def gEKPLS(xt, yt, xtest, ytest, funXLimits, ndim):
# 'n_comp' must be an integer in [1,ndim[, 'theta0' a list of n_comp values
t = GEKPLS(n_comp=2,
theta0=[1e-2, 1e-2],
xlimits=funXLimits,
delta_x=1e-2,
extra_points=1,
print_prediction=False)
t.set_training_values(xt, yt)
# Add the gradient information
for i in range(ndim):
t.set_training_derivatives(xt, yt[:, 1 + i].reshape((yt.shape[0], 1)),
i)
t.train()
# Prediction of the validation points
y = t.predict_values(xtest)
print('GEKPLS1, err: ' + str(compute_rms_error(t, xtest, ytest)))
title = ('GEKPLS model')
return t, title, xtest, ytest
# Prediction of the derivatives with regards to each direction space
yd_prediction = np.zeros((ntest, ndim))
for i in range(ndim):
yd_prediction[:, i] = t.predict_derivatives(xtest, kx=i).T
print('GEKPLS1, err of the ' + str(i + 1) + '-th derivative: ' +
str(compute_rms_error(t, xtest, ydtest[:, i], kx=i)))
if plot_status:
plt.plot(ydtest[:, i], ydtest[:, i], '-.')
plt.plot(ydtest[:, i], yd_prediction[:, i], '.')
if plot_status:
plt.show()
def train(self, X_train, y_train):
if self.flavour == 'plain':
self.smt_model = KRG(poly=self.poly,
corr=self.corr,
theta0=self.theta0)
elif self.flavour == 'pls':
self.smt_model = KPLS(poly=self.poly,
corr=self.corr,
theta0=self.theta0,
n_comp=self.n_comp)
elif self.flavour == 'plsk':
self.smt_model = KPLSK(poly=self.poly,
corr=self.corr,
theta0=self.theta0,
n_comp=self.n_comp)
elif self.flavour == 'gepls':
self.smt_model = GEKPLS(poly=self.poly,
corr=self.corr,
theta0=self.theta0,
n_comp=self.n_comp,
xlimits=self.xlimits,
delta_x=self.delta_x,
extra_points=self.extra_points)
super(KrigingModel, self).train(X_train, y_train)
def setUp(self):
ndim = 3
nt = 100
ne = 100
ncomp = 1
problems = OrderedDict()
problems['exp'] = TensorProduct(ndim=ndim, func='exp')
problems['tanh'] = TensorProduct(ndim=ndim, func='tanh')
problems['cos'] = TensorProduct(ndim=ndim, func='cos')
sms = OrderedDict()
sms['LS'] = LS()
sms['QP'] = QP()
sms['KRG'] = KRG(theta0=[1e-2] * ndim)
sms['KPLS'] = KPLS(theta0=[1e-2] * ncomp, n_comp=ncomp)
sms['KPLSK'] = KPLSK(theta0=[1] * ncomp, n_comp=ncomp)
sms['GEKPLS'] = GEKPLS(theta0=[1e-2] * ncomp,
n_comp=ncomp,
delta_x=1e-1)
if compiled_available:
sms['IDW'] = IDW()
sms['RBF'] = RBF()
sms['RMTC'] = RMTC()
sms['RMTB'] = RMTB()
t_errors = {}
t_errors['LS'] = 1.0
t_errors['QP'] = 1.0
t_errors['KRG'] = 1e-5
t_errors['KPLS'] = 1e-5
t_errors['KPLSK'] = 1e-5
t_errors['GEKPLS'] = 1e-5
if compiled_available:
t_errors['IDW'] = 1e-15
t_errors['RBF'] = 1e-2
t_errors['RMTC'] = 1e-1
t_errors['RMTB'] = 1e-1
e_errors = {}
e_errors['LS'] = 1.5
e_errors['QP'] = 1.5
e_errors['KRG'] = 1e-2
e_errors['KPLS'] = 1e-2
e_errors['KPLSK'] = 1e-2
e_errors['GEKPLS'] = 1e-2
if compiled_available:
e_errors['IDW'] = 1e0
e_errors['RBF'] = 1e0
e_errors['RMTC'] = 2e-1
e_errors['RMTB'] = 2e-1
self.nt = nt
self.ne = ne
self.ndim = ndim
self.problems = problems
self.sms = sms
self.t_errors = t_errors
self.e_errors = e_errors
def test_gekpls(self):
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from smt.surrogate_models import GEKPLS
from smt.problems import Sphere
from smt.sampling_methods import LHS
# Construction of the DOE
fun = Sphere(ndim=2)
sampling = LHS(xlimits=fun.xlimits, criterion="m")
xt = sampling(20)
yt = fun(xt)
# Compute the gradient
for i in range(2):
yd = fun(xt, kx=i)
yt = np.concatenate((yt, yd), axis=1)
# Build the GEKPLS model
n_comp = 2
sm = GEKPLS(
theta0=[1e-2] * n_comp,
xlimits=fun.xlimits,
extra_points=1,
print_prediction=False,
n_comp=n_comp,
)
sm.set_training_values(xt, yt[:, 0])
for i in range(2):
sm.set_training_derivatives(xt, yt[:, 1 + i].reshape((yt.shape[0], 1)), i)
sm.train()
# Test the model
X = np.arange(fun.xlimits[0, 0], fun.xlimits[0, 1], 0.25)
Y = np.arange(fun.xlimits[1, 0], fun.xlimits[1, 1], 0.25)
X, Y = np.meshgrid(X, Y)
Z = np.zeros((X.shape[0], X.shape[1]))
for i in range(X.shape[0]):
for j in range(X.shape[1]):
Z[i, j] = sm.predict_values(
np.hstack((X[i, j], Y[i, j])).reshape((1, 2))
)
fig = plt.figure()
ax = fig.gca(projection="3d")
surf = ax.plot_surface(X, Y, Z)
plt.show()
def dEKPLS(xt, yt, xtest, ytest, funXLimits, ndim):
# 'n_comp' must be an integer in [1,ndim[, 'theta0' a list of n_comp values
t = GEKPLS(n_comp=1,
theta0=[1e-2],
xlimits=funXLimits,
delta_x=1e-2,
extra_points=1,
print_prediction=False)
t.set_training_values(xt, yt)
# Add the gradient information
for i in range(ndim):
t.set_training_derivatives(xt, yt[:, 1 + i].reshape((yt.shape[0], 1)),
i)
t.train()
title = 'GEKPLS model'
return t, title, xtest, ytest
def initialize_ego_gek(func="exp", criterion="LCB"):
from smt.problems import TensorProduct
class TensorProductIndirect(TensorProduct):
def __init__(self, **kwargs):
super().__init__(**kwargs)
self.super = super()
def _evaluate(self, x, kx):
assert kx is None
response = self.super._evaluate(x, kx)
sens = np.hstack(
self.super._evaluate(x, ki) for ki in range(x.shape[1]))
return np.hstack((response, sens))
fun = TensorProductIndirect(ndim=2, func=func)
# Construction of the DOE
sampling = LHS(xlimits=fun.xlimits, criterion="m", random_state=42)
xdoe = sampling(20)
ydoe = fun(xdoe)
# Build the GEKPLS surrogate model
n_comp = 2
sm = GEKPLS(
theta0=[1e-2] * n_comp,
xlimits=fun.xlimits,
extra_points=1,
print_prediction=False,
n_comp=n_comp,
)
# Build the EGO optimizer and optimize
ego = EGO(
xdoe=xdoe,
ydoe=ydoe,
n_iter=5,
criterion=criterion,
xlimits=fun.xlimits,
surrogate=sm,
n_start=30,
enable_tunneling=False,
random_state=42,
)
return ego, fun
def setUp(self):
ndim = 3
nt = 100
ne = 100
ncomp = 1
problems = OrderedDict()
problems["exp"] = TensorProduct(ndim=ndim, func="exp")
problems["tanh"] = TensorProduct(ndim=ndim, func="tanh")
problems["cos"] = TensorProduct(ndim=ndim, func="cos")
sms = OrderedDict()
sms["LS"] = LS()
sms["QP"] = QP()
sms["KRG"] = KRG(theta0=[1e-2] * ndim)
sms["MFK"] = MFK(theta0=[1e-2] * ndim)
sms["KPLS"] = KPLS(theta0=[1e-2] * ncomp, n_comp=ncomp)
sms["KPLSK"] = KPLSK(theta0=[1] * ncomp, n_comp=ncomp)
sms["GEKPLS"] = GEKPLS(theta0=[1e-2] * ncomp,
n_comp=ncomp,
delta_x=1e-1)
sms["GENN"] = genn()
if compiled_available:
sms["IDW"] = IDW()
sms["RBF"] = RBF()
sms["RMTC"] = RMTC()
sms["RMTB"] = RMTB()
t_errors = {}
t_errors["LS"] = 1.0
t_errors["QP"] = 1.0
t_errors["KRG"] = 1e0
t_errors["MFK"] = 1e0
t_errors["KPLS"] = 1e0
t_errors["KPLSK"] = 1e0
t_errors["GEKPLS"] = 1e0
t_errors["GENN"] = 1e0
if compiled_available:
t_errors["IDW"] = 1e0
t_errors["RBF"] = 1e-2
t_errors["RMTC"] = 1e-1
t_errors["RMTB"] = 1e-1
e_errors = {}
e_errors["LS"] = 1.5
e_errors["QP"] = 1.5
e_errors["KRG"] = 1e-2
e_errors["MFK"] = 1e-2
e_errors["KPLS"] = 1e-2
e_errors["KPLSK"] = 1e-2
e_errors["GEKPLS"] = 1e-2
e_errors["GENN"] = 1e-2
if compiled_available:
e_errors["IDW"] = 1e0
e_errors["RBF"] = 1e0
e_errors["RMTC"] = 2e-1
e_errors["RMTB"] = 2e-1
self.nt = nt
self.ne = ne
self.ndim = ndim
self.problems = problems
self.sms = sms
self.t_errors = t_errors
self.e_errors = e_errors
l = 0
k += 1
else:
l += 1
if plot_status:
plt.show()
########### The GEKPLS model using 1 approximating points
# 'n_comp' and 'theta0' must be an integer in [1,ndim[ and a list of length n_comp, respectively.
t = GEKPLS(
n_comp=1,
theta0=[1e-2],
xlimits=fun.xlimits,
delta_x=1e-2,
extra_points=1,
print_prediction=False,
)
t.set_training_values(xt, yt[:, 0])
# Add the gradient information
for i in range(ndim):
t.set_training_derivatives(xt, yt[:, 1 + i].reshape((yt.shape[0], 1)), i)
t.train()
# Prediction of the validation points
y = t.predict_values(xtest)
print("GEKPLS1, err: " + str(compute_rms_error(t, xtest, ytest)))
if plot_status:
k, l = 0, 0