def test_lp_norm(self):
import numpy as np
import matplotlib.pyplot as plt
from smt.problems import LpNorm
ndim = 2
problem = LpNorm(ndim=ndim, order=2)
num = 100
x = np.ones((num, ndim))
x[:, 0] = np.linspace(-1., 1., num)
x[:, 1] = np.linspace(-1., 1., num)
y = problem(x)
yd = np.empty((num, ndim))
for i in range(ndim):
yd[:, i] = problem(x, kx=i).flatten()
print(y.shape)
print(yd.shape)
plt.plot(x[:, 0], y[:, 0])
plt.xlabel('x')
plt.ylabel('y')
plt.show()
def test_norm1_2d_200(self):
self.ndim = 2
self.nt = 200
self.ne = 200
prob = LpNorm(ndim=self.ndim)
# training data
sampling = FullFactorial(xlimits=prob.xlimits, clip=True)
np.random.seed(0)
xt = sampling(self.nt)
yt = prob(xt)
# mixture of experts
moe = MOE(smooth_recombination=False, n_clusters=5)
moe.set_training_values(xt, yt)
moe.train()
# validation data
np.random.seed(1)
xe = sampling(self.ne)
ye = prob(xe)
rms_error = compute_rms_error(moe, xe, ye)
self.assert_error(rms_error, 0.0, 1e-1)
if TestMOE.plot:
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
y = moe.predict_values(xe)
plt.figure(1)
plt.plot(ye, ye, "-.")
plt.plot(ye, y, ".")
plt.xlabel(r"$y$ actual")
plt.ylabel(r"$y$ prediction")
fig = plt.figure(2)
ax = fig.add_subplot(111, projection="3d")
ax.scatter(xt[:, 0], xt[:, 1], yt)
plt.title("L1 Norm")
plt.show()
def test_norm1_2d_200(self):
self.ndim = 2
self.nt = 200
self.ne = 200
prob = LpNorm(ndim=self.ndim)
# training data
sampling = FullFactorial(xlimits=prob.xlimits, clip=True)
np.random.seed(0)
xt = sampling(self.nt)
yt = prob(xt)
# mixture of experts
moe = MOE(smooth_recombination=False, n_clusters=5)
moe.set_training_values(xt, yt)
moe.train()
# validation data
np.random.seed(1)
xe = sampling(self.ne)
ye = prob(xe)
rms_error = compute_rms_error(moe, xe, ye)
self.assert_error(rms_error, 0., 1e-1)
if TestMOE.plot:
y = moe.predict_values(xe)
plt.figure(1)
plt.plot(ye, ye, '-.')
plt.plot(ye, y, '.')
plt.xlabel(r'$y$ actual')
plt.ylabel(r'$y$ prediction')
fig = plt.figure(2)
ax = fig.add_subplot(111, projection='3d')
ax.scatter(xt[:, 0], xt[:, 1], yt)
plt.title('L1 Norm')
plt.show()
def test_lp_norm(self):
self.run_test(LpNorm(ndim=2))
def run_moe_example():
import numpy as np
from smt.applications import MOE
from smt.problems import LpNorm
from smt.sampling_methods import FullFactorial
import sklearn
import matplotlib.pyplot as plt
from matplotlib import colors
from mpl_toolkits.mplot3d import Axes3D
ndim = 2
nt = 200
ne = 200
# Problem: L1 norm (dimension 2)
prob = LpNorm(ndim=ndim)
# Training data
sampling = FullFactorial(xlimits=prob.xlimits, clip=True)
np.random.seed(0)
xt = sampling(nt)
yt = prob(xt)
# Mixture of experts
moe = MOE(smooth_recombination=True, n_clusters=5)
moe.set_training_values(xt, yt)
moe.train()
# Validation data
np.random.seed(1)
xe = sampling(ne)
ye = prob(xe)
# Prediction
y = moe.predict_values(xe)
fig = plt.figure(1)
fig.set_size_inches(12, 11)
# Cluster display
colors_ = list(colors.cnames.items())
GMM = moe.cluster
weight = GMM.weights_
mean = GMM.means_
if sklearn.__version__ < "0.20.0":
cov = GMM.covars_
else:
cov = GMM.covariances_
prob_ = moe._proba_cluster(xt)
sort = np.apply_along_axis(np.argmax, 1, prob_)
xlim = prob.xlimits
x0 = np.linspace(xlim[0, 0], xlim[0, 1], 20)
x1 = np.linspace(xlim[1, 0], xlim[1, 1], 20)
xv, yv = np.meshgrid(x0, x1)
x = np.array(list(zip(xv.reshape((-1,)), yv.reshape((-1,)))))
prob = moe._proba_cluster(x)
plt.subplot(221, projection="3d")
ax = plt.gca()
for i in range(len(sort)):
color = colors_[int(((len(colors_) - 1) / sort.max()) * sort[i])][0]
ax.scatter(xt[i][0], xt[i][1], yt[i], c=color)
plt.title("Clustered Samples")
plt.subplot(222, projection="3d")
ax = plt.gca()
for i in range(len(weight)):
color = colors_[int(((len(colors_) - 1) / len(weight)) * i)][0]
ax.plot_trisurf(
x[:, 0], x[:, 1], prob[:, i], alpha=0.4, linewidth=0, color=color
)
plt.title("Membership Probabilities")
plt.subplot(223)
for i in range(len(weight)):
color = colors_[int(((len(colors_) - 1) / len(weight)) * i)][0]
plt.tricontour(x[:, 0], x[:, 1], prob[:, i], 1, colors=color, linewidths=3)
plt.title("Cluster Map")
plt.subplot(224)
plt.plot(ye, ye, "-.")
plt.plot(ye, y, ".")
plt.xlabel("actual")
plt.ylabel("prediction")
plt.title("Predicted vs Actual")
plt.show()
