source: sasmodels/sasmodels/weights.py @ 3c24ccd

core_shell_microgelsmagnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since 3c24ccd was 3c24ccd, checked in by Paul Kienzle <pkienzle@…>, 6 years ago

add -weights option to sascomp to show dispersity distribution

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1"""
2SAS distributions for polydispersity.
3"""
4# TODO: include dispersion docs with the disperser models
5from __future__ import division, print_function
6
7from math import sqrt  # type: ignore
8from collections import OrderedDict
9
10import numpy as np  # type: ignore
11from scipy.special import gammaln  # type: ignore
12
13# TODO: include dispersion docs with the disperser models
14
15class Dispersion(object):
16    """
17    Base dispersion object.
18
19    Subclasses should define *_weights(center, sigma, lb, ub)*
20    which returns the x points and their corresponding weights.
21    """
22    type = "base disperser"
23    default = dict(npts=35, width=0, nsigmas=3)
24    def __init__(self, npts=None, width=None, nsigmas=None):
25        self.npts = self.default['npts'] if npts is None else npts
26        self.width = self.default['width'] if width is None else width
27        self.nsigmas = self.default['nsigmas'] if nsigmas is None else nsigmas
28
29    def get_pars(self):
30        """
31        Return the parameters to the disperser as a dictionary.
32        """
33        pars = {'type': self.type}
34        pars.update(self.__dict__)
35        return pars
36
37    # pylint: disable=no-self-use
38    def set_weights(self, values, weights):
39        """
40        Set the weights on the disperser if it is :class:`ArrayDispersion`.
41        """
42        raise RuntimeError("set_weights is only available for ArrayDispersion")
43
44    def get_weights(self, center, lb, ub, relative):
45        """
46        Return the weights for the distribution.
47
48        *center* is the center of the distribution
49
50        *lb*, *ub* are the min and max allowed values
51
52        *relative* is True if the distribution width is proportional to the
53        center value instead of absolute.  For polydispersity use relative.
54        For orientation parameters use absolute.
55        """
56        sigma = self.width * center if relative else self.width
57        if not relative:
58            # For orientation, the jitter is relative to 0 not the angle
59            center = 0
60            pass
61        if sigma == 0 or self.npts < 2:
62            if lb <= center <= ub:
63                return np.array([center], 'd'), np.array([1.], 'd')
64            else:
65                return np.array([], 'd'), np.array([], 'd')
66        x, px = self._weights(center, sigma, lb, ub)
67        return x, px
68
69    def _weights(self, center, sigma, lb, ub):
70        """actual work of computing the weights"""
71        raise NotImplementedError
72
73    def _linspace(self, center, sigma, lb, ub):
74        """helper function to provide linear spaced weight points within range"""
75        npts, nsigmas = self.npts, self.nsigmas
76        x = center + np.linspace(-nsigmas*sigma, +nsigmas*sigma, npts)
77        x = x[(x >= lb) & (x <= ub)]
78        return x
79
80
81class GaussianDispersion(Dispersion):
82    r"""
83    Gaussian dispersion, with 1-\ $\sigma$ width.
84
85    .. math::
86
87        w = \exp\left(-\tfrac12 (x - c)^2/\sigma^2\right)
88    """
89    type = "gaussian"
90    default = dict(npts=35, width=0, nsigmas=3)
91    def _weights(self, center, sigma, lb, ub):
92        # TODO: sample high probability regions more densely
93        # i.e., step uniformly in cumulative density rather than x value
94        # so weight = 1/Npts for all weights, but values are unevenly spaced
95        x = self._linspace(center, sigma, lb, ub)
96        px = np.exp((x-center)**2 / (-2.0 * sigma * sigma))
97        return x, px
98
99
100class RectangleDispersion(Dispersion):
101    r"""
102    Uniform dispersion, with width $\sqrt{3}\sigma$.
103
104    .. math::
105
106        w = 1
107    """
108    type = "rectangle"
109    default = dict(npts=35, width=0, nsigmas=1.70325)
110    def _weights(self, center, sigma, lb, ub):
111        x = self._linspace(center, sigma, lb, ub)
112        x = x[np.fabs(x-center) <= np.fabs(sigma)*sqrt(3.0)]
113        return x, np.ones_like(x)
114
115
116class LogNormalDispersion(Dispersion):
117    r"""
118    log Gaussian dispersion, with 1-\ $\sigma$ width.
119
120    .. math::
121
122        w = \frac{\exp\left(-\tfrac12 (\ln x - c)^2/\sigma^2\right)}{x\sigma}
123    """
124    type = "lognormal"
125    default = dict(npts=80, width=0, nsigmas=8)
126    def _weights(self, center, sigma, lb, ub):
127        x = self._linspace(center, sigma, max(lb, 1e-8), max(ub, 1e-8))
128        # sigma in the lognormal function is in ln(R) space, thus needs converting
129        sig = np.fabs(sigma/center)
130        px = np.exp(-0.5*((np.log(x)-np.log(center))/sig)**2)/(x*sig)
131        return x, px
132
133
134class SchulzDispersion(Dispersion):
135    r"""
136    Schultz dispersion, with 1-\ $\sigma$ width.
137
138    .. math::
139
140        w = \frac{z^z\,R^{z-1}}{e^{Rz}\,c \Gamma(z)}
141
142    where $c$ is the center of the distribution, $R = x/c$ and $z=(c/\sigma)^2$.
143
144    This is evaluated using logarithms as
145
146    .. math::
147
148        w = \exp\left(z \ln z + (z-1)\ln R - Rz - \ln c - \ln \Gamma(z) \right)
149    """
150    type = "schulz"
151    default = dict(npts=80, width=0, nsigmas=8)
152    def _weights(self, center, sigma, lb, ub):
153        x = self._linspace(center, sigma, max(lb, 1e-8), max(ub, 1e-8))
154        R = x/center
155        z = (center/sigma)**2
156        arg = z*np.log(z) + (z-1)*np.log(R) - R*z - np.log(center) - gammaln(z)
157        px = np.exp(arg)
158        return x, px
159
160
161class ArrayDispersion(Dispersion):
162    r"""
163    Empirical dispersion curve.
164
165    Use :meth:`set_weights` to set $w = f(x)$.
166    """
167    type = "array"
168    default = dict(npts=35, width=0, nsigmas=1)
169    def __init__(self, npts=None, width=None, nsigmas=None):
170        Dispersion.__init__(self, npts, width, nsigmas)
171        self.values = np.array([0.], 'd')
172        self.weights = np.array([1.], 'd')
173
174    def set_weights(self, values, weights):
175        """
176        Set the weights for the given x values.
177        """
178        self.values = np.ascontiguousarray(values, 'd')
179        self.weights = np.ascontiguousarray(weights, 'd')
180        self.npts = len(values)
181
182    def _weights(self, center, sigma, lb, ub):
183        # TODO: rebin the array dispersion using npts
184        # TODO: use a distribution that can be recentered and scaled
185        x = self.values
186        #x = center + self.values*sigma
187        idx = (x >= lb) & (x <= ub)
188        x = x[idx]
189        px = self.weights[idx]
190        return x, px
191
192
193# dispersion name -> disperser lookup table.
194# Maintain order since this is used by sasview GUI to order the options in
195# the dispersion type combobox.
196MODELS = OrderedDict((d.type, d) for d in (
197    RectangleDispersion,
198    ArrayDispersion,
199    LogNormalDispersion,
200    GaussianDispersion,
201    SchulzDispersion,
202))
203
204
205def get_weights(disperser, n, width, nsigmas, value, limits, relative):
206    """
207    Return the set of values and weights for a polydisperse parameter.
208
209    *disperser* is the name of the disperser.
210
211    *n* is the number of points in the weight vector.
212
213    *width* is the width of the disperser distribution.
214
215    *nsigmas* is the number of sigmas to span for the dispersion convolution.
216
217    *value* is the value of the parameter in the model.
218
219    *limits* is [lb, ub], the lower and upper bound on the possible values.
220
221    *relative* is true if *width* is defined in proportion to the value
222    of the parameter, and false if it is an absolute width.
223
224    Returns *(value, weight)*, where *value* and *weight* are vectors.
225    """
226    if disperser == "array":
227        raise NotImplementedError("Don't handle arrays through get_weights; use values and weights directly")
228    cls = MODELS[disperser]
229    obj = cls(n, width, nsigmas)
230    v, w = obj.get_weights(value, limits[0], limits[1], relative)
231    return v, w/np.sum(w)
232
233
234def plot_weights(model_info, mesh):
235    # type: (ModelInfo, List[Tuple[float, np.ndarray, np.ndarray]]) -> None
236    """
237    Plot the weights returned by :func:`get_weights`.
238
239    *model_info* defines model parameters, etc.
240
241    *mesh* is a list of tuples containing (*value*, *dispersity*, *weights*)
242    for each parameter, where (*dispersity*, *weights*) pairs are the
243    distributions to be plotted.
244    """
245    import pylab
246
247    if any(len(dispersity)>1 for value, dispersity, weights in mesh):
248        labels = [p.name for p in model_info.parameters.call_parameters]
249        #pylab.interactive(True)
250        pylab.figure()
251        for (v,x,w), s in zip(mesh, labels):
252            if len(x) > 1:
253                pylab.plot(x, w, '-o', label=s)
254        pylab.grid(True)
255        pylab.legend()
256        #pylab.show()
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