dmdbase.py 文件源码

def _eig_from_lowrank_op(Atilde, Y, U, s, V, exact):
        """
        Private method that computes eigenvalues and eigenvectors of the
        high-dimensional operator from the low-dimensional operator and the
        input matrix.

        :param numpy.ndarray Atilde: the lowrank operator.
        :param numpy.ndarray Y: input matrix Y.
        :param numpy.ndarray U: 2D matrix that contains the left-singular
            vectors of X, stored by column.
        :param numpy.ndarray s: 1D array that contains the singular values of X.
        :param numpy.ndarray V: 2D matrix that contains the right-singular
            vectors of X, stored by row.
        :param bool exact: if True, the exact modes are computed; otherwise,
            the projected ones are computed.
        :return: eigenvalues, eigenvectors
        :rtype: numpy.ndarray, numpy.ndarray
        """
        lowrank_eigenvalues, lowrank_eigenvectors = np.linalg.eig(Atilde)

        # Compute the eigenvectors of the high-dimensional operator
        if exact:
            eigenvectors = (
                (Y.dot(V) * np.reciprocal(s)).dot(lowrank_eigenvectors)
            )
        else:
            eigenvectors = U.dot(lowrank_eigenvectors)

        # The eigenvalues are the same
        eigenvalues = lowrank_eigenvalues

        return eigenvalues, eigenvectors