How to run ODE45 with optimizing parameters and dependent variables on time

Hi all,

I am trying to run a ode45 solver for system of first order differential equations for chemical kinetics equations. I have set up a function called "myodefcn" defined as

function dx = myodefcn(T, X, kHEPSelf, kHEPSelfA, kHEPSelfB, kHEPHO2,...
                      kHOCH2O2, kHO2Self, kOO2, kHO2O3, kHO2Cl, kO3Cl, kClCEb, kClCEa, ...
                      kClO2, kClself, kHO2OH, kOHO, kOHO2, kOHClO)

which has all the differential equations in form dx/dt. Rest all are constants named like k___, these constants depend on parameters A and B defined as

X0(1)   = 0.4e14*num*B; %and similar
kHEPSelf = 3.5e-12*scale*A; % and similar

and these are defined in another function "myobjective" which calculates these k___ values and calls the myodefcn as,

f = @(T,X) myodefcn(T, X, kHEPSelf, kHEPSelfA, kHEPSelfB, kHEPHO2, kHOCH2O2, kHO2Self,...
  kOO2, kHO2O3, kHO2Cl, kO3Cl, kClCEb, kClCEa, kClO2, kClself, kHO2OH, kOHO, ...
  kOHO2, kOHClO);
T = bX;
options = odeset('RelTol',1e-4,'AbsTol',[1e-4 1e-4 1e-5]);
[ts,xs] = ode45(f,T, X0);
err = bY - xs(:,1);
SSE = sum(err.^2);

the call for function "myobjective" is as follows

 [ts,xs, SSE] = myobjective(P, bX, bY)

where

 A = P(1); B = P(2);

and bX and bY are experimentally determined time and data vectors.

Now the problem is when I try to call the "myobjective" function using the fminsearch to minimize error SSE

A = 10; B = 2; P0 = [A, B];
p = fminsearch(@(P) myobjective(P, bX, bY), P0);

and get the values for A and B. The optimization fails and gives this error

Subscripted assignment dimension mismatch.

Error in fminsearch (line 197)
fv(:,1) = funfcn(x,varargin{:});

Also, I tried curve fitting the bX-bY data using 1-order polyfit and use coefficients for A and B but that doesn't seems the right fit as fit is linear and if I go with higher order, I don't know how to relate them to A and B.

Can someone tell me how to solve this error and get the values for A, B and X? Or how to pass these parameters to ode45 solver where it can solve the diff eqns and optimize the values for A and B?

Thanks.

Answer 1

[Star Strider]

I believe the problem are the values returned from myobjective. It returns 3 outputs instead of the required 1. That would likely throw the error you are seeing.

From the documentation for fminsearch:

• fun is the function to be minimized. It accepts an input x and returns a scalar f, the objective function evaluated at x. The function fun can be specified as a function handle for a function file

Have it return a single output, and providing there are no other errors, fminsearch should be happy. (If you have constraints, consider using fmincon instead, if you have the Optimization Toolbox.)

[Vikas Asthana]

Yes I have 3 outputs from myobjective but I need all these 3 for further calculations.

Is there a way to directly pass these A and B to ode45 as parameters and it itself optimize these values and return values. I have another program (see figure attached) which does this but only one file at a time and I have more than 300 files. So motive was to automatize it as initial calculations are done in matlab for those files to make data smaller.

[Vikas Asthana]

as far as multiple outputs are concerned, I have had functions earlier which optimize and gave value for parameters as well as multiple outputs. One example being this:

x = fminsearch(@(x) systf(x,t_real, out_real), x0 );
[errorSim, ysim, tsim] = systf(x, t_real, out_real);

[Star Strider]

The problem is that fminsearch doesn’t use the other two and doesn’t want them. If you need them in another function (once you have optimised it), write two versions of myobjective, one for fminsearch and one for your other function. I don’t know the details of what you’re doing, but there are two possibilities:

1. Write a third function that only returns the scalar to fminsearch that it wants,
2. declare the other variables that you use elsewhere, but that fminsearch doesn’t want, as global variables — not the best programming practice in my opinion, but perhaps necessary here — and have myobjective return only what fminsearch wants to it.