linalg.py 文件源码

def lu_solve_AATI(A, rho, b, lu, piv):
    r"""
    Solve the linear system :math:`(A A^T + \rho I)\mathbf{x} = \mathbf{b}`
    or :math:`(A A^T + \rho I)X = B` using :func:`scipy.linalg.lu_solve`.

    Parameters
    ----------
    A : array_like
      Matrix :math:`A`
    rho : float
      Scalar :math:`\rho`
    b : array_like
      Vector :math:`\mathbf{b}` or matrix :math:`B`
    lu : array_like
      Matrix containing U in its upper triangle, and L in its lower triangle,
      as returned by :func:`scipy.linalg.lu_factor`
    piv : array_like
      Pivot indices representing the permutation matrix P, as returned by
      :func:`scipy.linalg.lu_factor`

    Returns
    -------
    x : ndarray
      Solution to the linear system.
    """

    N, M = A.shape
    if N >= M:
        x = (b - linalg.lu_solve((lu, piv), b.dot(A).T).T.dot(A.T)) / rho
    else:
        x = linalg.lu_solve((lu, piv), b.T).T
    return x