#!/usr/bin/env python
from optparse import OptionParser
import damask
import os,sys,math,re,random,string
import numpy as np
scriptID = string.replace('$Id$','\n','\\n')
scriptName = scriptID.split()[1]
# --- helper functions ---
def integerFactorization(i):
j = int(math.floor(math.sqrt(float(i))))
while (j>1 and int(i)%j != 0):
j -= 1
return j
def positiveRadians(angle):
angle = math.radians(float(angle))
while angle < 0.0:
angle += 2.0*math.pi
return angle
def getHeader(sizeX,sizeY,step):
return [ \
'# TEM_PIXperUM 1.000000', \
'# x-star 0.509548', \
'# y-star 0.795272', \
'# z-star 0.611799', \
'# WorkingDistance 18.000000', \
'#', \
'# Phase 1', \
'# MaterialName Al', \
'# Formula Fe', \
'# Info', \
'# Symmetry 43', \
'# LatticeConstants 2.870 2.870 2.870 90.000 90.000 90.000', \
'# NumberFamilies 4', \
'# hklFamilies 1 1 0 1 0.000000 1', \
'# hklFamilies 2 0 0 1 0.000000 1', \
'# hklFamilies 2 1 1 1 0.000000 1', \
'# hklFamilies 3 1 0 1 0.000000 1', \
'# Categories 0 0 0 0 0 ', \
'#', \
'# GRID: SquareGrid', \
'# XSTEP: ' + str(step), \
'# YSTEP: ' + str(step), \
'# NCOLS_ODD: ' + str(sizeX), \
'# NCOLS_EVEN: ' + str(sizeX), \
'# NROWS: ' + str(sizeY), \
'#', \
'# OPERATOR: ODFsammpling', \
'#', \
'# SAMPLEID: ', \
'#', \
'# SCANID: ', \
'#', \
]
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) """
nOptSamples = max(ODF['nNonZero'],nSamples) # random subsampling if too little samples requested
nInvSamples = 0
repetition = [None]*ODF['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
file['croak'].write('%i:(%12.11f,%12.11f) %i <= %i <= %i\n'\
%(nIter,scaleLower,scaleUpper,nInvSamplesLower,nOptSamples,nInvSamplesUpper))
nInvSamples = nInvSamplesUpper
scale = scaleUpper
file['croak'].write('created set of %i samples (%12.11f) with scaling %12.11f delivering %i\n'\
%(nInvSamples,float(nInvSamples)/nOptSamples-1.0,scale,nSamples))
repetition = [None]*ODF['nBins'] # preallocate and clear
for bin in range(ODF['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(ODF['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]*ODF['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['interval'])
Eulers = binAsEulers(bin,ODF['interval'],ODF['delta'],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'])
orientations = [None]*nSamples
reconstructedODF = [0.0]*ODF['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['limit']]
bins = EulersAsBins(Eulers,ODF['interval'],ODF['delta'],ODF['center'])
bin = binsAsBin(bins,ODF['interval'])
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'])
orientations = [None]*nSamples
reconstructedODF = [0.0]*ODF['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(ODF['nBins'] * random.random())
Eulers = binAsEulers(bin,ODF['interval'],ODF['delta'],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) """
orientations = [None]*nSamples
reconstructedODF = [0.0]*ODF['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(ODF['nBins']) :
cumdV_V += ODF['dV_V'][bin]
while indexSelector < nSamples and selectors[indexSelector] < cumdV_V:
Eulers = binAsEulers(bin,ODF['interval'],ODF['delta'],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
file['croak'].write('created set of %i when asked to deliver %i\n'%(countSamples,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 = scriptID)
parser.add_option('-n', '--nsamples', dest='number', type='int', metavar = 'int',
help='number of orientations to be generated [%default]')
parser.add_option('-a','--algorithm', dest='algorithm', type='string', metavar = 'string',
help='sampling algorithm. IA: direct inversion, STAT: Van Houtte, MC: Monte Carlo. [%default].') #make choice
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('-r', '--rnd', dest='randomSeed', type='int', metavar='int', \
help='seed of random number generator [%default]')
parser.add_option('--ang', dest='ang', action='store_true',
help='write .ang file [%default]')
parser.set_defaults(randomSeed = None)
parser.set_defaults(number = 500)
parser.set_defaults(algorithm = 'IA')
parser.set_defaults(phase = 1)
parser.set_defaults(crystallite = 1)
parser.set_defaults(ang = True)
(options,filenames) = parser.parse_args()
nSamples = options.number
methods = [options.algorithm]
#--- setup file handles ---------------------------------------------------------------------------
files = []
if filenames == []:
files.append({'name':'STDIN','input':sys.stdin,'output':sys.stdout,'outang':sys.stdout,'croak':sys.stderr})
else:
for name in filenames:
if os.path.exists(name):
files.append({'name':name,'input':open(name),'output':open(name+'_tmp','w'),'outang':open(name+'_ang_tmp','w'),'croak':sys.stdout})
#--- loop over input files ------------------------------------------------------------------------
for file in files:
file['croak'].write('\033[1m' + scriptName + '\033[0m: ' + (file['name'] if file['name'] != 'STDIN' else '') + '\n')
table = damask.ASCIItable(file['input'],file['output'],buffered = False)
table.head_read()
randomSeed = int(os.urandom(4).encode('hex'), 16) if options.randomSeed == None else options.randomSeed # radom seed per file for second phase
random.seed(randomSeed)
# --------------- figure out columns in table ----------- -----------------------------------------
column = {}
pos = 0
keys = ['phi1','Phi','phi2','intensity']
for key in keys:
if key not in table.labels:
file['croak'].write('column %s not found...\n'%key)
else:
column[key] = pos
pos+=1
if pos != 4: continue
binnedODF = table.data_readArray(keys)
# --------------- figure out limits (left/right), delta, and interval -----------------------------
ODF = {}
limits = np.array([[np.min(table.data[:,column['phi1']]),\
np.min(table.data[:,column['Phi']]),\
np.min(table.data[:,column['phi2']])],\
[np.max(table.data[:,column['phi1']]),\
np.max(table.data[:,column['Phi']]),\
np.max(table.data[:,column['phi2']])]])
ODF['limit'] = np.radians(limits[1,:])
if all(limits[0,:]<1e-8): # vertex centered
ODF['center'] = 0.0
else: # cell centered
ODF['center'] = 0.5
eulers = [{},{},{}]
for i in xrange(table.data.shape[0]):
for j in xrange(3):
eulers[j][str(table.data[i,column[keys[j]]])] = True # remember eulers along phi1, Phi, and phi2
ODF['interval'] = np.array([len(eulers[0]),len(eulers[1]),len(eulers[2]),],'i') # steps are number of distict values
ODF['nBins'] = ODF['interval'].prod()
ODF['delta'] = np.radians(np.array(limits[1,0:3]-limits[0,0:3])/(ODF['interval']-1))
if binnedODF[0] != ODF['nBins']:
file['croak'].write('expecting %i values but got %i'%(ODF['nBins'],len(linesBinnedODF)))
continue
# build binnedODF array
sumdV_V = 0.0
ODF['dV_V'] = [None]*ODF['nBins']
ODF['nNonZero'] = 0
dg = ODF['delta'][0]*2.0*math.sin(ODF['delta'][1]/2.0)*ODF['delta'][2]
for b in range(ODF['nBins']):
ODF['dV_V'][b] = \
max(0.0,table.data[b,column['intensity']]) * dg * \
math.sin(((b//ODF['interval'][2])%ODF['interval'][1]+ODF['center'])*ODF['delta'][1])
if ODF['dV_V'][b] > 0.0:
sumdV_V += ODF['dV_V'][b]
ODF['nNonZero'] += 1
for b in range(ODF['nBins']): ODF['dV_V'][b] /= sumdV_V # normalize dV/V
file['croak'].write('non-zero fraction: %12.11f (%i/%i)\n'\
%(float(ODF['nNonZero'])/ODF['nBins'],ODF['nNonZero'],ODF['nBins']))
file['croak'].write('Volume integral of ODF: %12.11f\n'%sumdV_V)
file['croak'].write('Reference Integral: %12.11f\n'\
%(ODF['limit'][0]*ODF['limit'][2]*(1-math.cos(ODF['limit'][1]))))
# call methods
Functions = {'IA': 'directInversion', 'STAT': 'TothVanHoutteSTAT', 'MC': 'MonteCarloBins'}
method = Functions[options.algorithm]
Orientations, ReconstructedODF = (globals()[method])(ODF,nSamples)
# calculate accuracy of sample
squaredDiff = {'orig':0.0,method:0.0}
squaredRelDiff = {'orig':0.0,method:0.0}
mutualProd = {'orig':0.0,method:0.0}
indivSum = {'orig':0.0,method:0.0}
indivSquaredSum = {'orig':0.0,method:0.0}
for bin in range(ODF['nBins']):
squaredDiff[method] += (ODF['dV_V'][bin] - ReconstructedODF[bin])**2
if ODF['dV_V'][bin] > 0.0:
squaredRelDiff[method] += (ODF['dV_V'][bin] - ReconstructedODF[bin])**2/ODF['dV_V'][bin]**2
mutualProd[method] += ODF['dV_V'][bin]*ReconstructedODF[bin]
indivSum[method] += ReconstructedODF[bin]
indivSquaredSum[method] += ReconstructedODF[bin]**2
indivSum['orig'] += ODF['dV_V'][bin]
indivSquaredSum['orig'] += ODF['dV_V'][bin]**2
file['croak'].write('sqrt(N*)RMSD of ODFs:\t %12.11f\n'% math.sqrt(nSamples*squaredDiff[method]))
file['croak'].write('RMSrD of ODFs:\t %12.11f\n'%math.sqrt(squaredRelDiff[method]))
file['croak'].write('rMSD of ODFs:\t %12.11f\n'%(squaredDiff[method]/indivSquaredSum['orig']))
file['croak'].write('nNonZero correlation slope:\t %12.11f\n'\
%((ODF['nNonZero']*mutualProd[method]-indivSum['orig']*indivSum[method])/\
(ODF['nNonZero']*indivSquaredSum['orig']-indivSum['orig']**2)))
file['croak'].write( 'nNonZero correlation confidence:\t %12.11f\n'\
%((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)))))
if method == 'IA' and nSamples < ODF['nNonZero']:
strOpt = '(%i)'%ODF['nNonZero']
formatwidth = 1
file['output'].write('#' + scriptID + ' ' + ' '.join(sys.argv[1:])+'\n')
file['output'].write('# random seed %i\n'%randomSeed)
file['output'].write('#-------------------#')
file['output'].write('\n<microstructure>\n')
file['output'].write('#-------------------#\n')
for i,ID in enumerate(xrange(nSamples)):
file['output'].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)))
file['output'].write('\n#-------------------#')
file['output'].write('\n<texture>\n')
file['output'].write('#-------------------#\n')
for ID in xrange(nSamples):
eulers = re.split(r'[\t]', Orientations[ID].strip())
file['output'].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])))
#--- output finalization --------------------------------------------------------------------------
if file['name'] != 'STDIN':
file['output'].close()
os.rename(file['name']+'_tmp',
os.path.splitext(file['name'])[0] +'_'+method+'%s'%('_material.config'))
# write ang file
if options.ang:
sizeY = integerFactorization(nSamples)
sizeX = nSamples / sizeY
print 'Writing .ang file: %i * %i = %i (== %i)'%(sizeX,sizeY,sizeX*sizeY,nSamples)
# write header
for line in getHeader(sizeX,sizeY,1.0):
file['outang'].write(line + '\n')
# write data
counter = 0
for line in Orientations:
eulers = re.split(r'[\t]', line.strip())
file['outang'].write(''.join(['%10.5f'%math.radians(float(angle)) for angle in eulers])+
''.join(['%10.5f'%coord for coord in [counter%sizeX,counter//sizeX]])+
' 100.0 1.0 0 1 1.0\n')
counter += 1
#--- output finalization --------------------------------------------------------------------------
if file['name'] != 'STDIN':
file['outang'].close()
os.rename(file['name']+'_ang_tmp',
os.path.splitext(file['name'])[0] +'_'+method+'%s'%('.ang'))