def test_theta_rule():
"""
Compare result from theta_rule against
precomputed arrays for theta=0, 0.5, 1.
"""
I=0.8; a=1.2; T=4; dt=0.5 # fixed parameters
precomputed = {
't': np.array([ 0. , 0.5, 1. , 1.5, 2. , 2.5,
3. , 3.5, 4. ]),
0.5: np.array(
[ 0.8 , 0.43076923, 0.23195266, 0.12489759,
0.06725255, 0.03621291, 0.01949926, 0.0104996 ,
0.00565363]),
0: np.array(
[ 8.00000000e-01, 3.20000000e-01,
1.28000000e-01, 5.12000000e-02,
2.04800000e-02, 8.19200000e-03,
3.27680000e-03, 1.31072000e-03,
5.24288000e-04]),
1: np.array(
[ 0.8 , 0.5 , 0.3125 , 0.1953125 ,
0.12207031, 0.07629395, 0.04768372, 0.02980232,
0.01862645]),
}
# Compare to 8 decimal places
for theta in 0, 0.5, 1:
u, t = decay.theta_rule(I, a, T, dt, theta=theta)
diff = np.abs(u - precomputed[theta]).max()
nt.assert_almost_equal(diff, 0, places=8,
msg='theta=%s' % theta)
def test_against_discrete_solution():
"""
Compare result from theta_rule against
formula for the discrete solution.
"""
def exact_discrete_solution(n, I, a, theta, dt):
factor = (1 - (1-theta)*a*dt)/(1 + theta*dt*a)
return I*factor**n
theta = 0.8; a = 2; I = 0.1; dt = 0.8
N = int(8/dt) # no of steps
u, t = decay.theta_rule(I=I, a=a, T=N*dt, dt=dt,
theta=theta)
u_de = np.array([exact_discrete_solution(n, I, a, theta, dt)
for n in range(N+1)])
diff = np.abs(u_de - u).max()
nt.assert_almost_equal(diff, 0, delta=1E-14)
