def cauchy_pt(g, hess, delta):
# General expression for the Cauchy point
crv = np.dot(g, right_multiply_hessian(hess, g))
gnorm = np.linalg.norm(g)
if crv <= 0.0:
alpha = delta / gnorm
else:
alpha = min(delta / gnorm, gnorm**2 / crv)
s = -alpha * g
red = calculate_model_value(g, hess, s)
crvmin = np.dot(s, right_multiply_hessian(hess, s)) / np.dot(s, s)
if crvmin < 0.0:
crvmin = -1.0
return s, red, crvmin
def runTest(self):
n = 3
g = np.array([1.0, 0.0, 1.0])
H = np.array([[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 2.0]])
Delta = 2.0
hess = to_upper_triangular_vector(H)
xopt = np.ones((n, )) # trying nonzero (since bounds inactive)
sl = xopt + np.array([-0.5, -10.0, -10.0])
su = xopt + np.array([10.0, 10.0, 10.0])
d, gnew, crvmin = trsbox(xopt, g, hess, sl, su, Delta)
true_d = np.array([-1.0, 0.0, -0.5])
est_min = calculate_model_value(g, hess, d)
true_min = calculate_model_value(g, hess, true_d)
# Hope to get actual correct answer for internal minimum?
# self.assertTrue(np.all(d == true_d), 'Wrong answer')
# self.assertAlmostEqual(est_min, true_min, 'Wrong min value')
s_cauchy, red_cauchy, crvmin_cauchy = cauchy_pt_box(
g, hess, Delta, sl - xopt, su - xopt)
# print(s_cauchy)
# print(d)
self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved')
self.assertTrue(np.all(gnew == g + right_multiply_hessian(hess, d)),
'Wrong gnew')
print(crvmin)
self.assertAlmostEqual(crvmin, -1.0, 'Wrong crvmin')
def cauchy_pt_box(g, hess, delta, lower, upper):
# General expression for the Cauchy point, lower <= s <= upper
crv = np.dot(g, right_multiply_hessian(hess, g))
gnorm = np.linalg.norm(g)
if crv <= 0.0:
alpha = delta / gnorm
else:
alpha = min(delta / gnorm, gnorm**2 / crv)
# print("alpha = %g" % alpha)
# Then cap with bounds:
for i in range(len(g)):
if g[i] > 0: # s[i] negative, will hit lower
alpha = min(alpha, -lower[i] / g[i])
elif g[i] < 0: # s[i] positive, will hit upper
alpha = min(alpha, -upper[i] / g[i])
# print("alpha = %g after i=%g" % (alpha, i))
s = -alpha * g
red = calculate_model_value(g, hess, s)
crvmin = np.dot(s, right_multiply_hessian(hess, s)) / np.dot(s, s)
if crvmin < 0.0:
crvmin = -1.0
return s, red, crvmin
def runTest(self):
n = 3
g = np.array([1.0, 0.0, 1.0])
H = np.array([[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 2.0]])
Delta = 5.0 / 12.0
hess = to_upper_triangular_vector(H)
xopt = np.zeros((n, ))
sl = -1e20 * np.ones((n, ))
su = 1e20 * np.ones((n, ))
d, gnew, crvmin = trsbox(xopt, g, hess, sl, su, Delta)
true_d = np.array([-1.0 / 3.0, 0.0, -0.25])
est_min = calculate_model_value(g, hess, d)
true_min = calculate_model_value(g, hess, true_d)
# Hope to get actual correct answer
# self.assertTrue(np.all(d == true_d), 'Wrong answer')
# self.assertAlmostEqual(est_min, true_min, 'Wrong min value')
s_cauchy, red_cauchy, crvmin_cauchy = cauchy_pt(g, hess, Delta)
self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved')
self.assertTrue(np.all(gnew == g + right_multiply_hessian(hess, d)),
'Wrong gnew')
self.assertAlmostEqual(crvmin, 0.0, 'Wrong crvmin')