queens.parameters.random_fields package#

Random fields.

Modules for random fields.

Submodules#

queens.parameters.random_fields.fourier module#

Fourier Random fields class.

class DimensionMethods1D[source]#

Bases: object

1D FOURIER expansion helper methods.

static calculate_basis(coordinates, basis_dimension, number_expansion_terms, convex_hull_size, covariance, index)[source]#

Calculate the fourier basis.

Parameters:

coordinates (ndarray) – Vector with coordinates of field
basis_dimension (int) – Dimension of the complete Fourier basis (not the latent space)
number_expansion_terms (int) – Number of frequencies
convex_hull_size (float) – Maximum length on the mesh
covariance (ndarray) – Transform of covariance matrix
index (ndarray) – Array indexing valid basis terms in accordance to the truncation threshold

Returns:

Transformed and truncated fourier basis

Return type:

ndarray

static calculate_covariance(number_expansion_terms, corr_length, convex_hull_size)[source]#

Calculate discrete fourier transform of the covariance kernel.

Based on the kernel description of the random field, build its covariance matrix using the external geometry and coordinates.

Parameters:

number_expansion_terms (int) – Number of frequencies
corr_length (float) – Typical length in the field
convex_hull_size (float) – Max distance on the grid

Returns:

Cosine transform of covariance matrix

Return type:

ndarray

static get_dim(trunc_threshold, number_expansion_terms)[source]#

Calculate dimension of latent space.

Parameters:

trunc_threshold (int) – Truncation threshold
number_expansion_terms (int) – Number of frequencies in the expansion

Returns:

Array indexing the covariance values below the truncation limit
Array indexing the basis terms corresponding to valid covariance values
Dimension of the complete Fourier basis up to the truncation threshold
Dimension of the latent space

Return type:

tuple[ndarray, ndarray, int, int]

class DimensionMethods2D[source]#

Bases: object

2D FOURIER expansion helper methods.

static calculate_basis(coordinates, basis_dimension, number_expansion_terms, convex_hull_size, covariance, index)[source]#

Calculate the fourier basis.

Parameters:

coordinates (ndarray) – Vector with coordinates of field
basis_dimension (int) – Dimension of the complete Fourier basis (not the latent space)
number_expansion_terms (int) – Number of frequencies
convex_hull_size (float) – Maximum length on the mesh
covariance (ndarray) – Transform of covariance matrix
index (ndarray) – Array indexing valid basis terms in accordance to the truncation threshold

Returns:

Transformed and truncated fourier basis

Return type:

ndarray

static calculate_covariance(number_expansion_terms, corr_length, convex_hull_size)[source]#

Calculate discrete fourier transform of the covariance kernel.

Based on the kernel description of the random field, build its covariance matrix using the external geometry and coordinates.

Parameters:

number_expansion_terms (int) – Number of frequencies
corr_length (float) – Typical length in the field
convex_hull_size (float) – Max distance on the grid

Returns:

Cosine transform of covariance matrix

Return type:

ndarray

static get_dim(trunc_threshold, number_expansion_terms)[source]#

Calculate dimension of latent space.

Parameters:

trunc_threshold (int) – Truncation threshold
number_expansion_terms (int) – Number of frequencies in the expansion

Returns:

Array indexing the covariance values below the truncation limit
Array indexing the basis terms corresponding to valid covariance values
Dimension of the complete Fourier basis up to the truncation threshold
Dimension of the latent space

Return type:

tuple[ndarray, ndarray, int, int]

class DimensionMethods3D[source]#

Bases: object

3D FOURIER expansion helper methods.

static calculate_basis(coordinates, basis_dimension, number_expansion_terms, convex_hull_size, covariance, index)[source]#

Calculate the fourier basis.

Parameters:

coordinates (ndarray) – Vector with coordinates of field
basis_dimension (int) – Dimension of the complete Fourier basis (not the latent space)
number_expansion_terms (int) – Number of frequencies
convex_hull_size (float) – Maximum length on the mesh
covariance (ndarray) – Transform of covariance matrix
index (ndarray) – Array indexing valid basis terms in accordance to the truncation threshold

Returns:

Transformed and truncated fourier basis

Return type:

ndarray

static calculate_covariance(number_expansion_terms, corr_length, convex_hull_size)[source]#

Calculate discrete fourier transform of the covariance kernel.

Based on the kernel description of the random field, build its covariance matrix using the external geometry and coordinates.

Parameters:

number_expansion_terms (int) – Number of frequencies
corr_length (float) – Typical length in the field
convex_hull_size (float) – Max distance on the grid

Returns:

Cosine transform of covariance matrix

Return type:

ndarray

static get_dim(trunc_threshold, number_expansion_terms)[source]#

Calculate dimension of latent space.

Parameters:

trunc_threshold (int) – Truncation threshold
number_expansion_terms (int) – Number of frequencies in the expansion

Returns:

Array indexing the covariance values below the truncation limit
Array indexing the basis terms corresponding to valid covariance values
Dimension of the complete Fourier basis up to the truncation threshold
Dimension of the latent space

Return type:

tuple[ndarray, ndarray, int, int]

class Fourier[source]#

Bases: RandomField

FOURIER expansion of random fields class.

mean#: Mean vector at nodes

std#: Hyperparameter for standard-deviation of random field

corr_length#: Hyperparameter for the correlation length

variability#: Explained variance by the fourier decomposition

trunc_threshold#: Truncation threshold for Fourier series

basis_dimension#: Dimension of the complete Fourier basis up to the truncation threshold (not the latent space)

latent_index#: Index array mapping latent space variables to covariance values

covariance_index#: Array indexing the covariance values below the truncation threshold

covariance#: Fourier transformed covariance kernel

basis#: Inverse cosine transformed fourier basis

coordinates#: Vector of all coordinates in random field

field_dimension#: Physical dimension of the random field

number_expansion_terms#: Number of frequencies in all directions

dimension#: Dimension of latent space

convex_hull_size#: Euclidean distance between furthest apart coordinates in the field

__init__(coords, mean=0.0, std=1.0, corr_length=0.3, variability=0.98, trunc_threshold=64)[source]#

Initialize Fourier object.

Parameters:

coords (dict) – Dictionary with coordinates of discretized random field and the corresponding keys
mean (_SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes]) – Mean vector at nodes
std (float) – Hyperparameter for standard-deviation of random field
corr_length (float) – Hyperparameter for the correlation length
variability (float) – Explained variance of by the eigen
trunc_threshold (int) – Truncation threshold for Fourier series.

check_convergence()[source]#

Check if truncated terms converge to variability.

Return type:: None

draw(num_samples)[source]#

Draw samples from the latent representation of the random field.

Parameters:: num_samples (int) – Number of draws of latent random samples
Returns:: Drawn samples
Return type:: ndarray

expanded_representation(samples)[source]#

Expand latent representation of samples.

Parameters:: samples (ndarray) – Latent representation of samples
Returns:: Expanded representation of samples
Return type:: ndarray

grad_logpdf(samples)[source]#

Get gradient of joint log-PDF of latent space.

Parameters:: samples (ndarray) – Samples for evaluating the gradient of the log-PDF
Returns:: Gradient of the log-PDF
Return type:: ndarray

latent_gradient(upstream_gradient)[source]#

Gradient with respect to the latent parameters.

Parameters:: upstream_gradient (ndarray) – Gradient with respect to all coords of the field
Returns:: Gradient of the realization of the random field with respect to the latent space – variables
Return type:: ndarray

logpdf(samples)[source]#

Get joint log-PDF of latent space.

Parameters:: samples (ndarray) – Samples for evaluating the log-PDF
Returns:: Log-PDF of the samples
Return type:: ndarray

queens.parameters.random_fields.karhunen_loeve module#

Karhunen-Loève Random fields class.

class KarhunenLoeve[source]#

Bases: RandomField

Karhunen Loeve RandomField class.

nugget_variance#: Nugget variance for the random field (lower bound for diagonal values of the covariance matrix).

explained_variance#: Explained variance by the eigen decomposition.

std#: Hyperparameter for standard-deviation of random field

corr_length#: Hyperparameter for the correlation length

cut_off#: Lower value limit of covariance matrix entries

mean#: Mean at coordinates of random field, can be a single constant

cov_matrix#: Covariance matrix to compute eigendecomposition on

eigenbasis#: Eigenvectors of covariance matrix, weighted by the eigenvalues

eigenvalues#: Eigenvalues of covariance matrix

eigenvectors#: Eigenvectors of covariance matrix

dimension#: Dimension of the latent space

__init__(coords, mean=0.0, std=1.0, corr_length=0.3, explained_variance=None, latent_dimension=None, cut_off=0.0)[source]#

Initialize KL object.

Parameters:

coords (dict) – Dictionary with coordinates of discretized random field and the
mean (_SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes]) – Mean at coordinates of random field, can be a single constant
std (float) – Hyperparameter for standard-deviation of random field
corr_length (float) – Hyperparameter for the correlation length
explained_variance (float | None) – Explained variance of by the eigen decomposition, mutually exclusive argument with latent_dimension
latent_dimension (int | None) – Dimension of the latent space, mutually exclusive argument with explained_variance
cut_off (float) – Lower value limit of covariance matrix entries

calculate_covariance_matrix()[source]#

Calculate discretized covariance matrix.

Based on the kernel description of the random field, build its covariance matrix using the external geometry and coordinates.

Return type:: None

draw(num_samples)[source]#

Draw samples from the latent representation of the random field.

Parameters:: num_samples (int) – Number of draws of latent random samples
Returns:: Drawn samples
Return type:: ndarray

eigendecomp_cov_matrix(latent_dimension=None)[source]#

Decompose and then truncate the random field.

According to desired variance fraction that should be covered/explained by the truncation. Also computes the dimension of the latent space if it is not provided.

Parameters:: latent_dimension (int | None) – Dimension of the latent space
Returns:: Dimension of the latent space
Return type:: int

expanded_representation(samples)[source]#

Expand latent representation of samples.

Parameters:: samples (ndarray) – Latent representation of samples
Returns:: Expanded representation of samples
Return type:: ndarray

grad_logpdf(samples)[source]#

Get gradient of joint log-PDF of latent space.

Parameters:: samples (ndarray) – Samples for evaluating the gradient of the log-PDF
Returns:: Gradient of the log-PDF
Return type:: ndarray

latent_gradient(upstream_gradient)[source]#

Gradient of the field with respect to the latent parameters.

Parameters:: upstream_gradient (ndarray) – Gradient with respect to all coords of the field
Returns:: Gradient of the field with respect to the latent parameters
Return type:: ndarray

logpdf(samples)[source]#

Get joint log-PDF of latent space.

Parameters:: samples (ndarray) – Samples for evaluating the log-PDF
Returns:: Log-PDF of the samples
Return type:: ndarray

queens.parameters.random_fields.piece_wise module#

Piece-wise random fields class.

class PieceWise[source]#

Bases: RandomField

Piece-wise random field class.

The field is constructed at each node or element which is given by the coordinates. Each piece is assumed independently. Equals creating random variables for each point in coords.

distribution#: Dummy distribution with correct dimension

latent_1d_distribution#: QUEENS distribution object of latent space variables

__init__(coords, latent_1d_distribution)[source]#

Initialize RF object.

Parameters:

coords (dict) – Dictionary with coordinates of discretized random field and the corresponding keys
latent_1d_distribution (Continuous | Discrete) – Latent 1d distribution that is used for all variables.

draw(num_samples)[source]#

Draw samples from the latent representation of the random field.

Parameters:: num_samples (int) – Number of draws of latent random samples
Returns:: Drawn samples
Return type:: ndarray

expanded_representation(samples)[source]#

Expand latent representation of samples.

Parameters:: samples (ndarray) – Latent representation of samples
Returns:: Expanded representation of samples
Return type:: ndarray

grad_logpdf(samples)[source]#

Get gradient of joint log-PDF of latent space.

Parameters:: samples (ndarray) – Latent space samples
Returns:: Gradient of the log-PDF of the samples
Return type:: ndarray

latent_gradient(upstream_gradient)[source]#

Gradient of the field with respect to the latent parameters.

Parameters:: upstream_gradient (ndarray) – Gradient with respect to all coords of the field
Returns:: Gradient of the field with respect to the latent parameters
Return type:: ndarray

logpdf(samples)[source]#

Get joint log-PDF of latent space.

Parameters:: samples (ndarray) – Latent space samples
Returns:: Log-PDF of the samples
Return type:: ndarray