def test_integrate_predefined(method, forgiveness, banded):
use_jac = method in requires_jac
k = k0, k1, k2 = 2.0, 3.0, 4.0
y0 = [0.7, 0.3, 0.5]
f, j = _get_f_j(k)
kwargs = {'method': method, 'dx0': 1e-10}
if use_jac:
if banded:
jac_callbacks = [bandify(j, 1, 0), None]
kwargs['lband'] = 1
kwargs['uband'] = 0
else:
jac_callbacks = [j, None]
else:
jac_callbacks = [None]
for j in jac_callbacks:
xout = np.linspace(0, 3, 31)
atol, rtol = 1e-8, 1e-8
# Run twice to catch possible side-effects:
yout, nfo = integrate_predefined(f, j, y0, xout, 1e-8, 1e-8, **kwargs)
yout, nfo = integrate_predefined(f, j, y0, xout, 1e-8, 1e-8, **kwargs)
yref = decay_get_Cref(k, y0, xout)
assert np.allclose(yout, yref,
rtol=forgiveness*rtol,
atol=forgiveness*atol)
assert nfo['nfev'] > 0
assert nfo['time_cpu'] > 1e-9
assert nfo['time_wall'] > 1e-9
if method in requires_jac and j is not None:
assert nfo['njev'] > 0
def test_rhs_unrecoverable_error():
def f(t, y, fout):
fout[0] = y[0]
return -1
kwargs = dict(dx0=0.0, atol=1e-8, rtol=1e-8, method='adams')
with pytest.raises(RuntimeError):
yout, info = integrate_predefined(f, None, [1], [0, 1, 2], **kwargs)
def test_rhs_unrecoverable_error():
def f(t, y, fout):
fout[0] = y[0]
return -1
kwargs = dict(dx0=0.0, atol=1e-8, rtol=1e-8, method='adams')
with pytest.raises(RuntimeError):
yout, info = integrate_predefined(f, None, [1], [0, 1, 2], **kwargs)
def integrate_ivp(u0=1.0, v0=0.0, mu=1.0, tend=10.0, dt0=1e-8, nt=0,
nsteps=600, t0=0.0, atol=1e-8, rtol=1e-8, plot=False,
savefig='None', method='bdf', dpi=100, verbose=False):
"""
Example program integrating an IVP problem of van der Pol oscillator
"""
f, j = get_f_and_j(mu)
if nt > 1:
tout = np.linspace(t0, tend, nt)
yout, nfo = integrate_predefined(
f, j, [u0, v0], tout, dt0, atol, rtol, nsteps=nsteps,
check_indexing=False, method=method)
else:
tout, yout, nfo = integrate_adaptive(
f, j, [u0, v0], t0, tend, dt0, atol, rtol, nsteps=nsteps,
check_indexing=False, method=method) # dfdt[:] also for len == 1
if verbose:
print(nfo)
if plot:
import matplotlib.pyplot as plt
plt.plot(tout, yout[:, 1], 'g--')
plt.plot(tout, yout[:, 0], 'k-', linewidth=2)
if savefig == 'None':
plt.show()
else:
plt.savefig(savefig, dpi=dpi)
def test_derivative_1():
def f(t, y, fout):
fout[0] = y[0]
kwargs = dict(dx0=0.0, atol=1e-8, rtol=1e-8, nderiv=1, method='adams')
yout, info = integrate_predefined(f, None, [1], [0, 1, 2], **kwargs)
assert yout.shape == (3, 2, 1)
ref = np.array([
[[exp(0)], [exp(0)]],
[[exp(1)], [exp(1)]],
[[exp(2)], [exp(2)]],
])
assert np.allclose(yout, ref)
with pytest.raises(RuntimeError) as excinfo:
integrate_predefined(f, None, [1], [0, 1, 2], nsteps=7, **kwargs)
assert 'too_much_work' in str(excinfo.value).lower()
assert '7' in str(excinfo.value).lower()
def test_derivative_1():
yout, info = integrate_predefined(_f1, None, [1], [0, 1, 2], **_kwargs1)
assert yout.shape == (3, 2, 1)
ref = np.array([
[[exp(0)], [exp(0)]],
[[exp(1)], [exp(1)]],
[[exp(2)], [exp(2)]],
])
assert np.allclose(yout, ref)
def test_derivative_1():
def f(t, y, fout):
fout[0] = y[0]
kwargs = dict(dx0=0.0, atol=1e-8, rtol=1e-8, nderiv=1, method='adams')
yout, info = integrate_predefined(f, None, [1], [0, 1, 2], **kwargs)
assert yout.shape == (3, 2, 1)
ref = np.array([
[[exp(0)], [exp(0)]],
[[exp(1)], [exp(1)]],
[[exp(2)], [exp(2)]],
])
assert np.allclose(yout, ref)
with pytest.raises(RuntimeError) as excinfo:
integrate_predefined(f, None, [1], [0, 1, 2], nsteps=7, **kwargs)
assert 'too_much_work' in str(excinfo.value).lower()
assert '7' in str(excinfo.value).lower()
def test_rhs_recoverable_error():
global idx
idx = -1
def f(t, y, fout):
global idx
fout[0] = y[0]
idx = idx + 1
return 1 if 0 < idx < 3 else 0
kwargs = dict(dx0=0.0, atol=1e-8, rtol=1e-8, method='adams')
yout, info = integrate_predefined(f, None, [1], [0, 1, 2], **kwargs)
def test_rhs_recoverable_error():
global idx
idx = -2
def f(t, y, fout):
global idx
fout[0] = y[0]
idx = idx + 1
return 1 if 0 < idx < 3 else 0
kwargs = dict(dx0=0.0, atol=1e-8, rtol=1e-8, method='adams')
yout, info = integrate_predefined(f, None, [1], [0, 1, 2], **kwargs)
def test_sparse_jac_predefined():
k = 2.0, 3.0, 4.0
y0 = [0.7, 0.3, 0.5]
xout = np.linspace(0, 3, 31)
atol, rtol = 1e-8, 1e-8
f, _, j_sparse, nnz = _get_f_j(k, with_sparse=True)
kwargs = dict(method='bdf', linear_solver='klu', nnz=nnz)
yout, info = integrate_predefined(f, j_sparse, y0, xout, 1.0e-8, 1.0e-8, **kwargs)
yref = decay_get_Cref(k, y0, xout - xout[0])
assert info['success']
assert info['njev'] > 0
assert np.allclose(yout, yref, rtol=10*rtol, atol=10*atol)
def test_integrate_predefined(method, forgiveness, banded):
use_jac = method in requires_jac
k = k0, k1, k2 = 2.0, 3.0, 4.0
y0 = [0.7, 0.3, 0.5]
f, j = _get_f_j(k)
kwargs = {'method': method, 'dx0': 1e-10}
if use_jac:
if banded:
jac_callbacks = [bandify(j, 1, 0), None]
kwargs['lband'] = 1
kwargs['uband'] = 0
else:
jac_callbacks = [j, None]
else:
jac_callbacks = [None]
for j in jac_callbacks:
xout = np.linspace(0, 3, 31)
if config['SUNDIALS_PRECISION'] == "single":
atol = [1e-4, 3e-5, 2e-5]
rtol = 1e-4
else:
atol = [1e-8, 3e-9, 2e-9]
rtol = 1e-8
if method == 'bdf':
kwargs['stab_lim_det'] = True
# Run twice to catch possible side-effects:
yout, nfo = integrate_predefined(f, j, y0, xout, atol, rtol, **kwargs)
yout, nfo = integrate_predefined(f, j, y0, xout, atol, rtol, **kwargs)
yref = decay_get_Cref(k, y0, xout)
assert np.allclose(yout,
yref,
rtol=forgiveness * rtol,
atol=forgiveness * max(atol))
assert np.allclose(nfo['atol'], atol) and np.isclose(nfo['rtol'], rtol)
assert nfo['nfev'] > 0
if method in requires_jac and j is not None:
assert nfo['njev'] > 0
if os.name == 'posix':
assert nfo['time_jac'] >= 0
def integrate_ivp(u0=1.0,
v0=0.0,
mu=1.0,
tend=10.0,
dt0=1e-8,
nt=0,
nsteps=600,
t0=0.0,
atol=1e-8,
rtol=1e-8,
plot=False,
savefig='None',
method='bdf',
dpi=100,
verbose=False):
"""
Example program integrating an IVP problem of van der Pol oscillator
"""
f, j = get_f_and_j(mu)
if nt > 1:
tout = np.linspace(t0, tend, nt)
yout, nfo = integrate_predefined(f,
j, [u0, v0],
tout,
dt0,
atol,
rtol,
nsteps=nsteps,
check_indexing=False,
method=method)
else:
tout, yout, nfo = integrate_adaptive(
f,
j, [u0, v0],
t0,
tend,
dt0,
atol,
rtol,
nsteps=nsteps,
check_indexing=False,
method=method) # dfdt[:] also for len == 1
if verbose:
print(nfo)
if plot:
import matplotlib.pyplot as plt
plt.plot(tout, yout[:, 1], 'g--')
plt.plot(tout, yout[:, 0], 'k-', linewidth=2)
if savefig == 'None':
plt.show()
else:
plt.savefig(savefig, dpi=dpi)
def test_integrate_predefined(method, forgiveness, banded):
use_jac = method in requires_jac
k = k0, k1, k2 = 2.0, 3.0, 4.0
y0 = [0.7, 0.3, 0.5]
f, j = _get_f_j(k)
kwargs = {'method': method, 'dx0': 1e-10}
if use_jac:
if banded:
jac_callbacks = [bandify(j, 1, 0), None]
kwargs['lband'] = 1
kwargs['uband'] = 0
else:
jac_callbacks = [j, None]
else:
jac_callbacks = [None]
for j in jac_callbacks:
xout = np.linspace(0, 3, 31)
atol, rtol = 1e-8, 1e-8
# Run twice to catch possible side-effects:
yout, nfo = integrate_predefined(f, j, y0, xout, [1e-8, 3e-9, 2e-9],
1e-8, **kwargs)
yout, nfo = integrate_predefined(f, j, y0, xout, [1e-8, 3e-9, 2e-9],
1e-8, **kwargs)
yref = decay_get_Cref(k, y0, xout)
assert np.allclose(yout,
yref,
rtol=forgiveness * rtol,
atol=forgiveness * atol)
assert nfo['atol'] == [1e-8, 3e-9, 2e-9] and nfo['rtol'] == 1e-8
assert nfo['nfev'] > 0
if os.name == 'posix':
assert nfo['time_cpu'] > 1e-9
assert nfo['time_wall'] > 1e-9
assert nfo['time_rhs'] > 1e-9
if method in requires_jac and j is not None:
assert nfo['njev'] > 0
if os.name == 'posix':
assert nfo['time_jac'] > 1e-9
def test_roots_predefined_autorestart():
def f(t, y, fout):
fout[0] = y[0]
def roots(t, y, out):
out[0] = y[0] - exp(1)
kwargs = dict(dx0=1e-12, atol=1e-12, rtol=1e-12, method='adams',
roots=roots, nroots=1, nsteps=3, autorestart=4)
xout = [0, 0.5, 1.5, 2]
yout, info = integrate_predefined(f, None, [1], xout, **kwargs)
discrepancy = np.exp(xout) - yout.flatten()
assert np.allclose(discrepancy, 0)
assert len(info['root_indices']) == 1
assert info['root_indices'][0] == 2
def test_derivative_2():
def f(t, y, fout):
fout[0] = y[0]
kwargs = dict(dx0=0.0, atol=1e-12, rtol=1e-12, nderiv=3, method='adams')
yout, info = integrate_predefined(f, None, [1], [0, 1, 2, 3, 4], **kwargs)
assert yout.shape == (5, 4, 1)
ref = np.array([
[[exp(0)], [exp(0)], [0], [0]], # higher order deriv. skipped for t0
[[exp(1)]]*4,
[[exp(2)]]*4,
[[exp(3)]]*4,
[[exp(4)]]*4,
])
assert np.allclose(yout, ref)
def test_roots_predefined():
def f(t, y, fout):
fout[0] = y[0]
def roots(t, y, out):
out[0] = y[0] - exp(1)
kwargs = dict(dx0=1e-12, atol=1e-12, rtol=1e-12, method='adams',
roots=roots, nroots=1)
xout = [0, 0.5, 1.5, 2]
yout, info = integrate_predefined(f, None, [1], xout, **kwargs)
discrepancy = np.exp(xout) - yout.flatten()
assert np.allclose(discrepancy, 0)
assert len(info['root_indices']) == 1
assert info['root_indices'][0] == 2
def test_derivative_2():
def f(t, y, fout):
fout[0] = y[0]
kwargs = dict(dx0=0.0, atol=1e-12, rtol=1e-12, nderiv=3, method='adams')
yout, info = integrate_predefined(f, None, [1], [0, 1, 2, 3, 4], **kwargs)
assert yout.shape == (5, 4, 1)
ref = np.array([
[[exp(0)], [exp(0)], [0], [0]], # higher order deriv. skipped for t0
[[exp(1)]]*4,
[[exp(2)]]*4,
[[exp(3)]]*4,
[[exp(4)]]*4,
])
assert np.allclose(yout, ref)
def test_predefined_ew_ele():
k = 2.0, 3.0, 4.0
y0 = [0.7, 0., 0.]
atol, rtol = 1e-8, 1e-8
kwargs = dict(dx0=1e-10, atol=atol, rtol=rtol, method='bdf', ew_ele=True)
f, j = _get_f_j(k)
xout = np.logspace(-3, 1)
yout, info = integrate_predefined(f, j, y0, xout, **kwargs)
yref = decay_get_Cref(k, y0, xout - xout[0])
assert np.allclose(yout, yref, rtol=10 * rtol, atol=10 * atol)
assert yout.shape[0] == xout.size
assert info['nfev'] > 0
assert info['njev'] > 0
assert info['success']
abs_ew_ele = np.abs(np.prod(info['ew_ele'], axis=1))
assert np.all(abs_ew_ele < 1)
def test_predefined_roots_output():
def f(t, y, fout):
fout[0] = y[0]
def roots(t, y, out):
out[0] = y[0] - exp(1)
kwargs = dict(dx0=1e-12, atol=1e-12, rtol=1e-12,
method='adams', roots=roots, nroots=1)
yout, info = integrate_predefined(f, None, [1], [0, 2], **kwargs)
assert len(info['root_indices']) == 1
roots_x, roots_y = info['roots_output']
assert roots_x.shape == (1,)
assert roots_y.shape == (1, 1)
assert abs(roots_x[-1] - 1) < 1e-11
assert abs(roots_y[-1, 0] - exp(1)) < 1e-11
def test_predefined_roots_output():
def f(t, y, fout):
fout[0] = y[0]
def roots(t, y, out):
out[0] = y[0] - exp(1)
kwargs = dict(dx0=1e-12, atol=1e-12, rtol=1e-12,
method='adams', roots=roots, nroots=1)
yout, info = integrate_predefined(f, None, [1], [0, 2], **kwargs)
assert len(info['root_indices']) == 1
roots_x, roots_y = info['roots_output']
assert roots_x.shape == (1,)
assert roots_y.shape == (1, 1)
assert abs(roots_x[-1] - 1) < 1e-11
assert abs(roots_y[-1, 0] - exp(1)) < 1e-11
def test_predefined_return_on_error():
k = 2.0, 3.0, 4.0
y0 = [0.7, 0., 0.]
atol, rtol = 1e-8, 1e-8
kwargs = dict(dx0=1e-10, atol=atol, rtol=rtol,
method='bdf', return_on_error=True, nsteps=7)
f, j = _get_f_j(k)
xout = np.logspace(-3, 1)
yout, info = integrate_predefined(f, j, y0, xout, **kwargs)
yref = decay_get_Cref(k, y0, xout - xout[0])
assert np.allclose(yout[:info['nreached'], :], yref[:info['nreached'], :],
rtol=10*rtol,
atol=10*atol)
assert 10 < info['nreached'] < 40
assert yout.shape[0] == xout.size
assert info['nfev'] > 0
assert info['njev'] > 0
assert info['success'] is False
def test_jtimes_predefined(linear_solver, with_jac):
g = 9.81
y0 = [1000.0, 0.0]
atol, rtol = 1e-8, 1e-8
f, jac, jtimes = _gravity_f_j_jtimes(g)
if not with_jac:
jac = None
kwargs = dict(atol=atol, rtol=rtol,
method='bdf', linear_solver=linear_solver,
jtimes=jtimes)
tout = np.linspace(0, 10, 100)
yout, info = integrate_predefined(f, jac, y0, tout, **kwargs)
yref = gravity_analytic(g, y0, tout)
assert np.allclose(yout, yref, rtol=10*rtol, atol=10*atol)
assert info['success']
assert info['njvev'] > 0
if not with_jac:
assert info['njev'] == 0
def test_predefined_return_on_error():
k = 2.0, 3.0, 4.0
y0 = [0.7, 0., 0.]
atol, rtol = 1e-8, 1e-8
kwargs = dict(dx0=1e-10, atol=atol, rtol=rtol,
method='bdf', return_on_error=True, nsteps=7)
f, j = _get_f_j(k)
xout = np.logspace(-3, 1)
yout, info = integrate_predefined(f, j, y0, xout, **kwargs)
yref = decay_get_Cref(k, y0, xout - xout[0])
assert np.allclose(yout[:info['nreached'], :], yref[:info['nreached'], :],
rtol=10*rtol,
atol=10*atol)
assert 10 < info['nreached'] < 40
assert yout.shape[0] == xout.size
assert info['nfev'] > 0
assert info['njev'] > 0
assert info['success'] is False
def test_quads_predefined():
k = 0.7
def f(t, y, fout):
fout[0] = -0.7*y[0]
def quads(t, y, out):
out[0] = t*y[0]
out[1] = y[0]**2
kwargs = dict(dx0=1e-12, atol=1e-12, rtol=1e-12, method='adams',
quads=quads, nquads=2)
A, t0, duration = 42, 0, 4
t = np.linspace(t0, duration, 37)
yout, info = integrate_predefined(f, None, [A, 0, 0], t, **kwargs)
assert np.allclose(yout[:, 0], 42*np.exp(-k*t))
q0 = A/k**2 + (-A*k**2*t - A*k)*np.exp(-k*t)/k**3
q1 = (1.0/2.0)*A**2/k - 1.0/2.0*A**2*np.exp(-2*k*t)/k
assert np.allclose(info['quads'][:, 0], q0)
assert np.allclose(info['quads'][:, 1], q1)
def test_predefined_autorestart():
k = k0, k1, k2 = 2.0, 3.0, 4.0
y0 = [0.7, 0.3, 0.5]
atol, rtol = 1e-8, 1e-8
x0, xend = 0, 3
kwargs = dict(dx0=1e-10, atol=atol, rtol=rtol,
method='BDF', nsteps=62,
autorestart=10)
f, j = _get_f_j(k)
xout = np.linspace(x0, xend)
yout, info = integrate_predefined(f, j, y0, xout, **kwargs)
yref = decay_get_Cref(k, y0, xout)
assert np.allclose(yout, yref,
rtol=10*rtol,
atol=10*atol)
assert xout[-1] > 1e-6
assert yout.shape[0] == xout.size
assert info['nfev'] > 0
assert info['njev'] > 0
assert info['success']
assert xout[-1] == xend
def test_predefined_autorestart():
k = k0, k1, k2 = 2.0, 3.0, 4.0
y0 = [0.7, 0.3, 0.5]
atol, rtol = 1e-8, 1e-8
x0, xend = 0, 3
kwargs = dict(dx0=1e-10, atol=atol, rtol=rtol,
method='BDF', nsteps=7,
autorestart=10)
f, j = _get_f_j(k)
xout = np.linspace(x0, xend)
yout, info = integrate_predefined(f, j, y0, xout, **kwargs)
yref = decay_get_Cref(k, y0, xout)
assert np.allclose(yout, yref,
rtol=10*rtol,
atol=10*atol)
assert xout[-1] > 1e-6
assert yout.shape[0] == xout.size
assert info['nfev'] > 0
assert info['njev'] > 0
assert info['success']
assert xout[-1] == xend
def test_derivative_1__exception():
with pytest.raises(RuntimeError) as excinfo:
integrate_predefined(_f1, None, [1], [0, 1, 2], nsteps=7, **_kwargs1)
assert 'too_much_work' in str(excinfo.value).lower()
assert '7' in str(excinfo.value).lower()
