def cell_and_euler_to_ub(self,cell,euler):
'''
cell = [a,b,c,alpha,beta,gamma]
euler= [phi1,PHI,phi2]
'''
U = tools.euler_to_u(euler[0],euler[1],euler[2])
B = tools.form_b_mat(cell)
return np.dot(U,B)
def test_ucell2B2ucell(self):
ucell = n.array([
3.5 + n.random.rand(), 3.5 + n.random.rand(),
3.5 + n.random.rand(), 89.5 + n.random.rand(),
89.5 + n.random.rand(), 89.5 + n.random.rand()
])
B = tools.form_b_mat(ucell)
ucell2 = tools.b_to_cell(B)
diff = n.abs(ucell - ucell2).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)
def extract_strain_and_directions(cell, wavelength, distance, pixelsize, g, flt, ymin, ystep, omegastep, NY ):
B = tools.form_b_mat(cell)
keys = [ (hkl[0], hkl[1], hkl[2], int(s))
for hkl, s in zip(g.hkl.T , g.etasigns)]
uni = uniq(keys)
akeys = np.array( keys )
strains = []
directions = []
all_omegas = []
dtys = []
all_tths = []
all_etas = []
weights = []
all_intensity = []
all_sc = []
all_Gws = []
all_hkl = []
for refi,u in enumerate(uni):
# h==h, k==k, l==l, sign==sign
mask = (akeys == u).astype(int).sum(axis=1) == 4
tths = flt.tth[g.mask][mask]
etas = flt.eta[g.mask][mask]
omegas = flt.omega[g.mask][mask]
scs = flt.sc[g.mask][mask]
detector_y_pos = flt.dty[ g.mask ][mask]
intensity = flt.sum_intensity[g.mask][mask]
scs = flt.sc[g.mask][mask]
G_ws = np.array( (flt.gx[g.mask][mask], flt.gy[g.mask][mask], flt.gz[g.mask][mask]) ).T
h = u[0]
k = u[1]
l = u[2]
for sc, dty, tth, eta, om, I, sc, G_w in zip( scs, detector_y_pos, tths, etas, omegas, intensity, scs, G_ws ):
all_hkl.append( [h,k,l] )
bragg_order, d_measured, d_original, eps = strain(B, h, k, l, tth, wavelength)
strains.append( eps )
directions.append( normal_omega(tth, eta, wavelength, om) )
all_omegas.append( om )
all_tths.append( tth )
all_etas.append( eta )
dtys.append( dty )
all_intensity.append( I )
all_sc.append( sc )
all_Gws.append(G_w)
weights.append( weight( d_measured, d_original, eps, tth, wavelength, bragg_order, distance, pixelsize ) )
return np.array(strains), np.array(directions), np.array(all_omegas), np.array(dtys), np.array(weights), np.array(all_tths), np.array(all_etas), np.array(all_intensity), np.array(all_sc), np.asarray(all_Gws), np.asarray(all_hkl)
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)
Bmat = tools.form_b_mat(cell)
ubi = n.linalg.inv(n.dot(Umat, Bmat)) * 2 * n.pi
(U1, B1) = tools.ubi_to_u_b(ubi)
diffU = n.abs(Umat - U1).sum()
diffB = n.abs(Bmat - B1).sum()
self.assertAlmostEqual(diffU, 0, 9)
self.assertAlmostEqual(diffB, 0, 9)
def test1(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)
Bmat = tools.form_b_mat(cell)
ubi = n.linalg.inv(n.dot(Umat, Bmat)) * 2 * n.pi
ubi2 = tools.u_to_ubi(Umat, cell)
(U2, B2) = tools.ubi_to_u_b(ubi2)
diff = n.abs(ubi - ubi2).sum()
self.assertAlmostEqual(diff, 0, 9)
diff = n.abs(Umat - U2).sum()
self.assertAlmostEqual(diff, 0, 9)
diff = n.abs(Bmat - B2).sum()
self.assertAlmostEqual(diff, 0, 9)
def build_B_from_Cif(ciffile):
"""
Builds a B-matrix based on information in a cif file
Parameter:
- cif file name
Returns
- B matrix, as in polyxsim (watch out for the 2pi factor!!)
Created: 12/2019, S. Merkel, Univ. Lille, France
"""
param['structure_phase_0'] = ciffile
xtal_structure = open_cif(param, 0)
unit_cell = param['unit_cell_phase_0']
B = tools.form_b_mat(unit_cell)
return B
def test_tth(self):
# generate random gvector
hkl = n.array([
round(n.random.rand() * 10 - 5),
round(n.random.rand() * 10 - 5),
round(n.random.rand() * 10 - 5)
])
ucell = n.array([
3.5 + n.random.rand(), 3.5 + n.random.rand(),
3.5 + n.random.rand(), 89.5 + n.random.rand(),
89.5 + n.random.rand(), 89.5 + n.random.rand()
])
B = tools.form_b_mat(ucell)
U = tools.euler_to_u(n.random.rand() * 2. * n.pi,
n.random.rand() * 2. * n.pi,
n.random.rand() * n.pi)
wavelength = 0.95 + n.random.rand() * 0.1
gvec = n.dot(U, n.dot(B, hkl))
tth = tools.tth(ucell, hkl, wavelength)
tth2 = tools.tth2(gvec, wavelength)
diff = n.abs(tth - tth2)
self.assertAlmostEqual(diff, 0, 9)
def test_find_omega_general_nowedge(self):
# generate random gvector
hkl = n.array([
round(n.random.rand() * 10 - 5),
round(n.random.rand() * 10 - 5),
round(n.random.rand() * 10 - 5)
])
ucell = n.array([
3.5 + n.random.rand(), 3.5 + n.random.rand(),
3.5 + n.random.rand(), 89.5 + n.random.rand(),
89.5 + n.random.rand(), 89.5 + n.random.rand()
])
B = tools.form_b_mat(ucell)
U = tools.euler_to_u(n.random.rand() * 2. * n.pi,
n.random.rand() * 2. * n.pi,
n.random.rand() * n.pi)
wavelength = 0.95 + n.random.rand() * 0.1
gvec = n.dot(U, n.dot(B, hkl))
tth = tools.tth(ucell, hkl, wavelength)
# calculate corresponding eta and Omega using tools.find_omega_general
(omega1,
eta1) = tools.find_omega_general(gvec * wavelength / (4. * n.pi), tth,
0, 0)
Om1 = []
for i in range(len(omega1)):
Om1.append(tools.form_omega_mat_general(omega1[i], 0, 0))
# calculate corresponding eta and Omega using tools.find_omega_wedge
omega2 = tools.find_omega(gvec, tth)
Om2 = []
for i in range(len(omega2)):
Om2.append(tools.form_omega_mat(omega2[i]))
#assert
for i in range(len(omega1)):
# print Om1[i]
# print Om2[i]
diff = n.abs(Om1[i] - Om2[i]).sum()
self.assertAlmostEqual(diff, 0, 9)
def rotations(crystal_system):
"""
rotations returns the set of unitary rotation matrices
corresponding to the indistinguasible lattice permutations
The values of the function only differ from permutations for
trigonal and hexagonal crystal systems
rot = rotations(crystal_system)
U_new = U*rot
U_new*B*perm*hkl = U*B*hkl, so U_new = U*B*perminv*Binv and
rot = B*perminv*Binv. If B or perm is diagonal, rot = perminv.
perminv included in perm, but to get the i'th entry of rot
to correspond to the i'th entry of perm one must use perminv.
crystal_system can be one of the following values
1: Triclinic
2: Monoclinic
3: Orthorhombic
4: Tetragonal
5: Trigonal
6: Hexagonal
7: Cubic
Jette Oddershede, Riso, 8/2/2010
"""
if crystal_system < 1 or crystal_system > 7:
raise ValueError('Crystal system shoud have a value between 1 and 7')
if crystal_system == 1: # Triclinic
rot = permutations(crystal_system)
for i in range(len(rot)):
rot[i] = inv(rot[i])
if crystal_system == 2: # Monoclinic
rot = permutations(crystal_system)
for i in range(len(rot)):
rot[i] = inv(rot[i])
if crystal_system == 3: # Orthorhombic
rot = permutations(crystal_system)
for i in range(len(rot)):
rot[i] = inv(rot[i])
if crystal_system == 4: # Tetragonal
rot = permutations(crystal_system)
for i in range(len(rot)):
rot[i] = inv(rot[i])
if crystal_system == 5: # Trigonal
perm = permutations(crystal_system)
B = tools.form_b_mat([1.,1.,1.,90.,90.,120.])
Binv = inv(B)
rot = zeros((6, 3, 3))
for i in range(len(perm)):
rot[i] = dot(B,dot(inv(perm[i]),Binv))
if crystal_system == 6: # Hexagonal
perm = permutations(crystal_system)
B = tools.form_b_mat([1.,1.,1.,90.,90.,120.])
Binv = inv(B)
rot = zeros((12, 3, 3))
for i in range(len(perm)):
rot[i] = dot(B,dot(inv(perm[i]),Binv))
if crystal_system == 7: # Cubic
rot = permutations(crystal_system)
for i in range(len(rot)):
rot[i] = inv(rot[i])
return rot
tilt_x = 0.0
tilt_y = 0.0
tilt_z = 0.0
wedge = 0.0
unit_cell = [4.04975, 4.04975, 4.04975, 90, 90, 90]
sgno = 225
U = n.array([
-0.52880000, 0.78460000, 0.32380000, -0.51780000, 0.00400000, -0.85550000,
-0.67250000, -0.62000000, 0.40410000
]).reshape(3, 3)
pos = [0.0, 0.0, 0.0]
hkl = n.array([1, 1, 1]) * 3
unit_cell = [4.04975, 4.04975, 4.04975, 90, 90, 90]
B = tools.form_b_mat(unit_cell)
Gc = n.dot(B, hkl)
Gw = n.dot(U, Gc)
wavedisp = 1e-3
sigma_limit = 2.
wavelength_0 = 0.4859292
wavelength = wavelength_0
tth = tools.tth2(Gw, wavelength)
(Omega, Eta) = tools.find_omega_wedge(Gw, tth, wedge)
omega_0 = Omega[1] * 180. / n.pi
Om = tools.form_omega_mat(Omega[1])
Gt = n.dot(Om, Gw)
(dety, detz) = detector.det_coor(Gt, n.cos(tth), wavelength, distance,
