scipy.stats.random_correlation — SciPy v1.15.2 Manual (original) (raw)

scipy.stats.random_correlation = <scipy.stats._multivariate.random_correlation_gen object>[source]#

A random correlation matrix.

Return a random correlation matrix, given a vector of eigenvalues.

The eigs keyword specifies the eigenvalues of the correlation matrix, and implies the dimension.

Parameters:

eigs1d ndarray

Eigenvalues of correlation matrix

seed{None, int, numpy.random.Generator, numpy.random.RandomState}, optional

If seed is None (or np.random), the numpy.random.RandomStatesingleton is used. If seed is an int, a new RandomState instance is used, seeded with seed. If seed is already a Generator or RandomState instance then that instance is used.

tolfloat, optional

Tolerance for input parameter checks

diag_tolfloat, optional

Tolerance for deviation of the diagonal of the resulting matrix. Default: 1e-7

Returns:

rvsndarray or scalar

Random size N-dimensional matrices, dimension (size, dim, dim), each having eigenvalues eigs.

Raises:

RuntimeError

Floating point error prevented generating a valid correlation matrix.

Notes

Generates a random correlation matrix following a numerically stable algorithm spelled out by Davies & Higham. This algorithm uses a single O(N) similarity transformation to construct a symmetric positive semi-definite matrix, and applies a series of Givens rotations to scale it to have ones on the diagonal.

References

[1]

Davies, Philip I; Higham, Nicholas J; “Numerically stable generation of correlation matrices and their factors”, BIT 2000, Vol. 40, No. 4, pp. 640 651

Examples

import numpy as np from scipy.stats import random_correlation rng = np.random.default_rng() x = random_correlation.rvs((.5, .8, 1.2, 1.5), random_state=rng) x array([[ 1. , -0.02423399, 0.03130519, 0.4946965 ], [-0.02423399, 1. , 0.20334736, 0.04039817], [ 0.03130519, 0.20334736, 1. , 0.02694275], [ 0.4946965 , 0.04039817, 0.02694275, 1. ]]) import scipy.linalg e, v = scipy.linalg.eigh(x) e array([ 0.5, 0.8, 1.2, 1.5])

Methods