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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

  If overwrite_a is disabled, this function matches `cholesky` and zeros the other triangle. If it is enabled, the returned matrix may contain random data in the entries not used by the Cholesky decomposition, saving out on the explicit putting to 0 done by `cholesky`.

  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: 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

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

    lower ndarray, bool

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

  Raises:
    LinAlgError

      Raised if decomposition fails.

  See also

  `cholesky`

    Compute the Cholesky decomposition and explicitly put the other triangle to 0.

  `cho_solve`

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

  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 cho_factor
      >>> A = np.array([[9, 3, 1, 5], [3, 7, 5, 1], [1, 5, 9, 2], [5, 1, 2, 6]],
      ...             dtype=float, order="F")
      >>> A_ref = np.copy(A)
      >>> c, low = cho_factor(A)
      >>> c
      array([[3.        , 1.        , 0.33333333, 1.66666667],
             [0.        , 2.44948974, 1.90515869, -0.27216553],
             [0.        , 0.        , 2.29330749, 0.8559528 ],
             [0.        , 0.        , 0.        , 1.55418563]])
      >>> np.allclose(c.T @ c - A, np.zeros((4, 4)))
      True
      >>> c, low = cho_factor(A, overwrite_a=True)
      >>> 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_ref, np.zeros((4, 4)))
      True