bet package

Subpackages

Submodules

bet.Comm module

This module provides a workaround for people without mpi4py installed to run BET.

class bet.Comm.MPI_for_no_mpi4py

Bases: object

Provides a fake MPI implementation so that the user need not install mpi4py.

BOOL

bool type

DOUBLE

float type

INT

int type

SUM

fake sum

class bet.Comm.comm_for_no_mpi4py

Bases: object

Provides a fake MPI.COMM_WORLD implementation so that the user need not install mpi4py.

Allgather(val, val2=None)
Parameters

val (object) – object to Allgather

Return type

object

Returns

val

Allreduce(val1, val2=None, op=None)
Parameters

  • val1 (object) – object to Allreduce

  • val2 (object) – object to Allreduce

  • op – None

Return type

object

Returns

val1

Barrier()

Does nothing in serial.

Bcast(val, root=0)
Parameters

  • val (object) – object to gather

  • root (int) – 0

Return type

object

Returns

val

Get_rank()
Return type

int

Returns

0

Get_size()
Return type

int

Returns

1

Scatter(val1, val2, root=0)
Parameters

  • val1 (object) – object to Scatter

  • val2 (object) – object to Scatter

  • root (int) – 0

Return type

object

Returns

val1

allgather(val)
Parameters

val (object) – object to allgather

Return type

object

Returns

val

allreduce(val1, op=None)
Parameters

val1 (object) – object to allreduce

Return type

object

Returns

val1

barrier()

Does nothing in serial.

bcast(val, root=0)
Parameters

  • val (object) – object to broadcast

  • root (int) – 0

Return type

object

Returns

val

gather(val1, root=0)
Parameters

  • val1 (object) – object to gather

  • root (int) – 0

Return type

object

Returns

val1

rank

rank, 0

scatter(val1, root=0)
Parameters

  • val1 (object) – object to scatter

  • root (int) – 0

Return type

object

Returns

val1

size

size, 1

bet.sample module

This module contains the main data structures and exceptions for BET. Notably:

class bet.sample.ball_sample_set(dim)

Bases: bet.sample.sample_set_base

A data structure containing arrays specific to a set of samples defining discretization containing a number of balls. Only returns the neighbors for which \(x_i \in A_k\).

A series of n balls \(A_i \subset \Lambda\) with \(A_i \cap A_j = \emptyset\) for \(i \neq j\). The last entry represents the remainder \(\Lambda \setminus ( \cup_{i-1}^n A_i)\).

append_error_estimates(new_error_estimates)

Does nothing for this type of sample set.

Note

Remember to update the other member attribute arrays so that check_num() does not fail.

Parameters

new_error_estimates (numpy.ndarray of shape (num,)) – New error_estimates to append.

append_jacobians(new_jacobians)

Does nothing for this type of sample set.

Note

Remember to update the other member attribute arrays so that check_num() does not fail.

Parameters

new_jacobians (numpy.ndarray of shape (num, other_dim, dim)) – New jacobians to append.

append_values(values)

Does nothing for this type of sample_set.

See also

numpy.concatenate()

Parameters

values (numpy.ndarray of shape (some_num, dim)) – values to append

append_values_local(values_local)

Does nothing for this type of sample_set.

See also

numpy.concatenate()

Parameters

values_local (numpy.ndarray of shape (some_num, dim)) – values to append

exact_volume()

Calculate the exact volume fraction given the given p-norm.

query(x, k=1)

Identify which value points x are associated with for discretization. The distance is set to 0 if it is in the rectangle and infinity if it is not. It is only considered in or out.

See also

scipy.spatial.KDTree.query()

Parameters

  • x (numpy.ndarray of shape (*, dim)) – points for query

  • k (int) – number of nearest neighbors to return

Return type

tuple

Returns

(dist, ptr)

setup(centers, radii)

Initialize.

Parameters

  • centers (iterable of shape (num-1, dim)) – centers of balls

  • radii (iterable of length num-1) – radii of balls

update_bounds(num=None)

Does nothing for this type of sample set.

update_bounds_local(num_local=None)

Does nothing for this type of sample set.

class bet.sample.cartesian_sample_set(dim)

Bases: bet.sample.rectangle_sample_set

Defines a hyperrectangle discretization based on a Cartesian grid.

setup(xi)

Initialize.

Parameters

xi (array_like) – x1, x2,…, xn, 1-D arrays representing the coordinates of a grid

See also

numpy.meshgrid()

exception bet.sample.dim_not_matching

Bases: Exception

Exception for when the dimension of the array is inconsistent.

class bet.sample.discretization(input_sample_set, output_sample_set, output_probability_set=None, emulated_input_sample_set=None, emulated_output_sample_set=None, output_observed_set=None)

Bases: object

A data structure to store all of the sample_set_base objects and associated pointers to solve an stochastic inverse problem.

check_nums()

Checks that self._input_sample_set and self._output_sample_set both have the same number of samples.

Return type

int

Returns

Number of samples

choose_inputs_outputs(inputs=None, outputs=None)

Slices the inputs and outputs of the discretization.

Parameters

  • inputs (list) – list of indices of input sample set to include

  • outputs (list) – list of indices of output sample set to include

Return type

discretization

Returns

sliced discretization

clip(cnum)

Creates and returns a discretization with the the first cnum entries of the input and output sample sets.

Parameters

cnum (int) – number of values of sample set to return

Return type

discretization

Returns

clipped discretization

copy()

Makes a copy using numpy.copy().

Return type

discretization

Returns

Copy of this discretization

estimate_input_volume_emulated()

Calculate the volume faction of cells approximately using Monte Carlo integration.

Note

This could be re-written to just use emulated_ii_ptr instead of _emulated_input_sample_set.

estimate_output_volume_emulated()

Calculate the volume faction of cells approximately using Monte Carlo integration.

Note

This could be re-written to just use emulated_oo_ptr instead of _emulated_output_sample_set.

get_emulated_ii_ptr()

Returns the pointer from self._emulated_input_sample_set to self._input_sample_set

See also

scipy.spatial.KDTree.query`()

Return type

numpy.ndarray of int of shape (self._output_sample_set._values.shape[0],)

Returns

self._emulated_ii_ptr

get_emulated_input_sample_set()

Returns a reference to the emulated_input sample set for this discretization.

Return type

sample_set_base

Returns

emulated_input sample set

get_emulated_oo_ptr()

Returns the pointer from self._emulated_output_sample_set to self._output_probability_set

See also

scipy.spatial.KDTree.query`()

Return type

numpy.ndarray of int of shape (self._output_sample_set._values.shape[0],)

Returns

self._emulated_ii_ptr

get_emulated_output_sample_set()

Returns a reference to the emulated_output sample set for this discretization.

Return type

sample_set_base

Returns

emulated_output sample set

get_input_sample_set()

Returns a reference to the input sample set for this discretization.

Return type

sample_set_base

Returns

input sample set

get_io_ptr()

Returns the pointer from self._output_sample_set to self._output_probability_set

See also

scipy.spatial.KDTree.query`()

Return type

numpy.ndarray of int of shape (self._output_sample_set._values.shape[0],)

Returns

self._io_ptr

get_output_observed_set()

Returns a reference to the output observed sample set for this discretization.

Return type

sample_set_base

Returns

output sample set

get_output_probability_set()

Returns a reference to the output probability sample set for this discretization.

Return type

sample_set_base

Returns

output probability sample set

get_output_sample_set()

Returns a reference to the output sample set for this discretization.

Return type

sample_set_base

Returns

output sample set

global_to_local()

Call global_to_local for input_sample_set and output_sample_set.

globalize_ptrs()

Globalizes discretization pointers.

local_to_global()

Call local_to_global for input_sample_set and output_sample_set.

merge(disc)

Merges a given discretization with this one by merging the input and output sample sets.

Parameters

disc (bet.sample.discretization) – Discretization object to merge with.

Return type

bet.sample.discretization

Returns

Merged discretization

sample_set_names = ['_input_sample_set', '_output_sample_set', '_emulated_input_sample_set', '_emulated_output_sample_set', '_output_probability_set', '_output_observed_set']

List of attribute names for attributes that are sample.sample_set_base

save(filename, globalize=True)

Save the discretization using pickle.

Returns

set_emulated_ii_ptr(globalize=True)

Creates the pointer from self._emulated_input_sample_set to self._input_sample_set

See also

scipy.spatial.KDTree.query`()

Parameters

  • globalize (bool) – flag whether or not to globalize self._output_sample_set

  • p (int) – Which Minkowski p-norm to use. (1 <= p <= infinity)

set_emulated_input_sample_set(emulated_input_sample_set)

Sets the emulated_input sample set for this discretization.

Parameters

emulated_input_sample_set (sample_set_base) – emupated input sample set.

set_emulated_oo_ptr(globalize=True)

Creates the pointer from self._emulated_output_sample_set to self._output_probability_set

See also

scipy.spatial.KDTree.query`()

Parameters

  • globalize (bool) – flag whether or not to globalize self._output_sample_set

  • p (int) – Which Minkowski p-norm to use. (1 <= p <= infinity)

set_emulated_output_sample_set(emulated_output_sample_set)

Sets the emulated_output sample set for this discretization.

Parameters

emulated_output_sample_set (sample_set_base) – emupated output sample set.

set_input_sample_set(input_sample_set)

Sets the input sample set for this discretization.

Parameters

input_sample_set (sample_set_base) – input sample set.

set_io_ptr(globalize=True)

Creates the pointer from self._output_sample_set to self._output_probability_set

Parameters

globalize (bool) – flag whether or not to globalize self._output_sample_set

set_output_observed_set(output_sample_set)

Sets the output observed sample set for this discretization.

Parameters

output_sample_set (sample_set_base) – output observed sample set.

set_output_probability_set(output_probability_set)

Sets the output probability sample set for this discretization.

Parameters

output_probability_set (sample_set_base) – output probability sample set.

set_output_sample_set(output_sample_set)

Sets the output sample set for this discretization.

Parameters

output_sample_set (sample_set_base) – output sample set.

vector_names = ['_io_ptr', '_io_ptr_local', '_emulated_ii_ptr', '_emulated_ii_ptr_local', '_emulated_oo_ptr', '_emulated_oo_ptr_local']

List of attribute names for attributes which are vectors or 1D numpy.ndarray

exception bet.sample.domain_not_matching

Bases: Exception

Exception for when the domain does not match.

bet.sample.evaluate_pdf(prob_type, prob_parameters, vals)

Evaluate the probability density function defined by prob_type and prob_parameters at points defined by vals.

Parameters

  • prob_type (str) – Type of probability description. Options are ‘kde’ (weighted kernel density estimate), ‘rv’ (random variable), ‘gmm’ (Gaussian mixture model), and ‘voronoi’.

  • prob_parameters – Parameters that define the probability measure of type prob_type

  • vals (numpy.ndarray) – Values at which to evaluate the PDF.

Returns

probability density evaluated at vals

:rtype numpy.ndarray

bet.sample.evaluate_pdf_marginal(prob_type, prob_parameters, vals, i)

Evaluate the marginal probability density function of index i defined by prob_type and prob_parameters at points defined by vals.

Parameters

  • prob_type (str) – Type of probability description. Options are ‘kde’ (weighted kernel density estimate), ‘rv’ (random variable), ‘gmm’ (Gaussian mixture model), and ‘voronoi’.

  • prob_parameters – Parameters that define the probability measure of type prob_type

  • vals (numpy.ndarray) – Values at which to evaluate the PDF.

  • i (int) – index of marginal

Returns

marginal probability density evaluated at vals

:rtype numpy.ndarray

exception bet.sample.length_not_matching

Bases: Exception

Exception for when the length of the array is inconsistent.

class bet.sample.rectangle_sample_set(dim)

Bases: bet.sample.sample_set_base

A data structure containing arrays specific to a set of samples defining a hyperrectangle discretization.

A series of n hyperrectangles \(A_i \subset \Lambda\) with \(A_i \cap A_j = \emptyset\) for \(i \neq j\). The last entry represents the remainder \(\Lambda \setminus ( \cup_{i-1}^n A_i)\).

append_error_estimates(new_error_estimates)

Does nothing for this type of sample set.

Note

Remember to update the other member attribute arrays so that check_num() does not fail.

Parameters

new_error_estimates (numpy.ndarray of shape (num,)) – New error_estimates to append.

append_jacobians(new_jacobians)

Does nothing for this type of sample set.

Note

Remember to update the other member attribute arrays so that check_num() does not fail.

Parameters

new_jacobians (numpy.ndarray of shape (num, other_dim, dim)) – New jacobians to append.

append_values(values)

Does nothing for this type of sample_set.

See also

numpy.concatenate()

Parameters

values (numpy.ndarray of shape (some_num, dim)) – values to append

append_values_local(values_local)

Does nothing for this type of sample_set.

See also

numpy.concatenate()

Parameters

values_local (numpy.ndarray of shape (some_num, dim)) – values to append

exact_volume_lebesgue()

Exactly calculates the Lebesgue volume fraction of the cells.

query(x, k=1)

Identify which value points x are associated with for discretization. Only returns the neighbors for which \(x_i \in A_k\). The distance is set to 0 if it is in the rectangle and infinity if it is not. It is only considered in or out.

See also

scipy.spatial.KDTree.query()

Parameters

  • x (numpy.ndarray of shape (*, dim)) – points for query

  • k (int) – number of nearest neighbors to return

Return type

tuple

Returns

(dist, ptr)

setup(maxes, mins)

Initialization

Parameters

  • maxes (iterable with components of length dim) – array or list of maxes for hyperrectangles

  • mins (iterable with components of length dim) – array or list of mins for hyperrectangles

update_bounds(num=None)

Does nothing for this type of sample set.

update_bounds_local(num_local=None)

Does nothing for this type of sample set.

class bet.sample.sample_set(dim)

Bases: bet.sample.voronoi_sample_set

Set Voronoi cells as the default for now.

class bet.sample.sample_set_base(dim)

Bases: object

A data structure containing values that define a set of samples.

append_error_estimates(new_error_estimates)

Appends the new_error_estimates to self._error_estimates.

Note

Remember to update the other member attribute arrays so that check_num() does not fail.

Parameters

new_error_estimates (numpy.ndarray of shape (num,)) – New error_estimates to append.

append_jacobians(new_jacobians)

Appends the new_jacobians to self._jacobians.

Note

Remember to update the other member attribute arrays so that check_num() does not fail.

Parameters

new_jacobians (numpy.ndarray of shape (num, other_dim, dim)) – New jacobians to append.

append_values(values)

Appends the values in _values to self._values.

See also

numpy.concatenate()

Parameters

values (numpy.ndarray of shape (some_num, dim)) – values to append

append_values_local(values_local)

Appends the values in _values_local to self._values.

See also

numpy.concatenate()

Parameters

values_local (numpy.ndarray of shape (some_num, dim)) – values to append

array_names = ['_values', '_volumes', '_probabilities', '_densities', '_jacobians', '_error_estimates', '_right', '_left', '_width', '_kdtree_values', '_radii', '_normalized_radii', '_region', '_error_id']

List of global attribute names for attributes that are numpy.ndarray

calculate_volumes()

Calculate the volumes of cells. Depends on sample set type.

check_num()

Checks that the number of entries in self._values, self._volumes, self._probabilities, self._jacobians, and self._error_estimates all match (assuming the named array exists).

Return type

int

Returns

num

check_num_local()

Checks that the number of entries in self._values_local, self._volumes_local, self._probabilities_local, self._jacobians_local, and self._error_estimates_local all match (assuming the named array exists).

Return type

int

Returns

num

clip(cnum)

Creates and returns a sample set with the the first cnum entries of the sample set.

Parameters

cnum (int) – number of values of sample set to return

Return type

sample_set

Returns

the clipped sample set

copy()

Makes a copy using numpy.copy().

Return type

sample_set_base

Returns

Copy of this sample_set_base

estimate_volume(n_mc_points=10000)

Calculate the volume faction of cells approximately using Monte Carlo integration.

Parameters

n_mc_points (int) – If estimate is True, number of MC points to use

estimate_volume_emulated(emulated_sample_set)

Calculate the volume faction of cells approximately using Monte Carlo integration.

Note

This could be re-written to just use an emulated_ii_ptr instead of an emulated_sample_set.

Parameters

emulated_sample_set (bet.sample.sample_set_base) – The set of samples used to approximate the volume measure.

estimate_volume_mc(globalize=True)

Give all cells the same volume fraction based on the Monte Carlo assumption.

get_bounding_box()

Get the bounding box of the values.

get_cluster_maps()

Returns cluster maps.

get_densities()

Returns sample densities.

Return type

numpy.ndarray of shape (num,)

Returns

sample densities

get_densities_local()

Returns sample local densities.

Return type

numpy.ndarray

Returns

sample local densities

get_dim()

Return the dimension of the sample space.

Return type

int

Returns

Dimension of the sample space.

get_domain()

Returns the sample domain,

Return type

numpy.ndarray of shape (dim, 2)

Returns

Sample domain

get_error_estimates()

Returns sample error_estimates.

Return type

numpy.ndarray of shape (num,)

Returns

sample error_estimates

get_error_estimates_local()

Returns sample error_estimates_local.

Return type

numpy.ndarray of shape (num,)

Returns

sample error_estimates_local

get_error_id()

Returns error identifiers.

get_error_id_local()

Returns local error identifier.

get_jacobians()

Returns sample jacobians.

Return type

numpy.ndarray of shape (num, other_dim, dim)

Returns

sample jacobians

get_jacobians_local()

Returns local sample jacobians.

Return type

numpy.ndarray of shape (num, other_dim, dim)

Returns

local sample jacobians

get_kdtree()

Returns a scipy.spatial.KDTree for this set of samples.

Return type

scipy.spatial.KDTree

Returns

scipy.spatial.KDTree for this set of samples.

get_label()

Returns label for set.

get_labels()

Returns labels for each dimension of set.

get_p_norm()

Returns p-norm for sample set

get_prob_parameters()

Returns the updated probability measure parameters.

get_prob_parameters_init()

Returns initial probability measure parameters.

get_prob_type()

Returns the type of updated probability measure.

get_prob_type_init()

Returns the type of initial probability measure.

get_probabilities()

Returns sample probabilities.

Return type

numpy.ndarray of shape (num,)

Returns

sample probabilities

get_probabilities_local()

Returns sample local probabilities.

Return type

numpy.ndarray

Returns

sample local probabilities

get_reference_value()

Returns the reference value of a sample set.

get_region()

Returns region.

get_region_local()

Returns local region.

get_values()

Returns sample values.

Return type

numpy.ndarray

Returns

sample values

get_values_local()

Returns sample local values.

Return type

numpy.ndarray

Returns

sample local values

get_volumes()

Returns sample cell volumes.

Return type

numpy.ndarray of shape (num,)

Returns

sample cell volumes

get_volumes_local()

Returns sample local volumes.

Return type

numpy.ndarray

Returns

sample local volumes

get_weights()

Returns weights of samples.

get_weights_init()

Returns initial weights of samples

global_to_local()

Makes local arrays from available global ones.

local_to_global()

Makes global arrays from available local ones.

marginal_pdf(vals, i)

Evaluate the marginal (with index i) probability density function of the updated probability measure at values.

Parameters

  • vals (numpy.ndarray of shape (num_vals, dim) or (num_vals, )) – Values at which to evaluated the PDF.

  • i (int) – index defining marginal

:return probability densities :rtype numpy.ndarray of shape (num_vals, )

marginal_pdf_init(vals, i)

Evaluate the marginal (with index i) probability density function of the initial probability measure at values.

Parameters

  • vals (numpy.ndarray of shape (num_vals, dim) or (num_vals, )) – Values at which to evaluated the PDF.

  • i (int) – index defining marginal

:return probability densities :rtype numpy.ndarray of shape (num_vals, )

meta_fields = ['_bounding_box', '_densities', '_densities_local', '_dim', '_domain', '_domain_original', '_error_estimates', '_error_estimates_local', '_error_id', '_error_id_local', '_jacobians', '_jacobians_local', '_kdtree_values', '_kdtree_values_local', '_left', '_left_local', '_local_index', '_normalized_radii', '_normalized_radii_local', '_p_norm', '_probabilities', '_probabilities_local', '_radii', '_radii_local', '_reference_value', '_region', '_region_local', '_right', '_right_local', '_values', '_values_local', '_volumes', '_volumes_local', '_width', '_width_local', '_prob_type', '_prob_type_init', '_prob_parameters', '_prob_parameters_init', '_label', '_labels', '_cluster_maps', '_weights', '_weights_init']
normalize_domain()

Normalize the domain and attributes to a unit hyperbox.

pdf(vals)

Evaluate the probability density function of the updated probability measure at values. :param vals: Values at which to evaluated the PDF. :type vals: numpy.ndarray of shape (num_vals, dim) :return probability densities :rtype numpy.ndarray of shape (num_vals, )

pdf_init(vals)

Evaluate the probability density function of the initial probability measure at values. :param vals: Values at which to evaluated the PDF. :type vals: numpy.ndarray of shape (num_vals, dim) :return probability densities :rtype numpy.ndarray of shape (num_vals, )

query(x, k=1)

Identify which value points x are associated with for discretization.

Parameters

  • x (numpy.ndarray of shape (*, dim)) – points for query

  • k (int) – number of nearest neighbors to return

save(filename, globalize=True)

Save the set using pickle.

Parameters

  • filename (str) – filename to save to

  • globalize (bool) – whether or not to globalize local variables before saving

set_bounding_box()

Set the bounding box of the values.

set_cluster_maps(cluster_maps)

Sets cluster maps (generally coming from LUQ).

Parameters

cluster_maps (list) – List of arrays containing values in each cluster.

set_densities(densities=None)

Set sample densities.

Parameters

densities (numpy.ndarray of shape (num,)) – sample densities

set_densities_local(densities_local=None)

Set sample local densities.

Parameters

densities_local (numpy.ndarray of shape (num,)) – local sample densities

set_domain(domain)

Sets the domain.

Parameters

domain (numpy.ndarray of shape (dim, 2)) – Sample domain

set_error_estimates(error_estimates)

Returns sample error estimates.

Parameters

error_estimates (numpy.ndarray of shape (num,)) – sample error estimates

set_error_estimates_local(error_estimates_local)

Returns local sample error estimates.

Parameters

error_estimates_local (numpy.ndarray of shape (num,)) – local sample error estimates

set_error_id(error_id)

Sets error_id for sample set.

Parameters

error_id (numpy.ndarray of shape (some_num, dim)) – array of error identifiers

set_error_id_local(error_id)

Sets local error id for sample set.

Parameters

error_id (numpy.ndarray of shape (some_num, dim)) – array of error identifiers

set_jacobians(jacobians)

Returns sample jacobians.

Parameters

jacobians (numpy.ndarray of shape (num, other_dim, dim)) – sample jacobians

set_jacobians_local(jacobians_local)

Returns local sample jacobians.

Parameters

jacobians_local (numpy.ndarray of shape (num, other_dim, dim)) – local sample jacobians

set_kdtree()

Creates a scipy.spatial.KDTree for this set of samples.

set_label(label)

Sets label for set. :param label: Label for set. :type label: str

set_labels(labels)

Sets labels for each dimension of set. :param labels: list or tuple containing strings which label parameters in each dimension. :type labels: list or tuple of length dim :return:

set_p_norm(p_norm)

Sets p-norm for sample set.

Parameters

p_norm (float) – p-norm to use

set_prob_parameters(prob_parameters)

Set updated probability measure parameters. :param prob_parameters: Updated probability measure parameters.

set_prob_parameters_init(prob_parameters_init)

Set initial probability measure parameters. :param prob_parameters_init: Initial probability measure parameters.

set_prob_type(prob_type)

Set the type of updated probability measure. :param prob_type: Type of updated probability measure (‘kde’, ‘gmm’, ‘voronoi’, ‘rv’) :type prob_type: str

set_prob_type_init(prob_type_init)

Set the type of initial probability measure. :param prob_type_init: Type of initial probability measure (‘kde’, ‘gmm’, ‘voronoi’, ‘rv’) :type prob_type_init: str

set_probabilities(probabilities)

Set sample probabilities.

Parameters

probabilities (numpy.ndarray of shape (num,)) – sample probabilities

set_probabilities_local(probabilities_local)

Set sample local probabilities.

Parameters

probabilities_local (numpy.ndarray of shape (num,)) – local sample probabilities

set_reference_value(ref_val)

Sets reference value for sample set.

Parameters

ref_val (numpy.ndarray of shape (dim,)) – reference value

set_region(region)

Sets region for sample set.

Parameters

region – array of regions

set_region_local(region)

Sets local region for sample set.

Parameters

region – array of regions

set_values(values)

Sets the sample values.

Parameters

values (numpy.ndarray of shape (num, dim)) – sample values

set_values_local(values_local)

Sets the local sample values.

Parameters

values_local (numpy.ndarray of shape (local_num, dim)) – sample local values

set_volumes(volumes)

Sets sample cell volumes.

Parameters

volumes (numpy.ndarray of shape (num,)) – sample cell volumes

set_volumes_local(volumes_local)

Sets local sample cell volumes.

Parameters

volumes_local (numpy.ndarray of shape (num,)) – local sample cell volumes

set_weights(weights)

Set weights for samples :type weights: numpy.ndarray of shape (num,) :param weights: weights of samples

set_weights_init(weights)

Set initial weights for samples :type weights: numpy.ndarray of shape (num,) :param weights: initial weights of samples

shape()

Returns the shape of self._values

Return type

tuple

Returns

(num, dim)

shape_local()

Returns the shape of self._values_local

Return type

tuple

Returns

(local_num, dim)

undo_normalize_domain()

Undoes normalization of the domain and attributes if they have been normalized.

update_bounds(num=None)

Creates self._right, self._left, self._width.

Parameters

num (int) – Determines shape of pointwise bounds (num, dim)

update_bounds_local(local_num=None)

Creates local versions of self._right, self._left, self._width (self._right_local, self._left_local, self._width_local).

Parameters

local_num (int) – Determines shape of local pointwise bounds (local_num, dim)

class bet.sample.voronoi_sample_set(dim)

Bases: bet.sample.sample_set_base

A data structure containing arrays specific to a set of samples defining a Voronoi tesselation.

estimate_local_volume(num_emulate_local=500, max_num_emulate=10000)

Estimates the volume fraction of the Voronoi cells associated with samples. Specifically we are calculating \(\mu_\Lambda(\mathcal(V)_{i,N} \cap A)/\mu_\Lambda(\Lambda)\). Here all of the samples are drawn from the generalized Lp uniform distribution.

Note

If this voronoi_sample_set has exact/estimated radii of the Voronoi cell associated with each sample for a domain normalized to the unit hypercube (_normalized_radii). Note that these are not centroidal Voronoi tesselations meaning that the centroid is NOT the generator of the Voronoi cell. What we desire for the radius is actually \(sup_{\lambda \in \mathcal{V}_{i, N}} d_v(\lambda, \lambda^{(i)})\).

Todo

When we move away from domains defined on hypercubes this will need to be updated to use whatever _in_domain method exists.

Volume of the L-p ball is obtained from Wang, X.. (2005). Volumes of Generalized Unit Balls. Mathematics Magazine, 78(5), 390-395. DOI 10.2307/30044198

Parameters

  • num_emulate_local (int) – The number of emulated samples.

  • max_num_emulate (int) – Maximum number of local emulated samples

estimate_radii(n_mc_points=10000, normalize=True)

Calculate the radii of cells approximately using Monte Carlo integration.

Todo

This currently presumes a uniform Lesbegue measure on the domain. Currently the way this is written emulated_input_sample_set is NOT used to calculate the volume. This should at least be an option.

Parameters

  • n_mc_points (int) – If estimate is True, number of MC points to use

  • normalize (bool) – estimate normalized radius

estimate_radii_and_volume(n_mc_points=10000, normalize=True)

Calculate the radii and volume faction of cells approximately using Monte Carlo integration.

Todo

This currently presumes a uniform Lesbegue measure on the domain. Currently the way this is written emulated_input_sample_set is NOT used to calculate the volume. This should at least be an option.

Parameters

  • n_mc_points (int) – If estimate is True, number of MC points to use

  • normalize (bool) – estimate normalized radius

exact_volume_1D()

Exactly calculates the volume fraction of the Voronoi cells. Specifically we are calculating \(\mu_\Lambda(\mathcal(V)_{i,N} \cap A)/\mu_\Lambda(\Lambda)\).

exact_volume_2D(side_ratio=0.25)

Exactly calculates the volume fraction of the Voronoi cells. Specifically we are calculating \(\mu_\Lambda(\mathcal(V)_{i,N} \cap A)/\mu_\Lambda(\Lambda)\).

Parameters

side_ratio (float) – ratio of width to reflect across boundary

merge(sset)

Merges a given sample set with this one by merging the values.

Parameters

sset (bet.sample.voronoi_sample_set) – Sample set object to merge with.

Return type

bet.sample.voronoi_sample_set

Returns

Merged discretization

query(x, k=1)

Identify which value points x are associated with for discretization.

Parameters

  • x (numpy.ndarray of shape (*, dim)) – points for query

  • k (int) – number of nearest neighbors to return

Return type

tuple

Returns

(dist, ptr)

exception bet.sample.wrong_input

Bases: Exception

Exception for when the input is of the wrong type.

exception bet.sample.wrong_p_norm

Bases: Exception

Exception for when the dimension of the array is inconsistent.

bet.surrogates module

This module provides methods for generating and using surrogate models.

class bet.surrogates.piecewise_polynomial_surrogate(input_disc)

Bases: object

This class provides methods for generating a piecewise polynomial surrogate.

calculate_prob_for_sample_set_region(s_set, regions, update_input=True)

Solves stochastic inverse problem based on surrogate points and the MC assumption. Calculates the probability of a regions of input space and error estimates for those probabilities.

Param

s_set: sample set for which to calculate error

Parameters

  • region (list) – list of regions of s_set for which to calculate error

  • update_input (bool) – whether or not to update probabilities and errror identifiers for input discretization

Return type

tuple

Returns

(probabilities, error_estimates), the probability and error estimates for the region

generate_for_input_set(input_sample_set, order=0)

Generates a surrogate discretization based on the input discretization, for a user-defined input sample set. The output sample set values and error estimates are piecewise polynomially defined over input sample set cells from the input discretization. For order 0, both are piecewise constant. For order 1, values are piecewise linear (assuming Jacobians exist), and error estimates are piecewise constant.

Parameters

  • input_sample_set – input sample set for surrogate discretization

  • order (int) – Polynomial order

Return type

discretization

Returns

discretization defining the surrogate model

bet.util module

This module contains general tools for BET including saving and loading objects, and reshaping objects. The most important methods are:

bet.util.clean_data(data)

Clean data so that NaN->0, inf-> maxfloat, -inf-> -maxfloat

Parameters

data (numpy.ndarray) – numerical object

Return type

numpy.ndarray

Returns

array of shape (data.shape)

bet.util.fix_dimensions_data(data, dim=None)

Fix the dimensions of an input so that it is a numpy.ndarray of shape (N, dim).

If dim is non-specified: If data is a non-iterable number assumes that dim==1. If data is a numpy array with len(shape) == 1 assumes that dim==1. If data is a numpy array with len(shape) == 2 assumes that dim==shape[1].

Parameters

  • data – numerical object

  • dim (int) – The dimension of the “data” space.

Return type

numpy.ndarray

Returns

array of shape (N, dim)

bet.util.fix_dimensions_domain(domain)

Fix the dimensions of an input so that it is a numpy.ndarray of shape (dim, 2).

Parameters

vector (collections.abc.Iterable) – numerical object of at least length 2

Return type

numpy.ndarray

Retuns

array of shape (dim, 2)

bet.util.fix_dimensions_vector(vector)

Fix the dimensions of an input so that it is a numpy.ndarray of shape (N,). :param vector: numerical object :rtype: numpy.ndarray :returns: array of shape (N,)

bet.util.fix_dimensions_vector_2darray(vector)

Fix the dimensions of an input so that it is a numpy.ndarray of shape (N,1).

Parameters

vector – numerical object

Return type

numpy.ndarray

Returns

array of shape (N,1)

bet.util.get_global_values(array, shape=None)

Concatenates local arrays into global array using np.vstack().

Parameters

array – Array.

Return type

ndarray

Returns

array

bet.util.load_object(file_name, localize=False)

Load saved objects.

Parameters

  • file_name (str) – Filename of object.

  • localize (bool) – Whether or not to localize parallel object.

Returns

The saved object

bet.util.load_object_parallel(file_name)

Load saved paralell objects.

Parameters

file_name (str) – Filename of object.

Returns

The saved object

bet.util.meshgrid_ndim(X)

Return coordinate matrix from two or more coordinate vectors. Handles a maximum of 10 vectors.

Make N-D coordinate arrays for vectorized evaluations of N-D scalar/vector fields over N-D grids, given one-dimensional coordinate arrays (x1, x2,…, xn).

Parameters

X (tuple) – A tuple containing the 1d coordinate arrays

Return type

ndarray of shape (num_grid_points,n)

Returns

X_new

bet.util.save_object(save_set, file_name, globalize=True)

Save BET object.

Parameters

  • save_set – Object to Save.

  • file_name (str) – Filename to save to.

  • globalize (bool) – Whether or not to globalize parallel objects.

Module contents

Butler, Estep, Tavener Method

This package provides tools for solving stochastic inverse problems using a measure-theoretic. It is named for the developers of the key algorithm in bet.calculateP.calculateP.

  • Comm provides a work around for users who do not which to install :program:mpi4py.

  • util provides some general use methods for creating grids, checking/fixing dimensions, and globalizing arrays.

  • calculateP provides tools to approximate probabilities.

  • sampling provides various sampling algorithms.

  • sensitivity provides tools for approximating derivatives and optimally choosing quantities of interest.

  • postProcess provides plotting tools and tools to sort samples by probabilities.

  • sample provides data structures to store sets of samples and their associated arrays.

  • surrogates provides methods for generating and using

    surrogate models.