def testHarmonicOscillator(self):
T, N = 10, 100
u0 = ad.array([1., 0.])
t = np.linspace(0, T, N)
u1 = pdeint(lambda u : ad.hstack([u[1], -u[0]]), u0, t)
u2 = pdeint(lambda u : ad.hstack([u[1], -u[0]]), u0, [0, T])
accuracy = np.linalg.norm(ad.value(u1[-1] - u2[-1]))
self.assertLess(accuracy, 5E-4)
def qoi(self, x):
# set the operator coefficients with the given x
self.set_coeff(x)
# solve the PDE
u = npd.solve(self.residual,
np.zeros([self.nx - 1, self.nx - 1]),
verbose=False)
# get the PDE solution on the boundary
u_bnd = u[:, -1]
# compute the average on the boundary
q = 0.5 * self.dx * np.sum(u_bnd[1:] + u_bnd[:-1])
# return a number from numpad
return npd.value(q)
def pdeint(f, u0, t, relTol=1E-4, absTol=1E-6, ret='array', disp=0):
'''
To be used like ode23s, using numpad for Jacobian
'''
def _roundTo2ToK(n):
log2n = np.log2(max(1, n))
return 2**int(round(log2n))
u = ad.array(u0).copy()
uHistory = [u]
uTrajectory = Trajectory(f, ad.value(u))
dt = t[1] - t[0]
for i in range(len(t) - 1):
iSubdiv, nSubdiv = 0, _roundTo2ToK((t[i+1] - t[i]) / dt)
dt = (t[i+1] - t[i]) / nSubdiv
while iSubdiv < nSubdiv:
uTmp1, uTmp2, u3rd, u2nd = step(f, u, dt)
uNorm = np.linalg.norm(ad.value(u))
errNorm = np.linalg.norm(ad.value(u3rd) - ad.value(u2nd))
if errNorm > max(absTol, relTol * uNorm):
dt, iSubdiv, nSubdiv = 0.5 * dt, 2 * iSubdiv, 2 * nSubdiv
else:
iSubdiv += 1
u = u3rd
uTrajectory.append(ad.value(uTmp1), ad.value(uTmp2),
ad.value(u), dt)
if ret == 'array':
u.obliviate()
if disp:
print(t[i] + (t[i+1] - t[i]) * iSubdiv / nSubdiv)
if errNorm < 0.25 * max(absTol, relTol * uNorm) and \
iSubdiv % 2 == 0 and nSubdiv > 1:
dt, iSubdiv, nSubdiv = 2 * dt, iSubdiv / 2, nSubdiv / 2
assert iSubdiv == nSubdiv
uHistory.append(u)
if ret == 'array':
return np.array([ad.value(u) for u in uHistory])
elif ret == 'list':
return uHistory
elif ret == 'trajectory':
return uTrajectory