[d1fe925] | 1 | """ |
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| 2 | SAS distributions for polydispersity. |
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| 3 | """ |
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| 4 | # TODO: include dispersion docs with the disperser models |
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| 5 | from math import sqrt |
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| 6 | import numpy as np |
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| 7 | from scipy.special import gammaln |
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| 8 | |
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| 9 | class Dispersion(object): |
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| 10 | """ |
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| 11 | Base dispersion object. |
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| 12 | |
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| 13 | Subclasses should define *_weights(center, sigma, lb, ub)* |
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| 14 | which returns the x points and their corresponding weights. |
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| 15 | """ |
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| 16 | type = "base disperser" |
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| 17 | default = dict(npts=35, width=0, nsigmas=3) |
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| 18 | def __init__(self, npts=None, width=None, nsigmas=None): |
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| 19 | self.npts = self.default['npts'] if npts is None else npts |
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| 20 | self.width = self.default['width'] if width is None else width |
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| 21 | self.nsigmas = self.default['nsigmas'] if nsigmas is None else nsigmas |
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| 22 | |
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| 23 | def get_pars(self): |
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| 24 | pars = {'type': self.type} |
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| 25 | pars.update(self.__dict__) |
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| 26 | return pars |
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| 27 | |
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| 28 | # pylint: disable=no-self-use |
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| 29 | def set_weights(self, values, weights): |
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| 30 | raise RuntimeError("set_weights is only available for ArrayDispersion") |
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| 31 | |
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| 32 | def get_weights(self, center, lb, ub, relative): |
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| 33 | """ |
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| 34 | Return the weights for the distribution. |
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| 35 | |
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| 36 | *center* is the center of the distribution |
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| 37 | |
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| 38 | *lb*,*ub* are the min and max allowed values |
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| 39 | |
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| 40 | *relative* is True if the distribution width is proportional to the |
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| 41 | center value instead of absolute. For polydispersity use relative. |
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| 42 | For orientation parameters use absolute. |
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| 43 | """ |
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| 44 | sigma = self.width * center if relative else self.width |
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| 45 | if sigma == 0 or self.npts < 2: |
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| 46 | if lb <= center <= ub: |
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| 47 | return np.array([center], 'd'), np.array([1.], 'd') |
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| 48 | else: |
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| 49 | return np.array([], 'd'), np.array([], 'd') |
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| 50 | return self._weights(center, sigma, lb, ub) |
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| 51 | |
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| 52 | def _weights(self, center, sigma, lb, ub): |
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| 53 | """actual work of computing the weights""" |
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| 54 | raise NotImplementedError |
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| 55 | |
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| 56 | def _linspace(self, center, sigma, lb, ub): |
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| 57 | """helper function to provide linear spaced weight points within range""" |
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| 58 | npts, nsigmas = self.npts, self.nsigmas |
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| 59 | x = center + np.linspace(-nsigmas*sigma, +nsigmas*sigma, npts) |
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| 60 | x = x[(x >= lb) & (x <= ub)] |
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| 61 | return x |
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| 62 | |
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| 63 | |
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| 64 | class GaussianDispersion(Dispersion): |
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| 65 | type = "gaussian" |
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| 66 | default = dict(npts=35, width=0, nsigmas=3) |
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| 67 | def _weights(self, center, sigma, lb, ub): |
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| 68 | x = self._linspace(center, sigma, lb, ub) |
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| 69 | px = np.exp((x-center)**2 / (-2.0 * sigma * sigma)) |
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| 70 | return x, px |
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| 71 | |
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| 72 | |
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| 73 | class RectangleDispersion(Dispersion): |
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| 74 | type = "rectangle" |
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| 75 | default = dict(npts=35, width=0, nsigmas=1.70325) |
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| 76 | def _weights(self, center, sigma, lb, ub): |
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| 77 | x = self._linspace(center, sigma*sqrt(3.0), lb, ub) |
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| 78 | px = np.ones_like(x) |
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| 79 | return x, px |
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| 80 | |
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| 81 | |
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| 82 | class LogNormalDispersion(Dispersion): |
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| 83 | type = "lognormal" |
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| 84 | default = dict(npts=80, width=0, nsigmas=8) |
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| 85 | def _weights(self, center, sigma, lb, ub): |
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| 86 | x = self._linspace(center, sigma, max(lb,1e-8), max(ub,1e-8)) |
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| 87 | px = np.exp(-0.5*(np.log(x)-center)**2)/sigma**2/(x*sigma) |
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| 88 | return x, px |
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| 89 | |
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| 90 | |
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| 91 | class SchulzDispersion(Dispersion): |
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| 92 | type = "schulz" |
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| 93 | default = dict(npts=80, width=0, nsigmas=8) |
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| 94 | def _weights(self, center, sigma, lb, ub): |
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| 95 | x = self._linspace(center, sigma, max(lb,1e-8), max(ub,1e-8)) |
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| 96 | R= x/center |
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| 97 | z = (center/sigma)**2 |
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| 98 | arg = z*np.log(z) + (z-1)*np.log(R) - R*z - np.log(center) - gammaln(z) |
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| 99 | px = np.exp(arg) |
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| 100 | return x, px |
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| 101 | |
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| 102 | |
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| 103 | class ArrayDispersion(Dispersion): |
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| 104 | type = "array" |
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| 105 | default = dict(npts=35, width=0, nsigmas=1) |
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| 106 | def __init__(self, npts=None, width=None, nsigmas=None): |
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| 107 | Dispersion.__init__(self, npts, width, nsigmas) |
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| 108 | self.values = np.array([0.], 'd') |
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| 109 | self.weights = np.array([1.], 'd') |
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| 110 | |
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| 111 | def set_weights(self, values, weights): |
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| 112 | self.values = np.ascontiguousarray(values, 'd') |
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| 113 | self.weights = np.ascontiguousarray(weights, 'd') |
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| 114 | self.npts = len(values) |
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| 115 | |
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| 116 | def _weights(self, center, sigma, lb, ub): |
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| 117 | # TODO: interpolate into the array dispersion using npts |
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| 118 | x = center + self.values*sigma |
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| 119 | idx = (x>=lb)&(x<=ub) |
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| 120 | x = x[idx] |
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| 121 | px = self.weights[idx] |
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| 122 | return x, px |
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| 123 | |
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| 124 | |
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| 125 | # dispersion name -> disperser lookup table. |
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| 126 | models = dict((d.type,d) for d in ( |
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| 127 | GaussianDispersion, RectangleDispersion, |
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| 128 | ArrayDispersion, SchulzDispersion, LogNormalDispersion |
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| 129 | )) |
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| 130 | |
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| 131 | |
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| 132 | def get_weights(disperser, n, width, nsigmas, value, limits, relative): |
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| 133 | """ |
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| 134 | Return the set of values and weights for a polydisperse parameter. |
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| 135 | |
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| 136 | *disperser* is the name of the disperser. |
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| 137 | |
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| 138 | *n* is the number of points in the weight vector. |
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| 139 | |
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| 140 | *width* is the width of the disperser distribution. |
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| 141 | |
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| 142 | *nsigmas* is the number of sigmas to span for the dispersion convolution. |
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| 143 | |
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| 144 | *value* is the value of the parameter in the model. |
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| 145 | |
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| 146 | *limits* is [lb, ub], the lower and upper bound of the weight value. |
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| 147 | |
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| 148 | *relative* is true if *width* is defined in proportion to the value |
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| 149 | of the parameter, and false if it is an absolute width. |
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| 150 | |
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| 151 | Returns *(value,weight)*, where *value* and *weight* are vectors. |
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| 152 | """ |
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| 153 | cls = models[disperser] |
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| 154 | obj = cls(n, width, nsigmas) |
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| 155 | v,w = obj.get_weights(value, limits[0], limits[1], relative) |
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| 156 | return v,w |
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| 157 | |
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| 158 | # Hack to allow sasview dispersion objects to interoperate with sasmodels |
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| 159 | dispersers = dict((v.__name__,k) for k,v in models.items()) |
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| 160 | dispersers['DispersionModel'] = RectangleDispersion.type |
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| 161 | |
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