def test_solver(self):
"""
Compare result from solver against
precomputed arrays for theta=0, 0.5, 1.
"""
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]),
}
for theta in 0, 0.5, 1:
u, t = dc_mod.solver(I=0.8, a=1.2, T=4, dt=0.5,
theta=theta)
diff = np.abs(u - precomputed[theta]).max()
# Precomputed numbers are known to 8 decimal places
self.assertAlmostEqual(diff, 0, places=8,
msg='theta=%s' % theta)
def test_solver():
"""
Compare result from solver 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
]),
}
for theta in 0, 0.5, 1:
u, t = dc_mod.solver(I, a, T, dt, theta=theta)
diff = np.abs(u - precomputed[theta]).max()
# Precomputed numbers are known to 8 decimal places
nt.assert_almost_equal(diff, 0, places=8, msg='theta=%s' % theta)
def test_potential_integer_division(self):
"""Choose variables that can trigger integer division."""
theta = 1; a = 1; I = 1; dt = 2
N = 4
u, t = dc_mod.solver(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()
self.assertAlmostEqual(diff, 0, delta=1E-14)
def test_potential_integer_division():
"""Choose variables that can trigger integer division."""
theta = 1
a = 1
I = 1
dt = 2
N = 4
u, t = dc_mod.solver(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)
def test_against_discrete_solution():
"""
Compare result from solver against
formula for the discrete solution.
"""
theta = 0.8; a = 2; I = 0.1; dt = 0.8
N = int(8/dt) # no of steps
u, t = dc_mod.solver(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)
def test_against_discrete_solution():
"""
Compare result from solver against
formula for the discrete solution.
"""
theta = 0.8
a = 2
I = 0.1
dt = 0.8
N = int(8 / dt) # no of steps
u, t = dc_mod.solver(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)