def test_2d_1fi_cokriging(self):
# CoKrigingSurrogate with one fidelity could be used as a KrigingSurrogate
# Same test as for KrigingSurrogate... well with predicted test value adjustment
def branin(x):
y = (x[1]-(5.1/(4.*pi**2.))*x[0]**2.+5.*x[0]/pi-6.)**2.+10.*(1.-1./(8.*pi))*cos(x[0])+10.
return y
x = array([[-2., 0.], [-0.5, 1.5], [1., 3.], [8.5, 4.5],
[-3.5, 6.], [4., 7.5], [-5., 9.], [5.5, 10.5],
[10., 12.], [7., 13.5], [2.5, 15.]])
y = array([branin(case) for case in x])
krig1 = MultiFiCoKrigingSurrogate()
krig1.train(x, y)
pred1 = krig1.predict([-2., 0.])
self.assertAlmostEqual(branin(x[0]), pred1.mu, places=5)
self.assertAlmostEqual(0., pred1.sigma, places=5)
pred2 = krig1.predict([5., 5.])
self.assertAlmostEqual(22, pred2.mu, delta=1)
self.assertAlmostEqual(13, pred2.sigma, delta=1)
# Test with theta setting instead of estimation
krig2 = MultiFiCoKrigingSurrogate(theta=[0.1])
krig1.train(x, y)
pred1 = krig1.predict([-2., 0.])
self.assertAlmostEqual(branin(x[0]), pred1.mu, places=5)
self.assertAlmostEqual(0., pred1.sigma, places=5)
pred2 = krig1.predict([5., 5.])
self.assertAlmostEqual(22, pred2.mu, delta=1)
self.assertAlmostEqual(13, pred2.sigma, delta=1)
def test_1d_2fi_cokriging(self):
# Example from Forrester: Engineering design via surrogate modelling
def f_expensive(x):
return ((x*6-2)**2)*sin((x*6-2)*2)
def f_cheap(x):
return 0.5*((x*6-2)**2)*sin((x*6-2)*2)+(x-0.5)*10. - 5
x = array([[[0.0], [0.4], [0.6], [1.0]],
[[0.1], [0.2], [0.3], [0.5], [0.7],
[0.8], [0.9], [0.0], [0.4], [0.6], [1.0]]])
y = array([[f_expensive(v) for v in array(x[0]).ravel()],
[f_cheap(v) for v in array(x[1]).ravel()]])
cokrig = MultiFiCoKrigingSurrogate()
cokrig.train_multifi(x, y)
new_x = array([0.75])
pred = cokrig.predict(new_x)
self.assertTrue(isinstance(pred, NormalDistribution))
self.assertAlmostEqual( f_expensive(new_x[0]), pred.mu, delta=0.05)
self.assertAlmostEqual(0., pred.sigma, delta=0.02)
def test_1d_1fi_cokriging(self):
# CoKrigingSurrogate with one fidelity could be used as a KrigingSurrogate
# Same test as for KrigingSurrogate... well with predicted test value adjustment
x = array([[0.05], [.25], [0.61], [0.95]])
y = array([0.738513784857542, -0.210367746201974, -0.489015457891476, 12.3033138316612])
krig1 = MultiFiCoKrigingSurrogate()
krig1.train(x, y)
new_x = array([0.5])
pred1 = krig1.predict(x[0])
self.assertTrue(isinstance(pred1, NormalDistribution))
self.assertAlmostEqual(y[0] , pred1.mu, places=4)
self.assertAlmostEqual(.0, pred1.sigma, places=4)
pred2 = krig1.predict(new_x)
self.assertTrue(isinstance(pred2, NormalDistribution))
self.assertAlmostEqual( -2.0279, pred2.mu, places=3)
self.assertAlmostEqual(1.3408, pred2.sigma, places=3)
# Test with theta setting instead of estimation
krig2 = MultiFiCoKrigingSurrogate(theta=0.1)
krig2.train(x, y)
pred1 = krig2.predict(x[0])
self.assertTrue(isinstance(pred1, NormalDistribution))
self.assertAlmostEqual(y[0] , pred1.mu, places=4)
self.assertAlmostEqual(.0, pred1.sigma, places=4)
pred2 = krig2.predict(new_x)
self.assertTrue(isinstance(pred2, NormalDistribution))
self.assertAlmostEqual( -1.2719, pred2.mu, places=3)
self.assertAlmostEqual(0.0439, pred2.sigma, places=3)
def test_2d_2fi_cokriging(self):
def branin(x):
x1 = 15*x[0]-5
x2 = 15*x[1]
return (x2-(5.1/(4.*pi**2.))*x1**2.+5.*x1/pi-6.)**2.+10.*(1.-1./(8.*pi))*cos(x1)+10.
# Add a linear error
def branin_low_fidelity(x):
return branin(x)+30.*x[1] + 10.
x = [[[ 0.13073587, 0.24909577], # expensive (hifi) doe
[ 0.91915571, 0.4735261 ],
[ 0.75830543, 0.13321705],
[ 0.51760477, 0.34594101],
[ 0.03531219, 0.77765831],
[ 0.27249206, 0.5306115 ],
[ 0.62762489, 0.65778471],
[ 0.3914706 , 0.09852519],
[ 0.86565585, 0.85350002],
[ 0.40806563, 0.91465314]],
[[ 0.91430235, 0.17029894], # cheap (lowfi) doe
[ 0.99329651, 0.76431519],
[ 0.2012252 , 0.35006032],
[ 0.61707854, 0.90210676],
[ 0.15113004, 0.0133355 ],
[ 0.07108082, 0.55344447],
[ 0.4483159 , 0.52182902],
[ 0.5926638 , 0.06595122],
[ 0.66305449, 0.48579608],
[ 0.47965045, 0.7407793 ],
[ 0.13073587, 0.24909577], # notice hifi doe inclusion
[ 0.91915571, 0.4735261 ],
[ 0.75830543, 0.13321705],
[ 0.51760477, 0.34594101],
[ 0.03531219, 0.77765831],
[ 0.27249206, 0.5306115 ],
[ 0.62762489, 0.65778471],
[ 0.3914706 , 0.09852519],
[ 0.86565585, 0.85350002],
[ 0.40806563, 0.91465314]]]
y = array([[branin(case) for case in x[0]],
[branin_low_fidelity(case) for case in x[1]]])
nfi=2
cokrig = MultiFiCoKrigingSurrogate()
cokrig.train_multifi(x, y)
pred = cokrig.predict([2./3., 1/3.])
self.assertAlmostEqual(26, pred.mu, places=0)
self.assertAlmostEqual(0.3, pred.sigma, places=0)
# Test with theta setting instead of theta estimation
cokrig2 = MultiFiCoKrigingSurrogate(theta=0.1)
cokrig2.train_multifi(x, y)
pred = cokrig2.predict([2./3., 1/3.])
self.assertAlmostEqual(21.7, pred.mu, places=0)
self.assertAlmostEqual(2.29, pred.sigma, places=0)
# Test with theta setting instead of theta estimation
cokrig2 = MultiFiCoKrigingSurrogate(theta=[0.1, 10])
cokrig2.train_multifi(x, y)
pred = cokrig2.predict([2./3., 1/3.])
self.assertAlmostEqual(21.01, pred.mu, places=0)
self.assertAlmostEqual(2.29, pred.sigma, places=0)
# Test bad theta setting
cokrig3 = MultiFiCoKrigingSurrogate(theta=[0.1])
try:
cokrig3.train_multifi(x, y)
except ValueError, err:
self.assertEqual(str(err),
"theta must be a list of 2 element(s).")
self.assertAlmostEqual( f_expensive(new_x[0]), pred.mu, delta=0.05)
self.assertAlmostEqual(0., pred.sigma, delta=0.02)
def test_2d_1fi_cokriging(self):
# CoKrigingSurrogate with one fidelity could be used as a KrigingSurrogate
# Same test as for KrigingSurrogate... well with predicted test value adjustment
def branin(x):
y = (x[1]-(5.1/(4.*pi**2.))*x[0]**2.+5.*x[0]/pi-6.)**2.+10.*(1.-1./(8.*pi))*cos(x[0])+10.
return y
x = array([[-2., 0.], [-0.5, 1.5], [1., 3.], [8.5, 4.5],
[-3.5, 6.], [4., 7.5], [-5., 9.], [5.5, 10.5],
[10., 12.], [7., 13.5], [2.5, 15.]])
y = array([branin(case) for case in x])
krig1 = MultiFiCoKrigingSurrogate()
krig1.train(x, y)
pred1 = krig1.predict([-2., 0.])
self.assertAlmostEqual(branin(x[0]), pred1.mu, places=5)
self.assertAlmostEqual(0., pred1.sigma, places=5)
pred2 = krig1.predict([5., 5.])
self.assertAlmostEqual(22, pred2.mu, delta=1)
self.assertAlmostEqual(13, pred2.sigma, delta=1)
# Test with theta setting instead of estimation
krig2 = MultiFiCoKrigingSurrogate(theta=[0.1])
krig1.train(x, y)
pred1 = krig1.predict([-2., 0.])
