def run_test3():
xmin, xmax = -5.0, 5.0
ymin, ymax = -5.0, 5.0
func = stybtang
xDOE = mt.read_tabulated_data_without_header('LHS10.txt')
xDOE = np.vstack([xDOE, [-5,-5]])
yDOE = np.array([func(xi) for xi in xDOE])
X1 = np.arange(xmin,xmax,0.25)
X2 = np.arange(ymin,ymax,0.25)
X1, X2 = np.meshgrid(X1,X2)
X = np.vstack([X1.flatten(),X2.flatten()])
X = np.transpose(X)
Y = np.array([t.jackknifing(xDOE,yDOE,xi) for xi in X])
Y = np.reshape(Y,X1.shape)
Y2 = np.array([t.jackknifing(xDOE,yDOE,xi) for xi in xDOE])
fig1 = plt.figure(1)
ax1 = fig1.add_subplot(111, projection='3d')
ax1.hold(True)
ax1.plot_surface(X1,X2,Y,cmap=cm.jet,rstride=1, cstride=1)
ax1.plot(xDOE[:,0],xDOE[:,1],Y2,'ro')
plt.show()
def objective(x, X, Y, jnTarget, dMean, surrogate=None):
jn = t.jackknifing(x, X, Y, surrogate)
dist = np.array([np.linalg.norm(xi-x) for xi in X])
dmin = np.sort(dist)
a = 2.0*dmin[:3]/dMean
f1 = np.exp(-8.0*a**2.0)
#return -(5.0*np.sum(f1) + jn/jnTarget)
return jn/jnTarget + np.sum(f1)
def objective_old(x, X, Y, surrogate=None, nFoldSamples=1, dmin=0.05):
f = -t.jackknifing(x, X, Y, surrogate, nFoldSamples)
dist = np.array([np.linalg.norm(x-xi) for xi in X])
g = dmin - dist
g = np.array([np.max([gi,0.0])**2.0 for gi in g])
#phi = f + 100.0*np.sum(G)
#G = np.min(dist)**2.0
# g = 100.0/(1.0+1e3*dist*dist)
G = np.sum(g)
phi = f + G
return phi
def objective(x, X, Y, surrogate=None, p=1, k=0, dmin=0.05):
f = -t.jackknifing(x, X, Y, surrogate, p,k)
dist = np.array([np.linalg.norm(x-xi) for xi in X])
g = dmin - dist
G = np.array([np.max([gi,0.0])**2.0 for gi in g])
# phi = f - 100.0*np.sum(G)
# G = np.min(dist)**2.0
# phi = f - 100.0*G
# g = 100.0/(1.0+1e4*dist*dist)
# G = np.sum(g)
phi = 10.0*f + 1e3*np.sum(G)
return phi
def get_ffd_jackknife(function, npts):
X1 = np.linspace(0,1,npts)
X2 = np.linspace(0,1,npts)
X1, X2 = np.meshgrid(X1,X2)
X = np.vstack([X1.flatten(),X2.flatten()])
X = np.transpose(X)
jn = np.zeros(len(X))
Y = np.zeros(len(X))
for i,x in enumerate(X):
Y[i] = function(X)
for i,x in enumerate(X):
jn[i] = t.jackknifing(x,X,Y)
return np.average(jn), np.max(jn)
def run_test1():
x = np.linspace(-0.05,1.05,100)
f = tf.Forrester()
y = np.array([f.high_fidelity(xi) for xi in x])
#xs = np.array([0.0, 0.25, 0.5, 0.75, 1.0])
xs = np.linspace(0.0,1.0,5)
ys = np.array([f.high_fidelity(xi) for xi in xs])
model = t.RbfMod(xs,ys)
ym = np.array([model(xi) for xi in x])
jn = np.array([t.jackknifing(xi, xs, ys, None, 1) for xi in x])
jns = np.array([t.jackknifing(xi, xs, ys, None, 1) for xi in xs])
plt.figure(1)
plt.hold(True)
plt.plot(x,y,'r-')
plt.plot(xs,ys,'rs')
plt.plot(x, ym, 'b--')
plt.plot(x,ym+0.5*jn, 'k:')
plt.plot(x,ym-0.5*jn, 'k:')
plt.fill_between(x,ym+0.5*jn,ym-0.5*jn,color='#dddddd')
plt.axis([min(x), max(x), None, None])
plt.legend(['Exact function','Sample points', 'RBF Approximation', 'Jackknife Variance'],loc='upper left')
plt.xlabel('x')
plt.ylabel('f(x)')
plt.figure(2)
plt.hold(True)
plt.grid(True)
plt.plot(x,jn,'k-')
plt.plot(xs,jns,'rs')
plt.axis([min(x), max(x), -5, None])
plt.legend(['Jackknife Variance', 'Sample points'],loc='upper left')
plt.xlabel('x')
plt.ylabel('Variance')
plt.show()
def get_jn_old(x, X, Y, surrogate=None, nFoldSamples=1):
return t.jackknifing(x, X, Y, surrogate, nFoldSamples)
def get_jn(x, X, Y, surrogate=None, p=1, k=1):
return t.jackknifing(x, X, Y, surrogate, p, k)
def objective(x, X, Y, surrogate=None):
jn = t.jackknifing(x, X, Y, surrogate)
return -jn
def run_test1():
fhigh = tf.ForresterND(0.40, 0.9, 2.0)
flow = tf.ForresterND(0.45, 1.0, 0.0)
tolLow = 0.1
tolHigh = 0.1
minDistance = 0.05
errHist = list()
xDOE = mt.read_tabulated_data_without_header('LHS30.txt')
xDOE += 5.0
xDOE *= 0.1
yl = np.array([flow(xi) for xi in xDOE])
xl = np.array([0.0, 0.0])
xu = np.array([1.0, 1.0])
bnds = np.transpose(np.vstack([xl,xu]))
X1 = np.linspace(xl[0],xu[0],50)
X2 = np.linspace(xl[1],xu[1],50)
X1, X2 = np.meshgrid(X1,X2)
X = np.vstack([X1.flatten(),X2.flatten()])
X = np.transpose(X)
X1v = np.linspace(xl[0],xu[0],3)
X2v = np.linspace(xl[1],xu[1],3)
X1v, X2v = np.meshgrid(X1v,X2v)
Xv = np.vstack([X1v.flatten(),X2v.flatten()])
Xv = np.transpose(Xv)
err = tolLow+1
while err>tolLow:
jn = np.array([t.jackknifing(xi, xDOE,yl) for xi in Xv])
jnsortedIdx = np.argsort(jn)
jnsortedIdx = np.flipud(jnsortedIdx)
match = True
idx = 0
while match:
x0 = Xv[jnsortedIdx[0]]
#cnstr = ({'type':'ineq','fun':constraint,'args':(X,)})
rslt = minimize(objective,x0,method='SLSQP',bounds=bnds,args=(xDOE,yl,))
# constraints=cnstr)
xnew = rslt.x
err = -rslt.fun
dist = np.array([np.linalg.norm(xi-xnew) for xi in xDOE])
dist = np.min(dist)
if dist <= minDistance:
match = True
idx += 1
else:
match = False
print err, xnew, x0, idx
errHist.append(err)
xDOE = np.vstack([xDOE,xnew])
yl = np.array([flow(xi) for xi in xDOE])
print len(xDOE)
print get_avg_jackknife(xDOE,yl)
Yl = np.array([flow(xi) for xi in X])
model = mt.RbfMod(xDOE, yl)
Ym = np.array([model(xi) for xi in X])
Yl = np.reshape(Yl,X1.shape)
Ym = np.reshape(Ym,X1.shape)
# fig1 = plt.figure(1)
# ax1 = fig1.add_subplot(111, projection='3d')
# ax1.hold(True)
# ax1.plot_wireframe(X1,X2,Yl,color='r')
# ax1.plot_wireframe(X1,X2,Ym,color='b')
# ax1.plot(xDOE[:,0],xDOE[:,1],yl,'ro')
# ax1.set_xlabel('X1')
#
# fig2 = plt.figure(2)
# ax2 = fig2.add_subplot(111)
# ax2.plot(range(len(errHist)),errHist,'rs-')
# ax2.set_yscale('log')
# plt.show()
#
# variable fidelity model construction
flowApprox = mt.RbfMod(xDOE,yl)
xDOEh = mt.read_tabulated_data_without_header('LHS20.txt')
xDOEh += 5.0
xDOEh *= 0.1
#xDOEh = np.array([[0.0,0.0], [0, 1], [1,1], [1,0], [0.5,0.5]])
yh = np.array([fhigh(xi) for xi in xDOEh])
yl = np.array([flowApprox(xi) for xi in xDOEh])
gamma = yh - yl
fscaling = HybridScaling(xDOEh,yh,yl,flowApprox,0.0)
# --- vf DOE ---
err = tolHigh+1.0
while err>tolHigh:
jn = np.array([t.jackknifing(xi, xDOEh,gamma) for xi in Xv])
jnsortedIdx = np.argsort(jn)
jnsortedIdx = np.flipud(jnsortedIdx)
match = True
idx = 0
while match:
x0 = Xv[jnsortedIdx[idx]]
rslt = minimize(objective,x0,method='SLSQP',bounds=bnds,args=(xDOEh,gamma))
xnew = rslt.x
err = -rslt.fun
dist = np.array([np.linalg.norm(xi-xnew) for xi in xDOEh])
dist = np.min(dist)
if dist <= minDistance:
match = True
idx += 1
else:
match = False
print err, xnew, x0, idx
errHist.append(err)
xDOEh = np.vstack([xDOEh,xnew])
yl = np.array([flow(xi) for xi in xDOEh])
yh = np.array([fhigh(xi) for xi in xDOEh])
gamma = yh-yl
fscaling = HybridScaling(xDOEh,yh,yl,flowApprox,1.0)
print len(xDOEh)
# --- plot ---
Yl = np.array([fhigh(xi) for xi in X])
Ym = np.array([fscaling(xi) for xi in X])
Yl = np.reshape(Yl,X1.shape)
Ym = np.reshape(Ym,X1.shape)
print get_avg_jackknife(xDOEh,gamma)
fig1 = plt.figure(1)
ax1 = fig1.add_subplot(111, projection='3d')
ax1.hold(True)
ax1.plot_wireframe(X1,X2,Yl,color='r')
ax1.plot_wireframe(X1,X2,Ym,color='b')
ax1.plot(xDOEh[:,0],xDOEh[:,1],yh,'ro')
ax1.legend(['high','scaled','samples-high'])
ax1.set_xlim(0,1)
ax1.set_ylim(0,1)
ax1.set_zlim(0,5)
ax1.set_xlabel('X1')
ax1.set_ylabel('X2')
plt.show()
def get_avg_jackknife(X,Y):
jn = np.zeros(len(X))
for i,x in enumerate(X):
jn[i] = t.jackknifing(x,X,Y)
return np.average(jn), np.max(jn)