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scipy.linalg.

# cholesky

scipy.linalg.cholesky(a, lower=False, overwrite_a=False, check_finite=True)

  Compute the Cholesky decomposition of a matrix.

  Returns the Cholesky decomposition, \(A = L L^*\) or \(A = U^* U\) of a Hermitian positive-definite matrix A.

  Parameters:
    a(…, M, M) array_like

      Matrix to be decomposed

    lower bool, optional

      Whether to compute the upper- or lower-triangular Cholesky factorization. During decomposition, only the selected half of the matrix is referenced. Default is upper-triangular.

    overwrite_a bool, optional

      Whether to overwrite data in a (may improve performance). Default is False. See overwrite_* arguments for details.

    check_finite bool, optional

      Whether to check that the entire input matrix contains only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs.

  Returns:
    c(…, M, M) ndarray

      Upper- or lower-triangular Cholesky factor of a.

  Raises:
    LinAlgError if decomposition fails.

  See also

  `cho_factor`

    Compute the Cholesky decomposition without explicitly setting the other triangle to 0.

  Notes

  During the finiteness check (if selected), the entire matrix a is checked. During decomposition, a is assumed to be symmetric or Hermitian (as applicable), and only the half selected by option lower is referenced. Consequently, if a is asymmetric/non-Hermitian, `cholesky` may still succeed if the symmetric/Hermitian matrix represented by the selected half is positive definite, yet it may fail if an element in the other half is non-finite.

  Examples

      >>> import numpy as np
      >>> from scipy.linalg import cholesky
      >>> a = np.array([[1,-2j],[2j,5]])
      >>> L = cholesky(a, lower=True)
      >>> L
      array([[ 1.+0.j,  0.+0.j],
             [ 0.+2.j,  1.+0.j]])
      >>> L @ L.T.conj()
      array([[ 1.+0.j,  0.-2.j],
             [ 0.+2.j,  5.+0.j]])