def runTest(self):
n = 2
npt = (n + 1) * (n + 2) // 2
x0 = np.array([1.0, 1.0])
xl = -1e2 * np.ones((n, ))
xu = 1e2 * np.ones((n, ))
model = Model(npt, x0, objfun(x0), xl, xu, 1)
x1 = x0 + np.array([1.0, 0.0])
model.change_point(1, x1 - model.xbase, objfun(x1))
x2 = x0 + np.array([0.1, 0.9])
model.change_point(2, x2 - model.xbase, objfun(x2))
x3 = x0 + np.array([-0.1, 0.0])
model.change_point(3, x3 - model.xbase, objfun(x3))
x4 = x0 + np.array([-0.1, 2.0])
model.change_point(4, x4 - model.xbase, objfun(x4))
x5 = x0 + np.array([-1.1, 1.0])
model.change_point(5, x5 - model.xbase, objfun(x5))
xopt = model.xopt()
for i in range(npt):
c, g, hess = model.lagrange_polynomial(i) # based at xopt
for j in range(npt):
dx = model.xpt(j) - xopt
lag_value = c + model_value(g, hess, dx)
expected_value = 1.0 if i == j else 0.0
self.assertAlmostEqual(
lag_value,
expected_value,
msg="Lagrange for x%g has bad value at x%g" % (i, j))
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
xopt = np.zeros((n, ))
sl = -1e20 * np.ones((n, ))
su = 1e20 * np.ones((n, ))
d, gnew, crvmin = trsbox(xopt, g, H, sl, su, Delta)
true_d = np.array([-1.0 / 3.0, 0.0, -0.25])
est_min = model_value(g, H, d)
true_min = model_value(g, H, 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, H, Delta)
self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved')
self.assertTrue(np.all(gnew == g + H.dot(d)), 'Wrong gnew')
self.assertAlmostEqual(crvmin, 0.0, 'Wrong crvmin')
def runTest(self):
n = 3
g = np.array([0.0, 0.0, 1.0])
H = np.array([[-2.0, 0.0, 0.0], [0.0, -1.0, 0.0], [0.0, 0.0, -1.0]])
Delta = sqrt(2.0)
hess = Hessian(n, vals=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, 0.0, -1.0]) # non-unique solution
est_min = model_value(g, hess, d)
true_min = 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 + hess.vec_mul(d)), 'Wrong gnew')
self.assertAlmostEqual(crvmin, 0.0, 'Wrong 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 = Hessian(n, vals=H)
xopt = np.ones((n, )) # trying nonzero (since bounds inactive)
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, 0.0, -0.5])
est_min = model_value(g, hess, d)
true_min = 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(g, hess, Delta)
self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved')
self.assertTrue(np.all(gnew == g + hess.vec_mul(d)), 'Wrong gnew')
self.assertAlmostEqual(crvmin, -1.0, 'Wrong 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 = Hessian(n, vals=H)
xopt = np.zeros((n,))
sl = xopt + np.array([-0.3, -0.01, -0.1])
su = xopt + np.array([10.0, 1.0, 10.0])
d, gnew, crvmin = trsbox(xopt, g, hess, sl, su, Delta)
true_d = np.array([-1.0 / 3.0, 0.0, -0.25])
est_min = model_value(g, hess, d)
true_min = 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_box(g, hess, Delta, sl - xopt, su - xopt)
self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved')
self.assertTrue(np.max(np.abs(gnew - g - hess.vec_mul(d))) < 1e-10, 'Wrong gnew')
print(crvmin)
self.assertAlmostEqual(crvmin, -1.0, 'Wrong crvmin')
def cauchy_pt(g, hess, delta):
# General expression for the Cauchy point
crv = np.dot(g, hess.vec_mul(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 = model_value(g, hess, s)
crvmin = np.dot(s, hess.vec_mul(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
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, H, sl, su, Delta)
true_d = np.array([-1.0, 0.0, -0.5])
est_min = model_value(g, H, d)
true_min = model_value(g, H, 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, H, 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 + H.dot(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, hess.vec_mul(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 = model_value(g, hess, s)
crvmin = np.dot(s, hess.vec_mul(s)) / np.dot(s, s)
if crvmin < 0.0:
crvmin = -1.0
return s, red, crvmin
def runTest(self):
n = 2
npt = n + 1
x0 = np.array([-1.2, 1.0])
xl = -1e2 * np.ones((n, ))
xu = 1e2 * np.ones((n, ))
model = Model(npt, x0, rosenbrock(x0), xl, xu, 1)
x1 = np.array([1.0, 0.9])
model.change_point(1, x1 - model.xbase, rosenbrock(x1))
x2 = np.array([2.0, 0.9])
model.change_point(2, x2 - model.xbase, rosenbrock(x2))
xopt = model.xopt()
for i in range(npt):
c, g, hess = model.lagrange_polynomial(i) # based at xopt
for j in range(npt):
dx = model.xpt(j) - xopt
lag_value = c + model_value(g, hess, dx)
expected_value = 1.0 if i == j else 0.0
self.assertAlmostEqual(
lag_value,
expected_value,
msg="Lagrange for x%g has bad value at x%g" % (i, j))
