Correlate

Correlate is a class to induce correlation to an uncorrelated standard normal vector \(\textbf{u}=[U_1,...,U_n]\), given the correlation matrix \(\textbf{C}_z=[\rho_{ij}]\). The correlated standard normal vector \(\textbf{z}=[Z_1,...,Z_n]\) can be calculated as:

\[\mathbf{z}^\intercal = \mathbf{H}\mathbf{u}^\intercal\]

where \(\mathbf{H}\) is the lower triangular matrix resulting from the Cholesky decomposition of the correlation matrix, i.e. \(\mathbf{C_z}=\mathbf{H}\mathbf{H}^\intercal\).

Correlate Class

The Correlate class is imported using the following command:

>>> from UQpy.transformations.Correlate import Correlate

Methods

class Correlate(samples_u, corr_z)[source]

A class to induce correlation to standard normal random variables.

Parameters:

samples_u (ndarray) – Uncorrelated standard normal vector of shape (nsamples, n_dimensions).
corr_z (ndarray) – The correlation matrix (\(\mathbf{C_Z}\)) of the standard normal random vector Z .

Attributes

Correlate.H: ndarray: The lower diagonal matrix resulting from the Cholesky decomposition of the correlation matrix (\(\mathbf{C_Z}\)).

Correlate.samples_z: ndarray: Correlated standard normal vector of shape (nsamples, n_dimensions).