def _test_NativeSys_two(NativeSys, nsteps=500):
native1 = NativeSys.from_callback(vdp_f, 2, 1)
tend2, k2, y02 = 2, [4, 3], (5, 4, 2)
atol2, rtol2 = 1e-11, 1e-11
native2 = NativeSys.from_callback(decay_dydt_factory(k2), len(k2) + 1)
xout1, yout1, info1 = native1.integrate([0, 1, 2], [1, 0],
params=[2.0],
nsteps=nsteps)
xout2, yout2, info2 = native2.integrate(tend2,
y02,
atol=atol2,
rtol=rtol2,
nsteps=nsteps)
# blessed values:
ref1 = [[1, 0], [0.44449086, -1.32847148], [-1.89021896, -0.71633577]]
assert np.allclose(yout1, ref1)
if 'nfev' in info1:
assert info1['nfev'] > 0
ref2 = np.array(bateman_full(y02, k2 + [0], xout2 - xout2[0],
exp=np.exp)).T
assert np.allclose(yout2, ref2, rtol=150 * rtol2, atol=150 * atol2)
def _test_return_on_error_success(NativeSys):
k, y0 = [4, 3], (5, 4, 2)
native = NativeSys.from_callback(decay_rhs,
len(k) + 1,
len(k),
namespace_override={
'p_rhs':
"""
f[0] = -m_p[0]*y[0];
f[1] = m_p[0]*y[0] - m_p[1]*y[1];
f[2] = m_p[1]*y[1];
if (x > 0.5) return AnyODE::Status::recoverable_error;
this->nfev++;
return AnyODE::Status::success;
"""
})
xout = [0, 0.2, 0.4, 0.6, 0.8, 1.0]
result = native.integrate(xout,
y0,
k,
atol=1e-11,
rtol=1e-11,
return_on_error=True,
dx_max=.05)
nreached = result.info['nreached']
assert nreached == 3
ref = np.array(
bateman_full(y0, k + [0], result.xout[:nreached] - xout[0],
exp=np.exp)).T
assert result.info['success'] is False
assert np.allclose(result.yout[:nreached, :], ref, rtol=1e-8, atol=1e-8)
def _test_symmetricsys_nativesys(NativeSys, nsteps=800, forgive=150):
logexp = (sp.log, sp.exp)
first_step = 1e-4
rtol = atol = 1e-7
k = [7., 3, 2]
class TransformedNativeSys(TransformedSys, NativeSys):
pass
SS = symmetricsys(logexp, logexp, SuperClass=TransformedNativeSys)
ts = SS.from_callback(decay_rhs, len(k) + 1, len(k))
y0 = [1e-20] * (len(k) + 1)
y0[0] = 1
xout, yout, info = ts.integrate([1e-12, 1],
y0,
k,
atol=atol,
rtol=rtol,
first_step=first_step,
nsteps=nsteps)
ref = np.array(bateman_full(y0, k + [0], xout - xout[0], exp=np.exp)).T
np.set_printoptions(linewidth=240)
assert np.allclose(yout, ref, rtol=rtol * forgive, atol=atol * forgive)
def _test_NativeSys__first_step_cb_source_code(NativeSys,
log10myconst,
should_succeed,
forgive=20,
**kwargs):
dec3 = _get_decay3()
odesys = NativeSys.from_other(
dec3,
namespace_override={
'p_first_step':
'return good_const()*y[0];',
'p_anon':
'double good_const(){ return std::pow(10, %.5g); }' % log10myconst
},
namespace_extend={'p_includes': ['<cmath>']})
y0, k = [.7, 0, 0], [1e23, 2, 3.]
xout, yout, info = odesys.integrate(5,
y0,
k,
integrator='native',
**kwargs)
ref = np.array(bateman_full(y0, k, xout - xout[0], exp=np.exp)).T
allclose_kw = dict(atol=kwargs['atol'] * forgive,
rtol=kwargs['rtol'] * forgive)
if should_succeed is None:
assert not np.allclose(yout, ref, **allclose_kw)
else:
assert info['success'] == should_succeed
info['nfev'] > 10 and info['nfev'] > 1 and info['time_cpu'] < 100
if should_succeed:
assert np.allclose(yout, ref, **allclose_kw)
def _test_NativeSys__band(NativeSys):
tend, k, y0 = 2, [4, 3], (5, 4, 2)
y = sp.symarray('y', len(k) + 1)
dydt = decay_dydt_factory(k)
f = dydt(0, y)
odesys = NativeSys(zip(y, f), band=(1, 0))
xout, yout, info = odesys.integrate(tend, y0, integrator='native')
ref = np.array(bateman_full(y0, k + [0], xout - xout[0], exp=np.exp)).T
assert np.allclose(yout, ref)
def _test_Decay_nonnegative(NativeSys):
odesys = NativeSys.from_other(_get_decay3(lower_bounds=[0] * 3))
y0, k = [3., 2., 1.], [3.5, 2.5, 0]
xout, yout, info = odesys.integrate([1e-10, 1], y0, k, integrator='native')
ref = np.array(bateman_full(y0, k, xout - xout[0], exp=np.exp)).T
assert info['success'] and info['nfev'] > 10 and info['nfev'] > 1 and info[
'time_cpu'] < 100
assert np.allclose(yout, ref) and np.allclose(np.sum(yout, axis=1),
sum(y0))
def _test_NativeSys__first_step_cb(NativeSys, forgive=20):
dec3 = _get_decay3()
dec3.first_step_expr = dec3.dep[0] * 1e-30
odesys = NativeSys.from_other(dec3)
y0, k = [.7, 0, 0], [1e23, 2, 3.]
kwargs = dict(atol=1e-8, rtol=1e-8)
xout, yout, info = odesys.integrate(5,
y0,
k,
integrator='native',
**kwargs)
ref = np.array(bateman_full(y0, k, xout - xout[0], exp=np.exp)).T
allclose_kw = dict(atol=kwargs['atol'] * forgive,
rtol=kwargs['rtol'] * forgive)
assert info['success'] and info['nfev'] > 10 and info['nfev'] > 1 and info[
'time_cpu'] < 100
assert np.allclose(yout, ref, **allclose_kw)
def _test_NativeSys__dep_by_name__single_varied(NativeSys):
tend, kf, y0 = 2, [4, 3], {'a': (5, 3, 7, 9, 1, 6, 11), 'b': 4, 'c': 2}
y = sp.symarray('y', len(kf) + 1)
dydt = decay_dydt_factory(kf)
f = dydt(0, y)
odesys = NativeSys(zip(y, f), names='a b c'.split(), dep_by_name=True)
results = odesys.integrate(tend, y0, integrator='native')
for idx in range(len(y0['a'])):
xout, yout, info = results[idx]
assert info['success']
assert xout.size == yout.shape[0] and yout.shape[1] == 3
ref = np.array(
bateman_full(
[y0[k][idx] if k == 'a' else y0[k] for k in odesys.names],
kf + [0],
xout - xout[0],
exp=np.exp)).T
assert np.allclose(yout, ref)
def _test_NativeSys_two(NativeSys, nsteps=500):
native1 = NativeSys.from_callback(vdp_f, 2, 1)
tend2, k2, y02 = 2, [4, 3], (5, 4, 2)
atol2, rtol2 = 1e-11, 1e-11
native2 = NativeSys.from_callback(decay_dydt_factory(k2), len(k2)+1)
xout1, yout1, info1 = native1.integrate([0, 1, 2], [1, 0], params=[2.0], nsteps=nsteps)
xout2, yout2, info2 = native2.integrate(tend2, y02, atol=atol2, rtol=rtol2, nsteps=nsteps)
# blessed values:
ref1 = [[1, 0], [0.44449086, -1.32847148], [-1.89021896, -0.71633577]]
assert np.allclose(yout1, ref1)
if 'nfev' in info1:
assert info1['nfev'] > 0
ref2 = np.array(bateman_full(y02, k2+[0], xout2 - xout2[0], exp=np.exp)).T
assert np.allclose(yout2, ref2, rtol=150*rtol2, atol=150*atol2)
def _test_ScaledSys_NativeSys(NativeSys, nsteps=1000):
class ScaledNativeSys(ScaledSys, NativeSys):
pass
k = k0, k1, k2 = [7., 3, 2]
y0, y1, y2, y3 = sp.symbols('y0 y1 y2 y3', real=True, positive=True)
# this is actually a silly example since it is linear
l = [(y0, -7 * y0), (y1, 7 * y0 - 3 * y1), (y2, 3 * y1 - 2 * y2),
(y3, 2 * y2)]
ss = ScaledNativeSys(l, dep_scaling=1e8)
y0 = [0] * (len(k) + 1)
y0[0] = 1
xout, yout, info = ss.integrate([1e-12, 1],
y0,
atol=1e-12,
rtol=1e-12,
nsteps=nsteps)
ref = np.array(bateman_full(y0, k + [0], xout - xout[0], exp=np.exp)).T
assert np.allclose(yout, ref, rtol=2e-11, atol=2e-11)
def _test_PartiallySolved_symmetric_native(NativeSys,
multiple=False,
forgive=1,
**kwargs):
trnsfsys = _get_transformed_partially_solved_system(NativeSys, multiple)
y0, k = [3., 2., 1.], [3.5, 2.5, 0]
xout, yout, info = trnsfsys.integrate([1e-10, 1],
y0,
k,
integrator='native',
**kwargs)
ref = np.array(bateman_full(y0, k, xout - xout[0], exp=np.exp)).T
assert info['success']
assert info['nfev'] > 10
assert info['nfev'] > 1
assert info['time_cpu'] < 100
allclose_kw = dict(atol=kwargs.get('atol', 1e-8) * forgive,
rtol=kwargs.get('rtol', 1e-8) * forgive)
assert np.allclose(yout, ref, **allclose_kw)
assert np.allclose(np.sum(yout, axis=1), sum(y0), **allclose_kw)
def _test_ScaledSys_NativeSys(NativeSys, nsteps=1000):
class ScaledNativeSys(ScaledSys, NativeSys):
pass
k = k0, k1, k2 = [7., 3, 2]
y0, y1, y2, y3 = sp.symbols('y0 y1 y2 y3', real=True, positive=True)
# this is actually a silly example since it is linear
l = [
(y0, -7*y0),
(y1, 7*y0 - 3*y1),
(y2, 3*y1 - 2*y2),
(y3, 2*y2)
]
ss = ScaledNativeSys(l, dep_scaling=1e8)
y0 = [0]*(len(k)+1)
y0[0] = 1
xout, yout, info = ss.integrate([1e-12, 1], y0,
atol=1e-12, rtol=1e-12, nsteps=nsteps)
ref = np.array(bateman_full(y0, k+[0], xout - xout[0], exp=np.exp)).T
assert np.allclose(yout, ref, rtol=2e-11, atol=2e-11)
def _test_symmetricsys_nativesys(NativeSys, nsteps=800, forgive=150):
logexp = (sp.log, sp.exp)
first_step = 1e-4
rtol = atol = 1e-7
k = [7., 3, 2]
class TransformedNativeSys(TransformedSys, NativeSys):
pass
SS = symmetricsys(logexp, logexp, SuperClass=TransformedNativeSys)
ts = SS.from_callback(decay_rhs, len(k)+1, len(k))
y0 = [1e-20]*(len(k)+1)
y0[0] = 1
xout, yout, info = ts.integrate(
[1e-12, 1], y0, k, atol=atol, rtol=rtol,
first_step=first_step, nsteps=nsteps)
ref = np.array(bateman_full(y0, k+[0], xout - xout[0], exp=np.exp)).T
np.set_printoptions(linewidth=240)
assert np.allclose(yout, ref, rtol=rtol*forgive, atol=atol*forgive)
def _test_PartiallySolvedSystem_Native(NativeSys, integrator):
class TransformedNativeSys(TransformedSys, NativeSys):
pass
logexp = get_logexp(1, 1e-24)
NativeLogLogSys = symmetricsys(logexp,
logexp,
SuperClass=TransformedNativeSys)
odesys = _get_decay3(lower_bounds=[0, 0, 0], linear_invariants=[[1, 1, 1]])
n_sys = NativeSys.from_other(odesys)
assert odesys.linear_invariants == n_sys.linear_invariants
scaledsys = ScaledSys.from_other(odesys, dep_scaling=42)
ns_sys = NativeSys.from_other(scaledsys)
partsys = PartiallySolvedSystem.from_linear_invariants(scaledsys)
np_sys = NativeSys.from_other(partsys)
LogLogSys = symmetricsys(logexp, logexp)
ll_scaledsys = LogLogSys.from_other(scaledsys)
ll_partsys = LogLogSys.from_other(partsys)
nll_scaledsys = NativeLogLogSys.from_other(scaledsys)
nll_partsys = NativeLogLogSys.from_other(partsys)
assert len(ll_scaledsys.nonlinear_invariants) > 0
assert ll_scaledsys.nonlinear_invariants == nll_scaledsys.nonlinear_invariants
y0 = [3.3, 2.4, 1.5]
k = [3.5, 2.5, 0]
systems = [
odesys, n_sys, scaledsys, ns_sys, partsys, np_sys, ll_scaledsys,
ll_partsys, nll_scaledsys, nll_partsys
]
for idx, system in enumerate(systems):
result = system.integrate([0, .3, .5, .7, .9, 1.3],
y0,
k,
integrator=integrator,
atol=1e-9,
rtol=1e-9)
ref = np.array(
bateman_full(y0, k, result.xout - result.xout[0], exp=np.exp)).T
assert result.info['success']
assert np.allclose(result.yout, ref)
def _test_PartiallySolved_symmetric_native_multi(NativeSys,
multiple=False,
forgive=1,
**kwargs):
trnsfsys = _get_transformed_partially_solved_system(NativeSys, multiple)
y0s = [[3., 2., 1.], [3.1, 2.1, 1.1], [3.2, 2.3, 1.2], [3.6, 2.4, 1.3]]
ks = [[3.5, 2.5, 0], [3.3, 2.4, 0], [3.2, 2.1, 0], [3.3, 2.4, 0]]
results = trnsfsys.integrate([(1e-10, 1)] * len(ks),
y0s,
ks,
integrator='native',
**kwargs)
allclose_kw = dict(atol=kwargs.get('atol', 1e-8) * forgive,
rtol=kwargs.get('rtol', 1e-8) * forgive)
for i, (y0, k) in enumerate(zip(y0s, ks)):
xout, yout, info = results[i]
ref = np.array(bateman_full(y0, k, xout - xout[0], exp=np.exp)).T
assert info['success']
assert info['nfev'] > 10
assert info['nfev'] > 1
assert info['time_cpu'] < 100
assert np.allclose(yout, ref, **allclose_kw)
assert np.allclose(np.sum(yout, axis=1), sum(y0), **allclose_kw)
def _test_NativeSys__get_dx_max_source_code(NativeSys, forgive=20, **kwargs):
dec3 = _get_decay3()
odesys = NativeSys.from_other(
dec3,
namespace_override={
'p_get_dx_max': 'AnyODE::ignore(y); return 1e-4*x + 1e-3;',
})
y0, k = [.7, 0, 0], [7., 2, 3.]
xout, yout, info = odesys.integrate(1,
y0,
k,
integrator='native',
get_dx_max_factor=1.0,
**kwargs)
ref = np.array(bateman_full(y0, k, xout - xout[0], exp=np.exp)).T
allclose_kw = dict(atol=kwargs['atol'] * forgive,
rtol=kwargs['rtol'] * forgive)
assert np.allclose(yout, ref, **allclose_kw)
assert info['success']
assert info['nfev'] > 10
if 'n_steps' in info:
print(info['n_steps'])
assert 750 < info['n_steps'] <= 1000
def _test_multiple_adaptive_chained(MySys, kw, **kwargs):
logexp = (sp.log, sp.exp)
# first_step = 1e-4
rtol, atol = 1e-14, 1e-12
ny = 4
ks = [[7e13, 3, 2], [2e5, 3e4, 12.7]]
y0s = [[1.0, 3.0, 2.0, 5.0], [2.0, 1.0, 3.0, 4.0]]
t0, tend = 1e-16, 7
touts = [(t0, tend)] * 2
class TransformedMySys(TransformedSys, MySys):
pass
SS = symmetricsys(logexp, logexp, SuperClass=TransformedMySys)
tsys = SS.from_callback(decay_rhs, ny, ny - 1)
osys = MySys.from_callback(decay_rhs, ny, ny - 1)
comb_res = integrate_chained([tsys, osys],
kw,
touts,
y0s,
ks,
atol=atol,
rtol=rtol,
**kwargs)
for y0, k, res in zip(y0s, ks, comb_res):
xout, yout = res.xout, res.yout
ref = np.array(bateman_full(y0, k + [0], xout - xout[0], exp=np.exp)).T
assert np.allclose(yout, ref, rtol=rtol * 1000, atol=atol * 1000)
for res in comb_res:
assert 0 <= res.info['time_cpu'] < 100
assert 0 <= res.info['time_wall'] < 100
assert res.info['success'] == True # noqa