def test_complex_to_real_jac():
z = np.array([[1 + 2j]])
r = _complex_to_real_jac(z)
yield assert_array_equal, r, np.array([[1, -2], [2, 1]])
z = np.array([[1 + 2j, 3 + 4j], [5 + 6j, 7 + 8j]])
r = _complex_to_real_jac(z)
expected = np.array([[1, -2, 3, -4], [2, 1, 4, 3], [5, -6, 7, -8],
[6, 5, 8, 7]])
yield assert_array_equal, r, expected
def test_complex_to_real_jac():
z = np.array([[1+2j]])
r = _complex_to_real_jac(z)
yield assert_array_equal, r, np.array([[1, -2], [2, 1]])
z = np.array([[1+2j, 3+4j],
[5+6j, 7+8j]])
r = _complex_to_real_jac(z)
expected = np.array([[1, -2, 3, -4],
[2, 1, 4, 3],
[5, -6, 7, -8],
[6, 5, 8, 7]])
yield assert_array_equal, r, expected
def funcz(y, t, c):
# Same calculation as `func`, but computed using real arrays,
# so the calculation in `dot` should follow the same code path
# for both the real and complex examples below.
creal = _complex_to_real_jac(c)
dydt = creal.dot(y.view(np.float64))
return dydt.view(np.complex128)
def system3_funcz(y, t, c):
# Same calculation as `system3_func`, but computed using real arrays,
# so the calculation in `dot` should follow the same code path for
# both the real and complex examples below.
creal = _complex_to_real_jac(c)
dydt = creal.dot(y.view(np.float64))
return dydt.view(np.complex128)
def test_system3():
c = np.array([[-20+1j, 5-1j, 0, 0],
[ 0, -0.1, 1+2.5j, 0],
[ 0, 0, -1, 0.5],
[ 0, 0, 0, -5+10j]])
z0 = np.arange(1,5.0) + 0.5j
t = np.linspace(0, 250, 11)
common_kwargs = dict(full_output=True, atol=1e-12, rtol=1e-10,
mxstep=1000)
sol0, info0 = odeintw(system3_funcz, z0, t, Dfun=system3_jac,
args=(c,), **common_kwargs)
nje0 = info0['nje']
x0 = z0.view(np.float64)
sol1, info1 = odeint(system3_func, x0, t, Dfun=system3_jac,
args=(_complex_to_real_jac(c),), **common_kwargs)
nje1 = info1['nje']
# Using assert_array_equal here is risky. The system definitions have
# been defined so the call to odeint in odeintw follows the same
# code path as the call to odeint above. Still, floating point operations
# aren't necessarily deterministic.
yield assert_array_equal, sol0.view(np.float64), sol1
yield assert_array_equal, nje0, nje1
def test_system3():
c = np.array([[-20 + 1j, 5 - 1j, 0, 0], [0, -0.1, 1 + 2.5j, 0],
[0, 0, -1, 0.5], [0, 0, 0, -5 + 10j]])
z0 = np.arange(1, 5.0) + 0.5j
t = np.linspace(0, 250, 11)
common_kwargs = dict(full_output=True, atol=1e-12, rtol=1e-10, mxstep=1000)
sol0, info0 = odeintw(system3_funcz,
z0,
t,
Dfun=system3_jac,
args=(c, ),
**common_kwargs)
nje0 = info0['nje']
x0 = z0.view(np.float64)
sol1, info1 = odeint(system3_func,
x0,
t,
Dfun=system3_jac,
args=(_complex_to_real_jac(c), ),
**common_kwargs)
nje1 = info1['nje']
# Using assert_array_equal here is risky. The system definitions have
# been defined so the call to odeint in odeintw follows the same
# code path as the call to odeint above. Still, floating point operations
# aren't necessarily deterministic.
yield assert_array_equal, sol0.view(np.float64), sol1
yield assert_array_equal, nje0, nje1
atol=1e-12,
rtol=1e-10,
mxstep=1000)
sol0, info0 = odeintw(funcz, z0, t, Dfun=jac, **common_kwargs)
print(info0['nje'])
rargs = common_kwargs.copy()
rargs.pop('args')
x0 = z0.view(np.float64)
solr, infor = odeint(func,
x0,
t,
Dfun=jac,
args=(_complex_to_real_jac(c), ),
**rargs)
print(infor['nje'])
print("-----")
solbnj, infobnj = odeintw(func, z0, t, ml=0, mu=1, **common_kwargs)
print(infobnj['nje'])
sol2, info2 = odeint(func,
x0,
t,
ml=1,
mu=3,
args=(_complex_to_real_jac(c), ),
**rargs)
print()
z0 = np.arange(1,5.0) + 0.5j
t = np.linspace(0, 250, 11)
common_kwargs = dict(args=(c,), full_output=True, atol=1e-12, rtol=1e-10, mxstep=1000)
sol0, info0 = odeintw(funcz, z0, t, Dfun=jac, **common_kwargs)
print(info0['nje'])
rargs = common_kwargs.copy()
rargs.pop('args')
x0 = z0.view(np.float64)
solr, infor = odeint(func, x0, t, Dfun=jac, args=(_complex_to_real_jac(c),), **rargs)
print(infor['nje'])
print("-----")
solbnj, infobnj = odeintw(func, z0, t, ml=0, mu=1, **common_kwargs)
print(infobnj['nje'])
sol2, info2 = odeint(func, x0, t, ml=1, mu=3, args=(_complex_to_real_jac(c),), **rargs)
print(info2['nje'])
print("-----")
sol1, info1 = odeintw(func, z0, t, Dfun=bjac_cols, ml=0, mu=1, col_deriv=True, **common_kwargs)
print(info1['nje'])
common_kwargs = dict(args=(c,),
full_output=True,
atol=1e-12,
rtol=1e-10,
mxstep=1000)
sol0, info0 = odeintw(funcz, z0, t, Dfun=jac, **common_kwargs)
print(info0['nje'])
rargs = common_kwargs.copy()
rargs.pop('args')
x0 = z0.view(np.float64)
solr, infor = odeint(func, x0, t, Dfun=jac,
args=(_complex_to_real_jac(c),), **rargs)
print(infor['nje'])
print("-----")
solbnj, infobnj = odeintw(func, z0, t, ml=0, mu=1, **common_kwargs)
print(infobnj['nje'])
sol2, info2 = odeint(func, x0, t, ml=1, mu=3,
args=(_complex_to_real_jac(c),), **rargs)
print(info2['nje'])
print("-----")
sol1, info1 = odeintw(func, z0, t, Dfun=bjac_cols, ml=0, mu=1,
col_deriv=True, **common_kwargs)
