Coverage for local_installation/dynasor/post_processing/spherical_average.py: 99%
82 statements
« prev ^ index » next coverage.py v7.3.2, created at 2023-11-30 21:04 +0000
1import numpy as np
3from copy import deepcopy
4from dynasor.logging_tools import logger
5from dynasor.sample import Sample
6from numpy.typing import NDArray
7from scipy.stats import norm
10def get_spherically_averaged_sample_smearing(
11 sample: Sample, q_norms: NDArray[float], q_width: float) -> Sample:
12 r"""
13 Compute a spherical average over q-points for all the correlation functions in :attr:`sample`.
15 In the gaussian average method each q-point contributes to the function value at
16 given :math:`\vec{q}` with a weight determined by a gaussian function. For example
18 .. math::
20 F(q) = \sum_i w(\boldsymbol{q}_i, q) F(\boldsymbol{q}_i)
22 where
24 .. math::
26 w(\boldsymbol{q}_i, q) \propto \exp{\left [ -\frac{1}{2} \left ( \frac{|\boldsymbol{q}_i|
27 - q}{q_{width}} \right)^2 \right ]}
29 and
31 .. math::
33 \sum_i w(\boldsymbol{q}_i, q) = 1.0
35 This corresponds to a gaussian smearing or convolution.
36 The input parameters are :attr:`q_norms`, setting to the values of :math:`|\vec{q}|`,
37 for which the function is evaluated and :attr:`q_width` specifying the
38 standard deviation of the gaussian smearing.
40 Parameters
41 ----------
42 sample
43 Input sample.
44 q_norms
45 Values of :math:`|\vec{q}|` at which to evaluate the correlation functions.
46 q_width
47 Standard deviation of the gaussian smearing.
48 """
49 if not isinstance(sample, Sample):
50 raise ValueError('Input sample is not a Sample object.')
52 # get q-points
53 q_points = sample.q_points
54 if q_points.shape[1] != 3:
55 raise ValueError('q-points array has the wrong shape.')
57 # setup new input dicts for new Sample, remove q_points, add q_norms
58 meta_data = deepcopy(sample.meta_data)
59 data_dict = dict()
60 for key in sample.dimensions:
61 if key == 'q_points':
62 continue
63 data_dict[key] = sample[key]
65 for key in sample.available_correlation_functions:
66 Z = getattr(sample, key)
67 averaged_data = _get_gaussian_average(q_points, Z, q_norms, q_width)
68 data_dict[key] = averaged_data
69 data_dict['q_norms'] = q_norms
71 return sample.__class__(data_dict, **meta_data)
74def get_spherically_averaged_sample_binned(sample: Sample, num_q_bins: int) -> Sample:
75 r"""
76 Compute a spherical average over q-points for all the correlation functions in `:attr:`sample`.
78 Here, a q-binning method is used to conduct the spherical average, meaning all q-points are
79 placed into spherical bins (shells).
80 The corresponding function is calculated as the average of all q-points in a bin.
81 If a q-bin does not contain any q-points, then its value is set to ``np.nan``.
82 The q_min and q_max are determined from min/max of ``|q_points|``, and will determine
83 the q-bin range.
84 These will be set as bin-centers for the first and last bins repsectivley.
85 The input parameter is the number of q-bins to use :attr:`num_q_bins`.
87 Parameters
88 ----------
89 sample
90 Input sample
91 num_q_bins
92 number of q-bins to use
93 """
95 if not isinstance(sample, Sample):
96 raise ValueError('input sample is not a Sample object.')
98 # get q-points
99 q_points = sample.q_points
100 if q_points.shape[1] != 3:
101 raise ValueError('q-points array has wrong shape.')
103 # setup new input dicts for new Sample, remove q_points, add q_norms
104 meta_data = deepcopy(sample.meta_data)
105 data_dict = dict()
106 for key in sample.dimensions:
107 if key == 'q_points':
108 continue
109 data_dict[key] = sample[key]
111 # compute spherical average for each correlation function
112 for key in sample.available_correlation_functions:
113 Z = getattr(sample, key)
114 q_bincenters, bin_counts, averaged_data = _get_bin_average(q_points, Z, num_q_bins)
115 data_dict[key] = averaged_data
116 data_dict['q_norms'] = q_bincenters
118 return sample.__class__(data_dict, **meta_data)
121def _get_gaussian_average(
122 q_points: np.ndarray, Z: np.ndarray, q_norms: np.ndarray, q_width: float):
124 q_norms_sample = np.linalg.norm(q_points, axis=1)
125 Z_average = []
126 for q in q_norms:
127 weights = _gaussian(q_norms_sample, x0=q, sigma=q_width).reshape(-1, 1)
128 norm = np.sum(weights)
129 if norm != 0: 129 ↛ 131line 129 didn't jump to line 131, because the condition on line 129 was never false
130 weights = weights / norm
131 Z_average.append(np.sum(weights * Z))
132 return np.array(Z_average)
135def _gaussian(x, x0, sigma):
136 dist = norm(loc=x0, scale=sigma)
137 return dist.pdf(x)
140def _get_bin_average(q_points: np.ndarray, data: np.ndarray, num_q_bins: int):
141 """
142 Compute a spherical average over q-points for the data using q-bins.
144 If a q-bin does not contain any q-points, then a np.nan is inserted.
146 The q_min and q_min are determined from min/max of |q_points|, and will determine the bin-range.
147 These will set as bin-centers for the first and last bins repsectivley.
149 Parameters
150 ----------
151 q_points
152 array of q-points shape ``(Nq, 3)``
153 data
154 data-array of shape ``(Nq, N)``, shape cannot be ``(Nq, )``
155 num_q_bins
156 number of radial q-point bins to use
158 Returns
159 -------
160 q
161 array of |q| bins of shape ``(num_q_bins, )``
162 data_averaged
163 averaged data-array of shape ``
164 """
165 N_qpoints = q_points.shape[0]
166 N_t = data.shape[1]
167 assert q_points.shape[1] == 3
168 assert data.shape[0] == N_qpoints
170 # q-norms
171 q_norms = np.linalg.norm(q_points, axis=1)
172 assert q_norms.shape == (N_qpoints,)
174 # setup bins
175 q_max = np.max(q_norms)
176 q_min = np.min(q_norms)
177 delta_x = (q_max - q_min) / (num_q_bins - 1)
178 q_range = (q_min - delta_x / 2, q_max + delta_x / 2)
179 bin_counts, edges = np.histogram(q_norms, bins=num_q_bins, range=q_range)
180 q_bincenters = 0.5 * (edges[1:] + edges[:-1])
182 # calculate average for each bin
183 averaged_data = np.zeros((num_q_bins, N_t))
184 for bin_index in range(num_q_bins):
185 # find q-indices that belong to this bin
186 bin_min = edges[bin_index]
187 bin_max = edges[bin_index + 1]
188 bin_count = bin_counts[bin_index]
189 q_indices = np.where(np.logical_and(q_norms >= bin_min, q_norms < bin_max))[0]
190 assert len(q_indices) == bin_count
191 logger.debug(f'bin {bin_index} contains {bin_count} q-points')
193 # average over q-indices, if no indices then np.nan
194 if bin_count == 0:
195 logger.warning(f'No q-points for bin {bin_index}')
196 data_bin = np.array([np.nan for _ in range(N_t)])
197 else:
198 data_bin = data[q_indices, :].mean(axis=0)
199 averaged_data[bin_index, :] = data_bin
201 return q_bincenters, bin_counts, averaged_data