how to get the function as the sum of other functions?

I have a function fitfun=@(x)energy(i)-laa(i)*(1-exp(-x)), where x is unknown, energy and laa are arrays of values. I need to obtain expression for the summ of the functions: sumf=@(x)energy(1)-laa(1)*(1-exp(-x))+energy(2)-laa(2)*(1-exp(-x))...energy(N)-laa(N)*(1-exp(-x)). Next I need to minimize the "sumf" i.e. to find "x" which would give the value for total_function ~0. Fminsearch works perfectly for the individual function "fitfun" but not for the total sumf. Here is the script:

>

>syms x;
>> for i=1:N
function=@(x)energy(i)-laa(i)*(1-exp(-x))
sumf=@(x)sumf(x)+fitfun(x)
end
>> [x,fval] = fminsearch(sumf,[0])
Subscript indices must either be real positive integers or logicals.

Error in @(x)sumf(x)+fitfun(x)

Error in @(x)sumf(x)+fitfun(x)

Error in @(x)sumf(x)+fitfun(x)

Error in @(x)sumf(x)+fitfun(x)

Error in @(x)sumf(x)+fitfun(x)

Error in @(x)sumf(x)+fitfun(x)

Error in fminsearch (line 191)
fv(:,1) = funfcn(x,varargin{:});

>> 
Thank you

Answer 1

[Greig]

The easiest way would be to set it up your function as something like...

sumf = @(x) sum(energy - laa .* (1-exp(-x)) )

Then call fminsearch. This also saves on the loop, but make sure that your dimensions of "energy" and "laa" are consistent.

Also, depending on your function values, you may want to minimise the sum of the squares. If the sum is <0 then you will end up far from zero.

[Oleksandr Oleksandras]

it works, thank you so much! Regarding loop the error was in missing dot "." function=@(x)energy(i)-laa(i).*(1-exp(-x)) P.S. and of course the whole expression should be squared function=@(x)(energy(i)-laa(i).*(1-exp(-x))).^2

UPD. loop works only for small N, for large value of N fminsearch gives an error "Maximum recursion limit of 500 reached." And after increasing limit Matlab is crashed.

[Greig]

This will be because you define the sumf function as

sumf=@(x)sumf(x)+fitfun(x)

which calls itself recursively.

Have you tried defining it as I have above? That is, without the recursive call.

[Oleksandr Oleksandras]

yes it works fine