def setUp(self):
ndim = 10
nt = 50
ne = 100
problems = OrderedDict()
problems["Branin"] = Branin(ndim=2)
problems["Rosenbrock"] = Rosenbrock(ndim=3)
problems["sphere"] = Sphere(ndim=ndim)
problems["exp"] = TensorProduct(ndim=ndim, func="exp")
problems["tanh"] = TensorProduct(ndim=ndim, func="tanh")
problems["cos"] = TensorProduct(ndim=ndim, func="cos")
sms = OrderedDict()
sms["KPLS"] = KPLS(eval_n_comp=True)
t_errors = {}
e_errors = {}
t_errors["KPLS"] = 1e-3
e_errors["KPLS"] = 2.5
n_comp_opt = {}
n_comp_opt["Branin"] = 2
n_comp_opt["Rosenbrock"] = 1
n_comp_opt["sphere"] = 1
n_comp_opt["exp"] = 3
n_comp_opt["tanh"] = 1
n_comp_opt["cos"] = 1
self.nt = nt
self.ne = ne
self.problems = problems
self.sms = sms
self.t_errors = t_errors
self.e_errors = e_errors
self.n_comp_opt = n_comp_opt
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_tensor_product(self):
import numpy as np
import matplotlib.pyplot as plt
from smt.problems import TensorProduct
ndim = 2
problem = TensorProduct(ndim=ndim, func='cos')
num = 100
x = np.ones((num, ndim))
x[:, 0] = np.linspace(-1, 1., num)
x[:, 1] = 0.
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_mfk(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)
sm = MFK(theta0=[1e-2] * self.ndim)
if sm.options.is_declared("xlimits"):
sm.options["xlimits"] = prob.xlimits
sm.options["print_global"] = False
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)
self.assert_error(e_error, 0.0, 1)
def test_mfk_1fidelity(self):
self.problems = ["exp", "tanh", "cos"]
for fname in self.problems:
prob = TensorProduct(ndim=self.ndim, func=fname)
sampling = LHS(xlimits=prob.xlimits, random_state=0)
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)
sampling = LHS(xlimits=prob.xlimits, random_state=1)
xv = sampling(self.ne)
yv = prob(xv)
sm = MFK(
theta0=[1e-2] * self.ndim,
print_global=False,
)
sm.set_training_values(xt, yt[:, 0])
with Silence():
sm.train()
t_error = compute_rms_error(sm)
e_error = compute_rms_error(sm, xv, yv)
self.assert_error(t_error, 0.0, 1e-6)
self.assert_error(e_error, 0.0, 1e-6)
def setUp(self):
ndim = 3
nt = 500
ne = 100
problems = OrderedDict()
problems['carre'] = Carre(ndim=ndim)
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['PA2'] = PA2()
sms['KRG'] = KPLS(name='KRG', n_comp=ndim, theta0=[1.0] * ndim)
if compiled_available:
sms['IDW'] = IDW()
sms['RBF'] = RBF()
sms['RMTS'] = RMTS(num_elements=6)
sms['RMTB'] = RMTB(order=4, num_ctrl_pts=10)
t_errors = {}
t_errors['LS'] = 1.0
t_errors['PA2'] = 1.0
t_errors['KRG'] = 1e-6
t_errors['IDW'] = 1e-15
t_errors['RBF'] = 1e-2
t_errors['RMTS'] = 1e-2
t_errors['RMTB'] = 1e-2
e_errors = {}
e_errors['LS'] = 1.5
e_errors['PA2'] = 1.5
e_errors['KRG'] = 1e-2
e_errors['IDW'] = 1e0
e_errors['RBF'] = 1e0
e_errors['RMTS'] = 2e-1
e_errors['RMTB'] = 2e-1
self.nt = nt
self.ne = ne
self.problems = problems
self.sms = sms
self.t_errors = t_errors
self.e_errors = e_errors
def setUp(self):
ndim = 10
nt = 500
ne = 100
problems = OrderedDict()
problems["sphere"] = Sphere(ndim=ndim)
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=[4e-1] * ndim)
sms["KPLS"] = KPLS()
if compiled_available:
sms["IDW"] = IDW()
sms["RBF"] = RBF()
t_errors = {}
t_errors["LS"] = 1.0
t_errors["QP"] = 1.0
t_errors["KRG"] = 1e-4
t_errors["IDW"] = 1e-15
t_errors["RBF"] = 1e-2
t_errors["KPLS"] = 1e-3
e_errors = {}
e_errors["LS"] = 2.5
e_errors["QP"] = 2.0
e_errors["KRG"] = 2.0
e_errors["IDW"] = 4
e_errors["RBF"] = 2
e_errors["KPLS"] = 2.5
self.nt = nt
self.ne = ne
self.problems = problems
self.sms = sms
self.t_errors = t_errors
self.e_errors = e_errors
def setUp(self):
ndim = 3
nt = 2500
ne = 500
problems = OrderedDict()
problems['carre'] = Carre(ndim=ndim)
problems['exp'] = TensorProduct(ndim=ndim, func='exp')
problems['tanh'] = TensorProduct(ndim=ndim, func='tanh')
problems['cos'] = TensorProduct(ndim=ndim, func='cos')
sms = OrderedDict()
if compiled_available:
sms['RMTS'] = RMTS(num_elements=6)
sms['RMTB'] = RMTB(order=4, num_ctrl_pts=10)
t_errors = {}
t_errors['RMTS'] = 1e-2
t_errors['RMTB'] = 1e-2
e_errors = {}
e_errors['RMTS'] = 1e-1
e_errors['RMTB'] = 1e-1
ge_t_errors = {}
ge_t_errors['RMTS'] = 1e-2
ge_t_errors['RMTB'] = 1e-2
ge_e_errors = {}
ge_e_errors['RMTS'] = 1e-2
ge_e_errors['RMTB'] = 1e-2
self.nt = nt
self.ne = ne
self.problems = problems
self.sms = sms
self.t_errors = t_errors
self.e_errors = e_errors
self.ge_t_errors = ge_t_errors
self.ge_e_errors = ge_e_errors
def setUp(self):
ndim = 3
nt = 5000
ne = 500
problems = OrderedDict()
problems["sphere"] = Sphere(ndim=ndim)
problems["exp"] = TensorProduct(ndim=ndim, func="exp")
problems["tanh"] = TensorProduct(ndim=ndim, func="tanh")
problems["cos"] = TensorProduct(ndim=ndim, func="cos")
sms = OrderedDict()
if compiled_available:
sms["RMTC"] = RMTC()
sms["RMTB"] = RMTB()
t_errors = {}
t_errors["RMTC"] = 1e-1
t_errors["RMTB"] = 1e-1
e_errors = {}
e_errors["RMTC"] = 1e-1
e_errors["RMTB"] = 1e-1
ge_t_errors = {}
ge_t_errors["RMTC"] = 1e-2
ge_t_errors["RMTB"] = 1e-2
ge_e_errors = {}
ge_e_errors["RMTC"] = 1e-2
ge_e_errors["RMTB"] = 1e-2
self.nt = nt
self.ne = ne
self.problems = problems
self.sms = sms
self.t_errors = t_errors
self.e_errors = e_errors
self.ge_t_errors = ge_t_errors
self.ge_e_errors = ge_e_errors
def setUp(self):
ndim = 3
nt = 5000
ne = 500
problems = OrderedDict()
problems['sphere'] = Sphere(ndim=ndim)
problems['exp'] = TensorProduct(ndim=ndim, func='exp')
problems['tanh'] = TensorProduct(ndim=ndim, func='tanh')
problems['cos'] = TensorProduct(ndim=ndim, func='cos')
sms = OrderedDict()
if compiled_available:
sms['RMTC'] = RMTC()
sms['RMTB'] = RMTB()
t_errors = {}
t_errors['RMTC'] = 1e-1
t_errors['RMTB'] = 1e-1
e_errors = {}
e_errors['RMTC'] = 1e-1
e_errors['RMTB'] = 1e-1
ge_t_errors = {}
ge_t_errors['RMTC'] = 1e-2
ge_t_errors['RMTB'] = 1e-2
ge_e_errors = {}
ge_e_errors['RMTC'] = 1e-2
ge_e_errors['RMTB'] = 1e-2
self.nt = nt
self.ne = ne
self.problems = problems
self.sms = sms
self.t_errors = t_errors
self.e_errors = e_errors
self.ge_t_errors = ge_t_errors
self.ge_e_errors = ge_e_errors
def setUp(self):
ndim = 10
nt = 500
ne = 100
problems = OrderedDict()
problems['sphere'] = Sphere(ndim=ndim)
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=[4e-1]*ndim)
if compiled_available:
sms['IDW'] = IDW()
sms['RBF'] = RBF()
t_errors = {}
t_errors['LS'] = 1.0
t_errors['QP'] = 1.0
t_errors['KRG'] = 1e-6
t_errors['IDW'] = 1e-15
t_errors['RBF'] = 1e-2
e_errors = {}
e_errors['LS'] = 2.5
e_errors['QP'] = 2.0
e_errors['KRG'] = 2.0
e_errors['IDW'] = 1.5
e_errors['RBF'] = 1.5
self.nt = nt
self.ne = ne
self.problems = problems
self.sms = sms
self.t_errors = t_errors
self.e_errors = e_errors
def setUp(self):
ndim = 10
nt = 500
ne = 100
problems = OrderedDict()
problems['carre'] = Carre(ndim=ndim)
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['PA2'] = PA2()
sms['KRG'] = KPLS(name='KRG', n_comp=ndim, theta0=[40e-2] * ndim)
if compiled_available:
sms['IDW'] = IDW()
sms['RBF'] = RBF()
t_errors = {}
t_errors['LS'] = 1.0
t_errors['PA2'] = 1.0
t_errors['KRG'] = 1e-6
t_errors['IDW'] = 1e-15
t_errors['RBF'] = 1e-2
e_errors = {}
e_errors['LS'] = 1.5
e_errors['PA2'] = 2.0
e_errors['KRG'] = 2.0
e_errors['IDW'] = 1.5
e_errors['RBF'] = 1.5
self.nt = nt
self.ne = ne
self.problems = problems
self.sms = sms
self.t_errors = t_errors
self.e_errors = e_errors
def setUp(self):
ndim = 2
nt = 10000
ne = 1000
problems = OrderedDict()
problems['sphere'] = Sphere(ndim=ndim)
problems['exp'] = TensorProduct(ndim=ndim, func='exp', width=5)
problems['tanh'] = TensorProduct(ndim=ndim, func='tanh', width=5)
problems['cos'] = TensorProduct(ndim=ndim, func='cos', width=5)
sms = OrderedDict()
sms['LS'] = LS()
sms['QP'] = QP()
if compiled_available:
sms['RMTC'] = RMTC(num_elements=20, energy_weight=1e-10)
sms['RMTB'] = RMTB(num_ctrl_pts=40, energy_weight=1e-10)
t_errors = {}
t_errors['LS'] = 1.0
t_errors['QP'] = 1.0
t_errors['RMTC'] = 1e-2
t_errors['RMTB'] = 1e-2
e_errors = {}
e_errors['LS'] = 1.5
e_errors['QP'] = 1.5
e_errors['RMTC'] = 1e-2
e_errors['RMTB'] = 1e-2
self.nt = nt
self.ne = ne
self.problems = problems
self.sms = sms
self.t_errors = t_errors
self.e_errors = e_errors
def setUp(self):
ndim = 2
nt = 10000
ne = 1000
problems = OrderedDict()
problems["sphere"] = Sphere(ndim=ndim)
problems["exp"] = TensorProduct(ndim=ndim, func="exp", width=5)
problems["tanh"] = TensorProduct(ndim=ndim, func="tanh", width=5)
problems["cos"] = TensorProduct(ndim=ndim, func="cos", width=5)
sms = OrderedDict()
sms["LS"] = LS()
sms["QP"] = QP()
if compiled_available:
sms["RMTC"] = RMTC(num_elements=20, energy_weight=1e-10)
sms["RMTB"] = RMTB(num_ctrl_pts=40, energy_weight=1e-10)
t_errors = {}
t_errors["LS"] = 1.0
t_errors["QP"] = 1.0
t_errors["RMTC"] = 1.0
t_errors["RMTB"] = 1.0
e_errors = {}
e_errors["LS"] = 1.5
e_errors["QP"] = 1.5
e_errors["RMTC"] = 1.0
e_errors["RMTB"] = 1.0
self.nt = nt
self.ne = ne
self.problems = problems
self.sms = sms
self.t_errors = t_errors
self.e_errors = e_errors
def setUp(self):
ndim = 2
nt = 10000
ne = 1000
problems = OrderedDict()
problems['carre'] = Carre(ndim=ndim)
problems['exp'] = TensorProduct(ndim=ndim, func='exp', width=5)
problems['tanh'] = TensorProduct(ndim=ndim, func='tanh', width=5)
problems['cos'] = TensorProduct(ndim=ndim, func='cos', width=5)
sms = OrderedDict()
sms['LS'] = LS()
sms['PA2'] = PA2()
if compiled_available:
sms['RMTS'] = RMTS(num_elements=30, nln_max_iter=20)
sms['RMTB'] = RMTB(order=6, num_ctrl_pts=30, nln_max_iter=20)
t_errors = {}
t_errors['LS'] = 1.0
t_errors['PA2'] = 1.0
t_errors['RMTS'] = 1e-2
t_errors['RMTB'] = 1e-2
e_errors = {}
e_errors['LS'] = 1.5
e_errors['PA2'] = 1.5
e_errors['RMTS'] = 1e-2
e_errors['RMTB'] = 1e-2
self.nt = nt
self.ne = ne
self.problems = problems
self.sms = sms
self.t_errors = t_errors
self.e_errors = e_errors
def test_exp(self):
self.run_test(TensorProduct(name="TP-exp", ndim=1, func="exp"))
self.run_test(TensorProduct(name="TP-exp", ndim=3, func="exp"))
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
def test_gaussian(self):
self.run_test(TensorProduct(name='TP-gaussian', ndim=1, func='gaussian'))
self.run_test(TensorProduct(name='TP-gaussian', ndim=3, func='gaussian'))
def test_cos(self):
self.run_test(TensorProduct(name='TP-cos', ndim=1, func='cos'))
self.run_test(TensorProduct(name='TP-cos', ndim=3, func='cos'))
def test_tanh(self):
self.run_test(TensorProduct(name='TP-tanh', ndim=1, func='tanh'))
self.run_test(TensorProduct(name='TP-tanh', ndim=3, func='tanh'))
def test_exp(self):
self.run_test(TensorProduct(name='TP-exp', ndim=1, func='exp'))
self.run_test(TensorProduct(name='TP-exp', ndim=3, func='exp'))
def test_gaussian(self):
self.run_test(TensorProduct(name="TP-gaussian", ndim=1, func="gaussian"))
self.run_test(TensorProduct(name="TP-gaussian", ndim=3, func="gaussian"))
def test_cos(self):
self.run_test(TensorProduct(name="TP-cos", ndim=1, func="cos"))
self.run_test(TensorProduct(name="TP-cos", ndim=3, func="cos"))
def test_tanh(self):
self.run_test(TensorProduct(name="TP-tanh", ndim=1, func="tanh"))
self.run_test(TensorProduct(name="TP-tanh", ndim=3, func="tanh"))