# Nested loop problem with the second index

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gianluca on 2 Jul 2019
Edited: Jan on 2 Jul 2019
Dear all,
the following code does not work well for index j > 1. I have two vectors cpx = 1-by-n and cpy = 1-by-m.
I would a new matrix cp with n-by-m rows and 2 columns with all the possible permutations of the elements in cpx and cpy. Where is the mistake?
for i = 1:length(cpx)
for j = 1:length(cpy)
cp(i.*j,:) = [cpx(i) cpy(j)];
end
end
The results are fine till row 55, so that the first cicle for i = 1:55 and j = 1 works well, then the results are incomprehensible.

Jan on 2 Jul 2019
Edited: Jan on 2 Jul 2019
The problem of you code was cp(i.*j,:). i*j is not a growing index. In the 1st iteration 1*1 is fine. For i=1 it works for the complete loop over j. But in the next iteration for i=2, j=1 you overwrite the value written by i=1, j=2. Better:
nx = numel(cpx);
ny = numel(cpy);
cp = zeros(nx * ny, 2); % Pre-allocation!!!
for i = 1:nx
for j = 1:ny
cp((i-1) * ny + j,:) = [cpx(i) cpy(j)];
end
end
But this can be written without loops:
cp = [repelem(cpx(:), numel(cpy), 1), repmat(cpy(:), numel(cpx), 1)];

#### 1 Comment

Jan on 2 Jul 2019
Some timings:
cpx = rand(1000, 1);
cpy = rand(1000, 1);
tic
cp = zeros(length(cpx)*length(cpy),2);
row = 0;
for i = 1:length(cpx)
for j = 1:length(cpy)
row = row + 1;
cp(row,:) = [cpx(i) cpy(j)];
end
end
toc
% 6.8 sec
tic;
[X,Y] = ndgrid(cpx,cpy);
M = [X(:),Y(:)];
toc
% 0.018 sec
tic;
nx = numel(cpx);
ny = numel(cpy);
cp = zeros(nx * ny, 2);
for i = 1:nx
for j = 1:ny
cp((i-1) * ny + j,:) = [cpx(i) cpy(j)];
end
end
toc
% 3.9 sec
tic
cp = [repmat(cpx(:), numel(cpy), 1), repelem(cpy(:), numel(cpx), 1)];
toc
% 0.022 sec
For 100x1 inputs, REPELEM/REPMAT is faster than NDGRID. For arrays > 1000 elements, NDGRID is faster - to my surprise, because it uses REPMAT twice also. In every case, they outperform the loops massively.

Torsten on 2 Jul 2019
Edited: Torsten on 2 Jul 2019
cp = zeros(length(cpx)*length(cpy),2);
row = 0;
for i = 1:length(cpx)
for j = 1:length(cpy)
row = row + 1;
cp(row,:) = [cpx(i) cpy(j)];
end
end

Stephen Cobeldick on 2 Jul 2019
Edited: Stephen Cobeldick on 2 Jul 2019
The simple MATLAB way:
>> cpx = [1,3,5,7];
>> cpy = [22,44,66];
>> [X,Y] = ndgrid(cpx,cpy);
>> M = [X(:),Y(:)]
M =
1 22
3 22
5 22
7 22
1 44
3 44
5 44
7 44
1 66
3 66
5 66
7 66