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DAMASK_EICMD
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DAMASK_EICMD/processing/pre/hybridIA_linODFsampling.py

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#!/usr/bin/env python
from optparse import OptionParser
import damask
import os,sys,math,re,random,string
scriptID = string.replace('$Id$','\n','\\n')
scriptName = scriptID.split()[1]
random.seed()
# --- helper functions ---
def binAsBins(bin,intervals):
""" explode compound bin into 3D bins list """
bins = [0]*3
bins[0] = (bin//(intervals[1] * intervals[2])) % intervals[0]
bins[1] = (bin//intervals[2]) % intervals[1]
bins[2] = bin % intervals[2]
return bins
def binsAsBin(bins,intervals):
""" implode 3D bins into compound bin """
return (bins[0]*intervals[1] + bins[1])*intervals[2] + bins[2]
def EulersAsBins(Eulers,intervals,deltas,center):
""" return list of Eulers translated into 3D bins list """
return [\
int((euler+(0.5-center)*delta)//delta)%interval \
for euler,delta,interval in zip(Eulers,deltas,intervals) \
]
def binAsEulers(bin,intervals,deltas,center):
""" compound bin number translated into list of Eulers """
Eulers = [0.0]*3
Eulers[2] = (bin%intervals[2] + center)*deltas[2]
Eulers[1] = (bin//intervals[2]%intervals[1] + center)*deltas[1]
Eulers[0] = (bin//(intervals[2]*intervals[1]) + center)*deltas[0]
return Eulers
def directInvRepetitions(probability,scale):
""" calculate number of samples drawn by direct inversion """
nDirectInv = 0
for bin in range(len(probability)): # loop over bins
nDirectInv += int(round(probability[bin]*scale)) # calc repetition
return nDirectInv
# --- sampling methods ---
# ----- efficient algorithm ---------
def directInversion (ODF,nSamples):
""" ODF contains 'dV_V' (normalized to 1), 'center', 'intervals', 'limits' (in radians) """
nBins = ODF['intervals'][0]*ODF['intervals'][1]*ODF['intervals'][2]
deltas = [limit/intervals for limit,intervals in zip(ODF['limits'],ODF['intervals'])]
# calculate repetitions of each orientation
if re.search(r'hybrid',sys.argv[0],re.IGNORECASE): # my script's name contains "hybrid"
nOptSamples = max(ODF['nNonZero'],nSamples) # random subsampling if too little samples requested
else: # blunt integer approximation
nOptSamples = nSamples
nInvSamples = 0
repetition = [None]*nBins
probabilityScale = nOptSamples # guess
scaleLower = 0.0
nInvSamplesLower = 0
scaleUpper = float(nOptSamples)
incFactor = 1.0
nIter = 0
nInvSamplesUpper = directInvRepetitions(ODF['dV_V'],scaleUpper)
while (\
(scaleUpper-scaleLower > scaleUpper*1e-15 or nInvSamplesUpper < nOptSamples) and \
nInvSamplesUpper != nOptSamples \
): # closer match required?
if nInvSamplesUpper < nOptSamples:
scaleLower,scaleUpper = scaleUpper,scaleUpper+incFactor*(scaleUpper-scaleLower)/2.0
incFactor *= 2.0
nInvSamplesLower,nInvSamplesUpper = nInvSamplesUpper,directInvRepetitions(ODF['dV_V'],scaleUpper)
else:
scaleUpper = (scaleLower+scaleUpper)/2.0
incFactor = 1.0
nInvSamplesUpper = directInvRepetitions(ODF['dV_V'],scaleUpper)
nIter += 1
print '%i:(%12.11f,%12.11f) %i <= %i <= %i'%(nIter,scaleLower,scaleUpper,nInvSamplesLower,nOptSamples,nInvSamplesUpper)
nInvSamples = nInvSamplesUpper
scale = scaleUpper
print 'created set of',nInvSamples,'samples (',float(nInvSamples)/nOptSamples-1.0,') with scaling',scale,'delivering',nSamples
repetition = [None]*nBins # preallocate and clear
for bin in range(nBins): # loop over bins
repetition[bin] = int(round(ODF['dV_V'][bin]*scale)) # calc repetition
# build set
set = [None]*nInvSamples
i = 0
for bin in range(nBins):
set[i:i+repetition[bin]] = [bin]*repetition[bin] # fill set with bin, i.e. orientation
i += repetition[bin] # advance set counter
orientations = [None]*nSamples
reconstructedODF = [0.0]*nBins
unitInc = 1.0/nSamples
for j in range(nSamples):
if (j == nInvSamples-1): ex = j
else: ex = int(round(random.uniform(j+0.5,nInvSamples-0.5)))
bin = set[ex]
bins = binAsBins(bin,ODF['intervals'])
Eulers = binAsEulers(bin,ODF['intervals'],deltas,ODF['center'])
orientations[j] = '%g\t%g\t%g' %( math.degrees(Eulers[0]),math.degrees(Eulers[1]),math.degrees(Eulers[2]) )
reconstructedODF[bin] += unitInc
set[ex] = set[j] # exchange orientations
return orientations, reconstructedODF
# ----- trial and error algorithms ---------
def MonteCarloEulers (ODF,nSamples):
""" ODF contains 'dV_V' (normalized to 1), 'center', 'intervals', 'limits' (in radians) """
countMC = 0
maxdV_V = max(ODF['dV_V'])
nBins = ODF['intervals'][0]*ODF['intervals'][1]*ODF['intervals'][2]
deltas = [limit/intervals for limit,intervals in zip(ODF['limits'],ODF['intervals'])]
orientations = [None]*nSamples
reconstructedODF = [0.0]*nBins
unitInc = 1.0/nSamples
for j in range(nSamples):
MC = maxdV_V*2.0
bin = 0
while MC > ODF['dV_V'][bin]:
countMC += 1
MC = maxdV_V*random.random()
Eulers = [limit*random.random() for limit in ODF['limits']]
bins = EulersAsBins(Eulers,ODF['intervals'],deltas,ODF['center'])
bin = binsAsBin(bins,ODF['intervals'])
orientations[j] = '%g\t%g\t%g' %( math.degrees(Eulers[0]),math.degrees(Eulers[1]),math.degrees(Eulers[2]) )
reconstructedODF[bin] += unitInc
return orientations, reconstructedODF, countMC
def MonteCarloBins (ODF,nSamples):
""" ODF contains 'dV_V' (normalized to 1), 'center', 'intervals', 'limits' (in radians) """
countMC = 0
maxdV_V = max(ODF['dV_V'])
nBins = ODF['intervals'][0]*ODF['intervals'][1]*ODF['intervals'][2]
deltas = [limit/intervals for limit,intervals in zip(ODF['limits'],ODF['intervals'])]
orientations = [None]*nSamples
reconstructedODF = [0.0]*nBins
unitInc = 1.0/nSamples
for j in range(nSamples):
MC = maxdV_V*2.0
bin = 0
while MC > ODF['dV_V'][bin]:
countMC += 1
MC = maxdV_V*random.random()
bin = int(nBins * random.random())
Eulers = binAsEulers(bin,ODF['intervals'],deltas,ODF['center'])
orientations[j] = '%g\t%g\t%g' %( math.degrees(Eulers[0]),math.degrees(Eulers[1]),math.degrees(Eulers[2]) )
reconstructedODF[bin] += unitInc
return orientations, reconstructedODF
def TothVanHoutteSTAT (ODF,nSamples):
""" ODF contains 'dV_V' (normalized to 1), 'center', 'intervals', 'limits' (in radians) """
nBins = ODF['intervals'][0]*ODF['intervals'][1]*ODF['intervals'][2]
deltas = [limit/intervals for limit,intervals in zip(ODF['limits'],ODF['intervals'])]
orientations = [None]*nSamples
reconstructedODF = [0.0]*nBins
unitInc = 1.0/nSamples
selectors = [random.random() for i in range(nSamples)]
selectors.sort()
indexSelector = 0
cumdV_V = 0.0
countSamples = 0
for bin in range(nBins) :
cumdV_V += ODF['dV_V'][bin]
while indexSelector < nSamples and selectors[indexSelector] < cumdV_V:
Eulers = binAsEulers(bin,ODF['intervals'],deltas,ODF['center'])
orientations[countSamples] = '%g\t%g\t%g' %( math.degrees(Eulers[0]),math.degrees(Eulers[1]),math.degrees(Eulers[2]) )
reconstructedODF[bin] += unitInc
countSamples += 1
indexSelector += 1
print 'created set of',countSamples,'when asked to deliver',nSamples
return orientations, reconstructedODF
# --------------------------------------------------------------------
# MAIN
# --------------------------------------------------------------------
parser = OptionParser(option_class=damask.extendableOption, usage='%prog options [file[s]]', description = """
Transform linear binned data into Euler angles.
""", version=string.replace(scriptID,'\n','\\n')
)
parser.add_option('-f', '--file', dest='file', type='string', metavar = 'string', \
help='file name, the input file is generated by the script "OIMlinear2linearODF.py"')
parser.add_option('-o', '--output', dest='output', type='string', metavar = 'string', \
help='the prefix of output files name.')
parser.add_option('-n', '--number', dest='number', type='int', metavar = 'int', \
help='the number of orientations needed to be generated, the default is [%default]')
parser.add_option('-a','--algorithm', dest='algorithm', type='string', metavar = 'string', \
help='''The algorithm adopted, three algorithms are provided,
that is:
[IA]: direct inversion,
[STAT]: Van Houtte,
[MC]: Monte Carlo.
the default is [%default].''')
parser.add_option('-p','--phase', dest='phase', type='int', metavar = 'int',
help='phase index to be used [%default]')
parser.add_option('--crystallite', dest='crystallite', type='int', metavar = 'int',
help='crystallite index to be used [%default]')
parser.add_option('-c', '--configuration', dest='config', action='store_true',
help='output material configuration [%default]')
parser.set_defaults(number = 500)
parser.set_defaults(output = 'texture')
parser.set_defaults(algorithm = 'IA')
parser.set_defaults(phase = 1)
parser.set_defaults(crystallite = 1)
options = parser.parse_args()[0]
# check usage
if not os.path.exists(options.file):
parser.error('binnedODF file does not exist'); sys.exit()
nameBinnedODF = options.file
nameSampledODF = options.output
nSamples = options.number
methods = [options.algorithm]
#open binned ODF
try:
fileBinnedODF = open(nameBinnedODF,'r')
except:
print 'unable to open binnedODF:', nameBinnedODF;
sys.exit(1);
# process header info
ODF = {}
ODF['limits'] = [math.radians(float(limit)) for limit in fileBinnedODF.readline().split()[0:3]]
ODF['deltas'] = [math.radians(float(delta)) for delta in fileBinnedODF.readline().split()[0:3]]
#ODF['intervals'] = [int(interval) for interval in fileBinnedODF.readline().split()[0:3]]
ODF['intervals'] = [int(round(limit/delta)) for limit,delta in zip(ODF['limits'],ODF['deltas'])]
nBins = ODF['intervals'][0]*ODF['intervals'][1]*ODF['intervals'][2]
print 'Limit: ', [math.degrees(limit) for limit in ODF['limits']]
print 'Delta: ', [math.degrees(delta) for delta in ODF['deltas']]
print 'Interval: ', [interval + 1 for interval in ODF['intervals']]
centering = fileBinnedODF.readline()
if re.search('cell',centering.lower()):
ODF['center'] = 0.5
print 'cell-centered data (offset %g)'%ODF['center']
else:
ODF['center'] = 0.0
print 'vertex-centered data (offset %g)'%ODF['center']
fileBinnedODF.readline() # skip blank delimiter
# read linear binned data
linesBinnedODF = fileBinnedODF.readlines()
fileBinnedODF.close()
if len(linesBinnedODF) != nBins:
print 'expecting', nBins, 'values but got', len(linesBinnedODF)
sys.exit(1)
# build binnedODF array
print 'reading',nBins,'values'
sumdV_V = 0.0
ODF['dV_V'] = [None]*nBins
ODF['nNonZero'] = 0
dg = ODF['deltas'][0]*2*math.sin(ODF['deltas'][1]/2.0)*ODF['deltas'][2]
for bin in range(nBins):
ODF['dV_V'][bin] = \
max(0.0,float(linesBinnedODF[bin])) * dg * \
math.sin(((bin//ODF['intervals'][2])%ODF['intervals'][1]+ODF['center'])*ODF['deltas'][1])
if ODF['dV_V'][bin] > 0.0:
sumdV_V += ODF['dV_V'][bin]
ODF['nNonZero'] += 1
for bin in range(nBins): ODF['dV_V'][bin] /= sumdV_V # normalize dV/V
print 'non-zero fraction:', float(ODF['nNonZero'])/nBins,'(%i/%i)'%(ODF['nNonZero'],nBins)
print 'Volume integral of ODF:', sumdV_V
print 'Reference Integral:', ODF['limits'][0]*ODF['limits'][2]*(1-math.cos(ODF['limits'][1]))
# call methods
Functions = {'IA': 'directInversion', 'STAT': 'TothVanHoutteSTAT', 'MC': 'MonteCarloBins'}
Orientations = {}
ReconstructedODF = {}
for method in methods:
Orientations[method], ReconstructedODF[method] = (globals()[Functions[method]])(ODF,nSamples)
# calculate accuracy of sample
squaredDiff = {}
squaredRelDiff = {}
mutualProd = {}
indivSum = {}
indivSquaredSum = {}
for method in ['orig']+methods:
squaredDiff[method] = 0.0
squaredRelDiff[method] = 0.0
mutualProd[method] = 0.0
indivSum[method] = 0.0
indivSquaredSum[method] = 0.0
for bin in range(nBins):
for method in methods:
squaredDiff[method] += (ODF['dV_V'][bin] - ReconstructedODF[method][bin])**2
if ODF['dV_V'][bin] > 0.0:
squaredRelDiff[method] += (ODF['dV_V'][bin] - ReconstructedODF[method][bin])**2/ODF['dV_V'][bin]**2
mutualProd[method] += ODF['dV_V'][bin]*ReconstructedODF[method][bin]
indivSum[method] += ReconstructedODF[method][bin]
indivSquaredSum[method] += ReconstructedODF[method][bin]**2
indivSum['orig'] += ODF['dV_V'][bin]
indivSquaredSum['orig'] += ODF['dV_V'][bin]**2
print 'sqrt(N*)RMSD of ODFs:\t', [math.sqrt(nSamples*squaredDiff[method]) for method in methods]
print 'RMSrD of ODFs:\t', [math.sqrt(squaredRelDiff[method]) for method in methods]
print 'rMSD of ODFs:\t', [squaredDiff[method]/indivSquaredSum['orig'] for method in methods]
#print 'correlation slope:\t', [(nBins*mutualProd[method]-indivSum['orig']*indivSum[method])/(nBins*indivSquaredSum['orig']-indivSum['orig']**2) for method in ('IA','STAT','MC')]
#print 'correlation confidence:\t', [(mutualProd[method]-indivSum['orig']*indivSum[method]/nBins)/\
# (nBins*math.sqrt((indivSquaredSum['orig']/nBins-(indivSum['orig']/nBins)**2)*(indivSquaredSum[method]/nBins-(indivSum[method]/nBins)**2))) for method in ('IA','STAT','MC')]
print 'nNonZero correlation slope:\t', [(ODF['nNonZero']*mutualProd[method]-indivSum['orig']*indivSum[method])/(ODF['nNonZero']*indivSquaredSum['orig']-indivSum['orig']**2) for method in methods]
print 'nNonZero correlation confidence:\t', [(mutualProd[method]-indivSum['orig']*indivSum[method]/ODF['nNonZero'])/\
(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]
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
if options.config:
try:
fileConfig = open(nameSampledODF+'.'+method+str(nSamples)+'.config', 'w') # write config file
formatwidth = 1
fileConfig.write('#-------------------#')
fileConfig.write('\n<microstructure>\n')
fileConfig.write('#-------------------#\n')
for i,ID in enumerate(xrange(nSamples)):
fileConfig.write('[Grain%s]\n'%(str(ID+1).zfill(formatwidth)) + \
'crystallite %i\n'%options.crystallite + \
'(constituent) phase %i texture %s fraction 1.0\n'%(options.phase,str(ID+1).rjust(formatwidth)))
fileConfig.write('\n#-------------------#')
fileConfig.write('\n<texture>\n')
fileConfig.write('#-------------------#\n')
for ID in xrange(nSamples):
eulers = re.split(r'[\t]', Orientations[method][ID].strip())
fileConfig.write('[Grain%s]\n'%(str(ID+1).zfill(formatwidth)) + \
'(gauss) phi1 %10.5f Phi %10.5f phi2 %10.6f scatter 0.0 fraction 1.0\n'\
%(float(eulers[0]),float(eulers[1]),float(eulers[2])))
fileConfig.close()
except:
print 'unable to write material.config file:', nameSampledODF+'.'+method+str(nSamples)+'.config'
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