def test_rod2U2rod(self):
rodvec = n.array([0.23, -0.34, 0.7])
Umat = tools.rod_to_u(rodvec)
rodvec2 = tools.u_to_rod(Umat)
diff = n.abs(rodvec - rodvec2).sum()
self.assertAlmostEqual(diff, 0, 9)
def test_U2rod2U(self):
phi1 = 0.2
PHI = 0.4
phi2 = 0.1
Umat = tools.euler_to_u(phi1, PHI, phi2)
rodvec = tools.u_to_rod(Umat)
Umat2 = tools.rod_to_u(rodvec)
diff = n.abs(Umat - Umat2).sum()
self.assertAlmostEqual(diff, 0, 9)
def write_errors(lsqr, i):
"""
Save the fitted grain error parameters, pos, U and eps
INPUT: The error set from the final fitting
OUTPUT: grainno mean_IA grainvolume x y z rodx rody rodz
U11 U12 U13 U21 U22 U23 U31 U32 U33
eps11 eps22 eps33 eps23 eps13 eps12
eps11_s eps22_s eps33_s eps23_s eps13_s eps12_s
sig11 sig22 sig33 sig23 sig13 sig12
sig11_s sig22_s sig33_s sig23_s sig13_s sig12_s
sig_tth sig_eta
Jette Oddershede, Risoe DTU, June 23 2008
"""
# error transformation into other coordinate system and from strain to stress under construction
U = tools.rod_to_u([
lsqr.inp.rod[i][0] + lsqr.m.values['rodx%s' % i],
lsqr.inp.rod[i][1] + lsqr.m.values['rody%s' % i],
lsqr.inp.rod[i][2] + lsqr.m.values['rodz%s' % i],
])
eps_ref = False
rodx_err = 0
rody_err = 0
rodz_err = 0
for key in lsqr.mg.covariance.keys():
if 'epsaa%s' % i in key:
eps_ref = True
break
if eps_ref == False:
cov_eps = n.zeros((6, 6))
else:
try:
free = lsqr.mg.fixed.values().count(False)
except:
free = lsqr.mg.fitarg.values().count(False)
assert free >= 6, 'wrong dimensions of covariance matrix'
covariance = n.zeros((free, free))
j1 = 0
for entry1 in lsqr.grains[i]:
try:
if lsqr.mg.fixed[entry1] == False:
j2 = 0
for entry2 in lsqr.grains[i]:
if lsqr.mg.fixed[entry2] == False:
covariance[j1][j2] = lsqr.mg.covariance[('%s' %
entry1,
'%s' %
entry2)]
j2 = j2 + 1
j1 = j1 + 1
except:
if lsqr.mg.fitarg["fix_%s" % entry1] == False:
j2 = 0
for entry2 in lsqr.grains[i]:
if lsqr.mg.fitarg["fix_%s" % entry2] == False:
covariance[j1][j2] = lsqr.mg.covariance[('%s' %
entry1,
'%s' %
entry2)]
j2 = j2 + 1
j1 = j1 + 1
if free == 6:
cov_eps = covariance
else:
#derivatives = n.linalg.inv(covariance)
#derivatives_rod = derivatives[len(derivatives)-9:len(derivatives)-6,len(derivatives)-9:len(derivatives)-6]
#cov_rod = n.linalg.inv(derivatives_rod)
#vars_rod = n.linalg.eig(cov_rod)[0]
#derivatives = derivatives[len(derivatives)-6:,len(derivatives)-6:]
#cov_eps = n.linalg.inv(derivatives)
cov_rod = covariance[len(covariance) - 9:len(covariance) - 6,
len(covariance) - 9:len(covariance) - 6]
vars_rod = n.linalg.eig(cov_rod)[0]
cov_eps = covariance[len(covariance) - 6:, len(covariance) - 6:]
# old way of doing it including covariances with orientations in strain errors
try:
cov_eps = n.array(
[[
lsqr.mg.covariance[('epsaa%s' % i, 'epsaa%s' % i)],
lsqr.mg.covariance[('epsaa%s' % i, 'epsbb%s' % i)],
lsqr.mg.covariance[('epsaa%s' % i, 'epscc%s' % i)],
lsqr.mg.covariance[('epsaa%s' % i, 'epsbc%s' % i)],
lsqr.mg.covariance[('epsaa%s' % i, 'epsac%s' % i)],
lsqr.mg.covariance[('epsaa%s' % i, 'epsab%s' % i)]
],
[
lsqr.mg.covariance[('epsbb%s' % i, 'epsaa%s' % i)],
lsqr.mg.covariance[('epsbb%s' % i, 'epsbb%s' % i)],
lsqr.mg.covariance[('epsbb%s' % i, 'epscc%s' % i)],
lsqr.mg.covariance[('epsbb%s' % i, 'epsbc%s' % i)],
lsqr.mg.covariance[('epsbb%s' % i, 'epsac%s' % i)],
lsqr.mg.covariance[('epsbb%s' % i, 'epsab%s' % i)]
],
[
lsqr.mg.covariance[('epscc%s' % i, 'epsaa%s' % i)],
lsqr.mg.covariance[('epscc%s' % i, 'epsbb%s' % i)],
lsqr.mg.covariance[('epscc%s' % i, 'epscc%s' % i)],
lsqr.mg.covariance[('epscc%s' % i, 'epsbc%s' % i)],
lsqr.mg.covariance[('epscc%s' % i, 'epsac%s' % i)],
lsqr.mg.covariance[('epscc%s' % i, 'epsab%s' % i)]
],
[
lsqr.mg.covariance[('epsbc%s' % i, 'epsaa%s' % i)],
lsqr.mg.covariance[('epsbc%s' % i, 'epsbb%s' % i)],
lsqr.mg.covariance[('epsbc%s' % i, 'epscc%s' % i)],
lsqr.mg.covariance[('epsbc%s' % i, 'epsbc%s' % i)],
lsqr.mg.covariance[('epsbc%s' % i, 'epsac%s' % i)],
lsqr.mg.covariance[('epsbc%s' % i, 'epsab%s' % i)]
],
[
lsqr.mg.covariance[('epsac%s' % i, 'epsaa%s' % i)],
lsqr.mg.covariance[('epsac%s' % i, 'epsbb%s' % i)],
lsqr.mg.covariance[('epsac%s' % i, 'epscc%s' % i)],
lsqr.mg.covariance[('epsac%s' % i, 'epsbc%s' % i)],
lsqr.mg.covariance[('epsac%s' % i, 'epsac%s' % i)],
lsqr.mg.covariance[('epsac%s' % i, 'epsab%s' % i)]
],
[
lsqr.mg.covariance[('epsab%s' % i, 'epsaa%s' % i)],
lsqr.mg.covariance[('epsab%s' % i, 'epsbb%s' % i)],
lsqr.mg.covariance[('epsab%s' % i, 'epscc%s' % i)],
lsqr.mg.covariance[('epsab%s' % i, 'epsbc%s' % i)],
lsqr.mg.covariance[('epsab%s' % i, 'epsac%s' % i)],
lsqr.mg.covariance[('epsab%s' % i, 'epsab%s' % i)]
]])
except:
cov_eps = n.zeros((6, 6))
cov_eps_s = conversion.CovarianceRotation(cov_eps, U)
cov_sig = conversion.CovarianceTransformation(cov_eps, lsqr.inp.C)
cov_sig_s = conversion.CovarianceRotation(cov_sig, U)
filename = '%s/%s_errors.gff' % (lsqr.inp.fit['direc'],
lsqr.inp.fit['stem'])
filename2 = '%s/%s_%s_errors.gff' % (
lsqr.inp.fit['direc'], lsqr.inp.fit['stem'], lsqr.inp.fit['goon'])
try:
f = open(filename, 'r')
lines = f.readlines()
f.close()
except:
f = open(filename, 'w')
out = "# grainno mean_IA grainvolume x y z rodx rody rodz U11 U12 U13 U21 U22 U23 U31 U32 U33 eps11 eps22 eps33 eps23 eps13 eps12 "
out = out + "eps11_s eps22_s eps33_s eps23_s eps13_s eps12_s sig11 sig22 sig33 sig23 sig13 sig12 sig11_s sig22_s sig33_s sig23_s sig13_s sig12_s sig_tth sig_eta\n"
f.write(out)
f.close()
f = open(filename, 'r')
lines = f.readlines()
f.close()
index = 0
for j in range(1, len(lines)):
if i + 1 == eval(split(lines[j])[0]):
index = j
break
if index == 0:
index = len(lines)
lines.append('')
format = "%d " * 1 + "%f " * 8 + "%0.12f " * 9 + "%e " * 24 + "%f " * 2 + "\n"
lines[index] = format % (
i + 1,
reject.spread(lsqr.inp.mean_ia[i]), #0
# reject.spread(lsqr.inp.volume[i]),
reject.median_absolute_deviation(lsqr.inp.volume[i]),
lsqr.mg.errors['x%s' % i] / 1000,
lsqr.mg.errors['y%s' % i] / 1000,
lsqr.mg.errors['z%s' % i] / 1000,
lsqr.mg.errors['rodx%s' % i],
lsqr.mg.errors['rody%s' % i],
lsqr.mg.errors['rodz%s' % i],
0,
0,
0,
0,
0,
0,
0,
0,
0,
n.sqrt(cov_eps[0][0]),
n.sqrt(cov_eps[1][1]),
n.sqrt(cov_eps[2][2]),
n.sqrt(cov_eps[3][3]),
n.sqrt(cov_eps[4][4]),
n.sqrt(cov_eps[5][5]),
n.sqrt(cov_eps_s[0][0]),
n.sqrt(cov_eps_s[1][1]),
n.sqrt(cov_eps_s[2][2]),
n.sqrt(cov_eps_s[3][3]),
n.sqrt(cov_eps_s[4][4]),
n.sqrt(cov_eps_s[5][5]),
n.sqrt(cov_sig[0][0]),
n.sqrt(cov_sig[1][1]),
n.sqrt(cov_sig[2][2]),
n.sqrt(cov_sig[3][3]),
n.sqrt(cov_sig[4][4]),
n.sqrt(cov_sig[5][5]),
n.sqrt(cov_sig_s[0][0]),
n.sqrt(cov_sig_s[1][1]),
n.sqrt(cov_sig_s[2][2]),
n.sqrt(cov_sig_s[3][3]),
n.sqrt(cov_sig_s[4][4]),
n.sqrt(cov_sig_s[5][5]),
reject.median_absolute_deviation(lsqr.inp.spr_tth[i]),
reject.median_absolute_deviation(lsqr.inp.spr_eta[i]))
f = open(filename, 'w')
for j in range(len(lines)):
f.write(lines[j])
f.close()
f = open(filename2, 'w')
for j in range(len(lines)):
f.write(lines[j])
f.close()
# Additional writing of file containing covariances
filename = '%s/%s_cov_eps_sig.gff' % (lsqr.inp.fit['direc'],
lsqr.inp.fit['stem'])
try:
f = open(filename, 'r')
lines = f.readlines()
f.close()
except:
f = open(filename, 'w')
out = "# grainno e11e11 e11e22 e11e33 e11e23 e11e13 e11e12 "
out = out + "e22e22 e22e33 e22e23 e22e13 e22e12 "
out = out + "e33e33 e33e23 e33e13 e33e12 "
out = out + "e23e23 e23e13 e23e12 e13e13 e13e12 e12e12 "
out = out + "e11e11_s e11e22_s e11e33_s e11e23_s e11e13_s e11e12_s "
out = out + "e22e22_s e22e33_s e22e23_s e22e13_s e22e12_s "
out = out + "e33e33_s e33e23_s e33e13_s e33e12_s "
out = out + "e23e23_s e23e13_s e23e12_s e13e13_s e13e12_s e12e12_s "
out = out + "s11s11 s11s22 s11s33 s11s23 s11s13 s11s12 "
out = out + "s22s22 s22s33 s22s23 s22s13 s22s12 "
out = out + "s33s33 s33s23 s33s13 s33s12 "
out = out + "s23s23 s23s13 s23s12 s13s13 s13s12 s12s12 "
out = out + "s11s11_s s11s22_s s11s33_s s11s23_s s11s13_s s11s12_s "
out = out + "s22s22_s s22s33_s s22s23_s s22s13_s s22s12_s "
out = out + "s33s33_s s33s23_s s33s13_s s33s12_s "
out = out + "s23s23_s s23s13_s s23s12_s s13s13_s s13s12_s s12s12_s \n"
f.write(out)
f.close()
f = open(filename, 'r')
lines = f.readlines()
f.close()
index = 0
for j in range(1, len(lines)):
if i + 1 == eval(split(lines[j])[0]):
index = j
break
if index == 0:
index = len(lines)
lines.append('')
format = "%d " * 1 + "%e " * 84 + "\n"
lines[index] = format % (
i + 1,
cov_eps[0][0],
cov_eps[0][1],
cov_eps[0][2],
cov_eps[0][3],
cov_eps[0][4],
cov_eps[0][5],
cov_eps[1][1],
cov_eps[1][2],
cov_eps[1][3],
cov_eps[1][4],
cov_eps[1][5],
cov_eps[2][2],
cov_eps[2][3],
cov_eps[2][4],
cov_eps[2][5],
cov_eps[3][3],
cov_eps[3][4],
cov_eps[3][5],
cov_eps[4][4],
cov_eps[4][5],
cov_eps[5][5],
cov_eps_s[0][0],
cov_eps_s[0][1],
cov_eps_s[0][2],
cov_eps_s[0][3],
cov_eps_s[0][4],
cov_eps_s[0][5],
cov_eps_s[1][1],
cov_eps_s[1][2],
cov_eps_s[1][3],
cov_eps_s[1][4],
cov_eps_s[1][5],
cov_eps_s[2][2],
cov_eps_s[2][3],
cov_eps_s[2][4],
cov_eps_s[2][5],
cov_eps_s[3][3],
cov_eps_s[3][4],
cov_eps_s[3][5],
cov_eps_s[4][4],
cov_eps_s[4][5],
cov_eps_s[5][5],
cov_sig[0][0],
cov_sig[0][1],
cov_sig[0][2],
cov_sig[0][3],
cov_sig[0][4],
cov_sig[0][5],
cov_sig[1][1],
cov_sig[1][2],
cov_sig[1][3],
cov_sig[1][4],
cov_sig[1][5],
cov_sig[2][2],
cov_sig[2][3],
cov_sig[2][4],
cov_sig[2][5],
cov_sig[3][3],
cov_sig[3][4],
cov_sig[3][5],
cov_sig[4][4],
cov_sig[4][5],
cov_sig[5][5],
cov_sig_s[0][0],
cov_sig_s[0][1],
cov_sig_s[0][2],
cov_sig_s[0][3],
cov_sig_s[0][4],
cov_sig_s[0][5],
cov_sig_s[1][1],
cov_sig_s[1][2],
cov_sig_s[1][3],
cov_sig_s[1][4],
cov_sig_s[1][5],
cov_sig_s[2][2],
cov_sig_s[2][3],
cov_sig_s[2][4],
cov_sig_s[2][5],
cov_sig_s[3][3],
cov_sig_s[3][4],
cov_sig_s[3][5],
cov_sig_s[4][4],
cov_sig_s[4][5],
cov_sig_s[5][5],
)
f = open(filename, 'w')
for j in range(len(lines)):
f.write(lines[j])
f.close()
def write_values(lsqr):
"""
Save the fitted grain parameters, pos, U and eps
INPUT: The parameter set from the final fitting
OUTPUT: grainno mean_IA grain_volume x y z rodx rody rodz
U11 U12 U13 U21 U22 U23 U31 U32 U33
eps11 eps22 eps33 eps23 eps13 eps12
eps11_s eps22_s eps33_s eps23_s eps13_s eps12_s
sig11 sig22 sig33 sig23 sig13 sig12
sig11_s sig22_s sig33_s sig23_s sig13_s sig12_s
sig_tth sig_eta
Jette Oddershede, Risoe DTU, April 21 2008
"""
filename = '%s/%s_%s.gff' % (lsqr.inp.fit['direc'], lsqr.inp.fit['stem'],
lsqr.inp.fit['goon'])
f = open(filename, 'w')
format = "%d " * 1 + "%f " * 8 + "%0.12f " * 9 + "%e " * 24 + "%f " * 2 + "\n"
out = "# grainno mean_IA grainvolume x y z rodx rody rodz U11 U12 U13 U21 U22 U23 U31 U32 U33 eps11 eps22 eps33 eps23 eps13 eps12 "
out = out + "eps11_s eps22_s eps33_s eps23_s eps13_s eps12_s sig11 sig22 sig33 sig23 sig13 sig12 sig11_s sig22_s sig33_s sig23_s sig13_s sig12_s sig_tth sig_eta\n"
f.write(out)
for i in range(lsqr.inp.no_grains):
if i + 1 in lsqr.inp.fit['skip']:
pass
else:
U = tools.rod_to_u([
lsqr.inp.rod[i][0] + lsqr.m.values['rodx%s' % i],
lsqr.inp.rod[i][1] + lsqr.m.values['rody%s' % i],
lsqr.inp.rod[i][2] + lsqr.m.values['rodz%s' % i],
])
eps = n.array([[
lsqr.m.values['epsaa%s' % i], lsqr.m.values['epsab%s' % i],
lsqr.m.values['epsac%s' % i]
],
[
lsqr.m.values['epsab%s' % i],
lsqr.m.values['epsbb%s' % i],
lsqr.m.values['epsbc%s' % i]
],
[
lsqr.m.values['epsac%s' % i],
lsqr.m.values['epsbc%s' % i],
lsqr.m.values['epscc%s' % i]
]])
eps_s = conversion.grain2sample(eps, U)
sig = conversion.strain2stress(eps, lsqr.inp.C)
sig_s = conversion.grain2sample(sig, U)
out = format % (
i + 1,
n.sum(lsqr.inp.mean_ia[i]) / len(lsqr.inp.mean_ia[i]), #0,
# sum(lsqr.inp.volume[i])/lsqr.inp.nrefl[i],
reject.median(lsqr.inp.volume[i]),
lsqr.m.values['x%s' % i] / 1000,
lsqr.m.values['y%s' % i] / 1000,
lsqr.m.values['z%s' % i] / 1000,
lsqr.inp.rod[i][0] + lsqr.m.values['rodx%s' % i],
lsqr.inp.rod[i][1] + lsqr.m.values['rody%s' % i],
lsqr.inp.rod[i][2] + lsqr.m.values['rodz%s' % i],
U[0, 0],
U[0, 1],
U[0, 2],
U[1, 0],
U[1, 1],
U[1, 2],
U[2, 0],
U[2, 1],
U[2, 2],
eps[0][0],
eps[1][1],
eps[2][2],
eps[1][2],
eps[0][2],
eps[0][1],
eps_s[0][0],
eps_s[1][1],
eps_s[2][2],
eps_s[1][2],
eps_s[0][2],
eps_s[0][1],
sig[0][0],
sig[1][1],
sig[2][2],
sig[1][2],
sig[0][2],
sig[0][1],
sig_s[0][0],
sig_s[1][1],
sig_s[2][2],
sig_s[1][2],
sig_s[0][2],
sig_s[0][1],
reject.median(lsqr.inp.spr_tth[i]),
reject.median(lsqr.inp.spr_eta[i]))
f.write(out)
f.close()
def setup_odf(self):
odf_scale = self.graindata.param['odf_scale']
if self.graindata.param['odf_type'] == 1:
odf_spread = self.graindata.param['mosaicity'] / 4
odf_spread_grid = odf_spread / odf_scale
sigma = odf_spread_grid * n.ones(3)
r1_max = int(n.ceil(3 * odf_spread_grid))
r1_range = r1_max * 2 + 1
r2_range = r1_max * 2 + 1
r3_range = r1_max * 2 + 1
mapsize = r1_range * n.ones(3)
odf_center = r1_max * n.ones(3)
print('size of ODF map', mapsize)
self.odf = generate_grains.gen_odf(sigma, odf_center, mapsize)
#from pylab import *
#imshow(self.odf[:,:,odf_center[2]])
#show()
elif self.graindata.param['odf_type'] == 3:
odf_spread = self.graindata.param['mosaicity'] / 4
odf_spread_grid = odf_spread / odf_scale
r1_max = n.ceil(3 * odf_spread_grid)
r2_max = n.ceil(3 * odf_spread_grid)
r3_max = n.ceil(3 * odf_spread_grid)
r1_range = r1_max * 2 + 1
r2_range = r2_max * 2 + 1
r3_range = r3_max * 2 + 1
print('size of ODF map', r1_range * n.ones(3))
odf_center = r1_max * n.ones(3)
self.odf = n.zeros((r1_range, r2_range, r3_range))
# Makes spheric ODF for debug purpuses
for i in range(self.odf.shape[0]):
for j in range(self.odf.shape[1]):
for k in range(self.odf.shape[2]):
r = [i - (r1_max), j - (r2_max), k - (r3_max)]
if n.linalg.norm(r) > r1_max:
self.odf[i, j, k] = 0
else:
self.odf[i, j, k] = 1
#from pylab import *
#imshow(self.odf[:,:,r3_max],interpolation=None)
#show()
elif self.graindata.param['odf_type'] == 2:
file = self.graindata.param['odf_file']
print('Read ODF from file_ %s' % file)
file = open(file, 'r')
(r1_range, r2_range, r3_range) = file.readline()[9:].split()
r1_range = int(r1_range)
r2_range = int(r2_range)
r3_range = int(r3_range)
odf_scale = float(file.readline()[10:])
oneD_odf = n.fromstring(file.readline(), sep=' ')
elements = r1_range * r2_range * r3_range
self.odf = oneD_odf[:elements].reshape(r1_range, r2_range,
r3_range)
if self.graindata.param['odf_sub_sample'] > 1:
sub = self.graindata.param['odf_sub_sample']
print('subscale =', sub)
r1_range_sub = r1_range * self.graindata.param['odf_sub_sample']
r2_range_sub = r2_range * self.graindata.param['odf_sub_sample']
r3_range_sub = r3_range * self.graindata.param['odf_sub_sample']
odf_fine = n.zeros((r1_range_sub, r2_range_sub, r3_range_sub))
for i in range(r1_range):
for j in range(r2_range):
for k in range(r3_range):
odf_fine[i * sub:(i + 1) * sub,
j * sub:(j + 1) * sub,
k * sub:(k + 1) * sub] = self.odf[i, j, k]
self.odf = odf_fine.copy() / (sub * sub * sub)
r1_range = r1_range_sub
r2_range = r2_range_sub
r3_range = r3_range_sub
odf_scale = odf_scale / sub
print('odf_scale', odf_scale)
#[r1_range, r2_range, r3_range] = self.odf.shape
odf_center = [(r1_range) / 2, r2_range / 2, r3_range / 2]
print(odf_center)
#self.odf[:,:,:] = 0.05
print(self.odf.shape)
#from pylab import *
#imshow(self.odf[:,:,odf_center[2]])
#show()
self.Uodf = n.zeros(r1_range*r2_range*r3_range*9).\
reshape(r1_range,r2_range,r3_range,3,3)
if self.graindata.param['odf_cut'] != None:
self.odf_cut = self.odf.max() * self.graindata.param['odf_cut']
else:
self.odf_cut = 0.0
for i in range(self.odf.shape[0]):
for j in range(self.odf.shape[1]):
for k in range(self.odf.shape[2]):
r = odf_scale*n.pi/180.*\
n.array([i-odf_center[0],
j-odf_center[1],
k-odf_center[2]])
self.Uodf[i, j, k, :, :] = tools.rod_to_u(r)
if self.graindata.param['odf_type'] != 2:
file = open(self.graindata.param['stem'] + '.odf', 'w')
file.write('ODF size: %i %i %i\n' % (r1_range, r2_range, r3_range))
file.write('ODF scale: %f\n' % (odf_scale))
for i in range(int(r1_range)):
self.odf[i, :, :].tofile(file, sep=' ', format='%f')
file.write(' ')
file.close()
return self.Uodf
def find_refl(inp):
"""
From U, (x,y,z) and B determined for the far-field case
calculate the possible reflection on the near-field detector
output[grainno][reflno]=[h,k,l,omega,dety,detz,tth,eta]
"""
S = n.array([[1, 0, 0],[0, 1, 0],[0, 0, 1]])
R = tools.detect_tilt(inp.param['tilt_x'],
inp.param['tilt_y'],
inp.param['tilt_z'])
inp.possible = []
# if structure info is given use this
if inp.files['structure_file'] != None:
inp.param['structure_phase_0'] = inp.files['structure_file']
xtal_structure = reflections.open_structure(inp.param,0)
HKL = reflections.gen_miller(inp.param,0)
else:
inp.param['unit_cell_phase_0'] = inp.unit_cell
inp.param['sgno_phase_0'] = inp.fit['sgno']
HKL = reflections.gen_miller(inp.param,0)
for grainno in range(inp.no_grains):
inp.possible.append([])
if grainno+1 not in inp.fit['skip']:
B = tools.epsilon_to_b(n.array([inp.values['epsaa%s' %grainno],
inp.values['epsab%s' %grainno],
inp.values['epsac%s' %grainno],
inp.values['epsbb%s' %grainno],
inp.values['epsbc%s' %grainno],
inp.values['epscc%s' %grainno]]),
inp.unit_cell)
U = tools.rod_to_u([inp.rod[grainno][0]+inp.values['rodx%s' %grainno],
inp.rod[grainno][1]+inp.values['rody%s' %grainno],
inp.rod[grainno][2]+inp.values['rodz%s' %grainno]])
gr_pos = n.array([inp.values['x%s' %grainno],
inp.values['y%s' %grainno],
inp.values['z%s' %grainno]])
for hkl in HKL:
Gc = n.dot(B,hkl[0:3])
Gw = n.dot(S,n.dot(U,Gc))
tth = tools.tth2(Gw,inp.param['wavelength'])
# print hkl[0:3],tth*180./n.pi
costth = n.cos(tth)
(Omega, Eta) = tools.find_omega_general(inp.param['wavelength']/(4.*n.pi)*Gw,
tth,
inp.values['wx']*n.pi/180,
inp.values['wy']*n.pi/180)
if len(Omega) > 0:
for solution in range(len(Omega)):
omega = Omega[solution]
eta = Eta[solution]
for i in range(len(inp.fit['w_limit'])//2):
if (inp.fit['w_limit'][2*i]*n.pi/180) < omega and\
omega < (inp.fit['w_limit'][2*i+1]*n.pi/180):
# form Omega rotation matrix
Om = tools.form_omega_mat_general(omega,inp.values['wx']*n.pi/180,inp.values['wy']*n.pi/180)
Gt = n.dot(Om,Gw)
# Calc crystal position at present omega
[tx,ty,tz]= n.dot(Om,gr_pos)
# Calc detector coordinate for peak
(dety, detz) = detector.det_coor(Gt,costth,
inp.param['wavelength'],
inp.param['distance'],
inp.param['y_size'],
inp.param['z_size'],
inp.param['y_center'],
inp.param['z_center'],
R,tx,ty,tz)
#If peak within detector frame store it in possible
if (-0.5 < dety) and\
(dety < inp.fit['dety_size']-0.5) and\
(-0.5 < detz) and\
(detz < inp.fit['detz_size']-0.5):
inp.possible[grainno].append([hkl[0],
hkl[1],
hkl[2],
omega*180/n.pi,
dety,
detz,
tth,
eta])
def read(file, sym, minimum, maximum, step):
data = ic.columnfile('%s.gff' % file)
#grain sizes
if "grainno" not in data.titles:
data.addcolumn(data.grain_id, 'grainno')
if "grainvolume" in data.titles:
scale = max(data.grainvolume**0.3333)
data.addcolumn(data.grainvolume**0.3333 / scale * 100, 'size')
else:
data.addcolumn(100. * np.ones(data.nrows), 'size')
rodx = []
rody = []
rodz = []
if "rodx" not in data.titles:
for i in range(data.nrows):
U = np.array([[data.U11[i], data.U12[i], data.U13[i]],
[data.U21[i], data.U22[i], data.U23[i]],
[data.U31[i], data.U32[i], data.U33[i]]])
rod = tools.u_to_rod(U)
rodx.append(rod[0])
rody.append(rod[1])
rodz.append(rod[2])
data.addcolumn(np.array(rodx), 'rodx')
data.addcolumn(np.array(rody), 'rody')
data.addcolumn(np.array(rodz), 'rodz')
if sym == "standard":
#grain colours, so that all orientations in Cubic space are allowed
maxhx = 62.8 * 3.14 / 180
minhx = -62.8 * 3.14 / 180
maxhy = 62.8 * 3.14 / 180
minhy = -62.8 * 3.14 / 180
maxhz = 62.8 * 3.14 / 180
minhz = -62.8 * 3.14 / 180
rr = data.rodx**2 + data.rody**2 + data.rodz**2
rr = np.sqrt(rr)
theta = 2 * np.arctan(rr)
r1 = data.rodx / rr
r2 = data.rody / rr
r3 = data.rodz / rr
# normalise colours
red = (r1 * theta - minhx) / (maxhx - minhx)
green = (r2 * theta - minhy) / (maxhy - minhy)
blue = (r3 * theta - minhz) / (maxhz - minhz)
elif sym == "orthorhombic":
# Fill orthorhombic stereographic triangle
red = []
green = []
blue = []
fig = pl.figure(10, frameon=False, figsize=pl.figaspect(1.0))
ax = pl.Axes(fig, [.2, .2, .7, .7])
ax.set_axis_off()
fig.add_axes(ax)
#plot triangle
xa = np.zeros((101))
ya = np.zeros((101))
for i in range(101):
xa[i] = np.cos(i * np.pi / 200.)
ya[i] = np.sin(i * np.pi / 200.)
pl.plot(xa, ya, 'black') # Curved edge
pl.plot([0, 1], [0, 0], 'black', linewidth=2) #lower line
pl.plot([0, 0], [1, 0], 'black', linewidth=2) #left line
pl.text(-0.02, -0.04, '[001]')
pl.text(0.95, -0.04, '[100]')
pl.text(-0.02, 1.01, '[010]')
# Grains
for i in range(data.nrows):
U = tools.rod_to_u([data.rodx[i], data.rody[i], data.rodz[i]])
axis = abs(U[2, :])
colour = np.zeros((3))
colour[0] = (2 * np.arcsin(abs(axis[2])) / np.pi)**1
colour[1] = (2 * np.arcsin(abs(axis[0])) / np.pi)**1
colour[2] = (2 * np.arcsin(abs(axis[1])) / np.pi)**1
mx = max(colour)
colour = colour / mx
red.append(colour[0])
green.append(colour[1])
blue.append(colour[2])
X = axis[0] / (1 + axis[2])
Y = axis[1] / (1 + axis[2])
pl.plot(X, Y, 'o', color=colour)
pl.xlim()
elif sym == "cubic":
# Fill cubic stereographic triangle
red = []
green = []
blue = []
fig = pl.figure(10, frameon=False, figsize=pl.figaspect(.9))
ax = pl.Axes(fig, [.2, .2, .7, .7])
ax.set_axis_off()
fig.add_axes(ax)
#plot triangle
xa = np.zeros((21))
ya = np.zeros((21))
for i in range(21):
ua = np.array([i / 20., 1., 1.])
UA = np.linalg.norm(ua)
za = ua[2] + UA
xa[i] = ua[1] / za
ya[i] = ua[0] / za
pl.plot(xa, ya, 'black') # Curved edge
pl.plot([0, xa[0]], [0, 0.0001], 'black', linewidth=2) #lower line
pl.plot([xa[20], 0], [ya[20], 0], 'black') # upper line
pl.text(-0.01, -0.02, '[100]')
pl.text(xa[0] - 0.01, -0.02, '[110]')
pl.text(xa[-1] - 0.01, ya[-1] + 0.005, '[111]')
# Grains
for i in range(data.nrows):
U = tools.rod_to_u([data.rodx[i], data.rody[i], data.rodz[i]])
axis = abs(U[2, :])
colour = np.zeros((3))
for j in range(3):
for k in range(j + 1, 3):
if (axis[j] > axis[k]):
colour[0] = axis[j]
axis[j] = axis[k]
axis[k] = colour[0]
rr = np.sqrt(axis[0] * axis[0] / ((axis[2] + 1)) /
((axis[2] + 1)) + (axis[1] / (axis[2] + 1) + 1) *
(axis[1] / (axis[2] + 1) + 1))
if axis[1] == 0:
beta = 0
else:
beta = np.arctan(axis[0] / axis[1])
colour[0] = ((np.sqrt(2.0) - rr) / (np.sqrt(2.0) - 1))**.5
colour[1] = ((1 - 4 * beta / np.pi) * ((rr - 1) /
(np.sqrt(2.0) - 1)))**.5
colour[2] = (4 * beta / np.pi * ((rr - 1) /
(np.sqrt(2.0) - 1)))**.5
mx = max(colour)
colour = colour / mx
red.append(colour[0])
green.append(colour[1])
blue.append(colour[2])
X = axis[1] / (1 + axis[2])
Y = axis[0] / (1 + axis[2])
pl.plot(X, Y, 'o', color=colour)
pl.xlim()
elif sym == "hexagonal":
## Fill hexagonal stereographic triangle
A = np.array([[0, 1, 0], [0, -np.sqrt(3), 1], [1, 0, 0]])
a0 = 1. / np.sqrt(3.)
a1 = 1.
a2 = 1.
red = []
green = []
blue = []
fig = pl.figure(10, frameon=False, figsize=pl.figaspect(0.5))
ax = pl.Axes(fig, [0.2, .2, 0.6, 0.6])
ax.set_axis_off()
fig.add_axes(ax)
## Plot triangle
ya = np.array(list(range(51))) / 100.
xa = np.sqrt(1 - ya**2)
pl.plot(xa, ya, 'black') # Curved edge
pl.plot([0, xa[0]], [0, 0.0001], 'black', linewidth=2) #lower line
pl.plot([xa[-1], 0], [ya[-1], 0], 'black') # upper line
## Label crystalographic directions
pl.text(-0.01, -0.02, '[0001]')
pl.text(xa[0] - 0.03, -0.02, '[2-1-10]')
pl.text(xa[-1] - 0.03, ya[-1] + 0.005, '[10-10]')
## Grains
r = symmetry.rotations(6)
for i in range(data.nrows):
U = tools.rod_to_u([data.rodx[i], data.rody[i], data.rodz[i]])
square = 1
angle = 0
frac = 1. / np.sqrt(3.)
for k in range(len(r)):
g = np.dot(U, r[k])
a = np.arccos((np.trace(g) - 1) / 2)
if g[2, 2] > 0:
uvw = g[2, :]
else:
uvw = -g[2, :]
## needed to switch these indices to get correct color and inv pf location
switch1 = uvw[0]
switch2 = uvw[1]
uvw[0] = switch2
uvw[1] = switch1
x = uvw[0] / (1 + uvw[2])
y = uvw[1] / (1 + uvw[2])
f = y / x
s = x * x + y * y
## Finds r (symmetry) which plots grain into triangle
if f <= frac and s <= square and x >= 0 and y >= 0:
angle = a
frac = f
square = s
UVW = uvw
X = x
Y = y
colour = np.dot(np.transpose(A), np.transpose(UVW))**0.7
colour[0] = colour[0] / a2
colour[1] = colour[1] / a1
colour[2] = colour[2] / a0
mx = max(colour)
colour = colour / mx
red.append(colour[0])
green.append(colour[1])
blue.append(colour[2])
pl.plot(X, Y, 'o', color=colour)
pl.xlim()
elif sym == "e11":
try:
colourbar(minimum, maximum, step, 'e-3')
norm = colors.normalize(minimum * 1e-3, maximum * 1e-3)
except:
colourbar(-1, 1, 1, 'e-3')
norm = colors.normalize(-1e-3, 1e-3)
color = cm.jet(norm(data.eps11_s))
red = color[:, 0]
green = color[:, 1]
blue = color[:, 2]
print(
"transverse strain:",
np.sum(data.grainvolume * data.eps11_s) /
np.sum(data.grainvolume))
elif sym == "e22":
try:
colourbar(minimum, maximum, step, 'e-3')
norm = colors.normalize(minimum * 1e-3, maximum * 1e-3)
except:
colourbar(-1, 1, 1, 'e-3')
norm = colors.normalize(-1e-3, 1e-3)
color = cm.jet(norm(data.eps22_s))
red = color[:, 0]
green = color[:, 1]
blue = color[:, 2]
print(
"transverse strain:",
np.sum(data.grainvolume * data.eps22_s) /
np.sum(data.grainvolume))
elif sym == "e33":
try:
colourbar(minimum, maximum, step, 'e-3')
norm = colors.normalize(minimum * 1e-3, maximum * 1e-3)
except:
colourbar(-1, 1, 1, 'e-3')
norm = colors.normalize(-1e-3, 1e-3)
color = cm.jet(norm(data.eps33_s))
red = color[:, 0]
green = color[:, 1]
blue = color[:, 2]
print(
"axial strain:",
np.sum(data.grainvolume * data.eps33_s) /
np.sum(data.grainvolume))
elif sym == "e12":
try:
colourbar(minimum, maximum, step, 'e-3')
norm = colors.normalize(minimum * 1e-3, maximum * 1e-3)
except:
colourbar(-1, 1, 1, 'e-3')
norm = colors.normalize(-1e-3, 1e-3)
color = cm.jet(norm(data.eps12_s))
red = color[:, 0]
green = color[:, 1]
blue = color[:, 2]
print(
"shear strain:",
np.sum(data.grainvolume * data.eps12_s) /
np.sum(data.grainvolume))
elif sym == "e13":
try:
colourbar(minimum, maximum, step, 'e-3')
norm = colors.normalize(minimum * 1e-3, maximum * 1e-3)
except:
colourbar(-1, 1, 1, 'e-3')
norm = colors.normalize(-1e-3, 1e-3)
color = cm.jet(norm(data.eps13_s))
red = color[:, 0]
green = color[:, 1]
blue = color[:, 2]
print(
"shear strain:",
np.sum(data.grainvolume * data.eps13_s) /
np.sum(data.grainvolume))
elif sym == "e23":
try:
colourbar(minimum, maximum, step, 'e-3')
norm = colors.normalize(minimum * 1e-3, maximum * 1e-3)
except:
colourbar(-1, 1, 1, 'e-3')
norm = colors.normalize(-1e-3, 1e-3)
color = cm.jet(norm(data.eps23_s))
red = color[:, 0]
green = color[:, 1]
blue = color[:, 2]
print(
"shear strain:",
np.sum(data.grainvolume * data.eps23_s) /
np.sum(data.grainvolume))
elif sym == "s33":
try:
colourbar(minimum, maximum, step, 'MPa')
norm = colors.normalize(minimum, maximum)
except:
colourbar(-50, 150, 50, 'MPa')
norm = colors.normalize(-50, 150)
color = cm.jet(norm(data.sig33_s))
red = color[:, 0]
green = color[:, 1]
blue = color[:, 2]
print(
"axial stress:",
np.sum(data.grainvolume * data.sig33_s) /
np.sum(data.grainvolume), "MPa")
elif sym == "s11":
try:
colourbar(minimum, maximum, step, 'MPa')
norm = colors.normalize(minimum, maximum)
except:
colourbar(-50, 150, 50, 'MPa')
norm = colors.normalize(-50, 150)
color = cm.jet(norm(data.sig11_s))
red = color[:, 0]
green = color[:, 1]
blue = color[:, 2]
print(
"transverse s11 stress:",
np.sum(data.grainvolume * data.sig11_s) /
np.sum(data.grainvolume), "MPa")
elif sym == "s22":
try:
colourbar(minimum, maximum, step, 'MPa')
norm = colors.normalize(minimum, maximum)
except:
colourbar(-50, 150, 50, 'MPa')
norm = colors.normalize(-50, 150)
color = cm.jet(norm(data.sig22_s))
red = color[:, 0]
green = color[:, 1]
blue = color[:, 2]
print(
"transverse s22 stress:",
np.sum(data.grainvolume * data.sig22_s) /
np.sum(data.grainvolume), "MPa")
elif sym == "s12":
try:
colourbar(minimum, maximum, step, 'MPa')
norm = colors.normalize(minimum, maximum)
except:
colourbar(-50, 50, 50, 'MPa')
norm = colors.normalize(-50, 50)
color = cm.jet(norm(data.sig12_s))
red = color[:, 0]
green = color[:, 1]
blue = color[:, 2]
print(
"shear s12 stress:",
np.sum(data.grainvolume * data.sig12_s) /
np.sum(data.grainvolume), "MPa")
elif sym == "s13":
try:
colourbar(minimum, maximum, step, 'MPa')
norm = colors.normalize(minimum, maximum)
except:
colourbar(-50, 50, 50, 'MPa')
norm = colors.normalize(-50, 50)
color = cm.jet(norm(data.sig13_s))
red = color[:, 0]
green = color[:, 1]
blue = color[:, 2]
print(
"shear s13 stress:",
np.sum(data.grainvolume * data.sig13_s) /
np.sum(data.grainvolume), "MPa")
elif sym == "s23":
try:
colourbar(minimum, maximum, step, 'MPa')
norm = colors.normalize(minimum, maximum)
except:
colourbar(-50, 50, 50, 'MPa')
norm = colors.normalize(-50, 50)
color = cm.jet(norm(data.sig23_s))
red = color[:, 0]
green = color[:, 1]
blue = color[:, 2]
print(
"shear s23 stress:",
np.sum(data.grainvolume * data.sig23_s) /
np.sum(data.grainvolume), "MPa")
elif sym == "latt_rot":
norm = colors.normalize(0, 0.5)
color = cm.jet(norm(data.latt_rot))
red = color[:, 0]
green = color[:, 1]
blue = color[:, 2]
colourbar(0.0, 0.5, 0.1, 'deg')
elif sym == "tz":
norm = colors.normalize(-0.1, 0.1)
color = cm.jet(norm(data.tz))
red = color[:, 0]
green = color[:, 1]
blue = color[:, 2]
elif sym == "vol":
norm = colors.normalize(0, 10)
color = cm.jet(norm(data.grainvolume / data.d_grainvolume))
red = color[:, 0]
green = color[:, 1]
blue = color[:, 2]
elif sym == "tth":
norm = colors.normalize(0.007, 0.009)
color = cm.jet(norm(data.sig_tth / data.grainvolume**.2))
red = color[:, 0]
green = color[:, 1]
blue = color[:, 2]
print(min(data.sig_tth / data.grainvolume**.2),
max(data.sig_tth / data.grainvolume**.2))
# pl.figure(8)
# pl.plot(np.log(data.grainvolume),np.log(data.sig_tth),'.')
elif sym == "eta":
norm = colors.normalize(0.08, 0.15)
color = cm.jet(norm(data.sig_eta / data.grainvolume**.2))
red = color[:, 0]
green = color[:, 1]
blue = color[:, 2]
print(min(data.sig_eta / data.grainvolume**.2),
max(data.sig_eta / data.grainvolume**.2))
# pl.figure(8)
# pl.plot(np.log(data.grainvolume),np.log(data.sig_eta),'.')
else:
np.random.seed(0)
red = np.random.rand(data.nrows)
np.random.seed(1)
green = np.random.rand(data.nrows)
np.random.seed(2)
blue = np.random.rand(data.nrows)
data.addcolumn(red, 'red')
data.addcolumn(green, 'green')
data.addcolumn(blue, 'blue')
return (data)
