Nested loop problem with the second index

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.

Answer 1

[Jan]

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)];

[Jan]

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.

Answer 2

[Torsten]

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

Answer 3

[Stephen23]

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