how to let a function call another functions and then optimize it

I really need your help about my problem. It is a little complicated so I hope I can explain it well. Firstly, I have decfine a function as

function [ pf ] = ambportfchc (r,lb1,lb2,lb3)

then I define another function

    function [ sumllh ] = binormal(hatpc,mu,s1,s12,s2)
    rn=size(mu,1);
    SIGMA =@(s1,s12,s2) [s1 s12; s12 s2];
    for i=1:rn
        llh(i,:)=log( mvnpdf(hatpc(i,:),mu(i,:),SIGMA));
    end
    sumllh=0;
    for i=1:size(mu,1)
        sumllh=sumllh+ llh(i,:)
    end
     end

which will call ambportfchc . At the end of day I want use fmincon to optimize binormal through the variables r,lb1,lb2,lb3,s1,s12,s2.

But it doesn't work at all! There are so many errors so I think I have done many things totally wrong. There are several points

1 when I define binormal, should I use mu (which will call function ambporfchc) or the orginal variables r,lb1,lb2,lb3 as input?

2 As you see in sumllh=sumllh+ llh(i,:), I actually want to sum up function handles (notice mu is a matrix, because it is the output of ambportfchc). What I am doing is wrong, isn't it? Then how should I do it right?

I would really appreciate your advice. I have been stuck in this program for a while....

[Walter Roberson]

?? It is not possible to sum function handles.

[xueqi]

Yeah I realize that it is impossible.But what should I do if I have to?

Answer 1

[Star Strider]

The problems I see are:

1. In the code you posted, ‘ambportfchc’ is missing an ‘end’ statement.
2. You are not calling ‘binormal’ inside ‘ambportfchc’, so you are not passing the arguments to ‘ambportfchc’ as arguments to ‘binormal’.
3. You are not assigning any value to ‘pf’ inside ‘ambportfchc’.

I refer you to this description of nested functions:

http://www.mathworks.com/help/techdoc/matlab_prog/f4-39683.html

and this demo:

http://www.mathworks.com/products/matlab/examples.html?file=/products/demos/shipping/matlab/nesteddemo.html

for details.

It is certainly possible to do what you intend. I have done something similar (integrate differential equations as nested functions inside an objective function) to do nonlinear parameter estimation for parametric curve fitting.

[xueqi]

Hi Star! I have read your reference demo and realize that I should put the nested function in the body of the main function.There are still some errors which I think stem from the parameter estimator part. Can I ask you how you do the parameter estimation? I have using the maximum likelihood so have to add up the probability dentisity function which causes a lot of difficulites. Thanks a lot:)

[Star Strider]

You seem to have the functions nested correctly as you list them in your original post, although you need to change your code as I suggested in my answer.

I still do not understand what you want to do. To use an optimization function, ‘ambportfchc’ would be your objective function. It will return ‘pf’ to your optimization function. For parameter estimation, you will need (x,y) data that ’pf’ will approximate for each value of ‘y’ as a function of ‘x’.

The ‘mle’ function requires only a vector of data, so you need to generate a vector describing a probability density function (the ‘data’ vector in the documentation for ‘mle’) and then let ‘mle’ fit it.

[xueqi]

Hi 'ambportfchc’ is for giving the relation between the independetn variables (r,lb1,lb2,lb3) and dependent variables 'pf'(actually there are two vaiables which I assume they are bivariable normal distributed). 'binormal' is for calculating the sum of log likelihood function. So 'ambportfchc' is nested in 'binormal' and 'binormal' is the objective function when doing optimization.It think it would be easier if I can use some built-in function in matlab to estimator parameters, but all of them seems un-applicable. Maybe I don't look them carefully. I will check if 'mle' works. Thanks:)