rc.data.samples

Functionality for Design of Experiments (DOE) and sampling.

Classes

DOE	Sampling methods for inputs.
GaussianNoise	Sample multivariate, zero-mean Gaussian noise.
Function	Sample a task.function.Vector.

Methods

permute_axes(new_order)	Provide a rotation matrix which reorders axes. Most use cases are to re-order input axes according to GSA.
PCA(root, csv)	Perform Principal Component Analysis on a Repo.

Module Contents

class DOE

Sampling methods for inputs.

static latin_hypercube(N, M, is_centered=True, **kwargs)

Latin Hypercube DOE.

Parameters:

• N (int) – The number of samples (rows).

• M (int) – The of input dimensions (columns).

• is_centered (bool) – Boolean ordinate whether to centre each sample in its Latin Hypercube cell. Default is False, which locates the sample randomly within its cell.

• kwargs – Passed directly to scipy.stats.qmc.LatinHypercube.

Returns: An (N,M) matrix of N samples of dimension M.

static full_factorial(N, M)

Full factorial DOE.

Parameters:

• N (int) – The number of samples (rows).

• M (int) – The of input dimensions (columns).

Returns: An (N,M) matrix of N samples of dimension M.

static space_filling_test(X, o)

Test whether X is a space-filling design matrix, by finding the distance to the nearest point in X for o test points.

Parameters:

• X (rc.base.Np.Matrix) – An (N,M) design matrix.

• o (int) – The number of test points used to assess whether X is a space-filling design.

Return type:

rc.base.Dict[str, float]

Returns: A dict of six measures: The theoretical hard upper bound, expected upper bound and

expected lower bound for a perfectly space-filling design matrix, followed by the max, mean and SD of the distance-to-nearest-in-X over the o test points.

class GaussianNoise(N, variance)

Sample multivariate, zero-mean Gaussian noise.

Parameters:

• N (int)

• variance (rc.base.Np.MatrixLike)

class Variance(L, magnitude, is_covariant=False, is_determined=True)

An artificially generated (co)variance matrix for GaussianNoise, with a useful labelling scheme.

Parameters:

• L (int)

• magnitude (float)

• is_covariant (bool)

• is_determined (bool)

property matrix: rc.base.Np.Matrix

Variance as an (L,L) covariance matrix, suitable for constructing GaussianNoise.

Return type:

rc.base.Np.Matrix

property meta: rc.base.Dict[str, rc.base.Any]

Meta matching the initials in self.__format__().

Return type:

rc.base.Dict[str, rc.base.Any]

__call__()

Variance as an (L,L) covariance matrix, suitable for constructing GaussianNoise. The constructor generates the matrix (perhaps stochastically), so repeated calls to any methods produce identical Variance.

Return type:

rc.base.Np.Matrix

__format__(format_spec)

The label for this Variance, to help name samples informatively. The description is d. (determined) or u. (undetermined), followed by v. (diagonal variance) or c. (non-diagonal covariance), followed by 100 * self.magnitude:.2f.

Parameters:

format_spec (rc.base.Any)

Return type:

str

__call__(repo=None)

Generate N samples of L-dimensional Gaussian noise, sampled from \(N[0,self.variance]\). The constructor generates the sample, so repeated calls to any method always refer to the same GaussianNoise.

Parameters:

repo (Repo | None) – An optional Repo which will have GaussianNoise added to Y in data.csv.

Return type:

rc.base.Np.Matrix

Returns: An (N,L) noise matrix, where (L,L) is the shape of self._variance.

class Function(root, doe, function_vector, N, M, noise_variance, ext=None, overwrite_existing=False, **kwargs)

Sample a task.function.Vector.

Parameters:

• root (rc.base.Path | str)

• doe (DOE)

• function_vector (Vector)

• N (int)

• M (int)

• noise_variance (GaussianNoise)

• ext (str | None)

• overwrite_existing (bool)

• kwargs (rc.base.Any)

property repo: Repo

The Repo containing the Function sample.

Return type:

Repo

collection(sub_folder)

Construct a Dict for task.results.Collect, with appropriate extra_columns.

Parameters:

• folder – The folder under self.repo.folder housing the csvs to collect.

• sub_folder (rc.base.Union[rc.base.Path, str])

Return type:

rc.base.Dict[str, rc.base.Any]

Returns: The Dict for self.repo.

un_rotate_folds()

Create an un-rotated Fold in the Repo, with index K+1.

Return type:

Function

permute_axes(new_order)

Provide a rotation matrix which reorders axes. Most use cases are to re-order input axes according to GSA.

Parameters:

new_order (rc.base.Sequence | None) – A Tuple or List containing a permutation of [0,...,M-1], for passing to np.transpose.

Return type:

rc.base.Np.Matrix | None

Returns: A rotation matrix which will reorder the axes to new_order. Returns None if new_order is None.

PCA(root, csv)

Perform Principal Component Analysis on a Repo.

Parameters:

• root (str | rc.base.Path) – The root folder.

• csv (str | rc.base.Path) – The csv to read.

• normalization – An optional csv file to use for normalization.

Return type:

rc.base.Path

Returns: The folder written to, namely root``/PCA``