def test_mu_m_lin():
J,grad_J = make_coef_J(1,100)
y0 = 1
yT = 1
T = 1
a = 1
import matplotlib.pyplot as plt
problem = Problem1(y0,yT,T,a,J,grad_J)
for N in [100]:
Mu = [0.2*N]
t = np.linspace(0,T,N+1)
res1 = problem.scipy_solver(N)
plt.plot(t,res1.x,'r--')
L2_diff = []
for m in [2,4,8,16]:
res2 = problem.scipy_penalty_solve(N,m,Mu)
error = np.sqrt(trapz((res1.x-res2.x[:N+1])**2,t))
L2_diff.append(error)
plt.plot(t,res2.x[:N+1])
print "||u1-um||_2 = %f for m=%d, error/m=%f" % (error,m,error/m)
plt.legend(['m=1','m=2','m=4','m=8','m=16'],loc=4)
plt.xlabel('t')
plt.ylabel('control')
plt.title('Controls for N='+str(N)+' and mu='+str(Mu[0]))
plt.show()
def test_LagAndPen():
y0 = 1
yT = 1
T = 1
a = 1
N = 700
m = 2
C = [1]
D = [0]
my = [0.1*N,0.7*N,2*N]
for i in range(len(C)):
for j in range(len(D)):
J,grad_J = make_coef_J(C[i],D[j])
problem = Problem1(y0,yT,T,a,J,grad_J)
opt = {"mem_lim" :40}
res1 = problem.penalty_solve(N,m,my,Lbfgs_options=opt)
try:
res2 = problem.lagrange_penalty_solve(N,m,my,Lbfgs_options=opt)
except:
res2 = [{'iteration':-1},{'iteration':-1},{'iteration':-1}]
print
print res1[0]['iteration'],res1[1]['iteration'],res1[2]['iteration']
print res2[0]['iteration'],res2[1]['iteration'],res2[2]['iteration']
def end_term_test():
y0 = 1
yT = 1
T = 1
a = 1
N = 1000
power = 4
coef = [1,0.5]
J, grad_J = make_coef_J(coef[0],coef[1],power=power)
def Jfunc(u,y,yT,T,power):
return J(u,y,yT,T)
problem = GeneralPowerY(y0,yT,T,a,power,Jfunc,grad_J)
problem.scipy_simple_test(N,make_plot=False)
def end_term_test():
y0 = 1
yT = 1
T = 1
a = 1
N = 1000
power = 4
coef = [1, 0.5]
J, grad_J = make_coef_J(coef[0], coef[1], power=power)
def Jfunc(u, y, yT, T, power):
return J(u, y, yT, T)
problem = GeneralPowerY(y0, yT, T, a, power, Jfunc, grad_J)
problem.scipy_simple_test(N, make_plot=False)
def test_constant_C():
J,grad_J = make_coef_J(1,100)
y0 = 1
yT = 1
T = 1
a = 1
problem = Problem1(y0,yT,T,a,J,grad_J)
problem.mu_to_N_relation(50,0.2)
problem2 = Explicit_quadratic(y0,yT,T,a,J,grad_J)
problem2.mu_to_N_relation(50,0.2)
def test_quadratic_manufactured_solution():
y0 = 1
yT = 1
T = 1
a = 1
solution = 3.1
J,grad_J = make_coef_J(1,solution)
problem = Explicit_quadratic(y0,yT,T,a,J,grad_J)
N = 200000
u = np.zeros(N+1) + solution
yT = problem.ODE_solver(u,N)[-1]
print "yT=%f"%yT
h_val = []
error = []
error2 = [[],[],[]]
M = [2,4,8]
import matplotlib.pyplot as plt
fig,ax = plt.subplots(2, 2)
teller = -1
for N in [50,100,150,200,500,1000]:
h_val.append(1./N)
problem = Explicit_quadratic(y0,yT,T,a,J,grad_J)
res = problem.scipy_solver(N,disp=False)
#u = np.zeros(N+1)
#problem.finite_diff(u,N)
t = np.linspace(0,T,N+1)
if N!= 100 and N!=500:
teller += 1
ax[teller/2,teller%2].plot(t,res.x)
err = max(abs(res.x-solution))
error.append(err)
print "max(|u-%.1f|)=%f for N=%d and iter=%d"%(solution,err,N,res.nit)
for i in range(len(M)):
res2 = problem.scipy_penalty_solve(N,M[i],[100])
err2 = max(abs(res2.x[:N+1]-solution))
print "m=%d: err=%f for N=%d and iter=%d"%(M[i],err2,N,res2.nit)
error2[i].append(err2)
if N!= 100 and N!=500:
ax[teller/2,teller%2].plot(t,res2.x[:N+1])
if N!= 100 and N!=500:
ax[teller/2,teller%2].legend(['m=1','m=2','m=4','m=8'],loc=4)
ax[teller/2,teller%2].set_title('N='+str(N))
plt.show()
Q = np.vstack([np.log(np.array(h_val)),np.ones(len(h_val))]).T
LS=linalg.lstsq(Q, np.log(np.array(error)))[0]
print LS[0],np.exp(LS[1])
plt.plot(np.log(np.array(h_val)),np.log(np.array(error)))
plt.xlabel('log(1/N)')
plt.ylabel('log(error)')
plt.show()
for i in range(len(M)):
Q = np.vstack([np.log(np.array(h_val)),np.ones(len(h_val))]).T
LS=linalg.lstsq(Q, np.log(np.array(error2[i])))[0]
print LS[0],np.exp(LS[1])
plt.plot(np.log(np.array(h_val)),np.log(np.array(error2[i])))
plt.show()
def test_manufactured_solution():
y0 = 1
yT = 2*np.exp(1) - 1
T = 1
a = 1
import matplotlib.pyplot as plt
J,grad_J = make_coef_J(1,1)
M = [2,4,8]
h_val = []
error = []
error2 = [[],[],[]]
fig,ax = plt.subplots(2, 2)
teller = -1
for N in [500,1000,1500,2000,5000,8000]:
h_val.append(1./N)
problem = Problem1(y0,yT,T,a,J,grad_J)
res = problem.scipy_solver(N,disp=False)
err = max(abs(res.x-1))
error.append(err)
print "max(|u-1|)=%f for N=%d and iter=%d"%(err,N,res.nit)
t = np.linspace(0,T,N+1)
if N!= 1000 and N!=5000:
teller += 1
ax[teller/2,teller%2].plot(t,res.x)
for i in range(len(M)):
res2 = problem.scipy_penalty_solve(N,M[i],[10])
err2 = max(abs(res2.x[:N+1]-1))
print "m=%d: err=%f for N=%d and iter=%d"%(M[i],err2,N,res2.nit)
error2[i].append(err2)
if N!= 1000 and N!=5000:
ax[teller/2,teller%2].plot(t,res2.x[:N+1])
if N!= 1000 and N!=5000:
ax[teller/2,teller%2].legend(['m=1','m=2','m=4','m=8'],loc=4)
ax[teller/2,teller%2].set_title('N='+str(N))
plt.show()
Q = np.vstack([np.log(np.array(h_val)),np.ones(len(h_val))]).T
LS=linalg.lstsq(Q, np.log(np.array(error)))[0]
print LS[0],np.exp(LS[1])
for i in range(len(M)):
Q = np.vstack([np.log(np.array(h_val)),np.ones(len(h_val))]).T
LS=linalg.lstsq(Q, np.log(np.array(error2[i])))[0]
print LS[0],np.exp(LS[1])
plt.plot(np.log(np.array(h_val)),np.log(np.array(error2[i])))
plt.show()
plt.plot(np.log(np.array(h_val)),np.log(np.array(error)))
plt.xlabel('log(1/N)')
plt.ylabel('log(error)')
plt.show()
def test_manufactured_resultChange_solution():
solution = 20
T = 1
y0 = 1
yT = (solution+1)*np.exp(T) - solution
a = 1
power = 4
J,grad_J = make_coef_J(1,solution,power=power)
def Jfunc(u,y,yT,T,power):
return J(u,y,yT,T)
import matplotlib.pyplot as plt
h_val = []
error = []
error2=[[],[],[]]
M=[2,4,8]
opt={'gtol': 1e-6, 'disp': False,'maxcor':10}
fig,ax = plt.subplots(2, 2)
teller = -1
for N in [50,100,150,200,500,1000]:
h_val.append(1./N)
t = np.linspace(0,T,N+1)
problem = GeneralPowerY(y0,yT,T,a,power,Jfunc,grad_J)
#u = np.zeros(N+1)
#problem.finite_diff(u,N)
res = problem.scipy_solver(N,disp=False,options=opt)
err = max(abs(res.x-solution))
error.append(err)
print "max(|u-%.1f|)=%f for N=%d and iter=%d"%(solution,err,N,res.nit)
#plt.plot(t,2*t+19)
if N!= 100 and N!=500:
teller += 1
ax[teller/2,teller%2].plot(t,res.x)
for i in range(len(M)):
res2 = problem.scipy_penalty_solve(N,M[i],[1],options=opt)
err2 = max(abs(res2.x[:N+1]-solution))
print "m=%d: err=%f for N=%d and iter=%d"%(M[i],err2,N,res2.nit)
error2[i].append(err2)
if N!= 100 and N!=500:
ax[teller/2,teller%2].plot(t,res2.x[:N+1])
if N!= 100 and N!=500:
ax[teller/2,teller%2].legend(['m=1','m=2','m=4','m=8'],loc=4)
ax[teller/2,teller%2].set_title('N='+str(N))
plt.show()
Q = np.vstack([np.log(np.array(h_val)),np.ones(len(h_val))]).T
LS=linalg.lstsq(Q, np.log(np.array(error)))[0]
print LS[0],np.exp(LS[1])
plt.plot(np.log(np.array(h_val)),np.log(np.array(error)))
plt.xlabel('log(1/N)')
plt.ylabel('log(error)')
plt.show()
for i in range(len(M)):
Q = np.vstack([np.log(np.array(h_val)),np.ones(len(h_val))]).T
LS=linalg.lstsq(Q, np.log(np.array(error2[i])))[0]
print LS[0],np.exp(LS[1])
plt.plot(np.log(np.array(h_val)),np.log(np.array(error2[i])))
plt.show()
