def setup_model(self):
"""perform all necessary steps to setup the model and make it ready to reproduce the experimental data"""
self.starting_concentration = self.update_starting_concentration()
self.model = self.create_reaction_system()
# create system of ordinary differential equations
self.odesys, extra = get_odesys(self.model, include_params=False)
self.time = self.exp_data.index
self.integration_times, self.org_time_index = self.expand_integration_times(
self.time)
def integration_with_sliders(
rsys,
tend,
c0,
parameters,
fig_kwargs=None,
slider_kwargs=None,
conc_bounds=None,
x_axis_type="linear",
y_axis_type="linear",
integrate_kwargs=None,
odesys_extra=None,
get_odesys_kw=None,
integrate=None,
):
"""
Parameters
----------
rsys : ReactionSystem
tend : float like
c0 : dict
Initial concentrations.
parameters : dict
Parameter values.
fig_kwargs : dict
Keyword-arguments passed to bokeh's ``Figure``.
slider_kwargs : dict
Keyword-arguments passed to bokeh's ``Slider``.
conc_bounds : dict of dicts
Mapping substance key to dict of bounds ('start', 'end', 'step').
x_axis_type : str
y_axis_type : str
integrate_kwargs : dict
Keyword-arguments passed to integrate.
odesys_extra : tuple
If odesys & extra have already been generated (avoids call to ``get_odesys``).
get_odesys_kw : dict
Keyword-arguments passed to ``get_odesys``.
integrate : callback
Defaults to ``odesys.integrate``.
"""
import numpy as np
from bokeh.plotting import Figure
from bokeh.models import ColumnDataSource, Column, Row
from bokeh.models.widgets import Slider
if slider_kwargs is None:
slider_kwargs = {}
if get_odesys_kw is None:
get_odesys_kw = {}
if odesys_extra is None:
odesys, extra = get_odesys(rsys, **get_odesys_kw)
else:
odesys, extra = odesys_extra
if integrate is None:
integrate = odesys.integrate
state_keys, rarg_keys, p_units = [
extra[k] for k in ("param_keys", "unique", "p_units")
]
output_conc_unit = get_odesys_kw.get("output_conc_unit", None)
output_time_unit = get_odesys_kw.get("output_time_unit", None)
unit_registry = get_odesys_kw.get("unit_registry", None)
if output_conc_unit is None:
if unit_registry is not None:
raise ValueError(
"if unit_registry is given, output_conc_unit must also be given"
)
output_conc_unit = 1
if output_time_unit is None:
if unit_registry is not None:
raise ValueError(
"if unit_registry is given, output_time_unit must also be given"
)
output_conc_unit = 1
param_keys = list(chain(state_keys, rarg_keys))
if x_axis_type == "linear":
tout = linspace(tend * 0, tend)
elif x_axis_type == "log":
tout = logspace_from_lin(tend * 1e-9, tend)
else:
raise NotImplementedError("Unknown x_axis_type: %s" % x_axis_type)
result = integrate(tout, c0, parameters, **(integrate_kwargs or {}))
sources = [
ColumnDataSource(
data={
"tout": to_unitless(result.xout, output_time_unit),
k: to_unitless(result.yout[:, idx], output_conc_unit),
}) for idx, k in enumerate(rsys.substances)
]
if fig_kwargs is None:
Cmax = np.max(result.yout)
x_range = list(
to_unitless([result.xout[0], result.xout[-1]], output_time_unit))
y_range = list(to_unitless([Cmax * 0, Cmax * 1.1], output_conc_unit))
fig_kwargs = dict(
plot_height=400,
plot_width=400,
title="C vs t",
tools="crosshair,pan,reset,save,wheel_zoom",
x_range=x_range,
y_range=y_range,
x_axis_type=x_axis_type,
y_axis_type=y_axis_type,
)
plot = Figure(**fig_kwargs)
colors = "red green blue black cyan magenta".split()
for idx, k in enumerate(rsys.substances):
plot.line(
"tout",
k,
source=sources[idx],
line_width=3,
line_alpha=0.6,
color=colors[idx % len(colors)],
)
def _C(k):
return to_unitless(c0[k], output_conc_unit)
if p_units is None:
p_units = [None] * len(param_keys)
p_ul = [
to_unitless(parameters[k], _u) for k, _u in zip(param_keys, p_units)
]
def _dict_to_unitless(d, u):
return {k: to_unitless(v, u) for k, v in d.items()}
c0_widgets = OrderedDict()
for k in rsys.substances:
if conc_bounds is not None and k in conc_bounds:
if k in slider_kwargs:
raise ValueError(
"Key '%s' both in slider_kwargs and conc_bounds" % k)
slider_defaults = _dict_to_unitless(conc_bounds[k],
output_conc_unit)
else:
ck = _C(k)
if ck == 0:
max_ = max(*[_C(k) for k in rsys.substances])
slider_defaults = dict(start=0, end=max_, step=max_ / 100)
else:
slider_defaults = dict(start=_C(k) / 2,
end=_C(k) * 2,
step=_C(k) / 10)
c0_widgets[k] = Slider(
title=(k + " / " + output_conc_unit.dimensionality.unicode)
if hasattr(output_conc_unit, "dimensionality") else k,
value=_C(k),
**slider_kwargs.get(k, slider_defaults))
param_widgets = OrderedDict([(
k,
Slider(title=k if u is None else k + " / " + u.dimensionality.unicode,
value=v,
**_dict_to_unitless(
slider_kwargs.get(
k, dict(start=v / 10, end=v * 10, step=v / 10)),
u,
)),
) for k, v, u in zip(param_keys, p_ul, p_units)])
all_widgets = list(chain(param_widgets.values(), c0_widgets.values()))
def update_data(attrname, old, new):
_c0 = defaultdict(lambda: 0 * output_conc_unit)
for k, w in c0_widgets.items():
_c0[k] = w.value * output_conc_unit
_params = {}
for (k, w), u in zip(param_widgets.items(), p_units):
_params[k] = w.value if u is None else w.value * u
_result = integrate(tout, _c0, _params)
for idx, k in enumerate(rsys.substances):
sources[idx].data = {
"tout": to_unitless(_result.xout, output_time_unit),
k: to_unitless(_result.yout[:, idx], output_conc_unit),
}
for w in all_widgets:
w.on_change("value", update_data)
inputs = Column(children=all_widgets)
return Row(children=[inputs, plot], width=800)
def integration_with_sliders(rsys,
tend,
c0,
parameters,
fig_kwargs=None,
unit_registry=None,
output_conc_unit=None,
output_time_unit=None,
slider_kwargs=None,
x_axis_type="linear",
y_axis_type="linear",
integrate_kwargs=None,
odesys_extra=None,
get_odesys_kw=None):
"""
Parameters
----------
odesys_extra : tuple of :class:`pyodesys.ODESys` & dict
From :func:`chempy.kinetics.ode.get_odesys`.
get_odesys_kw : dict
If odesys_extra is ``None`` the user may pass this for :func:`chempy.kinetics.ode.get_odesys`.
"""
import numpy as np
from bokeh.plotting import Figure
from bokeh.models import ColumnDataSource, HBox, VBoxForm
from bokeh.models.widgets import Slider
if slider_kwargs is None:
slider_kwargs = {}
if get_odesys_kw is None:
get_odesys_kw = {}
if odesys_extra is None:
odesys, extra = get_odesys(rsys, **get_odesys_kw)
else:
odesys, extra = odesys_extra
state_keys, rarg_keys, p_units = [
extra[k] for k in ('param_keys', 'unique', 'p_units')
]
if output_conc_unit is None:
output_conc_unit = 1
if output_time_unit is None:
output_conc_unit = 1
param_keys = list(chain(state_keys, rarg_keys))
if x_axis_type == 'linear':
tout = linspace(tend * 0, tend)
elif x_axis_type == 'log':
tout = logspace_from_lin(tend * 1e-9, tend)
else:
raise NotImplementedError("Unknown x_axis_type: %s" % x_axis_type)
tout, Cout, info = odesys.integrate(tout, c0, parameters,
**(integrate_kwargs or {}))
sources = [
ColumnDataSource(
data={
'tout': to_unitless(tout, output_time_unit),
k: to_unitless(Cout[:, idx], output_conc_unit)
}) for idx, k in enumerate(rsys.substances)
]
if fig_kwargs is None:
Cmax = np.max(Cout)
x_range = list(to_unitless([tend * 0, tend], output_time_unit))
y_range = list(to_unitless([Cmax * 0, Cmax * 1.1], output_conc_unit))
fig_kwargs = dict(plot_height=400,
plot_width=400,
title="C vs t",
tools="crosshair,pan,reset,resize,save,wheel_zoom",
x_range=x_range,
y_range=y_range,
x_axis_type=x_axis_type,
y_axis_type=y_axis_type)
plot = Figure(**fig_kwargs)
colors = 'red green blue black cyan magenta'.split()
for idx, k in enumerate(rsys.substances):
plot.line('tout',
k,
source=sources[idx],
line_width=3,
line_alpha=0.6,
color=colors[idx % len(colors)])
def _C(k):
return to_unitless(c0[k], output_conc_unit)
if p_units is None:
p_units = [None] * len(param_keys)
p_ul = [
to_unitless(parameters[k], _u) for k, _u in zip(param_keys, p_units)
]
c0_widgets = OrderedDict([
(k,
Slider(title=k if output_conc_unit is 1 else k + ' / ' +
output_conc_unit.dimensionality.unicode,
value=_C(k),
**slider_kwargs.get(
k, dict(start=_C(k) / 2, end=_C(k) * 2, step=_C(k) / 10))))
for k in rsys.substances
])
def _dict_to_unitless(d, u):
return {k: to_unitless(v, u) for k, v in d.items()}
param_widgets = OrderedDict([
(k,
Slider(title=k if u is None else k + ' / ' + u.dimensionality.unicode,
value=v,
**_dict_to_unitless(
slider_kwargs.get(
k, dict(start=v / 10, end=v * 10, step=v / 10)), u)))
for k, v, u in zip(param_keys, p_ul, p_units)
])
all_widgets = list(chain(param_widgets.values(), c0_widgets.values()))
def update_data(attrname, old, new):
_c0 = defaultdict(lambda: 0 * output_conc_unit)
for k, w in c0_widgets.items():
_c0[k] = w.value * output_conc_unit
_params = {}
for (k, w), u in zip(param_widgets.items(), p_units):
_params[k] = w.value if u is None else w.value * u
_tout, _Cout, _info = odesys.integrate(tout, _c0, _params)
for idx, k in enumerate(rsys.substances):
sources[idx].data = {
'tout': to_unitless(_tout, output_time_unit),
k: to_unitless(_Cout[:, idx], output_conc_unit)
}
for w in all_widgets:
w.on_change('value', update_data)
inputs = VBoxForm(children=all_widgets)
return HBox(children=[inputs, plot], width=800)
H2O = H+ + OH-; 10**-14/55.4
""")
arr, info, sane = eqsys.root(defaultdict(float, {'H2O': 55.4, 'HCO3-': 1e-2}))
conc = dict(zip(eqsys.substances, arr))
from math import log10
print("pH: %.2f" % -log10(conc['H+']))
# 测量离子浓度
from chempy import ReactionSystem # The rate constants below are arbitrary
rsys = ReactionSystem.from_string("""2 Fe+2 + H2O2 -> 2 Fe+3 + 2 OH-; 42
2 Fe+3 + H2O2 -> 2 Fe+2 + O2 + 2 H+; 17
H+ + OH- -> H2O; 1e10
H2O -> H+ + OH-; 1e-4""") # "[H2O]" = 1.0 (actually 55.4 at RT)
from chempy.kinetics.ode import get_odesys
odesys, extra = get_odesys(rsys)
from collections import defaultdict
import numpy as np
tout = sorted(np.concatenate((np.linspace(0, 23), np.logspace(-8, 1))))
c0 = defaultdict(float, {
'Fe+2': 0.05,
'H2O2': 0.1,
'H2O': 1.0,
'H+': 1e-2,
'OH-': 1e-12
})
result = odesys.integrate(tout, c0, atol=1e-12, rtol=1e-14)
import matplotlib.pyplot as plt
fig, axes = plt.subplots(1, 2, figsize=(12, 5))
for ax in axes:
_ = result.plot(names=[k for k in rsys.substances if k != 'H2O'], ax=ax)
def integrate_rd(tend=1e2, A0=1.0, B0=0.0, C0=0.0, k1=0.04, k2=1e4, k3=3e7,
t0=1e2, nt=100, N=1, nstencil=3, logt=False, logy=False,
plot=False, savefig='None', verbose=False, dump_expr='False',
use_chempy=False, D=2e-3):
if N == 1:
init_conc = (A0, B0, C0)
else:
init_conc = np.tile((A0, B0, C0), (N, 1))
init_conc /= np.linspace(1, 2, N).reshape((N, 1))**.5
rsys = ReactionSystem(get_reactions((k1, k2, k3)), 'ABC')
if verbose:
print([str(_) for _ in rsys.rxns])
if use_chempy:
from chempy.kinetics.ode import get_odesys
odesys = get_odesys(rsys, include_params=True)
if N != 1:
raise ValueError("ChemPy does not support diffusion")
odesys.integrate(np.logspace(log10(t0), log10(tend)), init_conc)
if plot:
odesys.plot_result(xscale='log', yscale='log')
result = None
else:
rd = ReactionDiffusion.from_ReactionSystem(
rsys, N=N, nstencil=1 if N == 1 else nstencil, logt=logt,
logy=logy, D=[D/2, D/3, D/5])
if dump_expr.lower() not in ('false', '0'):
from chemreac.symbolic import SymRD
import sympy as sp
cb = {'latex': sp.latex,
'ccode': sp.ccode}.get(dump_expr.lower(), str)
srd = SymRD.from_rd(rd, k=sp.symbols('k:3'))
print('dydx:')
print('\n'.join(map(cb, srd._f)))
print('jac:')
for ri, row in enumerate(srd.jacobian.tolist()):
for ci, expr in enumerate(row):
if expr == 0:
continue
print(ri, ci, cb(expr))
return None
if t0 == 0 and logt:
t0 = 1e-3*suggest_t0(rd, init_conc)
if verbose:
print("Using t0 = %12.5g" % t0)
t = np.logspace(np.log10(t0), np.log10(tend), nt)
print(t[0], t[-1])
integr = run(rd, init_conc, t)
if verbose:
import pprint
pprint.pprint(integr.info)
if plot:
if N == 1:
plot_C_vs_t(integr, xscale='log', yscale='log')
else:
import matplotlib.pyplot as plt
for idx, name in enumerate('ABC', 1):
plt.subplot(1, 3, idx)
rgb = [.5, .5, .5]
rgb[idx-1] = 1
plot_faded_time(integr, name, rgb=rgb, log_color=True)
result = integr
if plot:
save_and_or_show_plot(savefig=savefig)
return result
def integration_with_sliders(
rsys, tend, c0, parameters, fig_kwargs=None, slider_kwargs=None, conc_bounds=None,
x_axis_type="linear", y_axis_type="linear", integrate_kwargs=None, odesys_extra=None,
get_odesys_kw=None, integrate=None):
"""
Parameters
----------
rsys : ReactionSystem
tend : float like
c0 : dict
Initial concentrations.
parameters : dict
Parameter values.
fig_kwargs : dict
Keyword-arguments passed to bokeh's ``Figure``.
slider_kwargs : dict
Keyword-arguments passed to bokeh's ``Slider``.
conc_bounds : dict of dicts
Mapping substance key to dict of bounds ('start', 'end', 'step').
x_axis_type : str
y_axis_type : str
integrate_kwargs : dict
Keyword-arguments passed to integrate.
odesys_extra : tuple
If odesys & extra have already been generated (avoids call to ``get_odesys``).
get_odesys_kw : dict
Keyword-arguments passed to ``get_odesys``.
integrate : callback
Defaults to ``odesys.integrate``.
"""
import numpy as np
from bokeh.plotting import Figure
from bokeh.models import ColumnDataSource, Column, Row
from bokeh.models.widgets import Slider
if slider_kwargs is None:
slider_kwargs = {}
if get_odesys_kw is None:
get_odesys_kw = {}
if odesys_extra is None:
odesys, extra = get_odesys(rsys, **get_odesys_kw)
else:
odesys, extra = odesys_extra
if integrate is None:
integrate = odesys.integrate
state_keys, rarg_keys, p_units = [extra[k] for k in ('param_keys', 'unique', 'p_units')]
output_conc_unit = get_odesys_kw.get('output_conc_unit', None)
output_time_unit = get_odesys_kw.get('output_time_unit', None)
unit_registry = get_odesys_kw.get('unit_registry', None)
if output_conc_unit is None:
if unit_registry is not None:
raise ValueError("if unit_registry is given, output_conc_unit must also be given")
output_conc_unit = 1
if output_time_unit is None:
if unit_registry is not None:
raise ValueError("if unit_registry is given, output_time_unit must also be given")
output_conc_unit = 1
param_keys = list(chain(state_keys, rarg_keys))
if x_axis_type == 'linear':
tout = linspace(tend*0, tend)
elif x_axis_type == 'log':
tout = logspace_from_lin(tend*1e-9, tend)
else:
raise NotImplementedError("Unknown x_axis_type: %s" % x_axis_type)
result = integrate(tout, c0, parameters, **(integrate_kwargs or {}))
sources = [ColumnDataSource(data={
'tout': to_unitless(result.xout, output_time_unit),
k: to_unitless(result.yout[:, idx], output_conc_unit)
}) for idx, k in enumerate(rsys.substances)]
if fig_kwargs is None:
Cmax = np.max(result.yout)
x_range = list(to_unitless([result.xout[0], result.xout[-1]], output_time_unit))
y_range = list(to_unitless([Cmax*0, Cmax*1.1], output_conc_unit))
fig_kwargs = dict(plot_height=400, plot_width=400, title="C vs t",
tools="crosshair,pan,reset,save,wheel_zoom",
x_range=x_range, y_range=y_range, x_axis_type=x_axis_type,
y_axis_type=y_axis_type)
plot = Figure(**fig_kwargs)
colors = 'red green blue black cyan magenta'.split()
for idx, k in enumerate(rsys.substances):
plot.line('tout', k, source=sources[idx], line_width=3, line_alpha=0.6,
color=colors[idx % len(colors)])
def _C(k):
return to_unitless(c0[k], output_conc_unit)
if p_units is None:
p_units = [None]*len(param_keys)
p_ul = [to_unitless(parameters[k], _u) for k, _u in zip(param_keys, p_units)]
def _dict_to_unitless(d, u):
return {k: to_unitless(v, u) for k, v in d.items()}
c0_widgets = OrderedDict()
for k in rsys.substances:
if conc_bounds is not None and k in conc_bounds:
if k in slider_kwargs:
raise ValueError("Key '%s' both in slider_kwargs and conc_bounds" % k)
slider_defaults = _dict_to_unitless(conc_bounds[k], output_conc_unit)
else:
ck = _C(k)
if ck == 0:
max_ = max(*[_C(k) for k in rsys.substances])
slider_defaults = dict(start=0, end=max_, step=max_/100)
else:
slider_defaults = dict(start=_C(k)/2, end=_C(k)*2, step=_C(k)/10)
c0_widgets[k] = Slider(
title=k if output_conc_unit is 1 else k + ' / ' + output_conc_unit.dimensionality.unicode,
value=_C(k), **slider_kwargs.get(k, slider_defaults)
)
param_widgets = OrderedDict([
(k, Slider(title=k if u is None else k + ' / ' + u.dimensionality.unicode,
value=v, **_dict_to_unitless(
slider_kwargs.get(k, dict(start=v/10, end=v*10, step=v/10)),
u)))
for k, v, u in zip(param_keys, p_ul, p_units)])
all_widgets = list(chain(param_widgets.values(), c0_widgets.values()))
def update_data(attrname, old, new):
_c0 = defaultdict(lambda: 0*output_conc_unit)
for k, w in c0_widgets.items():
_c0[k] = w.value * output_conc_unit
_params = {}
for (k, w), u in zip(param_widgets.items(), p_units):
_params[k] = w.value if u is None else w.value * u
_result = integrate(tout, _c0, _params)
for idx, k in enumerate(rsys.substances):
sources[idx].data = {
'tout': to_unitless(_result.xout, output_time_unit),
k: to_unitless(_result.yout[:, idx], output_conc_unit)
}
for w in all_widgets:
w.on_change('value', update_data)
inputs = Column(children=all_widgets)
return Row(children=[inputs, plot], width=800)
def integration_with_sliders(
rsys, tend, c0, parameters, fig_kwargs=None, unit_registry=None, output_conc_unit=None,
output_time_unit=None, slider_kwargs=None, x_axis_type="linear", y_axis_type="linear",
integrate_kwargs=None, substitutions=None):
import numpy as np
from bokeh.plotting import Figure
from bokeh.models import ColumnDataSource, HBox, VBoxForm
from bokeh.models.widgets import Slider
if slider_kwargs is None:
slider_kwargs = {}
odesys, state_keys, rarg_keys, p_units = get_odesys(
rsys, unit_registry=unit_registry, substitutions=substitutions,
output_conc_unit=output_conc_unit,
output_time_unit=output_time_unit)[:4]
if output_conc_unit is None:
output_conc_unit = 1
if output_time_unit is None:
output_conc_unit = 1
param_keys = list(chain(state_keys, rarg_keys))
if x_axis_type == 'linear':
tout = linspace(tend*0, tend)
elif x_axis_type == 'log':
tout = logspace_from_lin(tend*1e-9, tend)
else:
raise NotImplementedError("Unknown x_axis_type: %s" % x_axis_type)
tout, Cout, info = odesys.integrate(tout, c0, parameters, **(integrate_kwargs or {}))
sources = [ColumnDataSource(data={
'tout': to_unitless(tout, output_time_unit),
k: to_unitless(Cout[:, idx], output_conc_unit)
}) for idx, k in enumerate(rsys.substances)]
if fig_kwargs is None:
Cmax = np.max(Cout)
x_range = list(to_unitless([tend*0, tend], output_time_unit))
y_range = list(to_unitless([Cmax*0, Cmax*1.1], output_conc_unit))
fig_kwargs = dict(plot_height=400, plot_width=400, title="C vs t",
tools="crosshair,pan,reset,resize,save,wheel_zoom",
x_range=x_range, y_range=y_range, x_axis_type=x_axis_type,
y_axis_type=y_axis_type)
plot = Figure(**fig_kwargs)
colors = 'red green blue black cyan magenta'.split()
for idx, k in enumerate(rsys.substances):
plot.line('tout', k, source=sources[idx], line_width=3, line_alpha=0.6,
color=colors[idx % len(colors)])
def _C(k):
return to_unitless(c0[k], output_conc_unit)
p_ul = [to_unitless(parameters[k], _u) for k, _u in zip(param_keys, p_units)]
c0_widgets = OrderedDict([
(k, Slider(
title=k if output_conc_unit is 1 else k + ' / ' + output_conc_unit.dimensionality.unicode,
value=_C(k), **slider_kwargs.get(k, dict(start=_C(k)/2, end=_C(k)*2, step=_C(k)/10))))
for k in rsys.substances])
def _dict_to_unitless(d, u):
return {k: to_unitless(v, u) for k, v in d.items()}
param_widgets = OrderedDict([
(k, Slider(title=k if u is None else k + ' / ' + u.dimensionality.unicode,
value=v, **_dict_to_unitless(
slider_kwargs.get(k, dict(start=v/10, end=v*10, step=v/10)),
u)))
for k, v, u in zip(param_keys, p_ul, p_units)])
all_widgets = list(chain(param_widgets.values(), c0_widgets.values()))
def update_data(attrname, old, new):
_c0 = defaultdict(lambda: 0*output_conc_unit)
for k, w in c0_widgets.items():
_c0[k] = w.value * output_conc_unit
_params = {}
for (k, w), u in zip(param_widgets.items(), p_units):
_params[k] = w.value if u is None else w.value * u
_tout, _Cout, _info = odesys.integrate(tout, _c0, _params)
for idx, k in enumerate(rsys.substances):
sources[idx].data = {
'tout': to_unitless(_tout, output_time_unit),
k: to_unitless(_Cout[:, idx], output_conc_unit)
}
for w in all_widgets:
w.on_change('value', update_data)
inputs = VBoxForm(children=all_widgets)
return HBox(children=[inputs, plot], width=800)