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 test_ubi2rod(self):
phi1 = 0.13
PHI = 0.4
phi2 = 0.21
cell = [3, 4, 5, 80, 95, 100]
Umat = tools.euler_to_u(phi1, PHI, phi2)
ubi = n.linalg.inv(n.dot(Umat, tools.form_b_mat(cell))) * 2 * n.pi
rodubi = tools.ubi_to_rod(ubi)
rodU = tools.u_to_rod(Umat)
diff = n.abs(rodubi - rodU).sum()
self.assertAlmostEqual(diff, 0, 9)
eps23 = []
eps13 = []
eps12 = []
titles = [
"grainno", "x", "y", "z", "rodx", "rody", "rodz", "U11", "U12", "U13",
"U21", "U22", "U23", "U31", "U32", "U33", "eps11", "eps22", "eps33",
"eps23", "eps13", "eps12"
]
for i in range(len(list_of_grains)):
grainno.append(eval(split(list_of_grains[i].name, ':')[0]))
x.append(list_of_grains[i].translation[0] / 1000.)
y.append(list_of_grains[i].translation[1] / 1000.)
z.append(list_of_grains[i].translation[2] / 1000.)
ubi = list_of_grains[i].ubi
(U, eps) = tools.ubi_to_u_and_eps(ubi, uc)
rod = tools.u_to_rod(U)
rodx.append(rod[0])
rody.append(rod[1])
rodz.append(rod[2])
U11.append(U[0, 0])
U12.append(U[0, 1])
U13.append(U[0, 2])
U21.append(U[1, 0])
U22.append(U[1, 1])
U23.append(U[1, 2])
U31.append(U[2, 0])
U32.append(U[2, 1])
U33.append(U[2, 2])
eps11.append(eps[0])
eps12.append(eps[1])
eps13.append(eps[2])
def ubi_to_gff(ubi,par):
from ImageD11 import grain as ig
from ImageD11 import parameters as ip
from string import split
from xfab import tools
from six.moves import range
list_of_grains = ig.read_grain_file(ubi)
p = ip.parameters()
p.loadparameters(par)
uc = [p.parameters['cell__a'],p.parameters['cell__b'],p.parameters['cell__c'],p.parameters['cell_alpha'],p.parameters['cell_beta'],p.parameters['cell_gamma']]
#print(uc)
grainno = []
x = []
y = []
z = []
rodx = []
rody = []
rodz = []
unitcell_a = []
unitcell_b = []
unitcell_c = []
unitcell_alpha = []
unitcell_beta = []
unitcell_gamma = []
U11 = []
U12 = []
U13 = []
U21 = []
U22 = []
U23 = []
U31 = []
U32 = []
U33 = []
eps11 = []
eps22 = []
eps33 = []
eps23 = []
eps13 = []
eps12 = []
titles = ["grainno","x","y","z","rodx","rody","rodz","U11","U12","U13","U21","U22","U23","U31","U32","U33","unitcell_a","unitcell_b","unitcell_c","unitcell_alpha","unitcell_beta","unitcell_gamma","eps11","eps22","eps33","eps23","eps13","eps12"]
for i in range(len(list_of_grains)):
if hasattr(list_of_grains,'name') == False:
grainno.append(i)
elif hasattr(list_of_grains,'name') == True:
grainno.append(eval(split(list_of_grains[i].name,':')[0]))
x.append(list_of_grains[i].translation[0]/1000.)
y.append(list_of_grains[i].translation[1]/1000.)
z.append(list_of_grains[i].translation[2]/1000.)
ubi = list_of_grains[i].ubi
(U,eps) = tools.ubi_to_u_and_eps(ubi,uc)
uc_a, uc_b, uc_c, uc_alpha, uc_beta, uc_gamma = tools.ubi_to_cell(ubi)
unitcell_a.append(uc_a)
unitcell_b.append(uc_b)
unitcell_c.append(uc_c)
unitcell_alpha.append(uc_alpha)
unitcell_beta.append(uc_beta)
unitcell_gamma.append(uc_gamma)
rod = tools.u_to_rod(U)
rodx.append(rod[0])
rody.append(rod[1])
rodz.append(rod[2])
U11.append(U[0,0])
U12.append(U[0,1])
U13.append(U[0,2])
U21.append(U[1,0])
U22.append(U[1,1])
U23.append(U[1,2])
U31.append(U[2,0])
U32.append(U[2,1])
U33.append(U[2,2])
eps11.append(eps[0])
eps12.append(eps[1])
eps13.append(eps[2])
eps22.append(eps[3])
eps23.append(eps[4])
eps33.append(eps[5])
gff = cl.newcolumnfile(titles)
gff.ncols = len(titles)
gff.nrows = len(grainno)
gff.bigarray = np.zeros((gff.ncols,gff.nrows))
gff.set_attributes()
gff.addcolumn(grainno,"grainno")
gff.addcolumn(x,"x")
gff.addcolumn(y,"y")
gff.addcolumn(z,"z")
gff.addcolumn(rodx,"rodx")
gff.addcolumn(rody,"rody")
gff.addcolumn(rodz,"rodz")
gff.addcolumn(U11,"U11")
gff.addcolumn(U12,"U12")
gff.addcolumn(U13,"U13")
gff.addcolumn(U21,"U21")
gff.addcolumn(U22,"U22")
gff.addcolumn(U23,"U23")
gff.addcolumn(U31,"U31")
gff.addcolumn(U32,"U32")
gff.addcolumn(U33,"U33")
gff.addcolumn(unitcell_a,"unitcell_a")
gff.addcolumn(unitcell_b,"unitcell_b")
gff.addcolumn(unitcell_c,"unitcell_c")
gff.addcolumn(unitcell_alpha,"unitcell_alpha")
gff.addcolumn(unitcell_beta,"unitcell_beta")
gff.addcolumn(unitcell_gamma,"unitcell_gamma")
gff.addcolumn(eps11,"eps11")
gff.addcolumn(eps22,"eps22")
gff.addcolumn(eps33,"eps33")
gff.addcolumn(eps23,"eps23")
gff.addcolumn(eps13,"eps13")
gff.addcolumn(eps12,"eps12")
return gff, uc
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)