Re: Wish to avoid multiple for loops, but don't know how to do it

[Ben Abbott]

On May 19, 2011, at 4:05 PM, Jordi Gutiérrez Hermoso wrote:

> On 19 May 2011 12:43, clustro <address@hidden> wrote:
>> for i = 1:N
>>        for j = 1:N
>>                for k = 1:N
>>                        for l = 1:N
>>                                xPoint = [x(i) x(j) x(k) x(l)]';
>>                                fEval_x = colville(xPoint);
>>                                if fEval_x < fmin
>>                                        fmin = fEval_x;
>>                                        xmin = xPoint;
>>                                endif
>>                        endfor
>>                endfor
>>        endfor
>> endfor
>> 
>> Where colville() is an optimization toy function.
>> 
>> Does anyone have a suggestion on how to avoid 20 nested for loops when
>> trying to scale this algorithm up to higher dimensions?
> 
> I don't understand the full extent of your problem, you basically want
> the minimum over the n-fold tensor product of a vector?
> 
> You might be able to do this with arrayfun, although I don't
> immediately see how to avoid the actual tensoring.
> 
> - Jordi G. H.

I'm not sure how to use arrayfun(), but using cellfun() ...

N = 4;
Nf = factorial (N);
input_permutations = mat2cell (perms (4), ones (Nf, 1), 4);
opt_fun = @(x) colville (x{:});
fEval_x = cellfun (opt_fun, input_permutations);
x_min = input_permutations (fEval_x == min (fEval_x));

The resulting x_min will be a cell array whose length is equal to the number of 
results equal to the minimum value.

Ben

p.s. I haven't tested this code, so there may be some typo.