scipy.stats.Covariance.colorize#
- Covariance.colorize(x)[source]#
Perform a colorizing transformation on data.
“Colorizing” (“color” as in “colored noise”, in which different frequencies may have different magnitudes) transforms a set of uncorrelated random variables into a new set of random variables with the desired covariance. When a coloring transform is applied to a sample of points distributed according to a multivariate normal distribution with identity covariance and zero mean, the covariance of the transformed sample is approximately the covariance matrix used in the coloring transform.
- Parameters:
- xarray_like
An array of points. The last dimension must correspond with the dimensionality of the space, i.e., the number of columns in the covariance matrix.
- Returns:
- x_array_like
The transformed array of points.
References
[1]“Whitening Transformation”. Wikipedia. https://en.wikipedia.org/wiki/Whitening_transformation
[2]Novak, Lukas, and Miroslav Vorechovsky. “Generalization of coloring linear transformation”. Transactions of VSB 18.2 (2018): 31-35. DOI:10.31490/tces-2018-0013
Examples
>>> import numpy as np >>> from scipy import stats >>> rng = np.random.default_rng() >>> n = 3 >>> A = rng.random(size=(n, n)) >>> cov_array = A @ A.T # make matrix symmetric positive definite >>> cholesky = np.linalg.cholesky(cov_array) >>> cov_object = stats.Covariance.from_cholesky(cholesky) >>> x = rng.multivariate_normal(np.zeros(n), np.eye(n), size=(10000)) >>> x_ = cov_object.colorize(x) >>> cov_data = np.cov(x_, rowvar=False) >>> np.allclose(cov_data, cov_array, rtol=3e-2) True