def test_mixed_int_krg(self):
import numpy as np
import matplotlib.pyplot as plt
from smt.surrogate_models import KRG
from smt.applications.mixed_integer import MixedIntegerSurrogateModel, INT
xt = np.array([0.0, 1.0, 2.0, 3.0, 4.0])
yt = np.array([0.0, 1.0, 1.5, 0.5, 1.0])
# xtypes = [FLOAT, INT, (ENUM, 3), (ENUM, 2)]
# FLOAT means x1 continuous
# INT means x2 integer
# (ENUM, 3) means x3, x4 & x5 are 3 levels of the same categorical variable
# (ENUM, 2) means x6 & x7 are 2 levels of the same categorical variable
sm = MixedIntegerSurrogateModel(xtypes=[INT],
xlimits=[[0, 4]],
surrogate=KRG(theta0=[1e-2]))
sm.set_training_values(xt, yt)
sm.train()
num = 100
x = np.linspace(0.0, 4.0, num)
y = sm.predict_values(x)
plt.plot(xt, yt, "o")
plt.plot(x, y)
plt.xlabel("x")
plt.ylabel("y")
plt.legend(["Training data", "Prediction"])
plt.show()
def test_mixed_gower(self):
from smt.applications.mixed_integer import MixedIntegerSurrogateModel, ENUM
from smt.surrogate_models import KRG
import matplotlib.pyplot as plt
import numpy as np
xt = np.linspace(1.0, 5.0, 5)
x_train = np.array(["%.2f" % i for i in xt], dtype=object)
yt = np.array([0.0, 1.0, 1.5, 0.5, 1.0])
xlimits = [["0.0", "1.0", " 2.0", "3.0", "4.0"]]
# Surrogate
sm = MixedIntegerSurrogateModel(
use_gower_distance=True,
xtypes=[(ENUM, 5)],
xlimits=xlimits,
surrogate=KRG(theta0=[1e-2]),
)
sm.set_training_values(x_train, yt)
sm.train()
# DOE for validation
num = 101
x = np.linspace(0, 5, num)
x_pred = np.array(["%.2f" % i for i in x], dtype=object)
y = sm.predict_values(x_pred)
plt.plot(xt, yt, "o")
plt.plot(x, y)
plt.xlabel("actual")
plt.ylabel("prediction")
plt.show()
def test_mixed_gower_krg(self):
from smt.applications.mixed_integer import (
MixedIntegerSurrogateModel,
ENUM,
GOWER,
)
from smt.surrogate_models import KRG
import matplotlib.pyplot as plt
import numpy as np
xt = np.array([0, 3, 4])
yt = np.array([0.0, 1.0, 1.5])
xlimits = [["0.0", "1.0", " 2.0", "3.0", "4.0"]]
# Surrogate
sm = MixedIntegerSurrogateModel(
categorical_kernel=GOWER,
xtypes=[(ENUM, 5)],
xlimits=xlimits,
surrogate=KRG(theta0=[1e-2]),
)
sm.set_training_values(xt, yt)
sm.train()
# DOE for validation
x = np.linspace(0, 5, 5)
y = sm.predict_values(x)
plt.plot(xt, yt, "o", label="data")
plt.plot(x, y, "d", color="red", markersize=3, label="pred")
plt.xlabel("x")
plt.ylabel("y")
plt.legend()
plt.show()
def run_mixed_integer_qp_example(self):
import numpy as np
import matplotlib.pyplot as plt
from smt.surrogate_models import QP
from smt.applications.mixed_integer import MixedIntegerSurrogateModel, ORD
xt = np.array([0.0, 1.0, 2.0, 3.0, 4.0])
yt = np.array([0.0, 1.0, 1.5, 0.5, 1.0])
# xtypes = [FLOAT, ORD, (ENUM, 3), (ENUM, 2)]
# FLOAT means x1 continuous
# ORD means x2 ordered
# (ENUM, 3) means x3, x4 & x5 are 3 levels of the same categorical variable
# (ENUM, 2) means x6 & x7 are 2 levels of the same categorical variable
sm = MixedIntegerSurrogateModel(xtypes=[ORD], xlimits=[[0, 4]], surrogate=QP())
sm.set_training_values(xt, yt)
sm.train()
num = 100
x = np.linspace(0.0, 4.0, num)
y = sm.predict_values(x)
plt.plot(xt, yt, "o")
plt.plot(x, y)
plt.xlabel("x")
plt.ylabel("y")
plt.legend(["Training data", "Prediction"])
plt.show()
def test_mixed_full_gaussian_3D(self):
from smt.applications.mixed_integer import (
MixedIntegerSurrogateModel,
ENUM,
FLOAT,
ORD,
FULL_GAUSSIAN,
)
from smt.surrogate_models import KRG
import matplotlib.pyplot as plt
import numpy as np
import itertools
xt = np.array([[0, 5, 0], [2, -1, 2], [4, 0.5, 1]])
yt = np.array([[0.0], [1.0], [1.5]])
xlimits = [
["0.0", "1.0", " 2.0", "3.0", "4.0"],
[-5, 5],
["0.0", "1.0", " 2.0", "3.0"],
]
# Surrogate
sm = MixedIntegerSurrogateModel(
categorical_kernel=FULL_GAUSSIAN,
xtypes=[(ENUM, 5), ORD, (ENUM, 4)],
xlimits=xlimits,
surrogate=KRG(theta0=[1e-2]),
)
sm.set_training_values(xt, yt)
sm.train()
# DOE for validation
x = np.linspace(0, 4, 5)
x2 = np.linspace(-5, 5, 21)
x3 = np.linspace(0, 3, 4)
x1 = []
for element in itertools.product(x, x2, x3):
x1.append(np.array(element))
x_pred = np.array(x1)
i = 0
for x in x_pred:
print(i, x)
i += 1
y = sm.predict_values(x_pred)
yvar = sm.predict_variances(x_pred)
# prediction are correct on known points
self.assertTrue(np.abs(np.sum(np.array([y[80], y[202], y[381]]) - yt)) < 1e-6)
self.assertTrue(
np.abs(np.sum(np.array([yvar[80], yvar[202], yvar[381]]))) < 1e-6
)
def test_mixed_int_krg(self):
import numpy as np
import matplotlib.pyplot as plt
from smt.surrogate_models import KRG
from smt.applications.mixed_integer import MixedIntegerSurrogateModel, INT
xt = np.array([0.0, 2.0, 3.0])
yt = np.array([0.0, 1.5, 0.9])
# xtypes = [FLOAT, INT, (ENUM, 3), (ENUM, 2)]
# FLOAT means x1 continuous
# INT means x2 integer
# (ENUM, 3) means x3, x4 & x5 are 3 levels of the same categorical variable
# (ENUM, 2) means x6 & x7 are 2 levels of the same categorical variable
sm = MixedIntegerSurrogateModel(xtypes=[INT],
xlimits=[[0, 4]],
surrogate=KRG(theta0=[1e-2]))
sm.set_training_values(xt, yt)
sm.train()
num = 500
x = np.linspace(0.0, 4.0, num)
y = sm.predict_values(x)
# estimated variance
s2 = sm.predict_variances(x)
fig, axs = plt.subplots(2)
axs[0].plot(xt, yt, "o")
axs[0].plot(x, y)
axs[0].set_xlabel("x")
axs[0].set_ylabel("y")
axs[0].legend(["Training data", "Prediction"])
# add a plot with variance
axs[1].plot(xt, yt, "o")
axs[1].plot(x, y)
axs[1].fill_between(
np.ravel(x),
np.ravel(y - 3 * np.sqrt(s2)),
np.ravel(y + 3 * np.sqrt(s2)),
color="lightgrey",
)
axs[1].set_xlabel("x")
axs[1].set_ylabel("y")
axs[1].legend(
["Training data", "Prediction", "Confidence Interval 99%"])
plt.show()
def test_mixed_gower_2D(self):
from smt.applications.mixed_integer import (
MixedIntegerSurrogateModel,
ENUM,
FLOAT,
GOWER,
)
from smt.surrogate_models import KRG
import matplotlib.pyplot as plt
import numpy as np
import itertools
xt = np.array([[0, 5], [2, -1], [4, 0.5]])
yt = np.array([[0.0], [1.0], [1.5]])
xlimits = [["0.0", "1.0", " 2.0", "3.0", "4.0"], [-5, 5]]
# Surrogate
sm = MixedIntegerSurrogateModel(
categorical_kernel=GOWER,
xtypes=[(ENUM, 5), FLOAT],
xlimits=xlimits,
surrogate=KRG(theta0=[1e-2], corr="abs_exp"),
)
sm.set_training_values(xt, yt)
sm.train()
# DOE for validation
x = np.linspace(0, 4, 5)
x2 = np.linspace(-5, 5, 21)
x1 = []
for element in itertools.product(x, x2):
x1.append(np.array(element))
x_pred = np.array(x1)
i = 0
for x in x_pred:
print(i, x)
i += 1
y = sm.predict_values(x_pred)
yvar = sm.predict_variances(x_pred)
# prediction are correct on known points
self.assertTrue(np.abs(np.sum(np.array([y[20], y[50], y[95]]) - yt)) < 1e-6)
self.assertTrue(np.abs(np.sum(np.array([yvar[20], yvar[50], yvar[95]]))) < 1e-6)
self.assertEqual(np.shape(y), (105, 1))
def test_mixed_gower_krg(self):
import numpy as np
import matplotlib.pyplot as plt
from smt.surrogate_models import KRG
from smt.applications.mixed_integer import MixedIntegerSurrogateModel
from smt.applications.mixed_integer import ENUM
# xtypes = [FLOAT, INT, (ENUM, 3), (ENUM, 2)]
# FLOAT means x1 continuous
# INT means x2 integer
# (ENUM, 3) means x3, x4 & x5 are 3 levels of the same categorical variable
# (ENUM, 2) means x6 & x7 are 2 levels of the same categorical variable
xt = np.linspace(1.0, 5.0, 5)
x_train = np.array(["%.2f" % i for i in xt], dtype=object)
yt = np.array([0.0, 1.0, 1.5, 0.5, 1.0])
xlimits = [["0.0", "1.0", " 2.0", "3.0", "4.0"]]
sm = MixedIntegerSurrogateModel(
use_gower_distance=True,
xtypes=[(ENUM, 5)],
xlimits=xlimits,
surrogate=KRG(theta0=[1e-2]),
)
sm.set_training_values(x_train, yt)
sm.train()
num = 101
x = np.linspace(0, 5, num)
x_pred = np.array(["%.2f" % i for i in x], dtype=object)
y = sm.predict_values(x_pred)
plt.plot(xt, yt, "o")
plt.plot(x, y)
plt.xlabel("x")
plt.ylabel("y")
plt.legend(["Training data", "Prediction"])
plt.show()