def opti(y0,a,T,yT,n,F,sol,adj,gr,printplot=False):
t=np.linspace(0,T,n+1)
dt=float(T)/n
x0 = SimpleVector(np.zeros(n+1))
szi_x0 = np.zeros(n+1)
def J(u):
return F(u,a,y0,yT,T)
def grad_J(u):
l = adj(y0,a,len(u)-1,u,T,yT)
return gr(u,l,dt)
def Mud_J(u):
y = SimpleVector(grad_J(u))
y2 = SimpleVector(np.zeros(len(u)))
s = SimpleVector(u)
s2 = SimpleVector(np.zeros(len(u)))
return MuVector([y,y2]),MuVector([s,s2])
res1 = minimize(J,szi_x0,method='L-BFGS-B', jac=grad_J,
options={'gtol': 1e-6, 'disp': False})
options={"beta":1,"mem_lim" : 10,"return_data":True,"jtol": 1e-6,}
S1 = Lbfgs(J,grad_J,x0,options=options)
S2 = MuLbfgs(J,grad_J,x0,Mud_J,options=options)
res2 = S1.solve()
res3 = S2.solve()
x1 = res1.x
x2 = res2['control'].array()
x3 = res3['control'].array()
if printplot == True:
print res1.nit,res2['iteration'],res3['iteration']
print l2_error(x1,x2,dt)
print l2_error(x1,x3,dt)
print l2_error(x2,x3,dt)
plot(t,x1)
plot(t,x2)
plot(t,x3)
legend(['scipy','lbfgs','mu'])
show()
return res1,res2,res3
def opti(y0, a, T, yT, n, F, sol, adj, gr, printplot=False):
t = np.linspace(0, T, n + 1)
dt = float(T) / n
x0 = SimpleVector(np.zeros(n + 1))
szi_x0 = np.zeros(n + 1)
def J(u):
return F(u, a, y0, yT, T)
def grad_J(u):
l = adj(y0, a, len(u) - 1, u, T, yT)
return gr(u, l, dt)
def Mud_J(u):
y = SimpleVector(grad_J(u))
y2 = SimpleVector(np.zeros(len(u)))
s = SimpleVector(u)
s2 = SimpleVector(np.zeros(len(u)))
return MuVector([y, y2]), MuVector([s, s2])
res1 = minimize(J,
szi_x0,
method='L-BFGS-B',
jac=grad_J,
options={
'gtol': 1e-6,
'disp': False
})
options = {
"beta": 1,
"mem_lim": 10,
"return_data": True,
"jtol": 1e-6,
}
S1 = Lbfgs(J, grad_J, x0, options=options)
S2 = MuLbfgs(J, grad_J, x0, Mud_J, options=options)
res2 = S1.solve()
res3 = S2.solve()
x1 = res1.x
x2 = res2['control'].array()
x3 = res3['control'].array()
if printplot == True:
print res1.nit, res2['iteration'], res3['iteration']
print l2_error(x1, x2, dt)
print l2_error(x1, x3, dt)
print l2_error(x2, x3, dt)
plot(t, x1)
plot(t, x2)
plot(t, x3)
legend(['scipy', 'lbfgs', 'mu'])
show()
return res1, res2, res3
def mini_solver(y0,a,T,yT,n,m,my_list,show_output=False,mem_limit=15):
t=np.linspace(0,T,n+1)
#initial guess for control and penalty control is set to be 0
x0 = SimpleVector(np.zeros(n+m))
dt = t[1]-t[0]
def ser_J(u):
return ser.Func(u,a,y0,yT,T)
def ser_grad_J(u):
l = ser.adjoint_solver(y0,a,len(u)-1,u,T,yT)
return ser.L2_grad(u,l,dt)
res1 = minimize(ser_J,np.zeros(n+1),method='L-BFGS-B', jac=ser_grad_J,
options={'gtol': 1e-6, 'disp': False})
res2 = []
res3 = []
H = None
#solve problem for increasing mu
for k in range(len(my_list)):
#define reduced functional dependent only on u
def J(u):
y,Y=solver(y0,a,n,m,u[:n+1],u[n+1:],T)
return Functional2(y,u[:n+1],u[n+1:],yT,T,my_list[k])
#define our gradient using by solving adjoint equation
def grad_J(u):
#adjoint_solver(y0,a,n,m,u,lam,T,yT,my)
l,L = adjoint_solver(y0,a,n,m,u[:n+1],u[n+1:],T,yT,my_list[k])
g = np.zeros(len(u))
g[:n+1]=dt*(u[:n+1]+L)
for i in range(m-1):
g[n+1+i]=l[i+1][0]-l[i][-1]
return g
def Mud_J(u):
l,L,y,Y = adjoint_solver(y0,a,n,m,u[:n+1],u[n+1:],T,yT,my_list[k],get_y=True)
u1 = u[:n+1]
l1 = u[n+1:]
du1 = float(T)*(u[:n+1]+L)/n
ADJ1 = np.zeros(m-1)
STA1 = np.zeros(m-1)
for i in range(m-1):
ADJ1[i] = l[i+1][0]
STA1[i] = y[i][-1]
y1 = np.zeros(len(u))
y2 = np.zeros(len(u))
y1[:n+1] = du1
y1[n+1:] = ADJ1
y2[n+1:] = l1 - STA1
Y1 = SimpleVector(y1)
Y2 = SimpleVector(y2)
S1 = SimpleVector(u)
S2 = SimpleVector(np.zeros(len(u)))
return MuVector([Y1,Y2]),MuVector([S1,S2])
#minimize J using initial guess x, and the gradient/functional above
"""
default = {"jtol" : 1e-4,
"rjtol" : 1e-6,
"gtol" : 1e-4,
"rgtol" : 1e-5,
"maxiter" : 200,
"display" : 2,
"line_search" : "strong_wolfe",
"line_search_options" : ls,
"mem_lim" : 5,
"Hinit" : "default",
"beta" : 1,
"mu_val" : 1,
"old_hessian" : None,
"penaly_number" : 1,
"return_data" : False, }
"""
#mem_limit = 10
options = {"mu_val": my_list[k], "old_hessian": H,
"return_data": True,"mem_lim":mem_limit, "beta":1,
"save_number":-1,"jtol" : 1e-4,}
options2={"mem_lim" : mem_limit,"return_data": True,"jtol" : 1e-4,}
S1 = MuLbfgs(J,grad_J,x0,Mud_J,Hinit=None,options=options)
S2 = Lbfgs(J,grad_J,x0,options=options2)
try:
data1 = S1.solve()
except Warning:
data1 = {'control' : x0, 'iteration' : -1, 'lbfgs': H }
except RuntimeError:
data1 = {'control' : x0, 'iteration' : -1, 'lbfgs': H }
try:
data2 = S2.solve()
except:
data2 = {'control' : x0, 'iteration' : -1, 'lbfgs': H }
res2.append(data1)
res3.append(data2)
H = data1['lbfgs']
if show_output==True:
x1 = data1['control']
plot(t,x1.array()[:n+1])
plot(t,res1.x)
legend(["mu","normal"])
print data1['iteration']
show()
return res1,res2,res3
