Nested loop problem with the second index

Question

gianluca 2019-7-2

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/469864-nested-loop-problem-with-the-second-index

编辑： Jan 2019-7-2

采纳的回答： Jan

Question.mat

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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.

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Answer 1

Jan 2019-7-2

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https://ww2.mathworks.cn/matlabcentral/answers/469864-nested-loop-problem-with-the-second-index#answer_381656

编辑：Jan 2019-7-2

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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)];

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Jan 2019-7-2

编辑：Jan 2019-7-2

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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.

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Answer 2

Torsten 2019-7-2

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https://ww2.mathworks.cn/matlabcentral/answers/469864-nested-loop-problem-with-the-second-index#answer_381622

编辑：Torsten 2019-7-2

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

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Answer 3

Stephen23 2019-7-2

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https://ww2.mathworks.cn/matlabcentral/answers/469864-nested-loop-problem-with-the-second-index#answer_381623

编辑：Stephen23 2019-7-2

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The simple MATLAB way:

>> cpx = [1,3,5,7];
>> cpy = [22,44,66];
>> [X,Y] = ndgrid(cpx,cpy);
>> M = [X(:),Y(:)]
M =
  22
  22
  22
  22
  44
  44
  44
  44
  66
  66
  66
  66