def compute_Sbar(b1, b2, b3, b4, b5, b6):
model = MosaicityParameterisation((b1, b2, b3, b4, b5, b6))
sigma = model.sigma()
sigmap = R * sigma * R.transpose()
sigma11 = matrix.sqr((sigmap[0], sigmap[1], sigmap[3], sigmap[4]))
sigma12 = matrix.col((sigmap[2], sigmap[5]))
sigma21 = matrix.col((sigmap[6], sigmap[7])).transpose()
sigma22 = sigmap[8]
return sigma11 - sigma12 * (1 / sigma22) * sigma21
def callback(self, x):
"""
Handle and update in parameter values
"""
parameterisation = MosaicityParameterisation(x)
sigma = parameterisation.sigma()
lnL = self.log_likelihood(x)
format_string = (
"( %.3g, %.3g, %.3g, %.3g, %.3g, %.3g, %.3g, %.3g, %.3g ): L = %f")
print(format_string % (tuple(sigma) + (lnL, )))
self.history.append(x)
def generate_predictions(self, experiment, reflections, parameters):
# Create the mosaicity model
parameterisation = MosaicityParameterisation(parameters)
# The crystal A and beam s0
A = matrix.sqr(experiment.crystal.get_A())
s0 = matrix.col(experiment.beam.get_s0())
s0_length = s0.length()
# Compute all the vectors
s1_cal = flex.vec3_double()
s2_cal = flex.vec3_double()
for i in range(len(reflections)):
# Compute the reciprocal lattice vector
h = matrix.col(reflections[i]["miller_index"])
r = A * h
s2 = s0 + r
# Rotate the covariance matrix
R = compute_change_of_basis_operation(s0, s2)
S = R * parameterisation.sigma() * R.transpose()
mu = R * s2
assert abs(1 - mu.normalize().dot(matrix.col((0, 0, 1)))) < 1e-7
# Partition the mean vector
mu1 = matrix.col((mu[0], mu[1]))
mu2 = mu[2]
# Partition the covariance matrix
S11 = matrix.sqr((S[0], S[1], S[3], S[4]))
S12 = matrix.col((S[2], S[5]))
S21 = matrix.col((S[6], S[7])).transpose()
S22 = S[8]
# Compute the conditional mean
mubar = mu1 + S12 * (1 / S22) * (s0_length - mu2)
# Compute the vector and rotate
v = matrix.col(
(mubar[0], mubar[1], s0_length)).normalize() * s0_length
s1 = R.transpose() * v
# Append the 2 vectors
s1_cal.append(s1)
s2_cal.append(s2)
# Return the predicted vectors
return s1_cal, s2_cal
def compute_L(b1, b2, b3, b4, b5, b6):
model = MosaicityParameterisation((b1, b2, b3, b4, b5, b6))
sigma = model.sigma()
sigmap = R * sigma * R.transpose()
sigma11 = matrix.sqr((sigmap[0], sigmap[1], sigmap[3], sigmap[4]))
sigma12 = matrix.col((sigmap[2], sigmap[5]))
sigma21 = matrix.col((sigmap[6], sigmap[7])).transpose()
sigma22 = sigmap[8]
sigma_bar = sigma11 - sigma12 * (1 / sigma22) * sigma21
d = r - mu2
A = log(sigma22)
B = (1 / sigma22) * d**2
C = log(sigma_bar.determinant()) * ctot
D = (sigma_bar.inverse() * Sobs).trace()
return -0.5 * (A + B + C + D)
def compute_sigma22(b1, b2, b3, b4, b5, b6):
model = MosaicityParameterisation((b1, b2, b3, b4, b5, b6))
sigma = model.sigma()
sigmap = R * sigma * R.transpose()
sigma22 = sigmap[8]
return sigma22