Multiple combinations of a matrix

I have a matrix m, with 2 columns, M= [1, 2; 3, 4; 5, 6].

I need to the combinations of column one with its assocated column two entry.

For example:

x = [1, 2, 3, 4; 1, 2, 5, 6; 3, 4, 5, 6]

[Turlough Hughes]

Do you want to be able to do this generally for any number of rows?

[Ulika Naidoo]

Yes, for any number of rows please.

Answer 1

[Turlough Hughes]

Try the following, it should work for any size of M.

function x = pairCombos(M)

numRows = size(M,1);
C = combnk(1:numRows,2); % Lists every pair combination of row indicies.
x = zeros(size(C,1),size(M,2)*2);  % Preallocate space for variable x.

for i = 1:size(C,1)
    x(i,:) = [M(C(i,1),:) M(C(i,2),:)]; % generate x as requested.
end

end

The final order depends the output from the combnk function. You might also consider using the sortrows function afterwards.

[Ulika Naidoo]

Brilliant! Thank you!!

[Turlough Hughes]

No problem :)

[Ulika Naidoo]

Hi Turlough,

I have another question, how would I then take x and find combinations with m?

This is what i have at the moment:

x = pairCombos(M)

numRows = size(x,1);

C = combnk(1:numRows,2); % Lists every pair combination of row indicies

b = zeros(size(C,1),4); % Preallocate space for variable b

for i = 1:size(C,1)

b(i,:) = [x(C(i,1),:) x(C(i,2),:)]; % generate b

a = [sum(b(i,[1 3])) sum(b(i,[2 4]));a] % I'm suming the values of column 1 & 3 and 2 & 4 of each row

end

l = max(a(:,1))

if l > 500

numRows = size(x,1);

bnumRows = size(b,1);

C1 = combnk(1:numRows,1:bnumRows); % Lists every pair combination of row indicies

b1 = zeros(size(C1,1),6); % Preallocate space for variable b

for i = 1:size(C1,2)

b1(i,:) = [x(C1(i,1),:) b(C1(i,2),:)]; % generate b

a1 = [sum(b1(i,[1 3])) sum(b1(i,[2 4]));a1] % Summing again

[~,ans] = (min(abs(a1 - x))) % trying to find the closest value to l.

end

end

But I get this error:

Error in combnk (line 36)

elseif n < 17 && (k > 3 || n-k < 4).

[Turlough Hughes]

What do you mean by take x and find combinations with m? Can you explain a bit more about what you're doing?

[Ulika Naidoo]

I'm trying to find the closest value from matrix M to a number L.

So where M = 1 2

3 4

5 6

and all combos so x = 1 2 3 4

1 2 5 6

3 4 5 6

But if I some column 1 and 3 then a= 4 6 8

However if any of these values from a are less than L, then to find combo's of X and M again and so on,

x1 = 1 2 3 4 1 2

1 2 5 6 1 2

3 4 5 6 1 2

1 2 3 4 3 4

1 2 5 6 3 4

3 4 5 6 3 4

I hope I made sense there. But then I realised I can just get combo's for X and X find the sum of column 1 and 3, if that is less than L , then sum 1, 3 and 5, if still less than L then finally sum 1, 3 , 5 and 7.

x2 =1 2 3 4 1 2 3 4

1 2 5 6 1 2 3 4

3 4 5 6 1 2 3 4

......

I was trying to find the optium number of batteries to use in a design with their associated costs, where L was the total voltage required, M column 1 was the volts and column 2 was the hours the batter can run for.

Thank you very much for your help!