# [SciPy-User] Problem with combining Fsolve and Integrate.Odeint

Warren Weckesser warren.weckesser@enthought....
Tue Oct 13 10:48:42 CDT 2009

```Whoops.  The code that I edited was from Johann, but I should have
addressed my response to Peter, since he was the original poster.

Warren

Warren Weckesser wrote:
> Hi Johann,
>
> You can do what you want by using the `args` argument of both fsolve
> and odeint.
>
> I have rewritten your example to do use `args`, and made several other
> changes that are more about my preferences than about getting it
> working.  In particular, if the differential equations depend on the
> parameters k1, k2, and k3, these should really be arguments to the
> function, not global variables.  Like fsolve, odeint also has an
> `args` argument that allows you to do this.
>
> Heres the code:
>
> ----------
>
> from numpy import empty, array, linspace
> from scipy.optimize import fsolve
> from scipy.integrate import odeint
> import pylab
>
>
> def de(X, t, k1, k2, k3):
>     Xdot = empty((2),'d')
>     Xdot[0] = k1 - k2*X[0]
>     Xdot[1] = k2*X[0] - k3*X[1]
>     return Xdot
>
>
> if __name__ == "__main__":
>     k1 = 10
>     k2 = 5
>     k3 = 8
>
>     init_val = array([10.,0.1])
>     t_range = linspace(0,1,21)
>
>     t_course = odeint(de, init_val, t_range, args=(k1,k2,k3))
>     fin_t_course = t_course[-1]
>
>     ss = fsolve(de, fin_t_course, args=(0, k1, k2, k3))
>     print ss
>
>     pylab.plot(t_range, t_course[:,0], t_range, t_course[:,1])
>     pylab.show()
>
> ----------
>
> Warren
>
> Johann Rohwer wrote:
>> Sending again - my previous reply doesn't seem to have made it to the
>> list...
>>
>> On Tuesday 13 October 2009, Peter Cimermančič wrote:
>>
>>> I'm trying to model system that is described with few ODEs.
>>> Function, where ODEs are in, is given as def function(y,t). It
>>> takes two arguments as you can see. y is an array of different
>>> species in the model, whereas t is an array of time steps. Then,
>>> I'd like to calculate steady state using fsolve, which takes
>>> function with one argument only. When trying to solve steady state,
>>> this error is raised: "TypeError: There is a mismatch between the
>>> input and output shape of diff_equations.". How could I solve my
>>> problem?
>>>
>>
>> Here is a self-contained example of 2 simple ODEs with mass action
>> kinetics, that calculates a time course with odeint and then uses the
>> final point of the time course as an initial estimate for a steady-
>> state calculation with fsolve. As you can see, the arguments of the
>> function de are handled OK between odeint and fsolve.
>>
>> BTW if you are interested in this problem in a more general way, you
>> might want to look at our PySCeS software (http://pysces.sf.net) which
>> is for simulation of (bio)chemical kinetic networks. It has high-level
>> functions to calculate time courses and steady states automatically
>> (amongst others) and runs on top of scipy.
>>
>> Regards
>> Johann
>>
>> ---------------------8-<--------------------------------
>>
>> import scipy
>> import pylab
>>
>> k1 = 10
>> k2 = 5
>> k3 = 8
>>
>> def de(X,t):
>>     Xdot = scipy.zeros((2),'d')
>>     Xdot[0] = k1 - k2*X[0]
>>     Xdot[1] = k2*X[0] - k3*X[1]
>>     return Xdot
>>
>> init_val = scipy.array([10.,0.1])
>> t_range = scipy.linspace(0,1,21)
>>
>> t_course = scipy.integrate.odeint(de, init_val, t_range)
>> fin_t_course = scipy.copy(t_course[-1])
>>
>> ss = scipy.optimize.fsolve(de, fin_t_course, args=None)
>> print ss
>>
>> pylab.plot(t_range, t_course[:,0], t_range, t_course[:,1])
>> pylab.show()
>>
>>
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>>
>
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```