def METHOD_NAME(self):
    """
    Matrix and RHS are inputs, solution vector is the output.
    """
    vec_size = self.options['vec_size']
    vec_size_A = self.vec_size_A = vec_size if self.options['vectorize_A'] else 1
    size = self.options['size']
    self._lup = []
    shape = (vec_size, size) if vec_size > 1 else (size, )
    shape_A = (vec_size_A, size, size) if vec_size_A > 1 else (size, size)
    init_A = np.eye(size)
    if vec_size_A > 1:
        init_A = np.repeat(init_A.reshape(1, size, size), vec_size_A, axis=0)
    self.add_input("A", val=init_A)
    self.add_input("b", val=np.ones(shape))
    self.add_output("x", shape=shape, val=.1)