Tricky matrix conversion question

Hey all,

I am trying to convert a matrix A into a new matrix B, by looking at each element in matrix A and whenever the next element (in a row) is different, make a pair and add it to the new matrix B. Also elements with number 0 should be ignored.

As an example: Suppose we have a matrix A, and we want the resulted matrix B.

A = [1 1 1 3 5      B = [1 3
     2 2 0 4 5           3 5
     2 2 0 0 5]          2 4
                         4 5
                         2 5]

This problem could be solved by using a for-loop over all elements in the matrix, however for computational time reasons i am looking for a faster way to convert this, any ideas are welcome :D

Answer 1

[Guillaume]

Actually, it can be done fairly easily without a loop. Whether or not it's faster than Adam's loop, I haven't tested.

A = [1 1 1 3 5;2 2 0 4 5; 2 2 0 0 5];

rows = repmat(1:size(A, 1), size(A, 2), 1);
At = A';
mask = At ~= 0;
Anz = At(mask);
pair1 = diff(Anz) ~= 0 & ~diff(rows(mask));
B = [Anz(pair1), Anz([false; pair1])]

[Adam Danz]

Slow clap! (+1)

@Niels de Vries, this version is 10x faster than mine when tested with my 1 million randi() data. Use this one.

Answer 2

[Adam Danz]

Sure, it's probably possible to avoid a loop entirely. But that doesn't mean it's practical.

This proposal loops through rows of A, removes 0s, differentiates to find changes, then extracts pairs and stores them in B to produce your desired results.

B = []; 
% Loop over rows of A
for i = 1:size(A,1)
    % remove 0s
    tempRow = A(i,A(i,:)~=0); 
    % differentiate
    d = diff(tempRow); 
    % Extract non=0 pairs
    pairedIdx = find(d~=0);
    % Detect pairs that differ and store in B
    pairedNums = [tempRow(pairedIdx)', tempRow(pairedIdx+1)']; 
    B(end + 1 : end + size(pairedNums,1),:) = pairedNums; 
end

In fact, when I change A to

A = randi(10, 1000, 1000)-1;

which contains 1 million elements in 1000 rows, it only takes ~1 sec using tic/toc.