Exemplo n.º 1
0
    def stationary_values(self):
        """
        Computes the limit of :math:`\Sigma_t` as t goes to infinity by
        solving the associated Riccati equation. Computation is via the
        doubling algorithm (see the documentation in
        `matrix_eqn.solve_discrete_riccati`).

        Returns
        -------
        Sigma_infinity : array_like or scalar(float)
            The infinite limit of :math:`\Sigma_t`
        K_infinity : array_like or scalar(float)
            The stationary Kalman gain.

        """
        # === simplify notation === #
        A, C, G, H = self.ss.A, self.ss.C, self.ss.G, self.ss.H
        Q, R = np.dot(C, C.T), np.dot(H, H.T)

        # === solve Riccati equation, obtain Kalman gain === #
        Sigma_infinity = solve_discrete_riccati(A.T, G.T, Q, R)
        temp1 = dot(dot(A, Sigma_infinity), G.T)
        temp2 = inv(dot(G, dot(Sigma_infinity, G.T)) + R)
        K_infinity = dot(temp1, temp2)

        # == record as attributes and return == #
        self.Sigma_infinity, self.K_infinity = Sigma_infinity, K_infinity
        return Sigma_infinity, K_infinity
Exemplo n.º 2
0
    def stationary_values(self):
        """
        Computes the limit of Sigma_t as t  goes to infinity by
        solving the associated Riccati equation.  Computation is via the
        doubling algorithm (see the documentation in
        `matrix_eqn.solve_discrete_riccati`).

        Returns
        -------
        Sigma_infinity : array_like or scalar(float)
            The infinite limit of Sigma_t
        K_infinity : array_like or scalar(float)
            The stationary Kalman gain.

        """
        # === simplify notation === #
        A, C, G, H = self.ss.A, self.ss.C, self.ss.G, self.ss.H
        Q, R = np.dot(C, C.T), np.dot(H, H.T)

        # === solve Riccati equation, obtain Kalman gain === #
        Sigma_infinity = solve_discrete_riccati(A.T, G.T, Q, R)
        temp1 = dot(dot(A, Sigma_infinity), G.T)
        temp2 = inv(dot(G, dot(Sigma_infinity, G.T)) + R)
        K_infinity = dot(temp1, temp2)

        # == record as attributes and return == #
        self.Sigma_infinity, self.K_infinity = Sigma_infinity, K_infinity
        return Sigma_infinity, K_infinity
Exemplo n.º 3
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def dare_test_tjm_1():
    A = [[0.0, 0.1, 0.0], [0.0, 0.0, 0.1], [0.0, 0.0, 0.0]]
    B = [[1.0, 0.0], [0.0, 0.0], [0.0, 1.0]]
    Q = [[10**5, 0.0, 0.0], [0.0, 10**3, 0.0], [0.0, 0.0, -10.0]]
    R = [[0.0, 0.0], [0.0, 1.0]]
    X = solve_discrete_riccati(A, B, Q, R)
    Y = np.diag((1e5, 1e3, 0.0))
    assert_allclose(X, Y, atol=1e-07)
Exemplo n.º 4
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def dare_test_tjm_2():
    A = [[0, -1], [0, 2]]
    B = [[1, 0], [1, 1]]
    Q = [[1, 0], [0, 0]]
    R = [[4, 2], [2, 1]]
    X = solve_discrete_riccati(A, B, Q, R)
    Y = np.zeros((2, 2))
    Y[0, 0] = 1
    assert_allclose(X, Y, atol=1e-07)
Exemplo n.º 5
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def dare_test_tjm_3():
    r = 0.5
    I = np.identity(2)
    A = [[2 + r**2, 0], [0, 0]]
    A = np.array(A)
    B = I
    R = [[1, r], [r, r * r]]
    Q = I - np.dot(A.T, A) + np.dot(A.T, np.linalg.solve(R + I, A))
    X = solve_discrete_riccati(A, B, Q, R)
    Y = np.identity(2)
    assert_allclose(X, Y, atol=1e-07)
Exemplo n.º 6
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def dare_test_tjm_3():
    r = 0.5
    I = np.identity(2)
    A = [[2 + r**2, 0],
         [0,        0]]
    A = np.array(A)
    B = I
    R = [[1, r],
         [r, r*r]]
    Q = I - np.dot(A.T, A) + np.dot(A.T, np.linalg.solve(R + I, A))
    X = solve_discrete_riccati(A, B, Q, R)
    Y = np.identity(2)
    assert_allclose(X, Y, atol=1e-07)
Exemplo n.º 7
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def dare_test_tjm_2():
    A = [[0, -1],
         [0, 2]]
    B = [[1, 0],
         [1, 1]]
    Q = [[1, 0],
         [0, 0]]
    R = [[4, 2],
         [2, 1]]
    X = solve_discrete_riccati(A, B, Q, R)
    Y = np.zeros((2, 2))
    Y[0, 0] = 1
    assert_allclose(X, Y, atol=1e-07)
Exemplo n.º 8
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def dare_test_tjm_1():
    A = [[0.0, 0.1, 0.0],
         [0.0, 0.0, 0.1],
         [0.0, 0.0, 0.0]]
    B = [[1.0, 0.0],
         [0.0, 0.0],
         [0.0, 1.0]]
    Q = [[10**5, 0.0, 0.0],
         [0.0, 10**3, 0.0],
         [0.0, 0.0, -10.0]]
    R = [[0.0, 0.0],
         [0.0, 1.0]]
    X = solve_discrete_riccati(A, B, Q, R)
    Y = np.diag((1e5, 1e3, 0.0))
    assert_allclose(X, Y, atol=1e-07)
Exemplo n.º 9
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    def stationary_values(self, method='doubling'):
        """
        Computes the limit of :math:`\Sigma_t` as t goes to infinity by
        solving the associated Riccati equation. The outputs are stored in the
        attributes `K_infinity` and `Sigma_infinity`. Computation is via the
        doubling algorithm (default) or a QZ decomposition method (see the
        documentation in `matrix_eqn.solve_discrete_riccati`).

        Parameters
        ----------
        method : str, optional(default="doubling")
            Solution method used in solving the associated Riccati
            equation, str in {'doubling', 'qz'}.

        Returns
        -------
        Sigma_infinity : array_like or scalar(float)
            The infinite limit of :math:`\Sigma_t`
        K_infinity : array_like or scalar(float)
            The stationary Kalman gain.

        """

        # === simplify notation === #
        A, C, G, H = self.ss.A, self.ss.C, self.ss.G, self.ss.H
        Q, R = np.dot(C, C.T), np.dot(H, H.T)

        # === solve Riccati equation, obtain Kalman gain === #
        Sigma_infinity = solve_discrete_riccati(A.T, G.T, Q, R, method=method)
        temp1 = np.dot(np.dot(A, Sigma_infinity), G.T)
        temp2 = inv(np.dot(G, np.dot(Sigma_infinity, G.T)) + R)
        K_infinity = np.dot(temp1, temp2)

        # == record as attributes and return == #
        self._Sigma_infinity, self._K_infinity = Sigma_infinity, K_infinity
        return Sigma_infinity, K_infinity
Exemplo n.º 10
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    def stationary_values(self, method='doubling'):
        """
        Computes the limit of :math:`\Sigma_t` as t goes to infinity by
        solving the associated Riccati equation. The outputs are stored in the
        attributes `K_infinity` and `Sigma_infinity`. Computation is via the
        doubling algorithm (default) or a QZ decomposition method (see the
        documentation in `matrix_eqn.solve_discrete_riccati`).

        Parameters
        ----------
        method : str, optional(default="doubling")
            Solution method used in solving the associated Riccati
            equation, str in {'doubling', 'qz'}.

        Returns
        -------
        Sigma_infinity : array_like or scalar(float)
            The infinite limit of :math:`\Sigma_t`
        K_infinity : array_like or scalar(float)
            The stationary Kalman gain.

        """

        # === simplify notation === #
        A, C, G, H = self.ss.A, self.ss.C, self.ss.G, self.ss.H
        Q, R = np.dot(C, C.T), np.dot(H, H.T)

        # === solve Riccati equation, obtain Kalman gain === #
        Sigma_infinity = solve_discrete_riccati(A.T, G.T, Q, R, method=method)
        temp1 = dot(dot(A, Sigma_infinity), G.T)
        temp2 = inv(dot(G, dot(Sigma_infinity, G.T)) + R)
        K_infinity = dot(temp1, temp2)

        # == record as attributes and return == #
        self._Sigma_infinity, self._K_infinity = Sigma_infinity, K_infinity
        return Sigma_infinity, K_infinity
Exemplo n.º 11
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def dare_golden_num_2d(method):
    A, B, R, Q = np.eye(2), np.eye(2), np.eye(2), np.eye(2)
    gold_diag = np.eye(2) * (1 + np.sqrt(5)) / 2.
    val = solve_discrete_riccati(A, B, R, Q, method=method)
    assert_allclose(val, gold_diag)
Exemplo n.º 12
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def dare_golden_num_float(method):
    val = solve_discrete_riccati(1.0, 1.0, 1.0, 1.0, method=method)
    gold_ratio = (1 + np.sqrt(5)) / 2.
    assert_allclose(val, gold_ratio)
Exemplo n.º 13
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def dare_test_golden_num_2d():
    A, B, R, Q = np.eye(2), np.eye(2), np.eye(2), np.eye(2)
    gold_diag = np.eye(2) * (1 + np.sqrt(5)) / 2.
    val = solve_discrete_riccati(A, B, R, Q)
    assert_allclose(val, gold_diag)
Exemplo n.º 14
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def dare_test_golden_num_float():
    val = solve_discrete_riccati(1.0, 1.0, 1.0, 1.0)
    gold_ratio = (1 + np.sqrt(5)) / 2.
    assert_allclose(val, gold_ratio)