Functional

This page describes the FunctionalModel methods.

Methods

F(x, y)

Calculate y = F(x) using armadillo library and write results to y without allocating new memory. This method is used only by the other components of the kernel.

Parameters:

  • x (ndarray) – Vector of the functional model parameters (L dimension).

  • y (ndarray) – Vector of results (D dimension).

getDimensionY()

Return the D dimension of the problem.

Returns:

The dimension D of the problem.

getDimensionX()

Return the L dimension of the problem.

Returns:

The dimension L of the problem.

toPhysic(x)

Transform the values of x from the mathematical space to the physical space.

Parameters:

x (ndarray) – The vector to normalize.

fromPhysic(x)

Transform the values of x from the physical space to the mathematical space.

Parameters:

x (ndarray) – The vector to normalize.

genData(N, generator_type, noise, seed)

Generate a complete learning dataset from the generator type and the FunctionalModel.

Parameters:

  • N (int) – Number of generated observations.

  • generator_type (str) – The type of the generator used to generate x_gen matrix values.

  • noise (float, ndarray) – Vector of dimension D corresponding to the y_i variances.

  • seed (int) – Seed number for random generators.

Returns:

A generated dataset composed of a pair (x_gen, y_gen) with x_gen of shape (L, N) and y_gen of shape (D, N).

importanceSampling(proposition_gmms, y, y_err, N_0, B=0, J=0, covariance=0, idx_gaussian=-1, verbose=1, seed=0)

Perform importance sampling with given parameters.

Parameters:

  • proposition_gmms (list[(1-D ndarray, 2-D ndarray, 3-D ndarray)], FullGMMResult, MergedGMMResult) –

    List of GMM propositions. The GMMs can be defined by the three following objects :

    • (list[(1-D ndarray, 2-D ndarray, 3-D ndarray)]) A Python list with length N_obs containing each GMM defined as a tuple of 3 elements:

      • weigths (ndarray of shape (K)),

      • means (ndarray of shape (L, K)),

      • covariance matrices (ndarray of shape (K, L, L)).

    • (FullGMMResult) The full GMM calculated with inverseDensities method.

    • (MergedGMMResult) The merged GMM calculated with inverseDensities method.

  • y (ndarray with shape(D, N_obs)) – Matrix y.

  • y_err (ndarray with shape(D, N_obs)) – Matrix of y errors.

  • N_0 (int) – Initial number of samples.

  • B (int) – (optional) Parameter B.

  • J (int) – (optional) Parameter J.

  • covariance (ndarray with shape(D)) – (optional) Covariance vector with shape (D).

  • idx_gaussian (int) – (optional) Index of the desired gaussian from the merged GMM. Starts from 0 and ends at K_merged - 1. Perform importance sampling with given parameters on the specified gaussian of the GMMs.

  • verbose (int) – (optional) The verbosity of the logging among {0, 1, 2}.

  • seed (int) – (optional) The seed for random generation. It helps with reproducibility.

Returns:

An instance of ImportanceSamplingResult containing the importance sampling results.