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# scipy.linalg.cho_factor

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

  Compute the Cholesky decomposition of a matrix, to use in cho_solve

  Returns a matrix containing the Cholesky decomposition, `A = L L*` or `A = U* U` of a Hermitian positive-definite matrix a. The return value can be directly used as the first parameter to cho_solve.

  Warning

  The returned matrix also contains random data in the entries not used by the Cholesky decomposition. If you need to zero these entries, use the function `cholesky` instead.

  Parameters:
    a(M, M) array_like

      Matrix to be decomposed

    lower bool, optional

      Whether to compute the upper or lower triangular Cholesky factorization (Default: 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

      Matrix whose upper or lower triangle contains the Cholesky factor of a. Other parts of the matrix contain random data.

    lower bool

      Flag indicating whether the factor is in the lower or upper triangle

  Raises:
    LinAlgError

      Raised if decomposition fails.

  See also

  `cho_solve`

    Solve a linear set equations using the Cholesky factorization of a matrix.

  Examples

      >>> import numpy as np
      >>> from scipy.linalg import cho_factor
      >>> A = np.array([[9, 3, 1, 5], [3, 7, 5, 1], [1, 5, 9, 2], [5, 1, 2, 6]])
      >>> c, low = cho_factor(A)
      >>> c
      array([[3.        , 1.        , 0.33333333, 1.66666667],
             [3.        , 2.44948974, 1.90515869, -0.27216553],
             [1.        , 5.        , 2.29330749, 0.8559528 ],
             [5.        , 1.        , 2.        , 1.55418563]])
      >>> np.allclose(np.triu(c).T @ np. triu(c) - A, np.zeros((4, 4)))
      True