volcapy.uq package

Submodules

volcapy.uq.azzimonti module

(DEPRECATED) Module implementing estimation of excursion sets and uncertainty quantification on them.

SHOULD BE ADAPTED TO THE NEW GAUSSIANPROCESS CLASS.

class volcapy.uq.azzimonti.GaussianProcess(mean, variance, covariance_func)

Bases: object

Implementation of Gaussian Process.

The underlying spatial structure is just a list of points, that is, we do not need to know the real spatial structure, the GP only know the mean/variance/covariance at points number i or j.

Parameters

mean: 1D array-like

List (or ndarray). Element i gives the mean at point i.

variance: 1D array-like

Variance at every point.

covariance_func: function

Two parameter function. F(i, j) should return the covariance between points i and j.

Methods

compute_excursion_probs(threshold)	Computes once and for all the probability of excursion above threshold for every point.
coverage_fct(i, threshold)	Coverage function (excursion probability) at a point.
expected_excursion_measure(threshold)	Get the expected measure of the excursion set above the given threshold.
vorobev_deviation(set_inds, threshold)	Compute the Vorob’ev deviation of a given set.
vorobev_expectation_inds(threshold)	Get cells belonging to the Vorobev expectation.
vorobev_quantile_inds(alpha, threshold)	Get the cells belonging Vorobev quantile alpha.

compute_excursion_probs(threshold)

Computes once and for all the probability of excursion above threshold for every point.

Parameters

threshold: float

Returns

List[float]

Excursion probabilities. Element i contains excursion probability (above threshold) for element i.

coverage_fct(i, threshold)

Coverage function (excursion probability) at a point.

Given a point in space, gives the probability that the value of the GP at that point is above some threshold.

Parameters

i: int

Index of the point to consider.

threshold: float

Returns

float

Probability that value of the field at point is above the threshold.

expected_excursion_measure(threshold)

Get the expected measure of the excursion set above the given threshold.

Parameters

threshold: float

Excursion threshold

Returns

flot

Expected size (in number of cells) of the excursion set above the given threshold.

vorobev_deviation(set_inds, threshold)

Compute the Vorob’ev deviation of a given set.

Parameters

set_inds: List[int]

Indices of the cells belonging to the set.

threshold: float

Excursion threshold.

Returns

float

Vorob’ev deviation of the set.

vorobev_expectation_inds(threshold)

Get cells belonging to the Vorobev expectation.

Parameters

threshold: float

Excursion threshold.

Returns

List[int]

List of the indices of the points that are in the Vorobev quantile.

vorobev_quantile_inds(alpha, threshold)

Get the cells belonging Vorobev quantile alpha.

Parameters

alpha: float

Level of the quantile to return. Will return points that have a prob greater than alpha to be in the excursion set.

threshold: float

Excursion threshold.

Returns

List[int]

List of the indices of the points that are in the Vorobev quantile.

volcapy.uq.example_azzimonti module

Run script for the Azzimonti techniques. It assumes posterior mean and variance have already been computed and stored as static files.

Module contents