def printas(tab, transpose=False):
"""Print a table using scipy formating"""
a = toarray(tab)
if transpose:
a = a.transpose()
print scipy.array2string(
a, separator=" ") #.replace("["," ").replace("]"," ")
def printas( tab, transpose=False):
"""Print a table using scipy formating"""
a = toarray(tab)
if transpose:
a = a.transpose()
print scipy.array2string(
a,
separator=" "
)#.replace("["," ").replace("]"," ")
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, 0, 0], [7, 1, 8, -9, 0, 0],
[8, 8, 3, 0, 0, 0], [9, -9, 0, 4, 0, 0],
[0, 0, 0, 0, 4, 9], [0, 0, 0, 0, 9, 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 "\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 .castep
(units,
thisStress) = castep.get_stress_dotcastep(seedname + "_cij__" +
str(patt + 1) + "__" +
str(a + 1) + ".castep")
# again, top right triangle
if a == 0:
stress = thisStress
else:
stress = S.row_stack((stress, thisStress))
"""
Both the stress and strain matrices use the IRE conventions to reduce the
3x3 matrices to 1x6 arrays. These 1D arrays are 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
# Should be zero? 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)
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)
def dumpXML(seedname):
import time
S.set_printoptions(threshold=S.nan) #don't skip printing parts of the array
if os.path.isfile(seedname+"-geomopt1.cml"):
# we'll inject the data into this file, then
basefile = seedname+"-geomopt1.cml"
print "Inserting CML into: "+ basefile
f = open(basefile, "r")
tree = etree.parse(f)
f.close()
fp = d["{http://www.castep.org/cml/dictionary/}finalProperties"]
finalproperties = fp.findin_context(tree)
assert len(finalproperties) == 1
startnode = finalproperties[0]
elif os.path.isfile(seedname+"-energy.cml"):
# we'll inject the data into this file, then
basefile = seedname+"-energy.cml"
print "Inserting CML into: "+ basefile
f = open(basefile, "r")
tree = etree.parse(f)
f.close()
fp = d["{http://www.castep.org/cml/dictionary/}finalProperties"]
finalproperties = fp.findin_context(tree)
assert len(finalproperties) == 1
startnode = finalproperties[0]
else:
basefile = seedname+"_cij_analysis.cml"
print "Outputting CML into: "+ basefile
# create a header
CML_NAMESPACE = "http://www.xml-cml.org/schema"
DC_NAMESPACE ="http://purl.org/dc/elements/1.1/"
CML = "{%s}" % CML_NAMESPACE
NSMAP = {None : CML_NAMESPACE, "dc" : DC_NAMESPACE}
startnode = etree.Element(CML +"cml", nsmap=NSMAP)
metadata = etree.Element("metadata")
metadata.attrib["name"] = "dc:date"
metadata.attrib["content"] = time.strftime("%Y-%m-%dT%H:%M:%S")
startnode.append(metadata)
metadata = etree.Element("metadata")
metadata.attrib["name"] = "dc:creator"
metadata.attrib["content"] = "MGElastics"
startnode.append(metadata)
metadata = etree.Element("metadata")
metadata.attrib["name"] = "dc:hasVersion"
metadata.attrib["content"] = str(version)
startnode.append(metadata)
metadata = etree.Element("metadata")
metadata.attrib["name"] = "dc:subject"
metadata.attrib["content"] = "Analysis file for Cij calculations"
startnode.append(metadata)
tree = etree.ElementTree(startnode)
# now append Cij data
cijnode = etree.Element("propertyList")
cijnode.attrib["title"] = "MaterialsGrid: Elastic Properties"
cijnode.attrib["dictRef"] = "castep:elastic_properties"
startnode.append(cijnode)
cijProp = etree.Element("property")
cijProp.attrib["dictRef"] = "castep:elastic_stiffness_constants"
cijProp.attrib["title"] = "Elastic Stiffness Constants"
cijnode.append(cijProp)
cijTensor = etree.Element("matrix")
cijTensor.attrib["rows"] = "6"
cijTensor.attrib["columns"] = "6"
cijTensor.attrib["dataType"] = "xsd:double"
cijTensor.attrib["units"] = "castepunits:"+ units.lower()
cijTensor.text = S.array2string(finalCijMatrix.reshape(1,36)[0],max_line_width=1000,suppress_small=True).strip("[] ")
cijProp.append(cijTensor)
sijProp = etree.Element("property")
sijProp.attrib["dictRef"] = "castep:elastic_compliance_constants"
sijProp.attrib["title"] = "Elastic Compliance Constants"
cijnode.append(sijProp)
sijTensor = etree.Element("matrix")
sijTensor.attrib["rows"] = "6"
sijTensor.attrib["columns"] = "6"
sijTensor.attrib["dataType"] = "xsd:double"
sijTensor.attrib["units"] = "castepunits:"+ units.lower()+"-1" #this has to be changed - i don't think the '/' is allowed
sijTensor.text = S.array2string(sij.reshape(1,36)[0],max_line_width=1000,suppress_small=True).strip("[] ")
sijProp.append(sijTensor)
#### Young's Moduli ####
youngsMod = etree.Element("propertyList")
youngsMod.attrib["dictRef"] = "castep:youngs_moduli"
youngsMod.attrib["title"] = "Young's Moduli"
cijnode.append(youngsMod)
# X
youngsModValX = etree.Element("property")
youngsModValX.attrib["title"] = "Young's Modulus X"
youngsModValX.attrib["dictRef"] = "castep:young_x"
youngsMod.append(youngsModValX)
youngsModValXScalar = etree.Element("scalar")
youngsModValXScalar.attrib["dataType"] = "xsd:double"
youngsModValXScalar.attrib["units"] = "castepunits:"+ units.lower()
youngsModValXScalar.text = str(youngX)
youngsModValX.append(youngsModValXScalar)
# Y
youngsModValY = etree.Element("property")
youngsModValY.attrib["title"] = "Young's Modulus Y"
youngsModValY.attrib["dictRef"] = "castep:young_y"
youngsMod.append(youngsModValY)
youngsModValYScalar = etree.Element("scalar")
youngsModValYScalar.attrib["dataType"] = "xsd:double"
youngsModValYScalar.attrib["units"] = "castepunits:"+ units.lower()
youngsModValYScalar.text = str(youngY)
youngsModValY.append(youngsModValYScalar)
# Z
youngsModValZ = etree.Element("property")
youngsModValZ.attrib["title"] = "Young's Modulus Z"
youngsModValZ.attrib["dictRef"] = "castep:young_z"
youngsMod.append(youngsModValZ)
youngsModValZScalar = etree.Element("scalar")
youngsModValZScalar.attrib["dataType"] = "xsd:double"
youngsModValZScalar.attrib["units"] = "castepunits:"+ units.lower()
youngsModValZScalar.text = str(youngZ)
youngsModValZ.append(youngsModValZScalar)
#### Poisson's Ratio ####
poissonMod = etree.Element("propertyList")
poissonMod.attrib["dictRef"] = "castep:poisson_ratio"
poissonMod.attrib["title"] = "Poisson Ratio"
cijnode.append(poissonMod)
# XY
poissonModValXY = etree.Element("property")
poissonModValXY.attrib["title"] = "Poisson Ratio XY"
poissonModValXY.attrib["dictRef"] = "castep:poisson_xy"
poissonModValXY.attrib["units"] = "castepunits:dimensionless"
poissonMod.append(poissonModValXY)
poissonModValXYScalar = etree.Element("scalar")
poissonModValXYScalar.attrib["dataType"] = "xsd:double"
poissonModValXYScalar.attrib["units"] = "castepunits:dimensionless"
poissonModValXYScalar.text = str(poissonXY)
poissonModValXY.append(poissonModValXYScalar)
# XZ
poissonModValXZ = etree.Element("property")
poissonModValXZ.attrib["title"] = "Poisson Ratio XZ"
poissonModValXZ.attrib["dictRef"] = "castep:poisson_xz"
poissonMod.append(poissonModValXZ)
poissonModValXZScalar = etree.Element("scalar")
poissonModValXZScalar.attrib["dataType"] = "xsd:double"
poissonModValXZScalar.attrib["units"] = "castepunits:dimensionless"
poissonModValXZScalar.text = str(poissonXZ)
poissonModValXZ.append(poissonModValXZScalar)
# YX
poissonModValYX = etree.Element("property")
poissonModValYX.attrib["title"] = "Poisson Ratio YX"
poissonModValYX.attrib["dictRef"] = "castep:poisson_yx"
poissonMod.append(poissonModValYX)
poissonModValYXScalar = etree.Element("scalar")
poissonModValYXScalar.attrib["dataType"] = "xsd:double"
poissonModValYXScalar.attrib["units"] = "castepunits:dimensionless"
poissonModValYXScalar.text = str(poissonYX)
poissonModValYX.append(poissonModValYXScalar)
# YZ
poissonModValYZ = etree.Element("property")
poissonModValYZ.attrib["title"] = "Poisson Ratio YZ"
poissonModValYZ.attrib["dictRef"] = "castep:poisson_yz"
poissonMod.append(poissonModValYZ)
poissonModValYZScalar = etree.Element("scalar")
poissonModValYZScalar.attrib["dataType"] = "xsd:double"
poissonModValYZScalar.attrib["units"] = "castepunits:dimensionless"
poissonModValYZScalar.text = str(poissonYZ)
poissonModValYZ.append(poissonModValYZScalar)
# ZX
poissonModValZX = etree.Element("property")
poissonModValZX.attrib["title"] = "Poisson Ratio ZX"
poissonModValZX.attrib["dictRef"] = "castep:poisson_zx"
poissonMod.append(poissonModValZX)
poissonModValZXScalar = etree.Element("scalar")
poissonModValZXScalar.attrib["dataType"] = "xsd:double"
poissonModValZXScalar.attrib["units"] = "castepunits:dimensionless"
poissonModValZXScalar.text = str(poissonZX)
poissonModValZX.append(poissonModValZXScalar)
# ZY
poissonModValZY = etree.Element("property")
poissonModValZY.attrib["title"] = "Poisson Ratio ZY"
poissonModValZY.attrib["dictRef"] = "castep:poisson_zy"
poissonMod.append(poissonModValZY)
poissonModValZYScalar = etree.Element("scalar")
poissonModValZYScalar.attrib["dataType"] = "xsd:double"
poissonModValZYScalar.attrib["units"] = "castepunits:dimensionless"
poissonModValZYScalar.text = str(poissonZY)
poissonModValZY.append(poissonModValZYScalar)
#### Polycrystalline Results ####
#bulk moduli
bulkModPL = etree.Element("propertyList")
bulkModPL.attrib["dictRef"] = "castep:polycrystalline_bulk_moduli"
bulkModPL.attrib["title"] = "Polycrystalline Bulk Moduli"
cijnode.append(bulkModPL)
bulkModVoigt = etree.Element("property")
bulkModVoigt.attrib["title"] = "Voigt"
bulkModVoigt.attrib["dictRef"] = "castep:bulk_modulus_voigt"
bulkModPL.append(bulkModVoigt)
bulkModReuss = etree.Element("property")
bulkModReuss.attrib["title"] = "Reuss"
bulkModReuss.attrib["dictRef"] = "castep:bulk_modulus_reuss"
bulkModPL.append(bulkModReuss)
bulkModHill = etree.Element("property")
bulkModHill.attrib["title"] = "Hill"
bulkModHill.attrib["dictRef"] = "castep:bulk_modulus_hill"
bulkModPL.append(bulkModHill)
bulkModVoigtScalar = etree.Element("scalar")
bulkModVoigtScalar.attrib["dataType"] = "xsd:double"
bulkModVoigtScalar.attrib["units"] = "castepunits:"+ units.lower()
bulkModVoigtScalar.text = str(voigtB)
bulkModVoigt.append(bulkModVoigtScalar)
bulkModReussScalar = etree.Element("scalar")
bulkModReussScalar.attrib["dataType"] = "xsd:double"
bulkModReussScalar.attrib["units"] = "castepunits:"+ units.lower()
bulkModReussScalar.text = str(reussB)
bulkModReuss.append(bulkModReussScalar)
bulkModHillScalar = etree.Element("scalar")
bulkModHillScalar.attrib["dataType"] = "xsd:double"
bulkModHillScalar.attrib["units"] = "castepunits:"+ units.lower()
bulkModHillScalar.text = str((voigtB+reussB)/2)
bulkModHill.append(bulkModHillScalar)
#shear moduli
shearModPL = etree.Element("propertyList")
shearModPL.attrib["dictRef"] = "castep:polycrystalline_shear_moduli"
shearModPL.attrib["title"] = "Polycrystalline Shear Moduli"
cijnode.append(shearModPL)
shearModVoigt = etree.Element("property")
shearModVoigt.attrib["title"] = "Voigt"
shearModVoigt.attrib["dictRef"] = "castep:shear_modulus_voigt"
shearModPL.append(shearModVoigt)
shearModReuss = etree.Element("property")
shearModReuss.attrib["title"] = "Reuss"
shearModReuss.attrib["dictRef"] = "castep:shear_modulus_reuss"
shearModPL.append(shearModReuss)
shearModHill = etree.Element("property")
shearModHill.attrib["title"] = "Hill"
shearModHill.attrib["dictRef"] = "castep:shear_modulus_hill"
shearModPL.append(shearModHill)
shearModVoigtScalar = etree.Element("scalar")
shearModVoigtScalar.attrib["dataType"] = "xsd:double"
shearModVoigtScalar.attrib["units"] = "castepunits:"+ units.lower()
shearModVoigtScalar.text = str(voigtG)
shearModVoigt.append(shearModVoigtScalar)
shearModReussScalar = etree.Element("scalar")
shearModReussScalar.attrib["dataType"] = "xsd:double"
shearModReussScalar.attrib["units"] = "castepunits:"+ units.lower()
shearModReussScalar.text = str(reussG)
shearModReuss.append(shearModReussScalar)
shearModHillScalar = etree.Element("scalar")
shearModHillScalar.attrib["dataType"] = "xsd:double"
shearModHillScalar.attrib["units"] = "castepunits:"+ units.lower()
shearModHillScalar.text = str((voigtG+reussG)/2)
shearModHill.append(shearModHillScalar)
if(options.debug):
print etree.tostring(startnode,pretty_print=True)
else:
# wrap it in an ElementTree instance, and save as XML
tree.write(basefile,pretty_print=True)
return
def main(input_options, libmode=False):
def dumpXML(seedname):
import time
S.set_printoptions(threshold=S.nan) #don't skip printing parts of the array
if os.path.isfile(seedname+"-geomopt1.cml"):
# we'll inject the data into this file, then
basefile = seedname+"-geomopt1.cml"
print "Inserting CML into: "+ basefile
f = open(basefile, "r")
tree = etree.parse(f)
f.close()
fp = d["{http://www.castep.org/cml/dictionary/}finalProperties"]
finalproperties = fp.findin_context(tree)
assert len(finalproperties) == 1
startnode = finalproperties[0]
elif os.path.isfile(seedname+"-energy.cml"):
# we'll inject the data into this file, then
basefile = seedname+"-energy.cml"
print "Inserting CML into: "+ basefile
f = open(basefile, "r")
tree = etree.parse(f)
f.close()
fp = d["{http://www.castep.org/cml/dictionary/}finalProperties"]
finalproperties = fp.findin_context(tree)
assert len(finalproperties) == 1
startnode = finalproperties[0]
else:
basefile = seedname+"_cij_analysis.cml"
print "Outputting CML into: "+ basefile
# create a header
CML_NAMESPACE = "http://www.xml-cml.org/schema"
DC_NAMESPACE ="http://purl.org/dc/elements/1.1/"
CML = "{%s}" % CML_NAMESPACE
NSMAP = {None : CML_NAMESPACE, "dc" : DC_NAMESPACE}
startnode = etree.Element(CML +"cml", nsmap=NSMAP)
metadata = etree.Element("metadata")
metadata.attrib["name"] = "dc:date"
metadata.attrib["content"] = time.strftime("%Y-%m-%dT%H:%M:%S")
startnode.append(metadata)
metadata = etree.Element("metadata")
metadata.attrib["name"] = "dc:creator"
metadata.attrib["content"] = "MGElastics"
startnode.append(metadata)
metadata = etree.Element("metadata")
metadata.attrib["name"] = "dc:hasVersion"
metadata.attrib["content"] = str(version)
startnode.append(metadata)
metadata = etree.Element("metadata")
metadata.attrib["name"] = "dc:subject"
metadata.attrib["content"] = "Analysis file for Cij calculations"
startnode.append(metadata)
tree = etree.ElementTree(startnode)
# now append Cij data
cijnode = etree.Element("propertyList")
cijnode.attrib["title"] = "MaterialsGrid: Elastic Properties"
cijnode.attrib["dictRef"] = "castep:elastic_properties"
startnode.append(cijnode)
cijProp = etree.Element("property")
cijProp.attrib["dictRef"] = "castep:elastic_stiffness_constants"
cijProp.attrib["title"] = "Elastic Stiffness Constants"
cijnode.append(cijProp)
cijTensor = etree.Element("matrix")
cijTensor.attrib["rows"] = "6"
cijTensor.attrib["columns"] = "6"
cijTensor.attrib["dataType"] = "xsd:double"
cijTensor.attrib["units"] = "castepunits:"+ units.lower()
cijTensor.text = S.array2string(finalCijMatrix.reshape(1,36)[0],max_line_width=1000,suppress_small=True).strip("[] ")
cijProp.append(cijTensor)
sijProp = etree.Element("property")
sijProp.attrib["dictRef"] = "castep:elastic_compliance_constants"
sijProp.attrib["title"] = "Elastic Compliance Constants"
cijnode.append(sijProp)
sijTensor = etree.Element("matrix")
sijTensor.attrib["rows"] = "6"
sijTensor.attrib["columns"] = "6"
sijTensor.attrib["dataType"] = "xsd:double"
sijTensor.attrib["units"] = "castepunits:"+ units.lower()+"-1" #this has to be changed - i don't think the '/' is allowed
sijTensor.text = S.array2string(sij.reshape(1,36)[0],max_line_width=1000,suppress_small=True).strip("[] ")
sijProp.append(sijTensor)
#### Young's Moduli ####
youngsMod = etree.Element("propertyList")
youngsMod.attrib["dictRef"] = "castep:youngs_moduli"
youngsMod.attrib["title"] = "Young's Moduli"
cijnode.append(youngsMod)
# X
youngsModValX = etree.Element("property")
youngsModValX.attrib["title"] = "Young's Modulus X"
youngsModValX.attrib["dictRef"] = "castep:young_x"
youngsMod.append(youngsModValX)
youngsModValXScalar = etree.Element("scalar")
youngsModValXScalar.attrib["dataType"] = "xsd:double"
youngsModValXScalar.attrib["units"] = "castepunits:"+ units.lower()
youngsModValXScalar.text = str(youngX)
youngsModValX.append(youngsModValXScalar)
# Y
youngsModValY = etree.Element("property")
youngsModValY.attrib["title"] = "Young's Modulus Y"
youngsModValY.attrib["dictRef"] = "castep:young_y"
youngsMod.append(youngsModValY)
youngsModValYScalar = etree.Element("scalar")
youngsModValYScalar.attrib["dataType"] = "xsd:double"
youngsModValYScalar.attrib["units"] = "castepunits:"+ units.lower()
youngsModValYScalar.text = str(youngY)
youngsModValY.append(youngsModValYScalar)
# Z
youngsModValZ = etree.Element("property")
youngsModValZ.attrib["title"] = "Young's Modulus Z"
youngsModValZ.attrib["dictRef"] = "castep:young_z"
youngsMod.append(youngsModValZ)
youngsModValZScalar = etree.Element("scalar")
youngsModValZScalar.attrib["dataType"] = "xsd:double"
youngsModValZScalar.attrib["units"] = "castepunits:"+ units.lower()
youngsModValZScalar.text = str(youngZ)
youngsModValZ.append(youngsModValZScalar)
#### Poisson's Ratio ####
poissonMod = etree.Element("propertyList")
poissonMod.attrib["dictRef"] = "castep:poisson_ratio"
poissonMod.attrib["title"] = "Poisson Ratio"
cijnode.append(poissonMod)
# XY
poissonModValXY = etree.Element("property")
poissonModValXY.attrib["title"] = "Poisson Ratio XY"
poissonModValXY.attrib["dictRef"] = "castep:poisson_xy"
poissonModValXY.attrib["units"] = "castepunits:dimensionless"
poissonMod.append(poissonModValXY)
poissonModValXYScalar = etree.Element("scalar")
poissonModValXYScalar.attrib["dataType"] = "xsd:double"
poissonModValXYScalar.attrib["units"] = "castepunits:dimensionless"
poissonModValXYScalar.text = str(poissonXY)
poissonModValXY.append(poissonModValXYScalar)
# XZ
poissonModValXZ = etree.Element("property")
poissonModValXZ.attrib["title"] = "Poisson Ratio XZ"
poissonModValXZ.attrib["dictRef"] = "castep:poisson_xz"
poissonMod.append(poissonModValXZ)
poissonModValXZScalar = etree.Element("scalar")
poissonModValXZScalar.attrib["dataType"] = "xsd:double"
poissonModValXZScalar.attrib["units"] = "castepunits:dimensionless"
poissonModValXZScalar.text = str(poissonXZ)
poissonModValXZ.append(poissonModValXZScalar)
# YX
poissonModValYX = etree.Element("property")
poissonModValYX.attrib["title"] = "Poisson Ratio YX"
poissonModValYX.attrib["dictRef"] = "castep:poisson_yx"
poissonMod.append(poissonModValYX)
poissonModValYXScalar = etree.Element("scalar")
poissonModValYXScalar.attrib["dataType"] = "xsd:double"
poissonModValYXScalar.attrib["units"] = "castepunits:dimensionless"
poissonModValYXScalar.text = str(poissonYX)
poissonModValYX.append(poissonModValYXScalar)
# YZ
poissonModValYZ = etree.Element("property")
poissonModValYZ.attrib["title"] = "Poisson Ratio YZ"
poissonModValYZ.attrib["dictRef"] = "castep:poisson_yz"
poissonMod.append(poissonModValYZ)
poissonModValYZScalar = etree.Element("scalar")
poissonModValYZScalar.attrib["dataType"] = "xsd:double"
poissonModValYZScalar.attrib["units"] = "castepunits:dimensionless"
poissonModValYZScalar.text = str(poissonYZ)
poissonModValYZ.append(poissonModValYZScalar)
# ZX
poissonModValZX = etree.Element("property")
poissonModValZX.attrib["title"] = "Poisson Ratio ZX"
poissonModValZX.attrib["dictRef"] = "castep:poisson_zx"
poissonMod.append(poissonModValZX)
poissonModValZXScalar = etree.Element("scalar")
poissonModValZXScalar.attrib["dataType"] = "xsd:double"
poissonModValZXScalar.attrib["units"] = "castepunits:dimensionless"
poissonModValZXScalar.text = str(poissonZX)
poissonModValZX.append(poissonModValZXScalar)
# ZY
poissonModValZY = etree.Element("property")
poissonModValZY.attrib["title"] = "Poisson Ratio ZY"
poissonModValZY.attrib["dictRef"] = "castep:poisson_zy"
poissonMod.append(poissonModValZY)
poissonModValZYScalar = etree.Element("scalar")
poissonModValZYScalar.attrib["dataType"] = "xsd:double"
poissonModValZYScalar.attrib["units"] = "castepunits:dimensionless"
poissonModValZYScalar.text = str(poissonZY)
poissonModValZY.append(poissonModValZYScalar)
#### Polycrystalline Results ####
#bulk moduli
bulkModPL = etree.Element("propertyList")
bulkModPL.attrib["dictRef"] = "castep:polycrystalline_bulk_moduli"
bulkModPL.attrib["title"] = "Polycrystalline Bulk Moduli"
cijnode.append(bulkModPL)
bulkModVoigt = etree.Element("property")
bulkModVoigt.attrib["title"] = "Voigt"
bulkModVoigt.attrib["dictRef"] = "castep:bulk_modulus_voigt"
bulkModPL.append(bulkModVoigt)
bulkModReuss = etree.Element("property")
bulkModReuss.attrib["title"] = "Reuss"
bulkModReuss.attrib["dictRef"] = "castep:bulk_modulus_reuss"
bulkModPL.append(bulkModReuss)
bulkModHill = etree.Element("property")
bulkModHill.attrib["title"] = "Hill"
bulkModHill.attrib["dictRef"] = "castep:bulk_modulus_hill"
bulkModPL.append(bulkModHill)
bulkModVoigtScalar = etree.Element("scalar")
bulkModVoigtScalar.attrib["dataType"] = "xsd:double"
bulkModVoigtScalar.attrib["units"] = "castepunits:"+ units.lower()
bulkModVoigtScalar.text = str(voigtB)
bulkModVoigt.append(bulkModVoigtScalar)
bulkModReussScalar = etree.Element("scalar")
bulkModReussScalar.attrib["dataType"] = "xsd:double"
bulkModReussScalar.attrib["units"] = "castepunits:"+ units.lower()
bulkModReussScalar.text = str(reussB)
bulkModReuss.append(bulkModReussScalar)
bulkModHillScalar = etree.Element("scalar")
bulkModHillScalar.attrib["dataType"] = "xsd:double"
bulkModHillScalar.attrib["units"] = "castepunits:"+ units.lower()
bulkModHillScalar.text = str((voigtB+reussB)/2)
bulkModHill.append(bulkModHillScalar)
#shear moduli
shearModPL = etree.Element("propertyList")
shearModPL.attrib["dictRef"] = "castep:polycrystalline_shear_moduli"
shearModPL.attrib["title"] = "Polycrystalline Shear Moduli"
cijnode.append(shearModPL)
shearModVoigt = etree.Element("property")
shearModVoigt.attrib["title"] = "Voigt"
shearModVoigt.attrib["dictRef"] = "castep:shear_modulus_voigt"
shearModPL.append(shearModVoigt)
shearModReuss = etree.Element("property")
shearModReuss.attrib["title"] = "Reuss"
shearModReuss.attrib["dictRef"] = "castep:shear_modulus_reuss"
shearModPL.append(shearModReuss)
shearModHill = etree.Element("property")
shearModHill.attrib["title"] = "Hill"
shearModHill.attrib["dictRef"] = "castep:shear_modulus_hill"
shearModPL.append(shearModHill)
shearModVoigtScalar = etree.Element("scalar")
shearModVoigtScalar.attrib["dataType"] = "xsd:double"
shearModVoigtScalar.attrib["units"] = "castepunits:"+ units.lower()
shearModVoigtScalar.text = str(voigtG)
shearModVoigt.append(shearModVoigtScalar)
shearModReussScalar = etree.Element("scalar")
shearModReussScalar.attrib["dataType"] = "xsd:double"
shearModReussScalar.attrib["units"] = "castepunits:"+ units.lower()
shearModReussScalar.text = str(reussG)
shearModReuss.append(shearModReussScalar)
shearModHillScalar = etree.Element("scalar")
shearModHillScalar.attrib["dataType"] = "xsd:double"
shearModHillScalar.attrib["units"] = "castepunits:"+ units.lower()
shearModHillScalar.text = str((voigtG+reussG)/2)
shearModHill.append(shearModHillScalar)
if(options.debug):
print etree.tostring(startnode,pretty_print=True)
else:
# wrap it in an ElementTree instance, and save as XML
tree.write(basefile,pretty_print=True)
return
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 getCMLStress(file):
def __castep(dict, term):
return dict["{http://www.castep.org/cml/dictionary/}%s" % term]
stress = __castep(d, "stress")
tree = etree.parse(file)
stress_xml = stress.findin(tree)
assert len(stress_xml) == 1
stressTensor = stress.getvalue(stress_xml[0])
return stressTensor, stressTensor.unit
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('--xml', '-x', action='store_true', help="CML mode")
p.add_option('--castep', '-c', action='store_true', help="CASTEP mode")
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)")
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.castep and options.xml:
p.error("options -x and -c are mutually exclusive")
elif not options.castep and not options.xml:
p.error("one of -x or -c is required")
# For some reason, golem/lxml needs to be imported first
if options.xml or options.force:
try:
# import golem, for use globally
global golem
import golem
# import etree, for use globally
global etree
from lxml import etree
# set dictionary, for use globally
global d
d = golem.loadDictionary("castepDict.xml")
except ImportError:
print >> sys.stderr, "You need to have golem and lxml installed for the --xml option"
sys.exit(1)
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)
if(options.castep):
print "Reading stress data from the .castep files"
elif(options.xml):
print "Reading stress data from the .xml files"
else:
print "Don't know where to get the stress data, please use flags --castep or --xml"
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"}
# regular expression which matches the whole stress tensor block from a .castep file
stressRE = re.compile("\s\*+\sSymmetrised\sStress\sTensor\s\*+\n.+\n.+?\((\w+)\).+\n.+\n.+\n.+\n\s\*\s+x\s+([\+\-]?\d+.\d+)\s+([\+\-]?\d+.\d+)\s+([\+\-]?\d+.\d+)\s+\*\n\s\*\s+y\s+[\+\-]?\d+.\d+\s+([\+\-]?\d+.\d+)\s+([\+\-]?\d+.\d+)\s+\*\n\s\*\s+z\s+[\+\-]?\d+.\d+\s+[\+\-]?\d+.\d+\s+([\+\-]?\d+.\d+)\s+\*\n")
# 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))
for patt in range(numStrainPatterns/numsteps):
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])])))
if(options.castep):
# now get corresponding stress data from .castep
dotCastep = open(seedname+"_cij__"+str(patt+1)+"__"+str(a+1)+".castep","r")
stressData = stressRE.findall(dotCastep.read())[0]
dotCastep.close()
units = stressData[0]
# again, top right triangle
if a == 0:
stress = S.array([float(stressData[1]),float(stressData[4]),float(stressData[6]),float(stressData[5]),float(stressData[3]),float(stressData[2])])
else:
stress = S.row_stack((stress,S.array([float(stressData[1]),float(stressData[4]),float(stressData[6]),float(stressData[5]),float(stressData[3]),float(stressData[2])])))
elif(options.xml):
# now get corresponding stress data from .xml (using Golem)
dotXMLfilename = seedname+"_cij__"+str(patt+1)+"__"+str(a+1)+"-geomopt1.cml"
cmlStressData, units = getCMLStress(dotXMLfilename)
if a == 0:
stress = S.array([float(cmlStressData[0][0]),float(cmlStressData[1][1]),float(cmlStressData[2][2]),float(cmlStressData[1][2]),float(cmlStressData[0][2]),float(cmlStressData[0][1])])
else:
stress = S.row_stack((stress,S.array([float(cmlStressData[0][0]),float(cmlStressData[1][1]),float(cmlStressData[2][2]),float(cmlStressData[1][2]),float(cmlStressData[0][2]),float(cmlStressData[0][1])]) ))
"""
Both the stress and strain matrices use the IRE conventions to reduce the
3x3 matrices to 1x6 arrays. These 1D arrays are 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])
# correct for scipy weirdness - see http://www.scipy.org/scipy/scipy/ticket/8
stderr = S.sqrt((numsteps * stderr**2)/(numsteps-2))
error = stderr/sqrt(sum(square(strain[:,index2-1])))
# print info about the fit
print '\n'
print 'Cij (gradient) : ',cijFitted
print 'Error in Cij : ', error
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
def __appendOrReplace(valList,val):
try:
valList.append(val)
return sum(valList)/len(valList)
except NameError:
return val
def __createListAndAppend(val):
newList = []
newList.append(val)
return val, newList
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] = __fit(1,1) # fit C11
finalCijs[6] = (__fit(2,1) + __fit(3,1))/2 # fit C21+C31
finalCijs[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...)
cij13 = []
cij13.append(__fit(1,3))
cij13.append(__fit(2,3))
finalCijs[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] = __fit(1,1) # fit C11
finalCijs[6] = __fit(2,1) # fit C21
finalCijs[7] = __appendOrReplace(cij13,__fit(3,1)) # fit C31
finalCijs[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] = __fit(1,1) # fit C11
finalCijs[6] = __fit(2,1) # fit C21
finalCijs[7] = __fit(3,1) # fit C31
finalCijs[8] = __fit(4,1) # fit C41
finalCijs[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] = __fit(3,3) # fit C33
finalCijs[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] = __fit(1,1) # fit C11
finalCijs[6] = __fit(2,1) # fit C21
finalCijs[7] = __fit(3,1) # fit C31
finalCijs[8] = __fit(4,1) # fit C41
finalCijs[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] = __fit(3,3) # fit C33
finalCijs[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] = __fit(1,1) # fit C11
finalCijs[6] = __fit(2,1) # fit C21
finalCijs[7] = __fit(3,1) # fit C31
finalCijs[10] = __fit(6,1) # fit C61
finalCijs[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] = __fit(3,3) # fit C33
finalCijs[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] = __fit(1,1) # fit C11
finalCijs[6], cij12 = __createListAndAppend(__fit(2,1)) # fit C21
finalCijs[7], cij13 = __createListAndAppend(__fit(3,1)) # fit C31
finalCijs[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] = __appendOrReplace(cij12,__fit(1,2)) # fit C12
finalCijs[1] = __fit(2,2) # fit C22
finalCijs[11], cij23 = __createListAndAppend(__fit(3,2)) # fit C32
finalCijs[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] = __appendOrReplace(cij13,__fit(1,3)) # fit C13
finalCijs[11] = __appendOrReplace(cij23,__fit(2,3)) # fit C23
finalCijs[2] = __fit(3,3) # fit C33
finalCijs[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] = __fit(1,1) # fit C11
finalCijs[6], cij12 = __createListAndAppend(__fit(2,1)) # fit C21
finalCijs[7], cij13 = __createListAndAppend(__fit(3,1)) # fit C31
finalCijs[3] = __fit(4,4) # fit C44
finalCijs[9], cij51 = __createListAndAppend(__fit(5,1)) # fit C51
finalCijs[19], cij64 = __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] = __appendOrReplace(cij13,__fit(1,3)) # fit C13
finalCijs[11], cij23 = __createListAndAppend(__fit(2,3)) # fit C23
finalCijs[2] = __fit(3,3) # fit C33
finalCijs[16], cij53 = __createListAndAppend(__fit(5,3)) # fit C53
finalCijs[19] = __appendOrReplace(cij64,__fit(4,6)) # fit C46
finalCijs[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] = __appendOrReplace(cij12,__fit(1,2)) # fit C12
finalCijs[1] = __fit(2,2) # fit C22
finalCijs[11] = __appendOrReplace(cij23,__fit(3,2)) # fit C32
finalCijs[13], cij52 = __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] = __appendOrReplace(cij51,__fit(1,5)) # fit C15
finalCijs[13] = __appendOrReplace(cij52,__fit(2,5)) # fit C25
finalCijs[16] = __appendOrReplace(cij53,__fit(3,5)) # fit C35
finalCijs[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] = __fit(1,1) # fit C11
finalCijs[6], cij12 = __createListAndAppend(__fit(2,1)) # fit C21
finalCijs[7], cij13 = __createListAndAppend(__fit(3,1)) # fit C31
finalCijs[8], cij14 = __createListAndAppend(__fit(4,1)) # fit C41
finalCijs[9], cij15 = __createListAndAppend(__fit(5,1)) # fit C51
finalCijs[10],cij16 = __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] = __appendOrReplace(cij12,__fit(1,2)) # fit C12
finalCijs[1] = __fit(2,2) # fit C22
finalCijs[11], cij23 = __createListAndAppend(__fit(3,2)) # fit C32
finalCijs[12], cij24 = __createListAndAppend(__fit(4,2)) # fit C42
finalCijs[13], cij25 = __createListAndAppend(__fit(5,2)) # fit C52
finalCijs[14], cij26 = __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] = __appendOrReplace(cij13,__fit(1,3)) # fit C13
finalCijs[11] = __appendOrReplace(cij23,__fit(2,3)) # fit C23
finalCijs[2] = __fit(3,3) # fit C33
finalCijs[15], cij34 = __createListAndAppend(__fit(4,3)) # fit C43
finalCijs[16], cij35 = __createListAndAppend(__fit(5,3)) # fit C53
finalCijs[17], cij36 = __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] = __appendOrReplace(cij14,__fit(1,4)) # fit C14
finalCijs[12] = __appendOrReplace(cij24,__fit(2,4)) # fit C24
finalCijs[15] = __appendOrReplace(cij34,__fit(3,4)) # fit C34
finalCijs[3] = __fit(4,4) # fit C44
finalCijs[18], cij45 = __createListAndAppend(__fit(5,4)) # fit C54
finalCijs[19], cij46 = __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] = __appendOrReplace(cij15,__fit(1,5)) # fit C15
finalCijs[13] = __appendOrReplace(cij25,__fit(2,5)) # fit C25
finalCijs[16] = __appendOrReplace(cij35,__fit(3,5)) # fit C35
finalCijs[18] = __appendOrReplace(cij45,__fit(4,5)) # fit C45
finalCijs[4] = __fit(5,5) # fit C55
finalCijs[20], cij56 = __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] = __appendOrReplace(cij16,__fit(1,6)) # fit C16
finalCijs[14] = __appendOrReplace(cij26,__fit(2,6)) # fit C26
finalCijs[17] = __appendOrReplace(cij36,__fit(3,6)) # fit C36
finalCijs[19] = __appendOrReplace(cij46,__fit(4,6)) # fit C46
finalCijs[20] = __appendOrReplace(cij56,__fit(5,6)) # fit C56
finalCijs[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])
c = cMatrix(symmetryType,TetrHigh)
# Generate the 6x6 matrix of elastic constants
# - negative values signify a symmetry relation
finalCijMatrix = 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]
elif index < 0:
finalCijMatrix[i,j] = -finalCijs[-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)
sij = S.linalg.inv(finalCijMatrix)
print "\nFinal Sij matrix ("+units+"-1):"
print S.array2string(sij,max_line_width=130,suppress_small=True)
# bulkModulus = (finalCijs[1]+2*finalCijs[7])/3 #cubic only
youngX = 1/sij[0,0]
youngY = 1/sij[1,1]
youngZ = 1/sij[2,2]
format = "%18s : %11.5f %8s"
print ""
# print format % ("Bulk Modulus", bulkModulus[0], units)
# print format % ("Compressibility", 1/bulkModulus[0], "1/"+ units)
print "\n x y z"
print "%18s : %11.5f %11.5f %11.5f %6s" % ("Young's Modulus", youngX, youngY, youngZ, units)
poissonXY = -1*sij[0,1]*youngX
poissonXZ = -1*sij[0,2]*youngX
poissonYX = -1*sij[1,0]*youngY
poissonYZ = -1*sij[1,2]*youngY
poissonZX = -1*sij[2,0]*youngZ
poissonZY = -1*sij[2,1]*youngZ
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 "\n<>--------------------- POLYCRYSTALLINE RESULTS -------------------------<>\n"
# These equations might be valid only for orthorhombic systems - check!
voigtB = (1.0/9)*(finalCijMatrix[0,0] + finalCijMatrix[1,1] + finalCijMatrix[2,2] ) \
+ (2.0/9)*(finalCijMatrix[0,1] + finalCijMatrix[0,2] + finalCijMatrix[1,2])
reussB = 1.0/((sij[0,0]+sij[1,1]+sij[2,2]) + 2*(sij[0,1]+sij[0,2]+sij[1,2]))
voigtG = (1.0/15)*(finalCijMatrix[0,0] + finalCijMatrix[1,1] + finalCijMatrix[2,2] - finalCijMatrix[0,1] - finalCijMatrix[0,2] - finalCijMatrix[1,2]) \
+ (1.0/5)*(finalCijMatrix[3,3] + finalCijMatrix[4,4] + finalCijMatrix[5,5])
reussG = 15.0/(4*(sij[0,0]+sij[1,1]+sij[2,2]) - 4*(sij[0,1]+sij[0,2]+sij[1,2]) + 3*(sij[3,3]+sij[4,4]+sij[5,5]))
format = "%16s : %11.5f %11.5f %11.5f %6s"
print " Voigt Reuss Hill"
print format % ("Bulk Modulus", voigtB, reussB, (voigtB+reussB)/2, units)
print format % ("Shear Modulus", voigtG, reussG, (voigtG+reussG)/2, units)
print "\n<>-----------------------------------------------------------------------<>\n"
"""
Here on in is just the XML output
"""
if(options.xml or options.force):
dumpXML(seedname)
enrichment=5,
max_burnup=50,
spectrum=SPECTRUM)
all_nuclides = study.get_all_nuclides()
num_nuclides = len(all_nuclides)
cycle_wts = sp.zeros((num_nuclides + 2, len(MOX_AT)))
cout = None
for i, mox_frac in enumerate(MOX_AT):
print(DESCRIPTOR[i], "Fuel")
print("Mox fraction: {:6.3%}".format(mox_frac))
if i == 0:
# Fresh fuel
cout = study.deplete_fresh(NSTEPS, plots=0)
else:
cin = study.reprocess(cout, ELEMENTS, mox_frac)
print(100 * cin / cin.sum())
cout = study.reload(cin, NSTEPS, verbose=True)
cycle_wts[:, i] = depletr.fuel.at_to_wt_arbitrary(all_nuclides, cout)
print()
fmt_dict = {'float_kind': "{:11.5e}".format}
print('\nWeight Fraction at EOC\n' + " " * 32, end=" ")
for desc in DESCRIPTOR:
print(desc, end=" " * 2)
print()
for j, nuc in enumerate(all_nuclides):
cycstr = sp.array2string(cycle_wts[j], formatter=fmt_dict, separator=" ")
nucstr = str(nuc)
print(nucstr + " " * (32 - len(nucstr)) + cycstr)
print('Отношение площади поверхности к объёму:', round(S / V, 3), 'м^-1')
if porosity_profile:
start_time = datetime.now().replace(microsecond=0)
fig, axs = plt.subplots(3, sharex=True, sharey=True, figsize=(16, 16))
fig.suptitle('Профиль пористости', fontsize=20)
phiX=ps.metrics.porosity_profile(im,0)
axs[0].plot(phiX, linewidth=3)
axs[0].set_xlabel('мкм', fontsize=20)
axs[0].set_ylabel('$\phi_x$', fontsize=20)
axs[0].grid()
axs[0].set_title('$E(\phi_x)=$'+sp.array2string(sp.mean(phiX),precision=2)+', $\sigma=$'+\
sp.array2string(sp.std(phiX),precision=2), fontsize=20)
phiY=ps.metrics.porosity_profile(im,1)
axs[1].plot(phiY, linewidth=3)
axs[1].set_xlabel('мкм', fontsize=20)
axs[1].set_ylabel('$\phi_y$', fontsize=20)
axs[1].grid()
axs[1].set_title('$E(\phi_y)=$'+sp.array2string(sp.mean(phiY),precision=2)+', $\sigma=$'+\
sp.array2string(sp.std(phiY),precision=2), fontsize=20)
phiZ=ps.metrics.porosity_profile(im,2)
axs[2].plot(phiZ, linewidth=3)
axs[2].set_xlabel('мкм', fontsize=20)
axs[2].set_ylabel('$\phi_z$', fontsize=20)
axs[2].grid()
def save(cls, network=None, phases=[], filename=''):
r"""
"""
# avoid printing truncated array
np.set_printoptions(threshold=np.inf)
project, network, phases = cls._parse_args(network=network,
phases=phases)
# Ensure network has PerGeos' expected properties
network = network[0]
if 'pore.EqRadius' not in network.props():
try:
network['pore.EqRadius'] = network['pore.diameter']/2
except KeyError:
network['pore.EqRadius'] = np.ones([network.Np, ])
# Add phase properties to network, if any
for phase in phases:
for item in phase.keys(mode='props', deep=True):
temp = item.split('.', 1)
new_name = temp[0] + '.' + phase.name + '.' + temp[1]
network[new_name] = phase[item]
s = ["# Avizo 3D ASCII 3.0\n\n"]
s.append("define VERTEX " + str(network.Np) + '\n')
s.append("define EDGE " + str(network.Nt) + '\n')
s.append("define POINT " + str(2*network.Nt) + '\n\n')
s.append("Parameters {\n\tContentType \"HxPoreNetworkModel\"\n}\n\n")
types = {'b': 'int', 'i': 'int', 'f': 'float'}
typemap = {}
namemap = {}
shapemap = {}
propmap = {}
i = 1
NumEdgePoints = 1
for item in network.keys():
typemap[item] = types[str(network[item].dtype)[0]]
ncols = int(network[item].size/network[item].shape[0])
if ncols > 1:
shapemap[item] = '[' + str(ncols) + ']'
else:
shapemap[item] = ''
if item.startswith('pore'):
element = 'pore', 'VERTEX'
if item.startswith('throat'):
element = 'throat', 'EDGE'
n = item.replace(element[0] + '.', '').replace('.', '_').split('_')
n = ''.join([i[0].upper()+i[1:] for i in n if len(i)])
namemap[item] = n
temp = element[1] + " { " + typemap[item] + shapemap[item] + " "\
+ namemap[item] + " } @" + str(i) + '\n'
if temp.find('EdgeConnectivity') == -1:
# replaces openpnm tags with the mandatory am file's tags
if "Conns" in temp:
temp = temp.replace("Conns", "EdgeConnectivity")
elif "Coords" in temp:
temp = temp.replace("Coords", "VertexCoordinates")
s.append(temp)
propmap[item] = str(i)
if "NumEdgePoints" in temp:
NumEdgePoints = 0
i += 1
if NumEdgePoints:
temp = "EDGE { int NumEdgePoints" + " } @" + str(i) + '\n'
s.append(temp)
tempat = "@" + str(i) + '\n'
i += 1
# Add POINT data
s.append("POINT { float[3] EdgePointCoordinates } @" + str(i))
s.append("\n\n# Data section follows")
for item in network.keys():
data = network[item]
if item != 'throat.EdgeConnectivity':
s.append('\n\n@' + propmap[item] + '\n')
if shapemap[item] == '':
data = sp.atleast_2d(data).T
if typemap[item] == 'float':
formatter = {'float_kind': lambda x: "%.15E" % x}
else:
formatter = None
if data.dtype == 'bool':
data = data.astype(int)
d = sp.array2string(data, formatter=formatter)
s.append(d.replace('[', '').replace(']', '').replace('\n ', '\n'))
# Add POINT data
s.append('\n\n@' + str(i) + '\n')
formatter = {'float_kind': lambda x: "%.15E" % x}
conns = network['throat.conns']
d = sp.array2string(network['pore.coords'][conns], formatter=formatter)
for r in (('[', ''), (']', ''), ('\n\n', '\n'), ('\n ', '\n'),
('\n ', '\n')):
d = d.replace(*r)
d += '\n'
s.append(d)
# Add NumEdgePoints
if NumEdgePoints:
s.append('\n\n' + tempat)
s.append(''.join(['2' + '\n']*network.Nt))
# Write to file
if filename == '':
filename = project.name
fname = cls._parse_filename(filename=filename, ext='am')
with open(fname, 'w') as f:
f.write(''.join(s))