How can I get the sums of all possible combinations of the values of a vector?

Dear all,

I would like to get the sums of all unique possible combinations of the values of a vector.

For example:

Input:

A = [10 20 30]

Output:

B = [10 20 30 (10+20) (10+30) (20+30) (10+20+30)]

If possible, I would also like to get the indices of the values used to get the sum, so:

C = [1 2 3 (1,2) (1,3) (2,3) (1,2,3)]

The output does not necessarily have to be a vector.

The length of the input vector (A) will vary from iterations to iterations, so I'm looking for a way to calculate B and C based on a changing vector A

All help would be greatly appreciated!

[Adam Danz]

It's clear that b will be vector but it's not clear what c should be. One possibility is a string:

c = "[ 1 2 3 (1 2) (1 3) (2 3) (1 2 3)]"

c = "[ 1 2 3 (1 2) (1 3) (2 3) (1 2 3)]"

Another possibility is a cellarray

c = {1 2 3 [1 2] [1 3] [2 3] [1 2 3]}

c = 1×7 cell array
    {[1]}    {[2]}    {[3]}    {[1 2]}    {[1 3]}    {[2 3]}    {[1 2 3]}

Or are you expecting something else? The decision should be made based on how you're going to use this variable.

[Tom de van der Schueren]

The values of vector B will later be used to see which sum comes closest to another given variable.

The indices of that closest sum will then be used in if statements, so a cellarray is probably preferable.

But at this moment I'm no able to construct either a vector with all the sums or a cellarray with the indices used to get these sums.

[Adam Danz]

Agreed, the cell array is the way to go. Simple indexing,

b(i)
c{i}

However, there could be multiple solutions to the problem you described. For example, a vector [1 2 3 4] will result in two values of 3 (3, 1+2), two values of 4 (4, 1+3), two values of five, two values of 6, and two values of 7. So if you're trying to find the closest value in b to some target value, there may be a problem.

Answer 1

[Adam Danz]

% Input: v, a row or column vector 
v = [2 4 6 8]; 

% create permutations and summation results
n = numel(v); 
vIdx = 1:n; 
results = cell(n,2);
for i = 1:n
    results{i,1} = num2cell(nchoosek(vIdx,i),2)';
    results{i,2} = sum(nchoosek(v,i),2)';
end

% Results
% b: 1xm row vector of summation results
% c: 1xm cell array of indicies of v for each summation
b = [results{:,2}]

b = 1×15

2 4 6 8 6 8 10 10 12 14 12 14 16 18 20

c = horzcat(results{:,1})

c = 1×15 cell array
    {[1]}    {[2]}    {[3]}    {[4]}    {[1 2]}    {[1 3]}    {[1 4]}    {[2 3]}    {[2 4]}    {[3 4]}    {[1 2 3]}    {[1 2 4]}    {[1 3 4]}    {[2 3 4]}    {[1 2 3 4]}

[Tom de van der Schueren]

Thank you very much!