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scipy.stats.Covariance.

# from_cholesky

static Covariance.from_cholesky(cholesky)

  Representation of a covariance provided via the (lower) Cholesky factor

  Parameters:
    cholesky array_like

      The lower triangular Cholesky factor of the covariance matrix.

  Notes

  Let the covariance matrix be \(A\) and \(L\) be the lower Cholesky factor such that \(L L^T = A\). Whitening of a data point \(x\) is performed by computing \(L^{-1} x\). \(\log\det{A}\) is calculated as \(2tr(\log{L})\), where the \(\log\) operation is performed element-wise.

  This `Covariance` class does not support singular covariance matrices because the Cholesky decomposition does not exist for a singular covariance matrix.

  Examples

  Prepare a symmetric positive definite covariance matrix `A` and a data point `x`.

      >>> import numpy as np
      >>> from scipy import stats
      >>> rng = np.random.default_rng()
      >>> n = 5
      >>> A = rng.random(size=(n, n))
      >>> A = A @ A.T  # make the covariance symmetric positive definite
      >>> x = rng.random(size=n)

  Perform the Cholesky decomposition of `A` and create the `Covariance` object.

      >>> L = np.linalg.cholesky(A)
      >>> cov = stats.Covariance.from_cholesky(L)

  Compare the functionality of the `Covariance` object against reference implementation.

      >>> from scipy.linalg import solve_triangular
      >>> res = cov.whiten(x)
      >>> ref = solve_triangular(L, x, lower=True)
      >>> np.allclose(res, ref)
      True
      >>> res = cov.log_pdet
      >>> ref = np.linalg.slogdet(A)[-1]
      >>> np.allclose(res, ref)
      True