def test_solver_linear_error_from_integration(atol):
class Dummy:
unit_registry = None
def expb(self, x):
return np.exp(x)
integr = Dummy()
integr.yout = np.array([1.0]).reshape((1, 1, 1))
print(integr.yout[slice(None), 0, 0])
integr.info = {'rtol': 1.0, 'atol': atol}
integr.rd = Dummy()
integr.rd.logy = False
assert np.allclose(solver_linear_error_from_integration(integr),
[[-1], [3]])
def plot_solver_linear_excess_error(integration, Cref, ax=None, x=None, ti=slice(None), bi=0, si=0, **kwargs):
"""
Plots the excess error commited by the intergrator, divided by the span
of the tolerances (atol + rtol*|y_i|).
Parameters
----------
integration: chemreac.integrate.Integration
result from integration.
Cref: array or float
analytic solution to compare with
ax: Axes instance or dict
if ax is a dict it is used as \*\*kwargs passed to
matplotlib.pyplot.axes (default: None)
x: array
(optional) x-values, when None it is deduced to be
either t or x (when ti or bi are slices repecitvely)
(default: None)
ti: slice
time indices
bi: slice
bin indices
si: integer
specie index
plot_kwargs: dict
keyword arguments passed to matplotlib.pyplot.plot (default: None)
fill_between_kwargs: dict
keyword arguments passed to matplotlib.pyplot.fill_between
(default: None)
scale_err: float
value with which errors are scaled. (default: 1.0)
fill: bool
whether or not to fill error span
\*\*kwargs:
common keyword arguments of plot_kwargs and fill_between_kwargs,
e.g. 'color', (default: None).
See Also
--------
plot_solver_linear_error
"""
if x is None:
if isinstance(ti, slice):
x = integration.tout[ti]
elif isinstance(bi, slice):
x = integration.rd.xcenters[bi]
else:
raise NotImplementedError("Failed to deduce x-axis.")
ax = _init_axes(ax)
le_l, le_u = solver_linear_error_from_integration(integration, ti, bi, si)
Eexcess_l = Cref[ti, bi, si] - le_l # Excessive if negative
Eexcess_u = Cref[ti, bi, si] - le_u # Excessive if positive
u_conc = get_derived_unit(integration.rd.unit_registry, "concentration")
Eexcess_l[np.argwhere(Eexcess_l >= 0)] = 0 * u_conc
Eexcess_u[np.argwhere(Eexcess_u <= 0)] = 0 * u_conc
fused = np.concatenate((Eexcess_l[..., np.newaxis], Eexcess_u[..., np.newaxis]), axis=-1)
indices = np.argmax(abs(fused), axis=-1)
Eexcess = fused[np.indices(indices.shape), indices][0, ...]
le_span = le_u - le_l
ax.plot(np.asarray(integration.tout), np.asarray(Eexcess / le_span), **kwargs)
return ax
def plot_solver_linear_error(
integration,
Cref=0,
ax=None,
x=None,
ti=slice(None),
bi=0,
si=0,
plot_kwargs=None,
fill_between_kwargs=None,
scale_err=1.0,
fill=True,
**kwargs
):
"""
Parameters
----------
integration: chemreac.integrate.Integration
result from integration.
Cref: array or float
analytic solution to compare with
ax: Axes instance or dict
if ax is a dict it is used as key word arguments passed to
matplotlib.pyplot.axes (default: None)
x: array
(optional) x-values, when None it is deduced to be
either t or x (when ti or bi are slices repecitvely)
(default: None)
ti: slice
time indices
bi: slice
bin indices
si: integer
specie index
plot_kwargs: dict
keyword arguments passed to matplotlib.pyplot.plot (default: None)
fill_between_kwargs: dict
keyword arguments passed to matplotlib.pyplot.fill_between
(default: None)
scale_err: float
value with which errors are scaled. (default: 1.0)
fill: bool
whether or not to fill error span
\*\*kwargs
common keyword arguments of plot_kwargs and fill_between_kwargs,
e.g. 'color', (default: None).
See Also
--------
plot_solver_linear_excess_error
"""
ax = _init_axes(ax)
Cerr = integration.Cout - to_unitless(Cref, get_derived_unit(integration.rd.unit_registry, "concentration"))
if x is None:
if isinstance(ti, slice):
x = integration.tout[ti]
elif isinstance(bi, slice):
x = integration.rd.xcenters[bi]
else:
raise NotImplementedError("Failed to deduce x-axis.")
plot_kwargs = plot_kwargs or {}
set_dict_defaults_inplace(plot_kwargs, kwargs)
plt.plot(np.asarray(x), np.asarray(scale_err * Cerr[ti, bi, si]), **plot_kwargs)
if fill:
le_l, le_u = solver_linear_error_from_integration(integration, ti=ti, bi=bi, si=si)
Cerr_u = le_u - Cref[ti, bi, si]
Cerr_l = le_l - Cref[ti, bi, si]
fill_between_kwargs = fill_between_kwargs or {}
set_dict_defaults_inplace(fill_between_kwargs, {"alpha": 0.2}, kwargs)
plt.fill_between(
np.asarray(x), np.asarray(scale_err * Cerr_l), np.asarray(scale_err * Cerr_u), **fill_between_kwargs
)
return ax
