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# scipy.stats.Covariance.whiten

Covariance.whiten(x)

  Perform a whitening transformation on data.

  “Whitening” (“white” as in “white noise”, in which each frequency has equal magnitude) transforms a set of random variables into a new set of random variables with unit-diagonal covariance. When a whitening transform is applied to a sample of points distributed according to a multivariate normal distribution with zero mean, the covariance of the transformed sample is approximately the identity matrix.

  Parameters:
    x array_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
      >>> precision = np.linalg.inv(cov_array)
      >>> cov_object = stats.Covariance.from_precision(precision)
      >>> x = rng.multivariate_normal(np.zeros(n), cov_array, size=(10000))
      >>> x_ = cov_object.whiten(x)
      >>> np.cov(x_, rowvar=False)  # near-identity covariance
      array([[0.97862122, 0.00893147, 0.02430451],
             [0.00893147, 0.96719062, 0.02201312],
             [0.02430451, 0.02201312, 0.99206881]])