How can I subtract columns for each row by using a for loop

Hi,

I have a matrix like this:

[1.011  1.004  1.054
1.008  0.998  1.042
0.984  0.988  1.024
1.026  1.006  1.016
1.000  0.996  0.977]

I would like to subtract each column for each row and store these results in a new matrix. How can I do this?

Thanks!

[Joseph Cheng]

can you expand on what you mean by subtract each column for each row? I do not understand what you're subtracting with.

[Jimmy]

Ok.

In this example I use 3 columns. I want to subtract the column for each possible combinations for each row. So lets say for row 1, I want subtract col 1 - 2, col 1 - 3, col 2 - 3 and so on. I want for row 2 the same subtractions.

Answer 1

[dpb]

nk=nchoosek(1:size(x,2),2);
dx=zeros(size(x,1),size(nk,1));
for i=1:size(nk,1)
  dx=x(:,nk(i,2))-x(:,nk(i,1));
end

Answer 2

[Joseph Cheng]

you can use combnk() or nchoosek to determine the combination of column subtraction and perform a for loop for each combination.

X = randi(10,4,3);

combin = combnk(1:size(X,2),2);
for ind = 1:size(X,2)
   newX(:,ind) = X(:,combin(ind,1))-X(:,combin(ind,2));
end

Answer 3

[Guillaume]

Use nchoosek to get all possible combinations of columns, and use that to calculate your differences:

m = [1.011  1.004  1.054
     1.008  0.998  1.042
     0.984  0.988  1.024
     1.026  1.006  1.016
     1.000  0.996  0.977];
colcomb = nchoosek(1:size(m, 2), 2);
coldiff = zeros(size(m, 1), size(colcomb, 1));
for comb = 1:size(colcomb, 1)
  coldiff(:, comb) = diff(m(:, colcomb(comb, :)), 1, 2);
end

[Jimmy]

Thanks! This works great!

Is it possible to give the columns names for each 'spread'? For instance column 1 is named as "1-2"?

[Guillaume]

Not in a matrix obviously, since it can only contain numbers. You could create a cell array of column names

colnames  = cell(size(colcomb, 1));
for comb = 1:size(colcomb, 1)
  colnames{comb} = sprintf('%d-%d', colcomb(comb, 2), colcomb(comb, 1));
end

Note that the difference calculated are 2-1, 3-1, 3-2, and I've represented that in the names.

[Jimmy]

Thanks a lot for the quick responses! It works pretty well!

[Jimmy]

Another interesting issue. Let suppose that I have 100 columns instead of 3. I want to store the best 10 combinations based on the combination value (where small is best). How can I achieve this? I also want to store the best combinations names like the 2-1.

Is this possible with Matlab?

(I accidentally clicked on the answer icon by dpb. I guess all the answers regarding the starter post are the correct answers!)

[Stephen23]

A table lets you put names on the columns.

[dpb]

For what working definition of small? But, basic idea is one of two choices...

a) go ahead and generate all pairs and then compute the comparison statistic and choose the N smallest of those, or,

b) compute each pair and the statistic at same time; after N replace the largest of those kept with the last if new is less; update the maxValue comparison value.

[Jimmy]

I choose for option a. Since the 10 smallest pairs are different for each row (the rows are basically the time line (t).) In the end I want to trade each pair for 125 days on a rolling window. For that reason I want to know which pairs I am trading.

Answer 4

[Andrei Bobrov]

X = [1.011  1.004  1.054
     1.008  0.998  1.042
     0.984  0.988  1.024
     1.026  1.006  1.016
     1.000  0.996  0.977];

n = nchoosek(1:size(X,2),2);
out = squeeze(diff(reshape(X(:,n'),[],2,3),1,2));