
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print 'Limit:', [math.degrees(limit) for limit in ODF['limits']]
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print 'Delta:', [math.degrees(delta) for delta in ODF['deltas']]
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print 'Interval:', ODF['intervals']
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centering = fileBinnedODF.readline()
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if re.search('cell',centering.lower()):
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ODF['center'] = 0.5
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print 'cell-centered data (offset %g)'%ODF['center']
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else:
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ODF['center'] = 0.0
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print 'vertex-centered data (offset %g)'%ODF['center']
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fileBinnedODF.readline() # skip blank delimiter
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# read linear binned data
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linesBinnedODF = fileBinnedODF.readlines()
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fileBinnedODF.close()
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if len(linesBinnedODF) != nBins:
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print 'expecting', nBins, 'values but got', len(linesBinnedODF)
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sys.exit(1)
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# build binnedODF array
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print 'reading',nBins,'values'
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sumdV_V = 0.0
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ODF['dV_V'] = [None]*nBins
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ODF['nNonZero'] = 0
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dg = ODF['deltas'][0]*2*math.sin(ODF['deltas'][1]/2.0)*ODF['deltas'][2]
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for bin in range(nBins):
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ODF['dV_V'][bin] = \
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max(0.0,float(linesBinnedODF[bin])) * dg * \
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math.sin(((bin//ODF['intervals'][2])%ODF['intervals'][1]+ODF['center'])*ODF['deltas'][1])
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if ODF['dV_V'][bin] > 0.0:
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sumdV_V += ODF['dV_V'][bin]
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ODF['nNonZero'] += 1
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for bin in range(nBins): ODF['dV_V'][bin] /= sumdV_V # normalize dV/V
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print 'non-zero fraction:', float(ODF['nNonZero'])/nBins,'(%i/%i)'%(ODF['nNonZero'],nBins)
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print 'Volume integral of ODF:', sumdV_V
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print 'Reference Integral:', ODF['limits'][0]*ODF['limits'][2]*(1-math.cos(ODF['limits'][1]))
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# call methods
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Functions = {'IA': 'directInversion', 'STAT': 'TothVanHoutteSTAT', 'MC': 'MonteCarloBins'}
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Orientations = {}
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ReconstructedODF = {}
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for method in methods:
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Orientations[method], ReconstructedODF[method] = (globals()[Functions[method]])(ODF,nSamples)
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# calculate accuracy of sample
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squaredDiff = {}
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squaredRelDiff = {}
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mutualProd = {}
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indivSum = {}
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indivSquaredSum = {}
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for method in ['orig']+methods:
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squaredDiff[method] = 0.0
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squaredRelDiff[method] = 0.0
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mutualProd[method] = 0.0
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indivSum[method] = 0.0
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indivSquaredSum[method] = 0.0
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for bin in range(nBins):
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for method in methods:
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squaredDiff[method] += (ODF['dV_V'][bin] - ReconstructedODF[method][bin])**2
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if ODF['dV_V'][bin] > 0.0:
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squaredRelDiff[method] += (ODF['dV_V'][bin] - ReconstructedODF[method][bin])**2/ODF['dV_V'][bin]**2
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mutualProd[method] += ODF['dV_V'][bin]*ReconstructedODF[method][bin]
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indivSum[method] += ReconstructedODF[method][bin]
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indivSquaredSum[method] += ReconstructedODF[method][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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print 'sqrt(N*)RMSD of ODFs:\t', [math.sqrt(nSamples*squaredDiff[method]) for method in methods]
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print 'RMSrD of ODFs:\t', [math.sqrt(squaredRelDiff[method]) for method in methods]
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print 'rMSD of ODFs:\t', [squaredDiff[method]/indivSquaredSum['orig'] for method in methods]
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#print 'correlation slope:\t', [(nBins*mutualProd[method]-indivSum['orig']*indivSum[method])/(nBins*indivSquaredSum['orig']-indivSum['orig']**2) for method in ('IA','STAT','MC')]
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#print 'correlation confidence:\t', [(mutualProd[method]-indivSum['orig']*indivSum[method]/nBins)/\
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# (nBins*math.sqrt((indivSquaredSum['orig']/nBins-(indivSum['orig']/nBins)**2)*(indivSquaredSum[method]/nBins-(indivSum[method]/nBins)**2))) for method in ('IA','STAT','MC')]
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print 'nNonZero correlation slope:\t', [(ODF['nNonZero']*mutualProd[method]-indivSum['orig']*indivSum[method])/(ODF['nNonZero']*indivSquaredSum['orig']-indivSum['orig']**2) for method in methods]
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print 'nNonZero correlation confidence:\t', [(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)*(indivSquaredSum[method]/ODF['nNonZero']-(indivSum[method]/ODF['nNonZero'])**2))) for method in methods]
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# write result
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try:
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|
nameSampledODF = sys.argv[3]
|
||
|
|
except:
|
||
|
|
sys.exit(0) # that's it folks
|
||
|
|
|
||
|
|
for method in methods:
|
||
|
|
if method == 'IA' and nSamples < ODF['nNonZero']:
|
||
|
|
strOpt = '(%i)'%ODF['nNonZero']
|
||
|
|
else:
|
||
|
|
strOpt = ''
|
||
|
|
try:
|
||
|
|
fileSampledODF = open(nameSampledODF+'.'+method+'sampled_'+str(nSamples)+strOpt, 'w')
|
||
|
|
fileSampledODF.write('%i\n'%nSamples)
|
||
|
|
fileSampledODF.write('\n'.join(Orientations[method])+'\n')
|
||
|
|
fileSampledODF.close()
|
||
|
|
except:
|
||
|
|
print 'unable to write sampledODF:', nameSampledODF+'.'+method+'sampled_'+str(nSamples)+strOpt
|
||
|
|
|
||
|
|
try:
|
||
|
|
fileRegressionODF = open(nameSampledODF+'.'+method+'regression_'+str(nSamples)+strOpt, 'w')
|
||
|
|
fileRegressionODF.write('\n'.join([a+'\t'+b for (a,b) in zip(map(str,ReconstructedODF[method]),map(str,ODF['dV_V']))])+'\n')
|
||
|
|
fileRegressionODF.close()
|
||
|
|
except:
|
||
|
|
print 'unable to write RegressionODF:', nameSampledODF+'.'+method+'regression_'+str(nSamples)+strOpt
|