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))
# For reference: model based around model.xbase
interp_ok, interp_cond_num, norm_chg_grad, norm_chg_hess, interp_error = model.interpolate_model(
verbose=True)
self.assertTrue(interp_ok, 'Interpolation failed')
self.assertAlmostEqual(interp_error,
0.0,
msg='Expect exact interpolation')
self.assertAlmostEqual(norm_chg_grad, np.linalg.norm(model.model_grad))
self.assertAlmostEqual(
norm_chg_hess, np.linalg.norm(model.model_hess.as_full(),
ord='fro'))
self.assertAlmostEqual(model.model_const,
objfun(model.xbase),
msg='Wrong constant term')
for xi in [x0, x1, x2, x3, x4, x5]:
self.assertAlmostEqual(model.model_value(xi - model.xbase,
d_based_at_xopt=False,
with_const_term=True),
objfun(xi),
msg='Wrong interp value at %s' % str(xi))
# Test some other parameter settings for model.model_value()
g, hess = model.build_full_model()
self.assertTrue(
np.allclose(
g, model.model_grad +
model.model_hess.vec_mul(model.xopt(abs_coordinates=False))),
'Bad gradient')
self.assertTrue(
np.allclose(hess.as_full(), model.model_hess.as_full()),
'Bad Hessian')
def runTest(self):
n = 2
npt = 2 * n + 1
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, precondition=False)
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))
# x2 is xopt in this situation
self.assertTrue(model.kopt == 2, 'Wrong xopt')
xs = [x0, x1, x3, x4]
xopt = x2
nxs = len(xs)
A = np.zeros((nxs + n, nxs + n))
for i in range(nxs):
for j in range(nxs):
A[i, j] = 0.5 * np.dot(xs[i] - xopt, xs[j] - xopt)**2
A[i, nxs:] = xs[i] - xopt
A[nxs:, i] = xs[i] - xopt
A2, left_scaling, right_scaling = model.interpolation_matrix()
# print("Expect", A)
# print("Got", A2)
self.assertTrue(np.allclose(A, A2), 'Interp matrix 1')
# For reference: model based around model.xbase
interp_ok, interp_cond_num, norm_chg_grad, norm_chg_hess, interp_error = model.interpolate_model(
verbose=True)
self.assertTrue(interp_ok, 'Interpolation failed')
self.assertAlmostEqual(interp_error,
0.0,
msg='Expect exact interpolation')
self.assertAlmostEqual(norm_chg_grad, np.linalg.norm(model.model_grad))
self.assertAlmostEqual(
norm_chg_hess, np.linalg.norm(model.model_hess.as_full(),
ord='fro'))
self.assertAlmostEqual(model.model_const,
objfun(model.xbase),
msg='Wrong constant term')
for xi in [x0, x1, x2, x3, x4]:
self.assertAlmostEqual(model.model_value(xi - model.xbase,
d_based_at_xopt=False,
with_const_term=True),
objfun(xi),
msg='Wrong interp value at %s' % str(xi))
# Test some other parameter settings for model.model_value()
g, hess = model.build_full_model()
self.assertTrue(
np.allclose(
g, model.model_grad +
model.model_hess.vec_mul(model.xopt(abs_coordinates=False))),
'Bad gradient')
self.assertTrue(
np.allclose(hess.as_full(), model.model_hess.as_full()),
'Bad Hessian')
# Build a new model
model2 = Model(npt, x0, objfun(x0), xl, xu, 1, precondition=False)
model2.change_point(1, x1 - model.xbase, objfun(x1))
model2.change_point(2, x2 - model.xbase, objfun(x2))
model2.change_point(3, x3 - model.xbase, objfun(x3))
model2.change_point(4, x4 - model.xbase, objfun(x4))
# Force Hessian to be something else
model2.model_hess = Hessian(n, vals=np.eye(n))
A2, left_scaling, right_scaling = model2.interpolation_matrix()
self.assertTrue(np.allclose(A, A2), 'Interp matrix 2')
interp_ok, interp_cond_num, norm_chg_grad, norm_chg_hess, interp_error = model2.interpolate_model(
)
self.assertTrue(interp_ok, 'Interpolation failed')
self.assertAlmostEqual(interp_error,
0.0,
msg='Expect exact interpolation')
self.assertAlmostEqual(model2.model_const,
objfun(model2.xbase),
msg='Wrong constant term')
for xi in [x0, x1, x2, x3, x4]:
self.assertAlmostEqual(model2.model_value(xi - model2.xbase,
d_based_at_xopt=False,
with_const_term=True),
objfun(xi),
msg='Wrong interp value at %s' % str(xi))
# Compare distance of hessians
h1 = Hessian(n).as_full()
h2 = Hessian(n, vals=np.eye(n)).as_full()
self.assertLessEqual(
np.linalg.norm(model.model_hess.as_full() - h1, ord='fro'),
np.linalg.norm(model2.model_hess.as_full() - h1, ord='fro'),
'Not min frob Hess 1')
self.assertLessEqual(
np.linalg.norm(model2.model_hess.as_full() - h2, ord='fro'),
np.linalg.norm(model.model_hess.as_full() - h2, ord='fro'),
'Not min frob Hess 2')
# print(model.model_hess.as_full())
# print(model2.model_hess.as_full())
# Build a new model
model3 = Model(npt, x0, objfun(x0), xl, xu, 1, precondition=False)
model3.change_point(1, x1 - model.xbase, objfun(x1))
model3.change_point(2, x2 - model.xbase, objfun(x2))
model3.change_point(3, x3 - model.xbase, objfun(x3))
model3.change_point(4, x4 - model.xbase, objfun(x4))
# Force Hessian to be something else
model3.model_hess = Hessian(n, vals=np.eye(n))
A2, left_scaling, right_scaling = model3.interpolation_matrix()
self.assertTrue(np.allclose(A, A2), 'Interp matrix 3')
interp_ok, interp_cond_num, norm_chg_grad, norm_chg_hess, interp_error = model3.interpolate_model(
min_chg_hess=False)
self.assertTrue(interp_ok, 'Interpolation failed')
self.assertAlmostEqual(interp_error,
0.0,
msg='Expect exact interpolation')
self.assertAlmostEqual(model3.model_const,
objfun(model3.xbase),
msg='Wrong constant term')
for xi in [x0, x1, x2, x3, x4]:
self.assertAlmostEqual(model3.model_value(xi - model3.xbase,
d_based_at_xopt=False,
with_const_term=True),
objfun(xi),
msg='Wrong interp value at %s' % str(xi))
self.assertTrue(
np.allclose(model.model_hess.as_full(),
model3.model_hess.as_full()),
'min_chg_hess=False not working')
def runTest(self):
n, m = 2, 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, precondition=False)
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))
A, left_scaling, right_scaling = model.interpolation_matrix()
A_expect = np.zeros((2, 2))
A_expect[0, :] = x0 - x1 # x1 is xopt in this situation
A_expect[1, :] = x2 - x1
self.assertTrue(array_compare(A, A_expect), 'Interp matrix 1')
# For reference: model based around model.xbase
interp_ok, interp_cond_num, norm_chg_grad, norm_chg_hess, interp_error = model.interpolate_model(
)
self.assertTrue(interp_ok, 'Interpolation failed')
self.assertAlmostEqual(interp_error,
0.0,
msg='Expect exact interpolation')
self.assertAlmostEqual(model.model_const,
rosenbrock(model.xbase),
msg='Wrong constant term')
self.assertTrue(
array_compare(model.model_value(x1 - model.xbase,
d_based_at_xopt=False,
with_const_term=True),
rosenbrock(x1),
thresh=1e-10), 'Wrong x1') # allow some inexactness
self.assertTrue(
array_compare(model.model_value(x2 - model.xbase,
d_based_at_xopt=False,
with_const_term=True),
rosenbrock(x2),
thresh=1e-10), 'Wrong x2')
# Test some other parameter settings for model.model_value()
self.assertTrue(
array_compare(model.model_value(x2 - x1,
d_based_at_xopt=True,
with_const_term=True),
rosenbrock(x2),
thresh=1e-10), 'Wrong x2 (from xopt)')
self.assertTrue(
array_compare(model.model_value(x2 - x1,
d_based_at_xopt=True,
with_const_term=False),
rosenbrock(x2) - rosenbrock(model.xbase),
thresh=1e-10), 'Wrong x2 (no constant)')
self.assertTrue(
array_compare(model.model_value(x2 - model.xbase,
d_based_at_xopt=False,
with_const_term=False),
rosenbrock(x2) - rosenbrock(model.xbase),
thresh=1e-10), 'Wrong x2 (no constant v2)')
g, hess = model.build_full_model()
self.assertTrue(
np.allclose(
g, model.model_grad +
model.model_hess.vec_mul(model.xopt(abs_coordinates=False))),
'Bad gradient')
self.assertTrue(
np.allclose(hess.as_full(), model.model_hess.as_full()),
'Bad Hessian')