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

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  1. POFitting data to system of ODEs using Python via Scipy & Numpy
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    <p>I am having some trouble translating my MATLAB code into Python via Scipy &amp; Numpy. I am stuck on how to find optimal parameter values (k0 and k1) for my system of ODEs to fit to my ten observed data points. I currently have an initial guess for k0 and k1. In MATLAB, I can using something called 'fminsearch' which is a function that takes the system of ODEs, the observed data points, and the initial values of the system of ODEs. It will then calculate a new pair of parameters k0 and k1 that will fit the observed data. I have included my code to see if you can help me implement some kind of 'fminsearch' to find the optimal parameter values k0 and k1 that will fit my data. I want to add whatever code to do this to my lsqtest.py file. </p> <p>I have three .py files - ode.py, lsq.py, and lsqtest.py </p> <p>ode.py: </p> <pre><code>def f(y, t, k): return (-k[0]*y[0], k[0]*y[0]-k[1]*y[1], k[1]*y[1]) </code></pre> <p>lsq.py: </p> <pre><code>import pylab as py import numpy as np from scipy import integrate from scipy import optimize import ode def lsq(teta,y0,data): #INPUT teta, the unknowns k0,k1 # data, observed # y0 initial values needed by the ODE #OUTPUT lsq value t = np.linspace(0,9,10) y_obs = data #data points k = [0,0] k[0] = teta[0] k[1] = teta[1] #call the ODE solver to get the states: r = integrate.odeint(ode.f,y0,t,args=(k,)) #the ODE system in ode.py #at each row (time point), y_cal has #the values of the components [A,B,C] y_cal = r[:,1] #separate the measured B #compute the expression to be minimized: return sum((y_obs-y_cal)**2) </code></pre> <p>lsqtest.py: </p> <pre><code>import pylab as py import numpy as np from scipy import integrate from scipy import optimize import lsq if __name__ == '__main__': teta = [0.2,0.3] #guess for parameter values k0 and k1 y0 = [1,0,0] #initial conditions for system y = [0.000,0.416,0.489,0.595,0.506,0.493,0.458,0.394,0.335,0.309] #observed data points data = y resid = lsq.lsq(teta,y0,data) print resid </code></pre>
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    1. COIs this what you're looking for? [scipy fmin](http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.fmin.html)
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    2. COAs on unrelated note, you don't _need_ to use matlab style one-function-with-the-same-name files in python.
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