def test_noninteractive(self):
"Test case for when agents don't interact with each other"
# Copied these values from test_lqcontrol
a = np.array([[.95, 0.], [0, .95]])
b1 = np.array([.95, 0.])
b2 = np.array([0., .95])
r1 = np.array([[-.25, 0.], [0., 0.]])
r2 = np.array([[0., 0.], [0., -.25]])
q1 = np.array([[-.15]])
q2 = np.array([[-.15]])
f1, f2, p1, p2 = nnash(a, b1, b2, r1, r2, q1, q2, 0, 0, 0, 0, 0, 0,
tol=1e-8, max_iter=10000)
alq = a[:1, :1]
blq = b1[:1].reshape((1, 1))
rlq = r1[:1, :1]
qlq = q1
lq_obj = LQ(qlq, rlq, alq, blq, beta=1.)
p, f, d = lq_obj.stationary_values()
assert_allclose(f1, f2[:, ::-1])
assert_allclose(f1[0, 0], f[0])
assert_allclose(p1[0, 0], p2[1, 1])
assert_allclose(p1[0, 0], p[0, 0])
def test_noninteractive(self):
"Test case for when agents don't interact with each other"
# Copied these values from test_lqcontrol
a = np.array([[.95, 0.], [0, .95]])
b1 = np.array([.95, 0.])
b2 = np.array([0., .95])
r1 = np.array([[-.25, 0.], [0., 0.]])
r2 = np.array([[0., 0.], [0., -.25]])
q1 = np.array([[-.15]])
q2 = np.array([[-.15]])
f1, f2, p1, p2 = nnash(a, b1, b2, r1, r2, q1, q2, 0, 0, 0, 0, 0, 0,
tol=1e-8, max_iter=10000)
alq = a[:1, :1]
blq = b1[:1].reshape((1, 1))
rlq = r1[:1, :1]
qlq = q1
lq_obj = LQ(qlq, rlq, alq, blq, beta=1.)
p, f, d = lq_obj.stationary_values()
assert_allclose(f1, f2[:, ::-1])
assert_allclose(f1[0, 0], f[0])
assert_allclose(p1[0, 0], p2[1, 1])
assert_allclose(p1[0, 0], p[0, 0])
def setUp(self):
# Initial Values
a_0 = 100
a_1 = 0.5
rho = 0.9
sigma_d = 0.05
beta = 0.95
c = 2
gamma = 50.0
theta = 0.002
ac = (a_0 - c) / 2.0
R = np.array([[0, ac, 0], [ac, -a_1, 0.5], [0., 0.5, 0]])
R = -R
Q = gamma / 2
Q_pf = 0.
A = np.array([[1., 0., 0.], [0., 1., 0.], [0., 0., rho]])
B = np.array([[0.], [1.], [0.]])
B_pf = np.zeros((3, 1))
C = np.array([[0.], [0.], [sigma_d]])
# the *_pf endings refer to an example with pure forecasting
# (see p171 in Robustness)
self.rblq_test = RBLQ(Q, R, A, B, C, beta, theta)
self.rblq_test_pf = RBLQ(Q_pf, R, A, B_pf, C, beta, theta)
self.lq_test = LQ(Q, R, A, B, C, beta)
self.methods = ['doubling', 'qz']
def setUp(self):
# Initial Values
a_0 = 100
a_1 = 0.5
rho = 0.9
sigma_d = 0.05
beta = 0.95
c = 2
gamma = 50.0
theta = 0.002
ac = (a_0 - c) / 2.0
R = np.array([[0, ac, 0],
[ac, -a_1, 0.5],
[0., 0.5, 0]])
R = -R
Q = gamma / 2
A = np.array([[1., 0., 0.],
[0., 1., 0.],
[0., 0., rho]])
B = np.array([[0.],
[1.],
[0.]])
C = np.array([[0.],
[0.],
[sigma_d]])
self.rblq_test = RBLQ(Q, R, A, B, C, beta, theta)
self.lq_test = LQ(Q, R, A, B, C, beta)
self.Fr, self.Kr, self.Pr = self.rblq_test.robust_rule()
def setUp(self):
# Initial Values
q = 1.
r = 1.
rf = 1.
a = .95
b = -1.
c = .05
beta = .95
T = 1
self.lq_scalar = LQ(q, r, a, b, C=c, beta=beta, T=T, Rf=rf)
Q = np.array([[0., 0.], [0., 1]])
R = np.array([[1., 0.], [0., 0]])
RF = np.eye(2) * 100
A = np.ones((2, 2)) * .95
B = np.ones((2, 2)) * -1
self.lq_mat = LQ(Q, R, A, B, beta=beta, T=T, Rf=RF)
density=gaussian_kde(betaols)
xs = np.linspace(-1,1)
plt.plot(xs,density(xs))
plt.show()
############
# AD-HOC #
###########
theta =2
R=-R
F, P, K = quantecon.robustlq.RBLQ(Q,R,A,B,C,beta,theta).robust_rule()
P = quantecon.solve_discrete_riccati(A, B, R, Q)
from quantecon.lqcontrol import LQ
I=np.eye(4)
lq = LQ(-beta*I*theta, R, A, C, beta=beta)
Ptest, ftest, dtest = lq.stationary_values()
theta =901
A=np.matrix([[rho1,0,0,0],
[0,rho2,0,0],
[0,0,rho3,0],
[0,0,0,rho4]])
B=np.zeros((4,4))
B = np.matrix([[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]) C = np.matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]) Q = np.matrix([[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]) R = np.matrix([[r1, 0, 0, 0], [0, r2, 0, 0], [0, 0, r3, 0], [0, 0, 0, r4]]) P = np.ones(4) I = np.ones(4) Z = np.zeros(4) quantecon.robustlq.RBLQ(Q, R, A, B, C, beta, theta).robust_rule() F, K, P = quantecon.robustlq.RBLQ.robust_rule() lq = LQ(-beta * I * theta, R, A, C, beta=beta) P, f, d = lq.stationary_values() #Define M for Schur-Decomposition M11 = A + C * np.linalg.inv(beta * theta * A) * C.T * R M12 = C * np.linalg.inv(beta * theta * A) * C.T M21 = np.linalg.inv(A) * R M22 = np.linalg.inv(A) M1 = np.hstack((M11, M12)) M2 = np.hstack((M21, M22)) M = np.vstack((M1, M2)) [T, Z, sdim] = scipy.linalg.schur(M, output='real', sort='iuc')
q = 1e6
# == Formulate as an LQ problem == #
Q = 1
R = np.zeros((2, 2))
Rf = np.zeros((2, 2))
Rf[0, 0] = q
A = [[1 + r, -c_bar + mu],
[0, 1]]
B = [[-1],
[0]]
C = [[sigma],
[0]]
# == Compute solutions and simulate == #
lq = LQ(Q, R, A, B, C, beta=beta, T=T, Rf=Rf)
x0 = (0, 1)
xp, up, wp = lq.compute_sequence(x0)
# == Convert back to assets, consumption and income == #
assets = xp[0, :] # a_t
c = up.flatten() + c_bar # c_t
income = wp[0, 1:] + mu # y_t
# == Plot results == #
n_rows = 2
fig, axes = plt.subplots(n_rows, 1, figsize=(12, 10))
plt.subplots_adjust(hspace=0.5)
for i in range(n_rows):
axes[i].grid()
