Fitting data to system of ODEs using Python via Scipy & Numpy

Question

I am having some trouble translating my MATLAB code into Python via Scipy & Numpy. I am stuck on how to find optimal parameter values (k0 and k1) for my system of ODEs to fi

Answer 1

    # cleaned up a bit to get my head around it - thanks for sharing 
    import pylab as pp
    import numpy as np
    from scipy import integrate, optimize

    class Parameterize_ODE():
        def __init__(self):
            self.X = np.linspace(0,9,10)
            self.y = np.array([0.000,0.416,0.489,0.595,0.506,0.493,0.458,0.394,0.335,0.309])
            self.y0 = [1,0,0] # inital conditions ODEs
        def ode(self, y, X, p):
            return (-p[0]*y[0],
                     p[0]*y[0]-p[1]*y[1],
                               p[1]*y[1])
        def model(self, X, p):
            return integrate.odeint(self.ode, self.y0, X, args=(p,))
        def f_resid(self, p):
            return self.y - self.model(self.X, p)[:,1]
        def optim(self, p_quess):
            return optimize.leastsq(self.f_resid, p_guess) # fit params

    po = Parameterize_ODE(); p_guess = [0.2, 0.3] 
    c, kvg = po.optim(p_guess)

    # --- show ---
    print "parameter values are ", c, kvg
    x = np.linspace(min(po.X), max(po.X), 2000)
    pp.plot(po.X, po.y,'.r',x, po.model(x, c)[:,1],'-b')
    pp.xlabel('X',{"fontsize":16}); pp.ylabel("y",{"fontsize":16}); pp.legend(('data','fit'),loc=0); pp.show()