Array rows differences and array filling in a loop

I have an array like A

A (n x m) = 
[a11 a12 a13 ... a1m; 
    a21 a22 a23 ... a2m;
    a31 a32 a33 ... a3m;
    a41 a42 a43 ... a4m
    ....................
    an1 an2 an3 ... anm]

I need to count the differences of all elements of the array row by row in all combinations and get an array like B

B (0.5*(n-1)*n x m) = 
                      [a21-a11 a22-a12 a23-a13 ... a2m-a1m;
                       a31-a11 a32-a12 a33-a13 ... a3m-a1m;
                       ....................................
                       an1-a11 an2-a12 an3-a13 ... anm-a1m;
                       a31-a21 a32-a22 a33-a23 ... a3m-a2m;
                       a41-a21 a42-a22 a43-a23 ... a4m-a2m;
                       ....................................
                       an1-a(n-1)1 an2-a(n-1)2 ... anm-a(n-1)m]

For example if

A =[1   3;
    2   5;
    4   6;
    7  10;
  100 150;
  230 270]

that result should be

B = [1 2; 
     3 3; 
     6 7; 
     99 147; 
     229 267; 
     2 1; 
     5 5; 
     98 145; 228 265; 3 4; 96 144; 226 264; 93 140; 223 260; 130 120]

I tried to start

clc

clear

A = [1 3;2 5;4 6;7 10;100 150;230 270]; % input array example
[n,m] = size(A); % additional variables to set the size of the output array B and the loop limits
B = zeros((n*(n-1)*0.5),m); % empty array for displaying results (n*(n-1)*0.5 - number of rows (differences) in the array)
for i = 1:n
    for j = 1:n
        B = diff(A(i:j:end,:))
        % but I don't understand how to configure the output of the results in a loop to array B after each iteration and with the desired order preserved
    end
end

Answer 1

[Stephen23]

No loops required, the simple MATLAB approach is to use NCHOOSEK:

A = [1,3;2,5;4,6;7,10;100,150;230,270]

A = 6×2

1 3 2 5 4 6 7 10 100 150 230 270

P = nchoosek(1:size(A,1),2);
B1 = A(P(:,2),:)-A(P(:,1),:)

B1 = 15×2

1 2 3 3 6 7 99 147 229 267 2 1 5 5 98 145 228 265 3 4

And checking against your expected output:

B0 = [1,2;3,3;6,7;99,147;229,267;2,1;5,5;98,145;228,265;3,4;96,144;226,264;93,140;223,260;130,120];
isequal(B0,B1)

ans = logical
   1

[Jon]

Wow, that is truly an elegant solution!

[Andrey Melnikov]

Thanks a lot! I knew about this function, but I couldn't understand how it works with arrays which have more than 1 column / row. ) Try to study on your example.

Answer 2

[Jon]

This would be one way to do it

A = [1 3;2 5;4 6;7 10;100 150;230 270]; % input array example
[n,m] = size(A); % additional variables to set the size of the output array B and the loop limits

% Make cell array to hold intermediate results
Bcell = cell(n-1,1);
for k = 2:n
    Bcell{k-1} = A(k:n,:) - A(k-1,:);
end

% Assign output B matrix
B = cell2mat(Bcell)

B = 15×2

1 2 3 3 6 7 99 147 229 267 2 1 5 5 98 145 228 265 3 4

[Jon]

You could also preallocate the B array as in your original code and assign the new rows directly into the B array instead of the cell array, but keeping track of the row indices is a little complicated (at least for me) and the above approach is straightforward

[Jon]

You could also define a recursive function to do this

A = [1 3;2 5;4 6;7 10;100 150;230 270]; % input array example
B = alldiff(A)

B = 15×2

1 2 3 3 6 7 99 147 229 267 2 1 5 5 98 145 228 265 3 4

function [B,A] = alldiff(A,B)
% recursive function to compute all row differences
% B = alldiff(A) computes matrix B with all of the row differences

% Check if completed
if size(A,1) == 1
    return
end
% Assign B on first entry
if nargin < 2
    B = [];
end

B = [B;A(2:end,:)-A(1,:)];
A = A(2:end,:);

% Make recursive call to continue
[B,A] = alldiff(A,B);
end

[Jon]

One minor comment, I think it is more conventional to refer to a matrix as having dimensions m by n, where we consider the rows as the "m's" and the columns as the "n's" but I stuck with your nomenclature.

Answer 3

[dpb]

The cell array @Jon shows is simpler to code and what first strikes, but the answer to the Q? as you posed it to store into the B array directly would look something like (I reformatted the original Q? code to be able to visualize what were actually trying to do more clearly, so that was on me... :) ) --

[nr,nc]=size(A);
B=zeros(nr*(nr-1)/2,nc);
k=0;
for j=1:nr-1                        % outer loop -- reference rows
  for i=j+1:nr                      % inner loop -- rows above reference to end
    k=k+1;                          % output row counter
    B(k,:)=A(i,:)-A(j,:);           % put the differences in that row
  end
end