def test_mfkplsk_derivs(self):
if self.ndim < 2:
print("To try test_mfkplsk_derivs the dimension must be greater than 1")
prob = Sphere(ndim=self.ndim)
sampling = LHS(xlimits=prob.xlimits)
# Modif MM
nt = 100
np.random.seed(0)
xt = sampling(nt)
yt = prob(xt)
dyt = {}
for kx in range(prob.xlimits.shape[0]):
dyt[kx] = prob(xt, kx=kx)
y_lf = 2 * prob(xt) + 2
x_lf = deepcopy(xt)
np.random.seed(1)
xe = sampling(self.ne)
ye = prob(xe)
dye = {}
for kx in range(prob.xlimits.shape[0]):
dye[kx] = prob(xe, kx=kx)
# modif MM
sm = MFKPLSK()
if sm.options.is_declared("xlimits"):
sm.options["xlimits"] = prob.xlimits
sm.options["print_global"] = False
# to test some options
sm.options["eval_noise"] = False
# modif MM
sm.options["n_comp"] = self.n_comp
sm.options["theta0"] = [1e-2] * self.n_comp
sm.set_training_values(xt, yt)
sm.set_training_values(x_lf, y_lf, name=0)
with Silence():
sm.train()
t_error = compute_rms_error(sm)
e_error = compute_rms_error(sm, xe, ye)
e_error0 = compute_rms_error(sm, xe, dye[0], 0)
e_error1 = compute_rms_error(sm, xe, dye[1], 1)
if print_output:
print(
"%8s %6s %18.9e %18.9e %18.9e %18.9e"
% (pname[:6], sname, t_error, e_error, e_error0, e_error1)
)
self.assert_error(e_error0, 0.0, 1e-1)
self.assert_error(e_error1, 0.0, 1e-1)
def run_mfkplsk_example():
import numpy as np
import matplotlib.pyplot as plt
from smt.applications.mfk import MFK, NestedLHS
from smt.applications.mfkplsk import MFKPLSK
# low fidelity modelk
def lf_function(x):
import numpy as np
return (
0.5 * ((x * 6 - 2) ** 2) * np.sin((x * 6 - 2) * 2)
+ (x - 0.5) * 10.0
- 5
)
# high fidelity model
def hf_function(x):
import numpy as np
return ((x * 6 - 2) ** 2) * np.sin((x * 6 - 2) * 2)
# Problem set up
xlimits = np.array([[0.0, 1.0]])
xdoes = NestedLHS(nlevel=2, xlimits=xlimits)
xt_c, xt_e = xdoes(7)
# Evaluate the HF and LF functions
yt_e = hf_function(xt_e)
yt_c = lf_function(xt_c)
# choice of number of PLS components
ncomp = 1
sm = MFKPLSK(n_comp=ncomp, theta0=np.array(ncomp * [1.0]))
# low-fidelity dataset names being integers from 0 to level-1
sm.set_training_values(xt_c, yt_c, name=0)
# high-fidelity dataset without name
sm.set_training_values(xt_e, yt_e)
# train the model
sm.train()
x = np.linspace(0, 1, 101, endpoint=True).reshape(-1, 1)
# query the outputs
y = sm.predict_values(x)
mse = sm.predict_variances(x)
derivs = sm.predict_derivatives(x, kx=0)
plt.figure()
plt.plot(x, hf_function(x), label="reference")
plt.plot(x, y, linestyle="-.", label="mean_gp")
plt.scatter(xt_e, yt_e, marker="o", color="k", label="HF doe")
plt.scatter(xt_c, yt_c, marker="*", color="g", label="LF doe")
plt.legend(loc=0)
plt.ylim(-10, 17)
plt.xlim(-0.1, 1.1)
plt.xlabel(r"$x$")
plt.ylabel(r"$y$")
plt.show()
def test_mfkplsk(self):
self.problems = ["exp", "tanh", "cos"]
for fname in self.problems:
prob = TensorProduct(ndim=self.ndim, func=fname)
sampling = FullFactorial(xlimits=prob.xlimits, clip=True)
np.random.seed(0)
xt = sampling(self.nt)
yt = prob(xt)
for i in range(self.ndim):
yt = np.concatenate((yt, prob(xt, kx=i)), axis=1)
y_lf = 2 * prob(xt) + 2
x_lf = deepcopy(xt)
np.random.seed(1)
xe = sampling(self.ne)
ye = prob(xe)
# Modif MM
sm = MFKPLSK()
if sm.options.is_declared("xlimits"):
sm.options["xlimits"] = prob.xlimits
sm.options["print_global"] = False
# modif MM
sm.options["n_comp"] = self.n_comp
sm.options["theta0"] = [1e-2] * self.n_comp
sm.set_training_values(xt, yt[:, 0])
sm.set_training_values(x_lf, y_lf[:, 0], name=0)
sm.set_training_values(xt, yt[:, 0])
sm.set_training_values(x_lf, y_lf[:, 0], name=0)
with Silence():
sm.train()
t_error = compute_rms_error(sm)
e_error = compute_rms_error(sm, xe, ye)
self.assert_error(t_error, 0.0, 1.5)
self.assert_error(e_error, 0.0, 1.5)
from smt.applications.mfkplsk import MFKPLSK from testbed_components import simple_1D_low, simple_1D_high # Problem set up xlimits = np.array([[0.0, 1.0]]) xdoes = NestedLHS(nlevel=2, xlimits=xlimits) xt_c, xt_e = xdoes(4) # Evaluate the HF and LF functions yt_e = simple_1D_high(xt_e) yt_c = simple_1D_low(xt_c) # choice of number of PLS components ncomp = 1 sm = MFKPLSK(n_comp=ncomp, theta0=np.array(ncomp * [1.0])) # low-fidelity dataset names being integers from 0 to level-1 sm.set_training_values(xt_c, yt_c, name=0) # high-fidelity dataset without name sm.set_training_values(xt_e, yt_e) # train the model sm.train() x = np.linspace(0, 1, 101, endpoint=True).reshape(-1, 1) # query the outputs y = sm.predict_values(x) mse = sm.predict_variances(x) derivs = sm.predict_derivatives(x, kx=0)