indexing a vector in a loop

Hi,

I have 5, 3x1 column vectors:

A1 = [a11; a12; a13]

A2 = [a21, a22, a23]

...

A5 = [an1, an2, an3]

and I would to define new vectors X_abcde, by summing these 5 column vectors in all possible ways:

X00001 = A1

...

X00005 = A5

...

X00012 = A1 + A2

...

X00045 = A5 + A4

...

X00123 = A1 + A2 + A3

...

X00345 = A3 + A4 + A5

...

X01234 = A1 + A2 + A3 + A4

...

X02345 = A2 + A2 + A3 + A5

...

X12345 = A1 + A2 + A2 + A3 + A5

My only problem is that I don't know if it's even possible to index the vectors in the following way:

for i = 1 : 5

X0000`i' = A`i'

end

and then:

for i = 1:5

for j > i & j <= 5

X000`i'`j' = A`i' + A`j'

end

end

etc...

Is there any way that I can define a vector X000`i'`j', where `i' and `j' are the letters used in the for loop?

Thank you very much in advance!

[Rik]

Yes, but you shouldn't. You should use an array (e.g. a cell array). Then your loop becomes way easier to write, Matlab will have a chance to optimize your code, code analysis tools like the m-lint will work and it will be easier to work with the result.

[Stephen23]

"My only problem is that I don't know if it's even possible to index the vectors in the following way:"

It is possible, but it is NOT recommended. Magically accessing variable names like that is how beginners force themselves into writing slow, complex, buggy code. Read this to know why:

https://www.mathworks.com/matlabcentral/answers/304528-tutorial-why-variables-should-not-be-named-dynamically-eval

See my answer for a much simpler and more efficient solution.

Answer 1

[Stephen23]

This is much simpler and more efficient that your idea of magically accessing variable names. I simply preallocate some cell arrays, use nchoosek to generate all of the combinations, and use each combination as basic indexing into the matrix of vectors:

N = 5; % number of vectors
M = randi(9,3,N); % N 3x1 vectors
C = cell(1,N);
for ii = 1:N
    X = nchoosek(1:N,ii);
    D = cell(2,size(X,1));
    for jj = 1:size(X,1)
        D{1,jj} = sum(M(:,X(jj,:)),2);
        D{2,jj} = X(jj,:);
     end
     C{ii} = D;
end
C = [C{:}];

The first row of C gives the summed vectors, the second row gives the vector combination. Lets check some of the outputs:

>> M % five 3x1 vectors in one matrix
M =
   5   2   5   1   9
   8   5   9   9   1
   4   1   4   2   6
>> C{:,1} % sum of vectors [1]
ans =
   5
   8
   4
ans =  1
>> C{:,2} % sum of vectors [2]
ans =
   2
   5
   1
ans =  2
>> C{:,6} % sum of vectors [1,2]
ans =
    7
   13
    5
ans =
   1   2
>> C{:,19} % sum of vectors [1,3,4]
ans =
   11
   26
   10
ans =
   1   3   4
>> C{:,31} % sum of vectors [1,2,3,4,5]
ans =
   22
   32
   17
ans =
   1   2   3   4   5