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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def b_operator(self, P):
 r""" The B operator, mapping P into .. math:: B(P) := R - \beta^2 A'PB(Q + \beta B'PB)^{-1}B'PA + \beta A'PA and also returning .. math:: F := (Q + \beta B'PB)^{-1} \beta B'PA Parameters P : array_like(float, ndim=2) A matrix that should be n x n Returns ------- F : array_like(float, ndim=2) The F matrix as defined above new_p : array_like(float, ndim=2) The matrix P after applying the B operator """

        A, B, Q, R, beta = self.A, self.B, self.Q, self.R, self.beta
        S1 = Q + beta * dot(B.T, dot(P, B))
        S2 = beta * dot(B.T, dot(P, A))
        S3 = beta * dot(A.T, dot(P, A))
        F = solve(S1, S2) if not self.pure_forecasting else np.zeros(
            (self.k, self.n))
        new_P = R - dot(S2.T, F) + S3

        return F, new_P