def run_test1():
f = Forrester()
x = np.linspace(0,1,100)
yh = f.high_fidelity(x)
yl = f.low_fidelity(x)
# case 1
xs1 = np.array([0.1, 0.3, 0.5, 0.7, 0.9])
yh1 = f.high_fidelity(xs1)
yl1 = f.low_fidelity(xs1)
gs1 = yh1 - yl1
fg1 = RbfMod(xs1,gs1)
yv1 = yl + np.array([fg1(xi) for xi in x])
# case 2
xs2 = np.array([0.15, 0.2, 0.25, 0.75, 0.8,0.85])
yh2 = f.high_fidelity(xs2)
yl2 = f.low_fidelity(xs2)
gs2 = yh2 - yl2
fg2 = RbfMod(xs2,gs2)
yv2 = yl + np.array([fg2(xi) for xi in x])
frbf = RbfMod(xs2, yh2)
yrbf2 = np.array([frbf(xi) for xi in x])
# case 3
xs3 = np.array([0.15, 0.2, 0.25])
yh3 = f.high_fidelity(xs3)
yl3 = f.low_fidelity(xs3)
gs3 = yh3 - yl3
p = sigmoid_fit(xs3,gs3)
yv3 = yl + sigmoid(x,p)
frbf3 = RbfMod(xs3, yh3)
yrbf3 = np.array([frbf3(xi) for xi in x])
# case 4
xs4 = np.linspace(0,1,8)
yh4 = f.high_fidelity(xs4)
f4 = RbfMod(xs4,yh4)
yv4 = np.array([f4(xi) for xi in x])
# case 5
bp1 = 0.5
gap = 0.05
x5l = np.linspace(0.0,bp1)
x5r = np.linspace(bp1,1.0)
y5l = f.low_fidelity(x5l)
y5r = f.high_fidelity(x5r)
xs5l = np.linspace(0.0,bp1-gap,8)
xs5r = np.linspace(bp1+gap,1.0,8)
ys5l = f.low_fidelity(xs5l)
ys5r = f.high_fidelity(xs5r)
d = y5l[-1] - y5r[0]
xs5 = np.hstack([xs5l, xs5r])
ys5 = np.hstack([ys5l, ys5r])
f5 = RbfMod(xs5,ys5)
yv5 = np.array([f5(xi) for xi in x])
plt.figure(1)
plt.hold(True)
plt.plot(x,yh,'k--',lw=2)
plt.plot(x,yl,'k:',lw=2)
plt.plot(x, yv1, 'r-',lw=2)
plt.plot(xs1, yh1, 'bo', markersize=9)
plt.legend(['High fidelity function','Low fidelity function','Data fusion','High fidelity samples'],loc='upper left')
plt.figure(2)
plt.hold(True)
plt.plot(x,yh,'k--',lw=2)
plt.plot(x,yl,'k:',lw=2)
plt.plot(x, yv2, 'r-',lw=2)
plt.plot(xs2, yh2, 'bo', markersize=9)
plt.plot(x,yrbf2,'g.-',markevery=2)
plt.legend(['High fidelity function','Low fidelity function','Data fusion (VF interpolation)','High fidelity samples','Conventional Interpolation (RBF)'],loc='upper left')
plt.figure(3)
plt.hold(True)
plt.plot(x,yh,'k--',lw=2)
plt.plot(x,yl,'k:',lw=2)
plt.plot(x, yv3, 'r-',lw=2)
plt.plot(xs3, yh3, 'bo', markersize=9)
plt.plot(x,yrbf3,'g.-',markevery=2)
plt.legend(['High fidelity function','Low fidelity function','Data fusion (VF extrapolation)','High fidelity samples','Conventional Extrapolation (RBF)'],loc='upper left')
plt.figure(4)
plt.hold(True)
plt.plot(x,yh,'k--',lw=2)
#plt.plot(x,yl,'k:',lw=2)
plt.plot(x, yv4, 'r-',lw=2)
plt.plot(xs4, yh4, 'bo', markersize=9)
plt.legend(['High fidelity function','Data fusion','High fidelity samples'],loc='upper left')
plt.figure(5)
plt.hold(True)
plt.plot(x5l,y5l,'k--',lw=2)
plt.plot(x5r,y5r,'k:',lw=2)
plt.plot(x, yv5, 'r-',lw=2)
plt.legend(['Low fidelity function','High fidelity function','Data fusion','High fidelity samples',],loc='upper left')
plt.axis([0,1,-10,20])
plt.show()
def run_test1():
f = Forrester()
xs = np.array([0.1, 0.3, 0.5, 0.7, 0.9])
x0 = 0.75
dx = 0.01
x = np.linspace(0,1,100)
yh = f.high_fidelity(x)
yl = f.low_fidelity(x)
yhs = f.high_fidelity(xs)
yls = f.low_fidelity(xs)
# constant
def objective(k):
yscaled = yls + k[1]
err = (yhs - yscaled)**2.0
return np.sum(err)
kopt = minimize(objective, [1.0,1.0]).x
yConst = kopt[0]*yl + kopt[1]
print kopt
# local
gamma0 = f.high_fidelity(x0) - f.low_fidelity(x0)
gamma1 = f.high_fidelity(x0+dx) - f.low_fidelity(x0+dx)
dGamma = (gamma1 - gamma0)/dx
yLocal = yl + gamma0 + dGamma*(x-x0)
# global
gamma = yhs - yls
model = RbfMod(xs,gamma)
yScaled = np.array([model(_x) for _x in x])
yGlobal = yl + yScaled
# rbf
model2 = RbfMod(xs,yhs)
yRbf = np.array([model2(_x) for _x in x])
plt.figure(1)
plt.hold(True)
plt.plot(x,yh,'gs-',markersize=3,markevery=2)
plt.plot(x,yl,'bo-',markersize=3,markevery=2)
plt.plot(xs,yhs,'rs',markersize=8)
plt.plot(x,yConst,'r-',linewidth=1.5)
plt.legend(['high-fidelity','low-fidelity','sample points','constant scaled function'],'upper left')
plt.figure(2)
plt.hold(True)
plt.plot(x,yh,'gs-',markersize=3,markevery=2)
plt.plot(x,yl,'bo-',markersize=3,markevery=2)
plt.plot(x0,f.high_fidelity(x0),'rs',markersize=8)
plt.plot(x,yLocal,'r-',linewidth=1.5)
plt.legend(['high-fidelity','low-fidelity','sample points','local scaled function'],'upper left')
plt.figure(3)
plt.hold(True)
plt.plot(x,yh,'gs-',markersize=3,markevery=2)
plt.plot(x,yl,'bo-',markersize=3,markevery=2)
plt.plot(xs,yhs,'rs',markersize=8)
plt.plot(x,yGlobal,'r-',linewidth=1.5)
plt.plot(x,yRbf,'k--',linewidth=1.5)
plt.legend(['high-fidelity','low-fidelity','sample points','global scaled function','RBF interpolation'],'upper left')
plt.figure(4)
plt.hold(True)
plt.plot(x,yh,'gs',markersize=3,markevery=2)
plt.plot(xs,yhs,'rs',markersize=8)
plt.plot(x,yRbf,'r-',linewidth=1.5)
plt.show()