class OperatorBase(object):
    @property
    def dtype(self):
        raise NotImplementedError

    @property
    def shape(self):
        raise NotImplementedError


class IdentityOperator(OperatorBase):
    def __init__(self, dtype, n):
        self.my_dtype = dtype
        self.n = n

    @property
    def dtype(self):
        return self.my_dtype

    @property
    def shape(self):
        return self.n, self.n

    def __call__(self, operand):
        return operand


class DiagonalPreconditioner(OperatorBase):
    def __init__(self, diagonal):
        self.diagonal = diagonal

    @property
    def dtype(self):
        return self.diagonal.dtype

    @property
    def shape(self):
        n = self.diagonal.shape[0]
        return n, n

    def __call__(self, operand):
        return self.diagonal * operand