34. Distribution functions

sasmodels.weights

SAS distributions for polydispersity.

class sasmodels.weights.ArrayDispersion(npts=None, width=None, nsigmas=None)

Bases: sasmodels.weights.Dispersion

Empirical dispersion curve.

Use set_weights() to set \(w = f(x)\).

get_pars()

Return the parameters to the disperser as a dictionary.

get_weights(center, lb, ub, relative)

Return the weights for the distribution.

center is the center of the distribution

lb, ub are the min and max allowed values

relative is True if the distribution width is proportional to the center value instead of absolute. For polydispersity use relative. For orientation parameters use absolute.

set_weights(values, weights)

Set the weights for the given x values.

default = {'npts': 35, 'nsigmas': 1, 'width': 0}

type = 'array'

class sasmodels.weights.BoltzmannDispersion(npts=None, width=None, nsigmas=None)

Bases: sasmodels.weights.Dispersion

Boltzmann dispersion, with \(\sigma=k T/E\).

\[w = \exp\left( -|x - c|/\sigma\right)\]

get_pars()

Return the parameters to the disperser as a dictionary.

get_weights(center, lb, ub, relative)

Return the weights for the distribution.

center is the center of the distribution

lb, ub are the min and max allowed values

relative is True if the distribution width is proportional to the center value instead of absolute. For polydispersity use relative. For orientation parameters use absolute.

set_weights(values, weights)

Set the weights on the disperser if it is ArrayDispersion.

default = {'npts': 35, 'nsigmas': 3, 'width': 0}

type = 'boltzmann'

class sasmodels.weights.Dispersion(npts=None, width=None, nsigmas=None)

Bases: object

Base dispersion object.

Subclasses should define _weights(center, sigma, lb, ub) which returns the x points and their corresponding weights.

get_pars()

Return the parameters to the disperser as a dictionary.

get_weights(center, lb, ub, relative)

Return the weights for the distribution.

center is the center of the distribution

lb, ub are the min and max allowed values

relative is True if the distribution width is proportional to the center value instead of absolute. For polydispersity use relative. For orientation parameters use absolute.

set_weights(values, weights)

Set the weights on the disperser if it is ArrayDispersion.

default = {'npts': 35, 'nsigmas': 3, 'width': 0}

type = 'base disperser'

class sasmodels.weights.GaussianDispersion(npts=None, width=None, nsigmas=None)

Bases: sasmodels.weights.Dispersion

Gaussian dispersion, with 1-\(\sigma\) width.

\[w = \exp\left(-\tfrac12 (x - c)^2/\sigma^2\right)\]

get_pars()

Return the parameters to the disperser as a dictionary.

get_weights(center, lb, ub, relative)

Return the weights for the distribution.

center is the center of the distribution

lb, ub are the min and max allowed values

relative is True if the distribution width is proportional to the center value instead of absolute. For polydispersity use relative. For orientation parameters use absolute.

set_weights(values, weights)

Set the weights on the disperser if it is ArrayDispersion.

default = {'npts': 35, 'nsigmas': 3, 'width': 0}

type = 'gaussian'

class sasmodels.weights.LogNormalDispersion(npts=None, width=None, nsigmas=None)

Bases: sasmodels.weights.Dispersion

log Gaussian dispersion, with 1-\(\sigma\) width.

\[w = \frac{\exp\left(-\tfrac12 (\ln x - c)^2/\sigma^2\right)}{x\sigma}\]

get_pars()

Return the parameters to the disperser as a dictionary.

get_weights(center, lb, ub, relative)

Return the weights for the distribution.

center is the center of the distribution

lb, ub are the min and max allowed values

relative is True if the distribution width is proportional to the center value instead of absolute. For polydispersity use relative. For orientation parameters use absolute.

set_weights(values, weights)

Set the weights on the disperser if it is ArrayDispersion.

default = {'npts': 80, 'nsigmas': 8, 'width': 0}

type = 'lognormal'

class sasmodels.weights.RectangleDispersion(npts=None, width=None, nsigmas=None)

Bases: sasmodels.weights.Dispersion

Uniform dispersion, with width \(\sqrt{3}\sigma\).

\[w = 1\]

get_pars()

Return the parameters to the disperser as a dictionary.

get_weights(center, lb, ub, relative)

Return the weights for the distribution.

center is the center of the distribution

lb, ub are the min and max allowed values

relative is True if the distribution width is proportional to the center value instead of absolute. For polydispersity use relative. For orientation parameters use absolute.

set_weights(values, weights)

Set the weights on the disperser if it is ArrayDispersion.

default = {'npts': 35, 'nsigmas': 1.73205, 'width': 0}

type = 'rectangle'

class sasmodels.weights.SchulzDispersion(npts=None, width=None, nsigmas=None)

Bases: sasmodels.weights.Dispersion

Schultz dispersion, with 1-\(\sigma\) width.

\[w = \frac{z^z\,R^{z-1}}{e^{Rz}\,c \Gamma(z)}\]

where \(c\) is the center of the distribution, \(R = x/c\) and \(z=(c/\sigma)^2\).

This is evaluated using logarithms as

\[w = \exp\left(z \ln z + (z-1)\ln R - Rz - \ln c - \ln \Gamma(z) \right)\]

get_pars()

Return the parameters to the disperser as a dictionary.

get_weights(center, lb, ub, relative)

Return the weights for the distribution.

center is the center of the distribution

lb, ub are the min and max allowed values

relative is True if the distribution width is proportional to the center value instead of absolute. For polydispersity use relative. For orientation parameters use absolute.

set_weights(values, weights)

Set the weights on the disperser if it is ArrayDispersion.

default = {'npts': 80, 'nsigmas': 8, 'width': 0}

type = 'schulz'

class sasmodels.weights.UniformDispersion(npts=None, width=None, nsigmas=None)

Bases: sasmodels.weights.Dispersion

Uniform dispersion, with width \(\sigma\).

\[w = 1\]

get_pars()

Return the parameters to the disperser as a dictionary.

get_weights(center, lb, ub, relative)

Return the weights for the distribution.

center is the center of the distribution

lb, ub are the min and max allowed values

relative is True if the distribution width is proportional to the center value instead of absolute. For polydispersity use relative. For orientation parameters use absolute.

set_weights(values, weights)

Set the weights on the disperser if it is ArrayDispersion.

default = {'npts': 35, 'nsigmas': None, 'width': 0}

type = 'uniform'

sasmodels.weights.get_weights(disperser, n, width, nsigmas, value, limits, relative)

Return the set of values and weights for a polydisperse parameter.

disperser is the name of the disperser.

n is the number of points in the weight vector.

width is the width of the disperser distribution.

nsigmas is the number of sigmas to span for the dispersion convolution.

value is the value of the parameter in the model.

limits is [lb, ub], the lower and upper bound on the possible values.

relative is true if width is defined in proportion to the value of the parameter, and false if it is an absolute width.

Returns (value, weight), where value and weight are vectors.

sasmodels.weights.load_weights(pattern: Optional[str] = None) → None

Load dispersion distributions matching the given glob pattern

sasmodels.weights.plot_weights(model_info: sasmodels.modelinfo.ModelInfo, mesh: List[Tuple[float, numpy.ndarray, numpy.ndarray]]) → None

Plot the weights returned by get_weights().

model_info defines model parameters, etc.

mesh is a list of tuples containing (value, dispersity, weights) for each parameter, where (dispersity, weights) pairs are the distributions to be plotted.