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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. Default is upper-triangular.

    overwrite_a bool, optional

      Whether to overwrite data in a (may improve performance).

    check_finite bool, optional

      Whether to check that the 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.

  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]])