def _get_diffracted_intensity(range_theta, range_stl, phase):
assert phase.type == "Phase", "Must be Phase!"
# Check probability model, if invalid return zeros instead of the actual pattern:
if not phase.valid_probs:
logger.debug("- calc: get_diffracted_intensity reports: 'Invalid probability found!'")
return np.zeros_like(range_stl)
else:
# Calculate CSDS distribution
CSDS_arr, CSDS_real_mean = calculate_distribution(phase.CSDS)
# Get absolute scale
abs_scale = get_absolute_scale(phase.components, CSDS_real_mean, phase.W)
# Create a helper function to 'expand' certain arrays, for
# results which are independent of the 2-theta range
stl_dim = range_stl.shape[0]
repeat_to_stl = lambda arr: np.repeat(arr[np.newaxis, ...], stl_dim, axis=0)
# Repeat junction probabilities & weight fractions
W = repeat_to_stl(phase.W).astype(np.complex_)
P = repeat_to_stl(phase.P).astype(np.complex_)
# Repeat & get SFa and SFb (transpose conjugate) structure factor matrices:
SF, PF = get_structure_factors(range_stl, phase.G, phase.components)
SFa = np.repeat(SF[..., np.newaxis, :], SF.shape[1], axis=1)
SFb = np.transpose(np.conjugate(SFa), axes=(0, 2, 1))
# Calculate the repetition factor for R+ probabilities:
rank = P.shape[1]
reps = rank / phase.G
# Calculate the structure factor matrix:
F = np.repeat(np.repeat(np.multiply(SFb, SFa), reps, axis=2), reps, axis=1)
# Create Q phase factor matrices:
PF = np.repeat(PF[..., np.newaxis, :], PF.shape[1], axis=1)
Q = np.multiply(np.repeat(np.repeat(PF, reps, axis=2), reps, axis=1), P)
Qn = get_Q_matrices(Q, phase.CSDS.maximum)
# Calculate the intensity:
sub_total = np.zeros(Q.shape, dtype=np.complex)
for n in range(phase.CSDS.minimum, phase.CSDS.maximum + 1):
progression_factor = 0
for m in range(n + 1, phase.CSDS.maximum + 1):
progression_factor += (m - n) * CSDS_arr[m]
sub_total += 2 * progression_factor * Qn[n - 1, ...]
CSDS_I = repeat_to_stl(np.identity(rank, dtype=np.complex) * CSDS_real_mean)
sub_total = (CSDS_I + sub_total)
sub_total = mmult(mmult(F, W), sub_total)
intensity = np.real(np.trace(sub_total, axis1=2, axis2=1))
return intensity * abs_scale
def get_Q_matrices(Q, CSDS_max):
Qn = np.zeros((CSDS_max + 1, ) + Q.shape, dtype=complex)
Qn[0, ...] = np.copy(Q)
for n in range(1, CSDS_max + 1):
Qn[n, ...] = mmult(Qn[n - 1, ...], Q)
return Qn
def _get_diffracted_intensity(range_theta, range_stl, phase):
assert phase.type == "Phase", "Must be Phase!"
# Check probability model, if invalid return zeros instead of the actual pattern:
if not phase.valid_probs:
logger.debug(
"- calc: get_diffracted_intensity reports: 'Invalid probability found!'"
)
return np.zeros_like(range_stl)
else:
# Calculate CSDS distribution
CSDS_arr, CSDS_real_mean = calculate_distribution(phase.CSDS)
# Get absolute scale
abs_scale = get_absolute_scale(phase.components, CSDS_real_mean,
phase.W)
# Create a helper function to 'expand' certain arrays, for
# results which are independent of the 2-theta range
stl_dim = range_stl.shape[0]
repeat_to_stl = lambda arr: np.repeat(
arr[np.newaxis, ...], stl_dim, axis=0)
# Repeat junction probabilities & weight fractions
W = repeat_to_stl(phase.W).astype(np.complex_)
P = repeat_to_stl(phase.P).astype(np.complex_)
# Repeat & get SFa and SFb (transpose conjugate) structure factor matrices:
SF, PF = get_structure_factors(range_stl, phase.G, phase.components)
SFa = np.repeat(SF[..., np.newaxis, :], SF.shape[1], axis=1)
SFb = np.transpose(np.conjugate(SFa), axes=(0, 2, 1))
# Calculate the repetition factor for R+ probabilities:
rank = P.shape[1]
reps = rank / phase.G
# Calculate the structure factor matrix:
F = np.repeat(np.repeat(np.multiply(SFb, SFa), reps, axis=2),
reps,
axis=1)
# Create Q phase factor matrices:
PF = np.repeat(PF[..., np.newaxis, :], PF.shape[1], axis=1)
Q = np.multiply(np.repeat(np.repeat(PF, reps, axis=2), reps, axis=1),
P)
Qn = get_Q_matrices(Q, phase.CSDS.maximum)
# Calculate the intensity:
sub_total = np.zeros(Q.shape, dtype=np.complex)
for n in range(phase.CSDS.minimum, phase.CSDS.maximum + 1):
progression_factor = 0
for m in range(n + 1, phase.CSDS.maximum + 1):
progression_factor += (m - n) * CSDS_arr[m]
sub_total += 2 * progression_factor * Qn[n - 1, ...]
CSDS_I = repeat_to_stl(
np.identity(rank, dtype=np.complex) * CSDS_real_mean)
sub_total = (CSDS_I + sub_total)
sub_total = mmult(mmult(F, W), sub_total)
intensity = np.real(np.trace(sub_total, axis1=2, axis2=1))
return intensity * abs_scale
def get_Q_matrices(Q, CSDS_max):
Qn = np.zeros((CSDS_max + 1,) + Q.shape, dtype=complex)
Qn[0, ...] = np.copy(Q)
for n in range(1, CSDS_max + 1):
Qn[n, ...] = mmult(Qn[n - 1, ...], Q)
return Qn