# Bumps 0.7.14 documentation

## Fitting an ODE

Bumps can fit black-box functions, such as odeint from scipy.

The following example is adapted from:

> https://people.duke.edu/~ccc14/sta-663/CalibratingODEs.html.

Instructor: Cliburn Chan cliburn.chan@duke..edu
Instructor: Janice McCarthy janice.mccarthy@duke.edu

    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.curvefit.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`.