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import numpy as np
from copy import deepcopy
from dynasor.logging_tools import logger
from dynasor.sample import Sample
from numpy.typing import NDArray
from scipy.stats import norm
def get_spherically_averaged_sample_smearing(
sample: Sample, q_norms: NDArray[float], q_width: float) -> Sample:
r"""
Compute a spherical average over q-points for all the correlation functions in :attr:`sample`.
In the gaussian average method each q-point contributes to the function value at
given :math:`\vec{q}` with a weight determined by a gaussian function. For example
.. math::
F(q) = \sum_i w(\boldsymbol{q}_i, q) F(\boldsymbol{q}_i)
where
.. math::
w(\boldsymbol{q}_i, q) \propto \exp{\left [ -\frac{1}{2} \left ( \frac{|\boldsymbol{q}_i|
- q}{q_{width}} \right)^2 \right ]}
and
.. math::
\sum_i w(\boldsymbol{q}_i, q) = 1.0
This corresponds to a gaussian smearing or convolution.
The input parameters are :attr:`q_norms`, setting to the values of :math:`|\vec{q}|`,
for which the function is evaluated and :attr:`q_width` specifying the
standard deviation of the gaussian smearing.
Parameters
----------
sample
Input sample.
q_norms
Values of :math:`|\vec{q}|` at which to evaluate the correlation functions.
q_width
Standard deviation of the gaussian smearing.
"""
if not isinstance(sample, Sample):
raise ValueError('Input sample is not a Sample object.')
# get q-points
q_points = sample.q_points
if q_points.shape[1] != 3:
raise ValueError('q-points array has the wrong shape.')
# setup new input dicts for new Sample, remove q_points, add q_norms
meta_data = deepcopy(sample.meta_data)
data_dict = dict()
for key in sample.dimensions:
if key == 'q_points':
continue
data_dict[key] = sample[key]
for key in sample.available_correlation_functions:
Z = getattr(sample, key)
averaged_data = _get_gaussian_average(q_points, Z, q_norms, q_width)
data_dict[key] = averaged_data
data_dict['q_norms'] = q_norms
return sample.__class__(data_dict, **meta_data)
def get_spherically_averaged_sample_binned(sample: Sample, num_q_bins: int) -> Sample:
r"""
Compute a spherical average over q-points for all the correlation functions in `:attr:`sample`.
Here, a q-binning method is used to conduct the spherical average, meaning all q-points are
placed into spherical bins (shells).
The corresponding function is calculated as the average of all q-points in a bin.
If a q-bin does not contain any q-points, then its value is set to ``np.nan``.
The q_min and q_max are determined from min/max of ``|q_points|``, and will determine
the q-bin range.
These will be set as bin-centers for the first and last bins repsectivley.
The input parameter is the number of q-bins to use :attr:`num_q_bins`.
Parameters
----------
sample
Input sample
num_q_bins
number of q-bins to use
"""
if not isinstance(sample, Sample):
raise ValueError('input sample is not a Sample object.')
# get q-points
q_points = sample.q_points
if q_points.shape[1] != 3:
raise ValueError('q-points array has wrong shape.')
# setup new input dicts for new Sample, remove q_points, add q_norms
meta_data = deepcopy(sample.meta_data)
data_dict = dict()
for key in sample.dimensions:
if key == 'q_points':
continue
data_dict[key] = sample[key]
# compute spherical average for each correlation function
for key in sample.available_correlation_functions:
Z = getattr(sample, key)
q_bincenters, bin_counts, averaged_data = _get_bin_average(q_points, Z, num_q_bins)
data_dict[key] = averaged_data
data_dict['q_norms'] = q_bincenters
return sample.__class__(data_dict, **meta_data)
def _get_gaussian_average(
q_points: np.ndarray, Z: np.ndarray, q_norms: np.ndarray, q_width: float):
q_norms_sample = np.linalg.norm(q_points, axis=1)
Z_average = []
for q in q_norms:
weights = _gaussian(q_norms_sample, x0=q, sigma=q_width).reshape(-1, 1)
norm = np.sum(weights)
if norm != 0:
weights = weights / norm
Z_average.append(np.sum(weights * Z, axis=0))
return np.array(Z_average)
def _gaussian(x, x0, sigma):
dist = norm(loc=x0, scale=sigma)
return dist.pdf(x)
def _get_bin_average(q_points: np.ndarray, data: np.ndarray, num_q_bins: int):
"""
Compute a spherical average over q-points for the data using q-bins.
If a q-bin does not contain any q-points, then a np.nan is inserted.
The q_min and q_min are determined from min/max of |q_points|, and will determine the bin-range.
These will set as bin-centers for the first and last bins repsectivley.
Parameters
----------
q_points
array of q-points shape ``(Nq, 3)``
data
data-array of shape ``(Nq, N)``, shape cannot be ``(Nq, )``
num_q_bins
number of radial q-point bins to use
Returns
-------
q
array of |q| bins of shape ``(num_q_bins, )``
data_averaged
averaged data-array of shape ``
"""
N_qpoints = q_points.shape[0]
N_t = data.shape[1]
assert q_points.shape[1] == 3
assert data.shape[0] == N_qpoints
# q-norms
q_norms = np.linalg.norm(q_points, axis=1)
assert q_norms.shape == (N_qpoints,)
# setup bins
q_max = np.max(q_norms)
q_min = np.min(q_norms)
delta_x = (q_max - q_min) / (num_q_bins - 1)
q_range = (q_min - delta_x / 2, q_max + delta_x / 2)
bin_counts, edges = np.histogram(q_norms, bins=num_q_bins, range=q_range)
q_bincenters = 0.5 * (edges[1:] + edges[:-1])
# calculate average for each bin
averaged_data = np.zeros((num_q_bins, N_t))
for bin_index in range(num_q_bins):
# find q-indices that belong to this bin
bin_min = edges[bin_index]
bin_max = edges[bin_index + 1]
bin_count = bin_counts[bin_index]
q_indices = np.where(np.logical_and(q_norms >= bin_min, q_norms < bin_max))[0]
assert len(q_indices) == bin_count
logger.debug(f'bin {bin_index} contains {bin_count} q-points')
# average over q-indices, if no indices then np.nan
if bin_count == 0:
logger.warning(f'No q-points for bin {bin_index}')
data_bin = np.array([np.nan for _ in range(N_t)])
else:
data_bin = data[q_indices, :].mean(axis=0)
averaged_data[bin_index, :] = data_bin
return q_bincenters, bin_counts, averaged_data
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