Fitting an ODE¶
Bumps can fit black-box functions, such as odeint from scipy.
The following example is adapted from:
from bumps.names import *
import numpy as np
from scipy.integrate import odeint
Define the ODE
def g(t, x0, a, b):
"""
Solution to the ODE x'(t) = f(t,x,k) with initial condition x(0) = x0
"""
return odeint(dfdt, x0, t, args=(a, b)).flatten()
def dfdt(x, t, a, b):
"""Receptor synthesis-internalization model."""
return a - b*x
Simulate some data.
Note that the function bumps.util.push_seed()
is to set the random
number generator to a known state so that this function will create the
same data every time the simulation is run. If not, then you wouldn’t
be able to resume a fit since each time you resumed you would be fitting
different data.
def simulate():
from bumps.util import push_seed
# Fake some data
a = 2.0
b = 0.5
x0 = 10.0
t = np.linspace(0, 10, 10)
dy = 0.2*np.ones_like(t)
with push_seed(1):
y = g(t, x0, a, b) + dy*np.random.normal(size=t.shape)
#print(a, b, x0, t, dt, gt)
return t, y, dy
t, y, dy = simulate()
Define the fit problem.
In this case bumps.curve.Curve
is initialized with plot_x
as a vector of length 1000. This is so that a smooth curve is drawn between
the ten data points that were simulated in the fit.
M = Curve(g, t, y, dy, x0=1., a=1., b=1.,
plot_x=np.linspace(t[0], t[-1], 1000))
M.x0.range(0, 100)
M.a.range(0, 10)
M.b.range(0, 10)
problem = FitProblem(M)
Download: ode.py
.