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DAMASK_EICMD
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DAMASK_EICMD/processing/pre/hybridIA_linODFsampling.py

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#!/usr/bin/env python3
# -*- coding: UTF-8 no BOM -*-
from optparse import OptionParser
import damask
import os,sys,math,random
import numpy as np
scriptName = os.path.splitext(os.path.basename(__file__))[0]
scriptID = ' '.join([scriptName,damask.version])
# --- 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 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']
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
damask.util.croak('%i:(%12.11f,%12.11f) %i <= %i <= %i'%(nIter,scaleLower,scaleUpper,
nInvSamplesLower,nOptSamples,nInvSamplesUpper))
nInvSamples = nInvSamplesUpper
scale = scaleUpper
damask.util.croak('created set of %i samples (%12.11f) with scaling %12.11f delivering %i'%(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 = np.zeros((nSamples,3),'f')
reconstructedODF = np.zeros(ODF['nBins'],'f')
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]
Eulers = binAsEulers(bin,ODF['interval'],ODF['delta'],ODF['center'])
orientations[j] = np.degrees(Eulers)
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 = np.zeros((nSamples,3),'f')
reconstructedODF = np.zeros(ODF['nBins'],'f')
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] = np.degrees(Eulers)
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 = np.zeros((nSamples,3),'f')
reconstructedODF = np.zeros(ODF['nBins'],'f')
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] = np.degrees(Eulers)
reconstructedODF[bin] += unitInc
return orientations, reconstructedODF
def TothVanHoutteSTAT (ODF,nSamples):
"""ODF contains 'dV_V' (normalized to 1), 'center', 'intervals', 'limits' (in radians)"""
orientations = np.zeros((nSamples,3),'f')
reconstructedODF = np.zeros(ODF['nBins'],'f')
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] = np.degrees(Eulers)
reconstructedODF[bin] += unitInc
countSamples += 1
indexSelector += 1
damask.util.croak('created set of %i when asked to deliver %i'%(countSamples,nSamples))
return orientations, reconstructedODF
# --------------------------------------------------------------------
# MAIN
# --------------------------------------------------------------------
parser = OptionParser(option_class=damask.extendableOption, usage='%prog options [file[s]]', description ="""
Transform linear binned ODF data into given number of orientations.
IA: integral approximation, STAT: Van Houtte, MC: Monte Carlo
""", version = scriptID)
algorithms = ['IA', 'STAT','MC']
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',
choices = algorithms, metavar = 'string',
help = 'sampling algorithm {%s} [IA]'%(', '.join(algorithms)))
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.set_defaults(randomSeed = None,
number = 500,
algorithm = 'IA',
phase = 1,
crystallite = 1,
ang = True,
)
(options,filenames) = parser.parse_args()
nSamples = options.number
methods = [options.algorithm]
# --- loop over input files -------------------------------------------------------------------------
if filenames == []: filenames = [None]
for name in filenames:
try:
table = damask.ASCIItable(name = name, buffered = False, readonly=True)
except:
continue
damask.util.report(scriptName,name)
randomSeed = int(os.urandom(4).hex(), 16) if options.randomSeed is None else options.randomSeed # random seed per file for second phase
random.seed(randomSeed)
# ------------------------------------------ read header and data ---------------------------------
table.head_read()
errors = []
labels = ['1_euler','2_euler','3_euler','intensity']
for i,index in enumerate(table.label_index(labels)):
if index < 0: errors.append('label {} not present.'.format(labels[i]))
if errors != []:
damask.util.croak(errors)
table.close(dismiss = True)
continue
table.data_readArray(labels)
# --------------- figure out limits (left/right), delta, and interval -----------------------------
ODF = {}
limits = np.array([np.min(table.data[:,0:3],axis=0),
np.max(table.data[:,0:3],axis=0)]) # min/max euler angles in degrees
ODF['limit'] = np.radians(limits[1,:]) # right hand limits in radians
ODF['center'] = 0.0 if all(limits[0,:]<1e-8) else 0.5 # vertex or cell centered
ODF['interval'] = np.array(list(map(len,[np.unique(table.data[:,i]) for i in range(3)])),'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)) # step size
if table.data.shape[0] != ODF['nBins']:
damask.util.croak('expecting %i values but got %i'%(ODF['nBins'],table.data.shape[0]))
continue
# ----- build binnedODF array and normalize ------------------------------------------------------
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,table.label_index('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
damask.util.croak(['non-zero fraction: %12.11f (%i/%i)'%(float(ODF['nNonZero'])/ODF['nBins'],
ODF['nNonZero'],
ODF['nBins']),
'Volume integral of ODF: %12.11f\n'%sumdV_V,
'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
damask.util.croak(['sqrt(N*)RMSD of ODFs:\t %12.11f'% math.sqrt(nSamples*squaredDiff[method]),
'RMSrD of ODFs:\t %12.11f'%math.sqrt(squaredRelDiff[method]),
'rMSD of ODFs:\t %12.11f'%(squaredDiff[method]/indivSquaredSum['orig']),
'nNonZero correlation slope:\t %12.11f'\
%((ODF['nNonZero']*mutualProd[method]-indivSum['orig']*indivSum[method])/\
(ODF['nNonZero']*indivSquaredSum['orig']-indivSum['orig']**2)),
'nNonZero correlation confidence:\t %12.11f'\
%((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+int(math.log10(nSamples))
materialConfig = [
'#' + scriptID + ' ' + ' '.join(sys.argv[1:]),
'# random seed %i'%randomSeed,
'#-------------------#',
'<microstructure>',
'#-------------------#',
]
for i,ID in enumerate(range(nSamples)):
materialConfig += ['[Grain%s]'%(str(ID+1).zfill(formatwidth)),
'crystallite %i'%options.crystallite,
'(constituent) phase %i texture %s fraction 1.0'%(options.phase,str(ID+1).rjust(formatwidth)),
]
materialConfig += [
'#-------------------#',
'<texture>',
'#-------------------#',
]
for ID in range(nSamples):
eulers = Orientations[ID]
materialConfig += ['[Grain%s]'%(str(ID+1).zfill(formatwidth)),
'(gauss) phi1 {} Phi {} phi2 {} scatter 0.0 fraction 1.0'.format(*eulers),
]
#--- output finalization --------------------------------------------------------------------------
with (open(os.path.splitext(name)[0]+'_'+method+'_'+str(nSamples)+'_material.config','w')) as outfile:
outfile.write('\n'.join(materialConfig)+'\n')
table.close()
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