def main(input_options, libmode=False):
def analysePatterns(strain):
# these are the IRE conventions, except that integers are 0->5 rather than 1->6
strainDict = {0:"xx",1:"yy",2:"zz",3:"yz", 4:"zx", 5:"xy"}
strainsUsed = S.zeros((6,1))
for a in range(0,S.size(strain)):
if strain[a] != 0.0:
print strainDict[a], "component is non-zero"
strainsUsed[a] = 1
else:
strainsUsed[a] = 0
return strainsUsed
def cMatrix(symmetryType,TetrHigh):
if symmetryType == "Cubic" :
return S.matrix([[1, 7, 7, 0, 0, 0],
[7, 1, 7, 0, 0, 0],
[7, 7, 1, 0, 0, 0],
[0, 0, 0, 4, 0, 0],
[0, 0, 0, 0, 4, 0],
[0, 0, 0, 0, 0, 4]])
elif symmetryType == "Trigonal-high/Hexagonal":
return S.matrix([[1, 7, 8, 9, 10, 0],
[7, 1, 8, 0,-9, 0],
[8, 8, 3, 0, 0, 0],
[9, -9, 0, 4, 0, 0],
[10, 0, 0, 0, 4, 0],
[0, 0, 0, 0, 0, 6]])
elif symmetryType == "Trigonal-low":
return S.matrix([[1, 7, 8, 9, 10, 0],
[7, 1, 8, -9, -10, 0],
[8, 8, 3, 0, 0, 0],
[9, -9, 0, 4, 0, -10],
[10,-10, 0, 0, 4, 9],
[0, 0, 0, -10, 9, 6]])
elif symmetryType == "Tetragonal":
if TetrHigh == "-1":
print "Higher-symmetry tetragonal (422,4mm,4-2m,4/mmm)"
return S.matrix([[1, 7, 8, 0, 0, 0],
[7, 1, 8, 0, 0, 0],
[8, 8, 3, 0, 0, 0],
[0, 0, 0, 4, 0, 0],
[0, 0, 0, 0, 4, 0],
[0, 0, 0, 0, 0, 6]])
else:
print "Lower-symmetry tetragonal (4,-4,4/m)"
return S.matrix([[1, 7, 8, 0, 0, 11],
[7, 1, 8, 0, 0, -11],
[8, 8, 3, 0, 0, 0],
[0, 0, 0, 4, 0, 0],
[0, 0, 0, 0, 4, 0],
[11, -11, 0, 0, 0, 6]])
elif symmetryType == "Orthorhombic":
return S.matrix([[ 1, 7, 8, 0, 0, 0],
[ 7, 2, 12, 0, 0, 0],
[ 8, 12, 3, 0, 0, 0],
[ 0, 0, 0, 4, 0, 0],
[ 0, 0, 0, 0, 5, 0],
[ 0, 0, 0, 0, 0, 6]])
elif symmetryType == "Monoclinic":
return S.matrix([[ 1, 7, 8, 0, 10, 0],
[ 7, 2, 12, 0, 14, 0],
[ 8, 12, 3, 0, 17, 0],
[ 0, 0, 0, 4, 0, 20],
[10, 14, 17, 0, 5, 0],
[ 0, 0, 0, 20, 0, 6]])
elif symmetryType == "Triclinic":
return S.matrix([[ 1, 7, 8, 9, 10, 11],
[ 7, 2, 12, 13, 14, 15],
[ 8, 12, 3, 16, 17, 18],
[ 9, 13, 16, 4, 19, 20],
[10, 14, 17, 19, 5, 21],
[11, 15, 18, 20, 21, 6]])
def get_options():
# deal with options
if not libmode:
p = optparse.OptionParser()
p.add_option('--force-cml-output','-f', action='store_true', help="Force CML output",dest="force")
p.add_option('--graphics', '-g', action='store_true', help="Show graphics (requires matplotlib)")
p.add_option('--debug', '-d', action='store_true', help="Debug mode (output to stdout rather than file)")
p.add_option('--latex', action='store_true', help="dump LaTeX formatted table to file",dest="latex")
p.add_option('--latex-nt', action='store_true', help="supress LaaTeX line titles", dest='latex_nt')
p.add_option('--txt', action='store', help="Append line to text file",dest="txt", type="string")
options,arguments = p.parse_args(args=input_options)
else:
class PotM_Options:
xml = True
graphics = True
castep = False
debug = False
options = PotM_Options()
taskRe = re.compile(r"(.+)-\w+\.cml")
arguments = taskRe.findall(input_options[1][0])
global outfile
outfile = input_options[0]
if options.graphics:
try:
global P
import pylab as P
except ImportError:
print >> sys.stderr, "You need to have matplotlib installed for the --graphics option"
sys.exit(1)
return options, arguments
options, arguments = get_options()
# Not sure why the lattice types are enumerated like this, but this is how .cijdat does it...
latticeTypes = {0:"Unknown", 1:"Triclinic", 2:"Monoclinic", 3:"Orthorhombic", \
4:"Tetragonal", 5:"Cubic", 6:"Trigonal-low", 7:"Trigonal-high/Hexagonal"}
# Get strain tensors
seedname = arguments[0]
cijdat = open(seedname+".cijdat","r")
print "\nReading strain data from ", seedname+".cijdat\n"
numStrainPatterns = (len(cijdat.readlines())-2)/4 #total for all strain patterns
#rewind
cijdat.seek(0)
# deal with those first four integers
latticeType,numsteps,TetrHigh,TrigHigh = cijdat.readline().split()
numsteps = int(numsteps)
symmetryType = latticeTypes[int(latticeType)]
print "System is", symmetryType,"\n"
# get maximum magnitude of strains
magnitude = float(cijdat.readline())
print numsteps, "steps of maximum magnitude",magnitude
# if using graphics, do some initial set-up
if options.graphics:
fig = P.figure(num=1, figsize=(9.5,8),facecolor='white')
fig.subplots_adjust(left=0.07,right=0.97,top=0.97,bottom=0.07,wspace=0.5,hspace=0.5)
colourDict = {0: '#BAD0EF', 1:'#FFCECE', 2:'#BDF4CB', 3:'#EEF093',4:'#FFA4FF',5:'#75ECFD'}
for index1 in range(6):
for index2 in range(6):
# position this plot in a 6x6 grid
sp = P.subplot(6,6,6*(index1)+index2+1)
sp.set_axis_off()
# change the labels on the axes
# xlabels = sp.get_xticklabels()
# P.setp(xlabels,'rotation',90,fontsize=7)
# ylabels = sp.get_yticklabels()
# P.setp(ylabels,fontsize=7)
P.text(0.4,0.4, "n/a")
print "\n<>---------------------------- ANALYSIS ---------------------------------<>"
# initialise 1d array to store all 21 unique elastic constants - will be transformed into 6x6 matrix later
finalCijs = S.zeros((21,1))
errors = S.zeros((21,1))
for patt in range(numStrainPatterns/numsteps):
print patt
print "\nAnalysing pattern", patt+1, ":"
for a in range(0,numsteps):
pattern = cijdat.readline()
# grab the strain data from the .cijdat file
line1 = cijdat.readline().split()
line2 = cijdat.readline().split()
line3 = cijdat.readline().split()
# only take from the top right triangle
# numbering according to IRE conventions (Proc IRE, 1949)
if a == 0:
strain = S.array([float(line1[0]),float(line2[1]),float(line3[2]),2*float(line2[2]),2*float(line1[2]),2*float(line1[1])])
else:
strain = S.row_stack((strain,S.array([float(line1[0]),float(line2[1]),float(line3[2]),2*float(line2[2]),2*float(line1[2]),2*float(line1[1])])))
# now get corresponding stress data from the output file
(units, thisStress) = espresso.get_stress(seedname+
"_cij__"+str(patt+1)+"__"+str(a+1))
# again, top right triangle
if a == 0:
stress = thisStress
else:
stress = S.row_stack((stress,thisStress))
print stress
print strain
"""
Both the stress and strain matrices use the IRE conventions to reduce the
3x3 matrices to 1x6 arrays. These 1D arrays aerror = sqrt((sum(square(stress[:,index1-1] - fit_str)) / \
(numsteps-2))/(sum(square(strain[:,index2-1]))))re then stacked to form a
Nx6 array, where N=number of steps.
Note that strain and stress arrays are numbered 0->5 rather than 1->6
"""
def __fit(index1, index2):
from scipy import stats, sqrt, square
# do the fit
(cijFitted,intercept,r,tt,stderr) = stats.linregress(strain[:,index2-1],stress[:,index1-1])
if (S.__version__ < '0.7.0'):
# correct for scipy weirdness - see http://www.scipy.org/scipy/scipy/ticket/8
# This was fixed before 0.7.0 release. Maybe in some versions of 0.6.x too -
# will report huge errors if the check is wrong
stderr = S.sqrt((numsteps * stderr**2)/(numsteps-2))
error = stderr/sqrt(sum(square(strain[:,index2-1])))
else:
# Work out the error ourselves as I cannot get it from
# stderr and this has been checked with gnuplot's fitter
fit_str = ((strain[:,index2-1] * cijFitted) + intercept)
error = sqrt((sum(square(stress[:,index1-1] - fit_str)) / \
(numsteps-2))/(sum(square(strain[:,index2-1]))))
# print info about the fit
print '\n'
print 'Cij (gradient) : ', cijFitted
print 'Error in Cij : ', error
print 'Intercept : ', intercept
if abs(r) > 0.9:
print 'Correlation coefficient : ',r
else:
print 'Correlation coefficient : ',r, ' <----- WARNING'
# if using graphics, add a subplot
if options.graphics:
# position this plot in a 6x6 grid
sp = P.subplot(6,6,6*(index1-1)+index2)
sp.set_axis_on()
# change the labels on the axes
xlabels = sp.get_xticklabels()
P.setp(xlabels,'rotation',90,fontsize=7)
ylabels = sp.get_yticklabels()
P.setp(ylabels,fontsize=7)
# colour the plot depending on the strain pattern
sp.set_axis_bgcolor(colourDict[patt])
# plot the data
P.plot([strain[0,index2-1],strain[numsteps-1,index2-1]],[cijFitted*strain[0,index2-1]+intercept,cijFitted*strain[numsteps-1,index2-1]+intercept])
P.plot(strain[:,index2-1],stress[:,index1-1],'ro')
return cijFitted, error
def __appendOrReplace(valList,erList,val):
try:
valList.append(val[0])
erList.append(val[1])
return (sum(valList)/len(valList)), (S.sqrt(sum([x**2 for x in erList])/len(erList)**2))
except NameError:
return val[0], val[1]
def __createListAndAppend(val):
newList = []
newList.append(val[0])
errorList = []
errorList.append(val[1])
return val[0], newList, val[1], errorList
cij = S.zeros(21)
# Analyse the patterns to see which strains were applied
strainsUsed = analysePatterns(strain[0,:])
# should check strains are as expected
if symmetryType == "Cubic":
if S.all(strainsUsed.transpose() == S.array([[1.0, 0.0, 0.0, 1.0, 0.0, 0.0]])): # strain pattern e1+e4
finalCijs[0], errors[0] = __fit(1,1) # fit C11
fit_21, fit_21_error = __fit(2,1)
fit_31, fit_31_error = __fit(3,1)
finalCijs[6] = (fit_21 + fit_31)/2 # fit C21+C31
errors[6] = S.sqrt((fit_21_error**2)/4 + (fit_31_error**2)/4)
finalCijs[3], errors[3] = __fit(4,4) # fit C44
else:
print "Unsupported strain pattern"
sys.exit(1)
elif symmetryType == "Trigonal-high/Hexagonal":
if S.all(strainsUsed.transpose() == S.array([[0.0, 0.0, 1.0, 0.0, 0.0, 0.0]])): # strain pattern e3 (hexagonal)
# fit C13 + C23, and add to list (more values coming...)
finalCijs[7], cij13, errors[7], er13 = __createListAndAppend(__fit(1,3))
finalCijs[7], cij13, errors[7], er13 = __createListAndAppend(__fit(2,3))
finalCijs[2], errors[2] = __fit(3,3) # fit C33
elif S.all(strainsUsed.transpose() == S.array([[1.0, 0.0, 0.0, 1.0, 0.0, 0.0]])): # strain pattern e1+e4 (hexagonal)
finalCijs[0], errors[0] = __fit(1,1) # fit C11
finalCijs[6], errors[6] = __fit(2,1) # fit C21
finalCijs[7], errors[7] = __appendOrReplace(cij13,er13,__fit(3,1)) # fit C31
finalCijs[3], errors[3] = __fit(4,4) # fit C44
elif S.all(strainsUsed.transpose() == S.array([[1.0, 0.0, 0.0, 0.0, 0.0, 0.0]])):
# strain pattern e1 (trigonal-high)
finalCijs[0], errors[0] = __fit(1,1) # fit C11
finalCijs[6], errors[6] = __fit(2,1) # fit C21
finalCijs[7], errors[7] = __fit(3,1) # fit C31
finalCijs[8], errors[8] = __fit(4,1) # fit C41
finalCijs[9], errors[9] = __fit(5,1) # fit C51
elif S.all(strainsUsed.transpose() == S.array([[0.0, 0.0, 1.0, 1.0, 0.0, 0.0]])):
# strain pattern e3+e4 (trigonal-high)
# could recalculate C13/C14/C23/C24/C46 here, but won't just now
finalCijs[2], errors[2] = __fit(3,3) # fit C33
finalCijs[3], errors[3] = __fit(4,4) # fit C44
else:
print "Unsupported strain pattern"
sys.exit(1)
elif symmetryType == "Trigonal-low":
if S.all(strainsUsed.transpose() == S.array([[1.0, 0.0, 0.0, 0.0, 0.0, 0.0]])):
# strain pattern e1
finalCijs[0], errors[0] = __fit(1,1) # fit C11
finalCijs[6], errors[6] = __fit(2,1) # fit C21
finalCijs[7], errors[7] = __fit(3,1) # fit C31
finalCijs[8], errors[8] = __fit(4,1) # fit C41
finalCijs[9], errors[9] = __fit(5,1) # fit C51
elif S.all(strainsUsed.transpose() == S.array([[0.0, 0.0, 1.0, 1.0, 0.0, 0.0]])):
# strain pattern e3+e4
# could recalculate C13/C14/C23/C24/C46 here, but won't just now
finalCijs[2], errors[2] = __fit(3,3) # fit C33
finalCijs[3], errors[3] = __fit(4,4) # fit C44
else:
print "Unsupported strain pattern"
sys.exit(1)
elif symmetryType == "Tetragonal":
if S.all(strainsUsed.transpose() == S.array([[1.0, 0.0, 0.0, 1.0, 0.0, 0.0]])): # strain pattern e1+e4
finalCijs[0], errors[0] = __fit(1,1) # fit C11
finalCijs[6], errors[6] = __fit(2,1) # fit C21
finalCijs[7], errors[7] = __fit(3,1) # fit C31
finalCijs[10], errors[10] = __fit(6,1) # fit C61
finalCijs[3], errors[3] = __fit(4,4) # fit C44
elif S.all(strainsUsed.transpose() == S.array([[0.0, 0.0, 1.0, 0.0, 0.0, 1.0]])): # strain pattern e3+e6
finalCijs[2], errors[2] = __fit(3,3) # fit C33
finalCijs[5], errors[5] = __fit(6,6) # fit C66
else:
print "Unsupported strain pattern"
sys.exit(1)
elif symmetryType == "Orthorhombic":
if S.all(strainsUsed.transpose() == S.array([[1.0, 0.0, 0.0, 1.0, 0.0, 0.0]])): # strain pattern e1+e4
finalCijs[0], errors[0] = __fit(1,1) # fit C11
finalCijs[6], cij12, errors[6], er12 = __createListAndAppend(__fit(2,1)) # fit C21
finalCijs[7], cij13, errors[7], er13 = __createListAndAppend(__fit(3,1)) # fit C31
finalCijs[3], errors[3] = __fit(4,4) # fit C44
elif S.all(strainsUsed.transpose() == S.array([[0.0, 1.0, 0.0, 0.0, 1.0, 0.0]])): # strain pattern e2+e5
finalCijs[6], errors[6] = __appendOrReplace(cij12,er12,__fit(1,2)) # fit C12
finalCijs[1], errors[1] = __fit(2,2) # fit C22
finalCijs[11], cij23, errors[11], er23 = __createListAndAppend(__fit(3,2)) # fit C32
finalCijs[4], errors[4] = __fit(5,5) # fit C55
elif S.all(strainsUsed.transpose() == S.array([[0.0, 0.0, 1.0, 0.0, 0.0, 1.0]])): # strain pattern e3+e6
finalCijs[7], errors[7] = __appendOrReplace(cij13,er13,__fit(1,3)) # fit C13
finalCijs[11], errors[11] = __appendOrReplace(cij23,er23,__fit(2,3)) # fit C23
finalCijs[2], errors[2] = __fit(3,3) # fit C33
finalCijs[5], errors[5] = __fit(6,6) # fit C66
else:
print "Unsupported strain pattern"
sys.exit(1)
elif symmetryType == "Monoclinic":
if S.all(strainsUsed.transpose() == S.array([[1.0, 0.0, 0.0, 1.0, 0.0, 0.0]])): # strain pattern e1+e4
finalCijs[0], errors[0] = __fit(1,1) # fit C11
finalCijs[6], cij12, errors[6], er12 = __createListAndAppend(__fit(2,1)) # fit C21
finalCijs[7], cij13, errors[7], er13 = __createListAndAppend(__fit(3,1)) # fit C31
finalCijs[3], errors[3] = __fit(4,4) # fit C44
finalCijs[9], cij51, errors[9], er51 = __createListAndAppend(__fit(5,1)) # fit C51
finalCijs[19], cij64, errors[19], er64 = __createListAndAppend(__fit(6,4)) # fit C64
elif S.all(strainsUsed.transpose() == S.array([[0.0, 0.0, 1.0, 0.0, 0.0, 1.0]])): # strain pattern e3+e6
finalCijs[7], errors[7] = __appendOrReplace(cij13,er13,__fit(1,3)) # fit C13
finalCijs[11], cij23, errors[11], er23 = __createListAndAppend(__fit(2,3)) # fit C23
finalCijs[2], errors[2] = __fit(3,3) # fit C33
finalCijs[16], cij53, errors[16], er53 = __createListAndAppend(__fit(5,3)) # fit C53
finalCijs[19], errors[19] = __appendOrReplace(cij64,er64,__fit(4,6)) # fit C46
finalCijs[5], errors[5] = __fit(6,6) # fit C66
elif S.all(strainsUsed.transpose() == S.array([[0.0, 1.0, 0.0, 0.0, 0.0, 0.0]])): # strain pattern e2
finalCijs[6], errors[6] = __appendOrReplace(cij12,er12,__fit(1,2)) # fit C12
finalCijs[1], errors[1] = __fit(2,2) # fit C22
finalCijs[11],errors[11] = __appendOrReplace(cij23,er23,__fit(3,2)) # fit C32
finalCijs[13], cij52, errors[13], er52 = __createListAndAppend(__fit(5,2)) # fit C52
elif S.all(strainsUsed.transpose() == S.array([[0.0, 0.0, 0.0, 0.0, 1.0, 0.0]])): # strain pattern e5
finalCijs[9], errors[9] = __appendOrReplace(cij51,er51,__fit(1,5)) # fit C15
finalCijs[13],errors[13] = __appendOrReplace(cij52,er52,__fit(2,5)) # fit C25
finalCijs[16],errors[16] = __appendOrReplace(cij53,er53,__fit(3,5)) # fit C35
finalCijs[4], errors[4] = __fit(5,5) # fit C55
else:
print "Unsupported strain pattern"
sys.exit(1)
elif symmetryType == "Triclinic":
if S.all(strainsUsed.transpose() == S.array([[1.0, 0.0, 0.0, 0.0, 0.0, 0.0]])): # strain pattern e1
finalCijs[0], errors[0] = __fit(1,1) # fit C11
finalCijs[6], cij12, errors[6], er12 = __createListAndAppend(__fit(2,1)) # fit C21
finalCijs[7], cij13, errors[7], er13 = __createListAndAppend(__fit(3,1)) # fit C31
finalCijs[8], cij14, errors[8], er14 = __createListAndAppend(__fit(4,1)) # fit C41
finalCijs[9], cij15, errors[9], er15 = __createListAndAppend(__fit(5,1)) # fit C51
finalCijs[10],cij16, errors[10],er16 = __createListAndAppend(__fit(6,1)) # fit C61
elif S.all(strainsUsed.transpose() == S.array([[0.0, 1.0, 0.0, 0.0, 0.0, 0.0]])): # strain pattern e2
finalCijs[6], errors[6] = __appendOrReplace(cij12,er12,__fit(1,2)) # fit C12
finalCijs[1], errors[1] = __fit(2,2) # fit C22
finalCijs[11], cij23, errors[11], er23 = __createListAndAppend(__fit(3,2)) # fit C32
finalCijs[12], cij24, errors[12], er24 = __createListAndAppend(__fit(4,2)) # fit C42
finalCijs[13], cij25, errors[13], er25 = __createListAndAppend(__fit(5,2)) # fit C52
finalCijs[14], cij26, errors[14], er26 = __createListAndAppend(__fit(6,2)) # fit C62
elif S.all(strainsUsed.transpose() == S.array([[0.0, 0.0, 1.0, 0.0, 0.0, 0.0]])): # strain pattern e3
finalCijs[7], errors[7] = __appendOrReplace(cij13,er13,__fit(1,3)) # fit C13
finalCijs[11], errors[11] = __appendOrReplace(cij23,er23,__fit(2,3)) # fit C23
finalCijs[2], errors[2] = __fit(3,3) # fit C33
finalCijs[15], cij34, errors[15], er34 = __createListAndAppend(__fit(4,3)) # fit C43
finalCijs[16], cij35, errors[16], er35 = __createListAndAppend(__fit(5,3)) # fit C53
finalCijs[17], cij36, errors[17], er36 = __createListAndAppend(__fit(6,3)) # fit C63
elif S.all(strainsUsed.transpose() == S.array([[0.0, 0.0, 0.0, 1.0, 0.0, 0.0]])): # strain pattern e4
finalCijs[8], errors[8] = __appendOrReplace(cij14,er14,__fit(1,4)) # fit C14
finalCijs[12], errors[12] = __appendOrReplace(cij24,er24,__fit(2,4)) # fit C24
finalCijs[15], errors[15] = __appendOrReplace(cij34,er34,__fit(3,4)) # fit C34
finalCijs[3], errors[3] = __fit(4,4) # fit C44
finalCijs[18], cij45, errors[18], er45 = __createListAndAppend(__fit(5,4)) # fit C54
finalCijs[19], cij46, errors[19], er46 = __createListAndAppend(__fit(6,4)) # fit C64
elif S.all(strainsUsed.transpose() == S.array([[0.0, 0.0, 0.0, 0.0, 1.0, 0.0]])): # strain pattern e5
finalCijs[9], errors[9] = __appendOrReplace(cij15,er15,__fit(1,5)) # fit C15
finalCijs[13], errors[13] = __appendOrReplace(cij25,er25,__fit(2,5)) # fit C25
finalCijs[16], errors[16] = __appendOrReplace(cij35,er35,__fit(3,5)) # fit C35
finalCijs[18], errors[18] = __appendOrReplace(cij45,er45,__fit(4,5)) # fit C45
finalCijs[4], errors[4] = __fit(5,5) # fit C55
finalCijs[20], cij56, errors[20], er56 = __createListAndAppend(__fit(6,5)) # fit C65
elif S.all(strainsUsed.transpose() == S.array([[0.0, 0.0, 0.0, 0.0, 0.0, 1.0]])): # strain pattern e6
finalCijs[10], errors[10] = __appendOrReplace(cij16,er16,__fit(1,6)) # fit C16
finalCijs[14], errors[14] = __appendOrReplace(cij26,er26,__fit(2,6)) # fit C26
finalCijs[17], errors[17] = __appendOrReplace(cij36,er36,__fit(3,6)) # fit C36
finalCijs[19], errors[19] = __appendOrReplace(cij46,er46,__fit(4,6)) # fit C46
finalCijs[20], errors[20] = __appendOrReplace(cij56,er56,__fit(5,6)) # fit C56
finalCijs[5], errors[5] = __fit(6,6) # fit C66
else:
print "Unsupported strain pattern"
sys.exit(1)
else:
print "Unsupported symmetry type. Exiting"
sys.exit(1)
if options.graphics:
P.savefig(os.path.basename(seedname)+'_fits')
cijdat.close()
if symmetryType == "Trigonal-high/Hexagonal" or symmetryType == "Trigonal-low":
# for these systems, C66 is calculated as a combination of the other Cijs.
finalCijs[5] = 0.5*(finalCijs[0]-finalCijs[6])
errors[5] = S.sqrt(0.25*(errors[0]**2+errors[6]**2))
c = cMatrix(symmetryType,TetrHigh)
# Generate the 6x6 matrix of elastic constants
# - negative values signify a symmetry relation
finalCijMatrix = S.zeros((6,6))
finalErrors = S.zeros((6,6))
for i in range(0,6):
for j in range(0,6):
index = int(c[i,j])
if index > 0:
finalCijMatrix[i,j] = finalCijs[index-1]
finalErrors[i,j] = errors[index-1]
elif index < 0:
finalCijMatrix[i,j] = -finalCijs[-index-1]
finalErrors[i,j] = -errors[-index-1]
# Tests
if symmetryType == "Cubic":
if finalCijs[3] <= 0:
print "\n *** WARNING: C44 is less than or equal to zero ***\n"
if finalCijs[0] <= abs(finalCijs[6]):
print "\n *** WARNING: C11 is less than or equal to |C12| ***\n"
if (finalCijs[0]+2*finalCijs[6]) <= 0:
print "\n *** WARNING: C11+2C12 is less than or equal to zero ***\n"
print "\n<>---------------------------- RESULTS ----------------------------------<>\n"
print "Final Cij matrix ("+units+"):"
print S.array2string(finalCijMatrix,max_line_width=130,suppress_small=True)
print "\nErrors on Cij matrix ("+units+"):"
print S.array2string(finalErrors,max_line_width=130,suppress_small=True)
(sij, esij, covsij) = CijUtil.invertCij(finalCijMatrix,finalErrors)
print "\nFinal Sij matrix ("+units+"-1):"
print S.array2string(sij,max_line_width=130,suppress_small=True)
print "\nErrors on Sij matrix ("+units+"-1):"
print S.array2string(esij,max_line_width=130,suppress_small=True)
print"\n<>----------------------------------------------------------------------<>\n"
if symmetryType == "Cubic":
print " Zener anisotropy index : %6.5f +/- %6.5f" % (CijUtil.zenerAniso(finalCijMatrix,finalErrors))
print " Universal anisotropy index : %6.5f +/- %6.5f" % (CijUtil.uAniso(finalCijMatrix,finalErrors))
print " (Rangnthn and Ostoja-Starzewski, PRL 101, 055504)\n"
(youngX, youngY, youngZ, eyoungX, eyoungY, eyoungZ,
poissonXY, poissonXZ, poissonYX, poissonYZ, poissonZX, poissonZY,
epoissonXY, epoissonXZ, epoissonYX, epoissonYZ, epoissonZX, epoissonZY) = CijUtil.youngsmod(finalCijMatrix,finalErrors)
format = "%18s : %11.5f %8s"
print "\n x y z"
print "%18s : %11.5f %11.5f %11.5f %6s" % ("Young's Modulus", youngX, youngY, youngZ, units)
print "%18s : %11.5f %11.5f %11.5f " % (" +/- ", eyoungX, eyoungY, eyoungZ)
print "\n xy xz yx yz zx zy"
format = "%18s : %6.5f %6.5f %6.5f %6.5f %6.5f %6.5f"
print format % ("Poisson's Ratios", poissonXY, poissonXZ, poissonYX, poissonYZ, poissonZX, poissonZY)
print format % (" +/-", epoissonXY, epoissonXZ, epoissonYX, epoissonYZ, epoissonZX, epoissonZY)
print "\n<>--------------------- POLYCRYSTALLINE RESULTS -------------------------<>\n"
(voigtB, reussB, voigtG, reussG, hillB, hillG, evB, erB, evG, erG, ehB, ehG) = CijUtil.polyCij(finalCijMatrix, finalErrors)
format = "%16s : %11.5f %11.5f %11.5f %11.5f %11.5f %11.5f %6s"
print " Voigt +/- Reuss +/- Hill +/-"
print format % ("Bulk Modulus", voigtB, evB, reussB, erB, hillB, ehB, units)
print format % ("Shear Modulus", voigtG, evG, reussG, erG, hillG, ehG, units)
print "\n<>-----------------------------------------------------------------------<>\n"
S.savetxt(seedname + '_cij.txt', finalCijMatrix)
if options.latex:
CijUtil.latexCij(finalCijMatrix, finalErrors, seedname + '.tex', options.latex_nt)
if options.txt:
CijUtil.txtCij(finalCijMatrix, options.txt)
4:"Tetragonal", 5:"Cubic", 6:"Trigonal-low", 7:"Trigonal-high/Hexagonal"}
symmetryType = latticeTypes[int(latticeType)]
magnitude = float(cijdat.readline())
for patt in range(1):
for a in range(0,numsteps):
pattern =cijdat.readline()
line1 = cijdat.readline().split()
line2 = cijdat.readline().split()
line3 = cijdat.readline().split()
if a == 0:
strain = S.array([float(line1[0]),float(line2[1]),float(line3[2]),2*float(line2[2]),2*float(line1[2]),2*float(line1[1])])
else:
strain = S.row_stack(S.array((strain,[float(line1[0]),float(line2[1]),float(line3[2]),2*float(line2[2]),2*float(line1[2]),2*float(line1[1])])))
(units, thisStress) = espresso.get_stress("MgO_cij__"+str(patt+1)+"__"+str(a+1))
if a == 0:
stress = thisStress
else:
stress = S.row_stack((stress,thisStress))
def __fit(index1,index2):
from scipy import stats, sqrt, square
print strain
print stress
(cijFitted,intercept,r,tt,stderr) = stats.linregress(strain[:,index2-1],stress[:,index1-1])
if (S.__version__ < '0.7.0'):
stderr = S.sqrt((numsteps * stderr**2)/(numsteps-2))
error = stderr/sqrt(sum(square(strain[:,index2-1])))
else:
fit_str = ((strain[index2-1,:] * cijFitted) + intercept)