subtraction of each row with every other row

I want to subtract each row of the matrix with every other row and store it in a different bigger size matrix, for example-

A=[1,2,3:4,5,6:7,8,9];

B[1-4,2-5,3-6; 1-7,2-8,3-9; 4-1,5-2,6-3; 4-7,5-8,6-9; 7-1,8-2,9-3; 7-4,8-5,9-6];

That means if the original matrix is of size 3×3 then the answer matrix would be 6×3.

My original matrix is of size 40×150.

[Paul Hoffrichter]

>> A=[1,2,3:4,5,6:7,8,9]
A =
     1     2     3     4     5     6     7     8     9

I assume you meant

>> A=[1,2,3;4,5,6;7,8,9]
A =
     1     2     3
     4     5     6
     7     8     9

Not sure where the row: -3 -4 -5, comes from.

>> B=[1-4,2-5,3-6; 1-7,2-8,3-9; 4-1,5-2,6-3; 4-7,4-8,4-9; 7-1,8-2,9-3; 7-4,8-5,9-6]
B =
    -3    -3    -3
    -6    -6    -6
     3     3     3
    -3    -4    -5  % <-- How do you get this?
     6     6     6
     3     3     3

[ST]

That was a typo, apology. Thanks for your efforts though.

[Paul Hoffrichter]

Could you fix up your OP removing any typos, and show the desired results.

Answer 1

[Paul Hoffrichter]

B = repmat(A, N,1) - repelem(A,N,1);

Answer 2

[Paul Hoffrichter]

A=[1,2,3,4,5; 6,7,8,9,10; 11, 12, 13, 14, 15;16, 17, 18, 19, 20];

c = nchoosek(1:size(A, 1),2);
c2 = [c; fliplr(c)];
B = zeros( length(c2), size(A,2));

for ii = 1: size(c2,1)
   [r1 r2] = deal( c2(ii,1), c2(ii,2) );
   B(ii,:) = A(r1,:) - A(r2,:);
end
B
B =
    -5    -5    -5    -5    -5
   -10   -10   -10   -10   -10
   -15   -15   -15   -15   -15
    -5    -5    -5    -5    -5
   -10   -10   -10   -10   -10
    -5    -5    -5    -5    -5
     5     5     5     5     5
    10    10    10    10    10
    15    15    15    15    15
     5     5     5     5     5
    10    10    10    10    10
     5     5     5     5     5

[ST]

I did this-

N=20;

step=50;

A=rand(N,step);

B=zeros(N*N,step);

count=1;

jj=1:(N*N);

n=N;

for ii=1:N

B(jj(count:count+n-1),:)=A-A(ii,:);

count=count+N;

end

[Paul Hoffrichter]

I kept the numbers more manageable to compare results.

METHOD_ONE = 0
N=20;
step=50;
N=3;
step=4;
rng(10);
A=randi(5*N, N, step);
if METHOD_ONE
   c = nchoosek(1:size(A, 1),2);
   c2 = [c; fliplr(c)];
   B = zeros( length(c2), size(A,2));
   
   for ii = 1: size(c2,1)
      [r1 r2] = deal( c2(ii,1), c2(ii,2) );
      B(ii,:) = A(r1,:) - A(r2,:);
   end
else
   B=zeros(N*N,step);
   count=1;
   jj=1:(N*N);
   n=N;
   for ii=1:N
      rowNums = jj(count:count+n-1);
      B( rowNums ,:) = A - A(ii, :);
      count=count+N;
   end
end
A
B

Output:

METHOD_ONE =
     0
A =
    12    12     3     2
     1     8    12    11
    10     4     3    15
B =
     0     0     0     0
   -11    -4     9     9
    -2    -8     0    13
    11     4    -9    -9
     0     0     0     0
     9    -4    -9     4
     2     8     0   -13
    -9     4     9    -4
     0     0     0     0

METHOD_ONE =
     1
A =
    12    12     3     2
     1     8    12    11
    10     4     3    15
B =
    11     4    -9    -9
     2     8     0   -13
    -9     4     9    -4
   -11    -4     9     9
    -2    -8     0    13
     9    -4    -9     4

As you can see, your code has rows of 0's when you subtract a row from itself. The ordering of rows of B are different between the two versions.

Also, half of the rows are just the negation of the other half. Do you need both halves?

[ST]

Yes, I need zero rows too. Thanks for your answer.