def test_unit_box():
ackley = Ackley(dim=1)
np.random.seed(0)
x = np.random.rand(30, 1)
fX = np.expand_dims([ackley.eval(y) for y in x], axis=1)
xx = np.expand_dims(np.linspace(0, 1, 100), axis=1)
# RBF with internal scaling to unit hypercube
rbf1 = RBFInterpolant(dim=1, lb=np.zeros(1), ub=100 * np.ones(1), eta=1e-6)
rbf1.add_points(x, fX)
# Normal RBF
rbf2 = RBFInterpolant(dim=1, lb=np.zeros(1), ub=100 * np.ones(1), eta=1e-6)
rbf2.add_points(x, fX)
assert np.max(np.abs(rbf1.predict(xx) - rbf2.predict(xx))) < 1e-10
assert np.max(
np.abs(rbf1.predict_deriv(x[0, :]) -
rbf2.predict_deriv(x[0, :]))) < 1e-10
assert np.max(np.abs(rbf1.X - rbf2.X)) < 1e-10
assert np.max(np.abs(rbf1.fX - rbf2.fX)) < 1e-10
rbf1.reset()
assert rbf1.num_pts == 0 and rbf1.dim == 1
assert rbf1.X.size == 0 and rbf1.fX.size == 0
def test_capped():
def ff(x):
return (6 * x - 2)**2 * np.sin(12 * x - 4)
np.random.seed(0)
x = np.random.rand(30, 1)
fX = ff(x)
xx = np.expand_dims(np.linspace(0, 1, 100), axis=1)
# RBF with capping adapter
rbf1 = RBFInterpolant(dim=1,
lb=np.zeros(1),
ub=np.ones(1),
output_transformation=median_capping,
eta=1e-6)
rbf1.add_points(x, fX)
# RBF fitted to capped value
fX_capped = fX.copy()
fX_capped[fX > np.median(fX)] = np.median(fX)
rbf2 = RBFInterpolant(dim=1, lb=np.zeros(1), ub=np.ones(1), eta=1e-6)
rbf2.add_points(x, fX_capped)
assert np.max(np.abs(rbf1.predict(xx) - rbf2.predict(xx))) < 1e-10
assert np.max(
np.abs(rbf1.predict_deriv(x[0, :]) -
rbf2.predict_deriv(x[0, :]))) < 1e-10
rbf1.reset()
assert rbf1.num_pts == 0 and rbf1.dim == 1
assert rbf1.X.size == 0 and rbf1.fX.size == 0
class RBF:
""" Radial Basis Function """
def __init__(self, kernel='cubic', tail='linear'):
self.kernel = kernel
self.tail = tail
self.name = 'rbf'
self.model = None
def fit(self, train_data, train_label):
if self.kernel == 'cubic':
kernel = CubicKernel
elif self.kernel == 'tps':
kernel = TPSKernel
else:
raise NotImplementedError("unknown RBF kernel")
if self.tail == 'linear':
tail = LinearTail
elif self.tail == 'constant':
tail = ConstantTail
else:
raise NotImplementedError("unknown RBF tail")
self.model = RBFInterpolant(dim=train_data.shape[1],
kernel=kernel(),
tail=tail(train_data.shape[1]))
for i in range(len(train_data)):
self.model.add_points(train_data[i, :], train_label[i])
def predict(self, test_data):
assert self.model is not None, "RBF model does not exist, call fit to obtain rbf model first"
return self.model.predict(test_data)
def test_capped():
def ff(x):
return (6 * x - 2)**2 * np.sin(12 * x - 4)
np.random.seed(0)
x = np.random.rand(30, 1)
fX = ff(x)
xx = np.expand_dims(np.linspace(0, 1, 100), axis=1)
# RBF with capping adapter
rbf1 = SurrogateCapped(RBFInterpolant(dim=1, eta=1e-6))
rbf1.add_points(x, fX)
# RBF fitted to capped value
fX_capped = fX.copy()
fX_capped[fX > np.median(fX)] = np.median(fX)
rbf2 = RBFInterpolant(dim=1, eta=1e-6)
rbf2.add_points(x, fX_capped)
assert (np.max(np.abs(rbf1.predict(xx) - rbf2.predict(xx))) < 1e-10)
assert (np.max(
np.abs(rbf1.predict_deriv(x[0, :]) - rbf2.predict_deriv(x[0, :]))) <
1e-10)
rbf1.reset()
assert (rbf1.num_pts == 0 and rbf1.dim == 1)
assert (rbf1.X.size == 0 and rbf1.fX.size == 0)
def test_rbf():
X = make_grid(30) # Make uniform grid with 30 x 30 points
rbf = RBFInterpolant(dim=2, lb=np.zeros(2), ub=np.ones(2), eta=1e-6)
assert isinstance(rbf, Surrogate)
fX = f(X)
rbf.add_points(X, fX)
# Derivative at random points
np.random.seed(0)
Xs = np.random.rand(10, 2)
fhx = rbf.predict(Xs)
dfhx = rbf.predict_deriv(Xs)
fx = f(Xs)
dfx = df(Xs)
assert np.max(np.abs(fx - fhx)) < 1e-4
assert la.norm(dfx - dfhx) < 1e-2
# Derivative at previous points
dfhx = rbf.predict_deriv(X[0, :])
assert la.norm(df(np.atleast_2d(X[0, :])) - dfhx) < 1e-1
# Reset the surrogate
rbf.reset()
assert rbf.num_pts == 0 and rbf.dim == 2
# Now add 100 points at a time and test reallocation + LU
for i in range(9):
rbf.add_points(X[i * 100:(i + 1) * 100, :], fX[i * 100:(i + 1) * 100])
rbf.predict(Xs) # Force fit
# Derivative at random points
np.random.seed(0)
Xs = np.random.rand(10, 2)
fhx = rbf.predict(Xs)
dfhx = rbf.predict_deriv(Xs)
fx = f(Xs)
dfx = df(Xs)
assert np.max(np.abs(fx - fhx)) < 1e-4
assert la.norm(dfx - dfhx) < 1e-2
# Derivative at previous points
dfhx = rbf.predict_deriv(X[0, :])
assert la.norm(df(np.atleast_2d(X[0, :])) - dfhx) < 1e-1
