def transonic_airfoil():
#x0 = array([0.119087477, 0.160950359,0.203634413,0.192468212,-0.200580639, -0.126010045, 0.107256400e-18])
x0 = array([0.17042532,0.14831629,0.14576823,0.134351,-0.15162484,-0.13875406,-0.14055989])
tol = 1.0e-4
gtol = 1.0e-4
maxIter = 50
xDoe = read_samples('LHC_transonic_af.txt')
aa = AirfoilAnalysis()
aa._upd_cst(x0)
lb = x0 - 0.075
ub = x0 + 0.075
err = tol+1.
niter = 0
gConverged = False
xConverged = False
delta = min([min(xu-x,x-xl) for x,xu,xl in zip(x0,ub,lb)])
trustRegion = TrustRegionManagement(delta, 0.25, 0.75, 1.25, 0.3, 2.0)
xDoe = denormalize(xDoe,lb,ub,0)
fscaled = ScaledFunction(aa.fLow, aa.fHigh,0,'add')
gscaled = ScaledFunction(aa.gLow, aa.gHigh,0,'add')
fscaled._initialize_by_doe_points(xDoe)
#gscaled._initialize_by_doe_points(xDoe)
def print_header():
print '\nx1\tx2\tf\trho\tdelta\terr\tgScaled\tgHigh'
while err>tol:
fscaled.construct_scaling_model(x0)
#gscaled.construct_scaling_model(x0)
bnds = get_bounds(x0,delta,lb,ub)
cnstr = ({'type':'ineq','fun':aa.g3},{'type':'ineq','fun':aa.g2},)
rslt = minimize(fscaled,x0,method='SLSQP',bounds=bnds,constraints=cnstr,tol=1e-10,jac=aa.fLowDeriv)
#rslt = minimize(fscaled,x0,method='SLSQP',bounds=bnds,tol=1e-10)
xnew = rslt.x
fnew = rslt.fun
#gScaledNew = gscaled(xnew)
rho1, fHighNew = fscaled.get_trust_region_ratio(xnew)
#rho2, gHighNew = gscaled.get_trust_region_ratio(xnew)
#rho = min([rho1,rho2])
rho = rho1
err = np.linalg.norm([x0-xnew])
delta = trustRegion.adjust(rho,err)
x0 = xnew
#print '\n%.4f\t%.4f\t%.4f\t'%(x0[0],x0[1],fnew),'%.2f\t%.2e\t'%(rho,delta),'%.2e'%err
print '\n',fnew, rho, delta, err
niter += 1
# if (-gtol<=gHighNew<=gtol and gScaledNew<=gtol) or (gHighNew>=0.0 and gScaledNew>gtol):
# gConverged = True
# else:
# gConverged = False
fscaled.funcHi.display()
fscaled.funcLo.display()
gscaled.funcHi.display()
gscaled.funcLo.display()
def numerical_example_2():
# fHigh = lambda x: np.exp(x[0]/3) + np.exp(x[1]/5) - x[0]
# fLow = lambda x: x[0] + x[1]
# def fHigh(x):
# x = 0.1*x
# return ForresterFunc(np.linalg.norm(x)/1.2)+5.*(x[0]+x[1])
# fLow = lambda x: np.exp(x[0]/3) + np.exp(x[1]/5) - x[0]
g1High = lambda x: x[0]**2*x[1]/20. - 1
g1Low = lambda x: x[0]**2*x[1]/20. + (x[0]+x[1])/5. - 2
g2 = lambda x: (x[0]+x[1]-5)**2/30 + (x[0]-x[1]-12)**2/120 - 1
forrester = lambda x: (5.0*x-2.0)**2.0*np.sin(12.*x-4.)
def fHigh(x):
x = np.array(x)*0.08
return forrester(np.linalg.norm(x)) + 5.*np.linalg.norm(x)# + 10.*(x[0]+x[1])
def fLow(x):
x = np.array(x)*0.085
return forrester(np.linalg.norm(x)) + 1.*np.linalg.norm(x)
tol = 1.0e-3
gtol = 1.0e-3
maxIter = 50
lb = np.array([0.0,0.0])
ub = np.array([10.,10.])
x0 = np.array([5.0,5.0])
# dx = 0.1
# xmsh = ymsh = np.arange(-0.5,10.5,dx)
# Xmsh, Ymsh = np.meshgrid(xmsh,ymsh)
# zs1 = np.array([fHigh(np.array([x,y])) for x,y in zip(np.ravel(Xmsh),np.ravel(Ymsh))])
# zs2 = np.array([g1High(np.array([x,y])) for x,y in zip(np.ravel(Xmsh),np.ravel(Ymsh))])
# zs3 = np.array([g2(np.array([x,y])) for x,y in zip(np.ravel(Xmsh),np.ravel(Ymsh))])
# Z1 = zs1.reshape(Xmsh.shape)
# Z2 = zs2.reshape(Xmsh.shape)
# Z3 = zs3.reshape(Xmsh.shape)
#plt.show()
#nDoe = 5 # nDoe>20 creates numerical noise and fails to converge
err = tol+1.
niter = 0
gConverged = False
xConverged = False
delta = min([min(xu-x,x-xl) for x,xu,xl in zip(x0,ub,lb)])
trustRegion = TrustRegionManagement(delta, 0.25, 0.75, 1.25, 0.3, 2.0)
#xDoe = lhs(len(x0),nDoe)
#xDoe = ff2n(2)
xDoe = read_samples('2DLHC.txt')
#xDoe = read_samples()
xDoe = denormalize(xDoe,lb,ub)
#print xDoe
fscaled = ScaledFunction(fLow, fHigh,4,'add')
gscaled = ScaledFunction(g1Low, g1High,4,'add')
fscaled._initialize_by_doe_points(xDoe)
gscaled._initialize_by_doe_points(xDoe)
def print_header():
print 'x1\tx2\tf\trho\tdelta\terr\tgScaled\tgHigh'
while xConverged==False or gConverged==False:
fscaled.construct_scaling_model(x0)
gscaled.construct_scaling_model(x0)
bnds = get_bounds(x0,delta,lb,ub)
cnstr = ({'type':'ineq','fun':gscaled},{'type':'ineq','fun':g2})
rslt = minimize(fscaled,x0,method='SLSQP',bounds=bnds,constraints=cnstr,tol=1e-10)
xnew = rslt.x
fnew = rslt.fun
gScaledNew = gscaled(xnew)
rho1, fHighNew = fscaled.get_trust_region_ratio(xnew)
rho2, gHighNew = gscaled.get_trust_region_ratio(xnew)
rho = min([rho1,rho2])
err = np.linalg.norm([x0-xnew])
delta = trustRegion.adjust(rho,err)
x0 = xnew
if niter%5==0:
print_header()
print '%.4f\t%.4f\t%.4f\t'%(x0[0],x0[1],fnew),'%.2f\t%.2e\t'%(rho,delta),'%.2e'%err,'%.4f\t%.4f\t'%(gScaledNew,gHighNew)
niter += 1
if err<=tol or niter>maxIter:
xConverged=True
else:
xConverged=False
if (-gtol<=gHighNew<=gtol and gScaledNew<=gtol) or (gHighNew>=0.0 and gScaledNew>gtol):
gConverged = True
else:
gConverged = False
xbounds = np.array([bnds[0][0],bnds[0][0],bnds[0][1],bnds[0][1],bnds[0][0]])
ybounds = np.array([bnds[1][0],bnds[1][1],bnds[1][1],bnds[1][0],bnds[1][0]])
# fig = plt.figure(1)
# ax = fig.add_subplot(111)
# ax.hold(True)
# zs4 = np.array([fscaled(np.array([x,y])) for x,y in zip(np.ravel(Xmsh),np.ravel(Ymsh))])
# zs5 = np.array([gscaled(np.array([x,y])) for x,y in zip(np.ravel(Xmsh),np.ravel(Ymsh))])
# Z4 = zs4.reshape(Xmsh.shape)
# Z5 = zs5.reshape(Xmsh.shape)
# cs1 = ax.contour(Xmsh,Ymsh,Z1,colors='m')#,levels=[0,2,4,6,9,12,15]
# ax.contour(Xmsh,Ymsh,Z2,colors='r',levels=[0])
# ax.contour(Xmsh,Ymsh,Z3,colors='k',levels=[0])
# cs2 = ax.contour(Xmsh,Ymsh,Z4,colors='g')
# cs3 = ax.contour(Xmsh,Ymsh,Z5,colors='b',levels=[0])
# tmpx, tmpy = [-5,-5],[1,2]
# ax.plot(tmpx,tmpy,'m')
# ax.plot(tmpx,tmpy,'g')
# ax.plot(tmpx,tmpy,'r')
# ax.plot(tmpx,tmpy,'b')
# ax.plot(tmpx,tmpy,'k')
# ax.plot(np.array(fscaled.xPrev)[:,0],np.array(fscaled.xPrev)[:,1],'ko')
# ax.plot(xbounds,ybounds,'k--')
# ax.axis([-0.5,10.5,-0.5,10.5])
# plt.clabel(cs1, fontsize=9, inline=1)
# plt.clabel(cs2, fontsize=9, inline=1)
# plt.clabel(cs3, fontsize=9, inline=1)
# ax.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
# plt.legend(['Hifi objective','Lowfi objective','Hifi constraint 1','Lofi constraint 1','constraint 2','Hifi sample points','Trust region'])
# plt.show()
# plt.cla()
#print xConverged, gConverged, xConverged and gConverged
fscaled.funcHi.display()
fscaled.funcLo.display()
gscaled.funcHi.display()
gscaled.funcLo.display()
print niter
xexact = np.array([ 3.11388573, 2.06264578])
print np.linalg.norm(xexact-xnew)
print fnew-2.5367139107528409
