bet.sampling package¶

Submodules¶

bet.sampling.LpGeneralizedSamples module¶

This module provides methods to sample from Lp generalized normal, uniform, and beta distributions on the nD ball.

Adapted from natter.LpSphericallySymmetric.py https://github.com/fabiansinz/natter

bet.sampling.LpGeneralizedSamples.Lp_generalized_beta(dim, num, p=2, d=2, scale=1.0, loc=None)¶

Generate samples from an Lp generalized beta distribution. When p=d then this is simly the Lp generalized uniform distribution.

Parameters

p (float) – \(0 < p \leq \infty\), p for the lp norm where infinity is numpy.inf
d (float) – shape parameter
dim (int) – Dimension of the space
num (int) – Number of samples to generate
scale (float, int, or numpy.ndarray) – Radius to scale the samples by
loc (numpy.ndarray of shape (dim,)) – Location of the center of the samples

bet.sampling.LpGeneralizedSamples.Lp_generalized_normal(dim, num, p=2, scale=1.0, loc=None)¶

Generate samples from an Lp generalized normal distribution.

Parameters

p (float) – \(0 < p \leq \infty\), p for the lp norm where infinity is numpy.inf
dim (int) – Dimension of the space
num (int) – Number of samples to generate
scale (float, int, or numpy.ndarray) – Radius to scale the samples by
loc (numpy.ndarray of shape (dim,)) – Location of the center of the samples

bet.sampling.LpGeneralizedSamples.Lp_generalized_uniform(dim, num, p=2, scale=1.0, loc=None)¶

Generate samples from an Lp generalized uniform distribution.

Parameters

p (float) – \(0 < p \leq \infty\), p for the lp norm where infinity is numpy.inf
dim (int) – Dimension of the space
num (int) – Number of samples to generate
scale (float, int, or numpy.ndarray) – Radius to scale the samples by
loc (numpy.ndarray of shape (dim,)) – Location of the center of the samples

bet.sampling.basicSampling module¶

This module contains functions for sampling. We assume we are given access to a model, a parameter space, and a data space. The model is a map from the parameter space to the data space. We desire to build up a set of samples to solve an inverse problem thus giving information about the inverse mapping. Each sample consists for a parameter coordinate, data coordinate pairing. We assume the measure on both spaces is Lebesgue.

exception bet.sampling.basicSampling.bad_object¶

Bases: Exception

Exception for when the wrong type of object is used.

bet.sampling.basicSampling.lhs_sample_set(input_obj, num_samples, criterion, globalize=True)¶

Sampling algorithm for generating samples from a Latin hypercube in the domain present with input_obj (a default unit hypercube is used if no domain has been specified)

Parameters

input_obj (sample_set or numpy.ndarray of shape (dim, 2) or int) – sample_set object containing the dimension or domain to sample from, the domain to sample from, or the dimension
num_samples (int) – number of samples
criterion (str) – latin hypercube criterion see PyDOE <http://pythonhosted.org/pyDOE/randomized.html>
globalize (bool) – Whether or not to globalize local variables.

Return type

sample_set

Returns

sample_set

bet.sampling.basicSampling.random_sample_set(rv, input_obj, num_samples, globalize=True)¶

Create a sample set by sampling random variates from continuous distributions from scipy.stats.rv_continuous. See https://docs.scipy.org/doc/scipy/reference/stats.html.

rv can take multiple types of formats depending on type of distribution.

A string is used for the same distribution with default parameters in each dimension. ex. rv = ‘uniform’ or rv = ‘beta’

A list or tuple of length 2 is used for the same distribution with user-defined parameters in each dimension as a dictionary. ex. rv = [‘uniform’, {‘loc’:-2, ‘scale’:5}] or rv = [‘beta’, {‘a’: 2, ‘b’:5, ‘loc’:-2, ‘scale’:5}]

A list of length dim which entries of lists or tuples of length 2 is used for different distributions with user-defined parameters in each dimension as a dictionary. ex. rv = [[‘uniform’, {‘loc’:-2, ‘scale’:5}],

[‘beta’, {‘a’: 2, ‘b’:5, ‘loc’:-2, ‘scale’:5}]]

Parameters

rv (str, list, or tuple) – Type and parameters for continuous random variables.
input_obj (sample_set or int or numpy.ndarray) – sample_set object containing the dimension to sample from, or the dimension.
num_samples (int) – Number of samples
globalize (bool) – Whether or not to globalize vectors.

bet.sampling.basicSampling.regular_sample_set(input_obj, num_samples_per_dim=1)¶

Sampling algorithm for generating a regular grid of samples taken on the domain present with input_obj (a default unit hypercube is used if no domain has been specified)

Parameters

input_obj (sample_set or numpy.ndarray of shape (dim, 2) or int) – sample_set object containing the dimension or domain to sample from, the domain to sample from, or the dimension
num_samples_per_dim (ndarray of dimension (input_sample_set._dim,)) – number of samples per dimension

Return type

sample_set

Returns

sample_set object which contains input num_samples

bet.sampling.basicSampling.sample_from_updated(input_set, num_samples, globalize=True)¶

Create a new sample set from resampling from the updated probability measure of another sample set.

Parameters

input_set (sample_set or discretization) – Sample set or discretization containing updated probability measure from which to sample.
num_samples (int) – Number of new samples to create.
globalize – Whether or not to globalize objects.

:type bool :return: Sample set containing new samples :rtype: sample_set

class bet.sampling.basicSampling.sampler(lb_model, error_estimates=False, jacobians=False)¶

Bases: object

This class provides methods for sampling of parameter space to provide samples to be used by algorithms to solve inverse problems.

compute_QoI_and_create_discretization(input_sample_set=None, savefile=None, globalize=True)¶: Dummy function for compute_qoi_and_create_discretization.

compute_qoi_and_create_discretization(input_sample_set=None, savefile=None, globalize=True)¶

Samples the model at input_sample_set and saves the results.

Note: There are many ways to generate samples on a regular grid in Numpy and other Python packages. Instead of reimplementing them here we provide sampler that utilizes user specified samples.

Parameters

input_sample_set (sample_set with num_samples) – samples to evaluate the model at
savefile (string) – filename to save samples and data
globalize (bool) – Makes local variables global.

Return type

discretization

Returns

discretization object which contains input and output of length num_samples

copy()¶: Returns a copy of the sampler object.

create_random_discretization(rv, input_obj, savefile=None, num_samples=None, globalize=True)¶

Create a sample set by sampling random variates from continuous distributions from scipy.stats.rv_continuous. See https://docs.scipy.org/doc/scipy/reference/stats.html, and evaluate the model to calculate quantities of interest and make a discretization.

rv can take multiple types of formats depending on type of distribution.

A string is used for the same distribution with default parameters in each dimension. ex. rv = ‘uniform’ or rv = ‘beta’

A list or tuple of length 2 is used for the same distribution with user-defined parameters in each dimension as a dictionary. ex. rv = [‘uniform’, {‘loc’:-2, ‘scale’:5}] or rv = [‘beta’, {‘a’: 2, ‘b’:5, ‘loc’:-2, ‘scale’:5}]

A list of length dim which entries of lists or tuples of length 2 is used for different distributions with user-defined parameters in each dimension as a dictionary. ex. rv = [[‘uniform’, {‘loc’:-2, ‘scale’:5}],

[‘beta’, {‘a’: 2, ‘b’:5, ‘loc’:-2, ‘scale’:5}]]

Parameters

rv (str, list, or tuple) – Type and parameters for continuous random variables.
input_obj (sample_set or int) – sample_set object containing the dimension to sample from, or the dimension.
savefile (string) – filename to save discretization
num_samples (int) – Number of samples
globalize (bool) – Whether or not to globalize vectors.

Return type

discretization

Returns

discretization object which contains input and output sample sets with num_samples total samples

lhs_sample_set(input_obj, num_samples, criterion, globalize=True)¶

Sampling algorithm for generating samples from a Latin hypercube in the domain present with input_obj (a default unit hypercube is used if no domain has been specified)

Parameters

input_obj (sample_set or numpy.ndarray of shape (dim, 2) or int) – sample_set object containing the dimension or domain to sample from, the domain to sample from, or the dimension
num_samples (int) – number of samples
criterion (str) – latin hypercube criterion see PyDOE <http://pythonhosted.org/pyDOE/randomized.html>
globalize (bool) – Whether or not to globalize local variables.

Return type

sample_set

Returns

sample_set

local_to_global()¶: Globalize local variables.

random_sample_set(rv, input_obj, num_samples, globalize=True)¶

Create a sample set by sampling random variates from continuous distributions from scipy.stats.rv_continuous. See https://docs.scipy.org/doc/scipy/reference/stats.html.

rv can take multiple types of formats depending on type of distribution.

A string is used for the same distribution with default parameters in each dimension. ex. rv = ‘uniform’ or rv = ‘beta’

A list or tuple of length 2 is used for the same distribution with user-defined parameters in each dimension as a dictionary. ex. rv = [‘uniform’, {‘loc’:-2, ‘scale’:5}] or rv = [‘beta’, {‘a’: 2, ‘b’:5, ‘loc’:-2, ‘scale’:5}]

A list of length dim which entries of lists or tuples of length 2 is used for different distributions with user-defined parameters in each dimension as a dictionary. ex. rv = [[‘uniform’, {‘loc’:-2, ‘scale’:5}],

[‘beta’, {‘a’: 2, ‘b’:5, ‘loc’:-2, ‘scale’:5}]]

Parameters

rv (str, list, or tuple) – Type and parameters for continuous random variables.
input_obj (sample_set or int) – sample_set object containing the dimension to sample from, or the dimension.
num_samples (int) – Number of samples
globalize (bool) – Whether or not to globalize vectors.

Returns

regular_sample_set(input_obj, num_samples_per_dim=1)¶

Sampling algorithm for generating a regular grid of samples taken on the domain present with input_obj (a default unit hypercube is used if no domain has been specified)

Parameters

input_obj (sample_set or numpy.ndarray of shape (dim, 2) or int) – sample_set object containing the dimension or domain to sample from, the domain to sample from, or the dimension
num_samples_per_dim (ndarray of dimension (input_sample_set._dim,)) – number of samples per dimension

Return type

sample_set

Returns

sample_set object which contains input num_samples

bet.sampling.useLUQ module¶

The module contains a class for interfacing between BET and LUQ.

exception bet.sampling.useLUQ.missing_module¶

Bases: Exception

Exception for when a module cannot be imported.

bet.sampling.useLUQ.myModel(inputs, times)¶: Example for interfacing a time series model with LUQ. :param inputs: Parameter values at which to evaluate the model. :type inputs: numpy.ndarray of shape (num_inputs, num_params) :param times: Times at which to output results. :type times: numpy.ndarray of shape (num_times, ) :return: Time series data :rtype: numpy.ndarray of shape (num_inputs, num_times)

class bet.sampling.useLUQ.useLUQ(predict_set, lb_model, times, obs_set=None)¶

Bases: object

Wrappers for interfacing BET with LUQ. Allows for the simple creation of bet.sample.discretization objects from LUQ output.

clean_data(**kwargs)¶: Wrapper for luq.luq.LUQ.clean_data

dynamics(**kwargs)¶: Wrapper for luq.luq.LUQ.dynamics

get_obs()¶: Evaluate the model for the predicted time series.

get_predictions()¶: Evaluate the model for the predicted time series.

initialize(predicted_time_series=None, obs_time_series=None, times=None)¶

Initialize the LUQ object. This can be used manually if time series are pre-computed.

Parameters

predicted_time_series (numpy.ndarray of shape (num_predict_samples, num_times)) – Time series solutions for predicted values.
obs_time_series (numpy.ndarray of shape (num_obs_samples, num_times)) – Time series solutions for predicted values.
times (numpy.ndarray with shape (num_times, )) – Times at which the series are output.

learn_qois_and_transform(**kwargs)¶: Wrapper for luq.luq.LUQ.learn_qois_and_transform

local_to_global()¶: Dummy function for saving.

make_disc()¶: Construct bet.sample.discretization objects for predict and obs sets. :return: predict_disc, obs_disc :rtype: bet.sample.discretization, bet.sample.discretization or None if no observation set.

save(savefile)¶: Save the object to a Pickle file. :param savefile: Name of file to save to. :type savefile: str

set_observed_time_series(obs_time_series)¶: Set observed time series data manually. :param obs_time_series: time series data :type obs_time_series: :return: numpy.ndarray with shape (num_obs, num_times)

setup()¶: Setup LUQ object all at once.

Module contents¶

This subpackage contains

basicSampling a general class and associated set of methods that sample spaces and solve models through an interface.
sampler requests data (QoI) at a specified set of parameter samples.
LpGeneralizedSamples provides methods for sampling on balls in Lp spaces.
useLUQ provides methods for interfacing with the LUQ package.