def test_short_distance_bound_linear_in_df1dx1_constant(self):
bounder_low = bound.OrdinaryPointBoundCalculator(
f_lipshitz_constant=100,
df1_dx1_lipshitz_constant=1,
)
bounder_hi = bound.OrdinaryPointBoundCalculator(
f_lipshitz_constant=100,
df1_dx1_lipshitz_constant=2,
)
dx = 1e-3
self.assertAlmostEqual(
2 * bounder_low.bound(dx),
bounder_hi.bound(dx),
places=13)
def test_long_distance_bound_linear_in_df1dx1_constant(self):
bounder_low = bound.OrdinaryPointBoundCalculator(
f_lipshitz_constant=1,
df1_dx1_lipshitz_constant=1,
)
bounder_hi = bound.OrdinaryPointBoundCalculator(
f_lipshitz_constant=2,
df1_dx1_lipshitz_constant=1,
)
long_distance = 100
dx = 1e-3
slope_low = (bounder_low.bound(long_distance + dx) -
bounder_low.bound(long_distance))
slope_hi = (bounder_hi.bound(long_distance + dx) -
bounder_hi.bound(long_distance))
self.assertAlmostEqual(2 * slope_low, slope_hi, places=13)
def test_bounds_quadratic_at_short_distances(self):
bounder = bound.OrdinaryPointBoundCalculator(
f_lipshitz_constant=1.0,
df1_dx1_lipshitz_constant=1.0,
)
dx = 1e-3
bound1 = bounder.bound(dx)
bound2 = bounder.bound(2 * dx)
self.assertAlmostEqual(4 * bound1, bound2, places=13)
def test_valid_bounds_when_f_constant_is_inf(self):
df1_dx1_lipshitz_constant = 1.0
bounder = bound.OrdinaryPointBoundCalculator(
f_lipshitz_constant=np.inf,
df1_dx1_lipshitz_constant=df1_dx1_lipshitz_constant,
)
dx = 1
bounds = bounder.bound(dx)
correct = 0.5 * df1_dx1_lipshitz_constant * dx**2
self.assertAlmostEqual(bounds, correct, places=13)
def test_bounds_linear_at_long_distances(self):
bounder = bound.OrdinaryPointBoundCalculator(
f_lipshitz_constant=1.0,
df1_dx1_lipshitz_constant=1.0,
)
long_distance = 100
dx = 1e-3
bound0 = bounder.bound(long_distance)
bound1 = bounder.bound(long_distance + dx)
bound2 = bounder.bound(long_distance + 2 * dx)
self.assertAlmostEqual(bound2 - bound1, bound1 - bound0, places=13)
def test_bounds_continuous_at_cutoff_distance(self):
np.random.seed(1432)
bounder = bound.OrdinaryPointBoundCalculator(
f_lipshitz_constant=np.random.randn(),
df1_dx1_lipshitz_constant=np.random.randn(),
)
cutoff_distance = bounder._cutoff_dist
places = 5
dx = 10**(-places - 1)
bound_below = bounder.bound(cutoff_distance - dx)
bound_above = bounder.bound(cutoff_distance + dx)
self.assertAlmostEqual(bound_below, bound_above, places)
def test_bounds_correctly(self):
np.random.seed(1459)
point_bounder = bound.OrdinaryPointBoundCalculator(*np.random.randn(2))
simplex_bounder = bound.MaxPointSimplexBoundCalculator(point_bounder)
simplex = make_simplex(dimension=10)
result = simplex_bounder.bound(simplex)
index = np.argmax([fp.value for fp in simplex.function_points])
vertex_max_f = simplex.function_points[index].value
max_dist_from_vertex = max([
np.linalg.norm(fp.point - simplex.function_points[index].point)
for fp in simplex.function_points])
correct = vertex_max_f - point_bounder.bound(max_dist_from_vertex)
self.assertAlmostEqual(result, correct, places=13)