# Create a permutation of elements in the same position

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Salwa Mostafa on 15 Feb 2022
Commented: Salwa Mostafa on 15 Feb 2022
I have coordinates of points x = [x_1 x_2], y =[ y_1 y_2 ] z = [z_1 z_2 ]
I want to create a matrix with all permutation but the coordinates are in the same position
[ x_1 y_1 z_2;
x_1 y_2 z_2;
x_1 y_1 z_1;
x_1 y_2 z_2;
x_2 y_1 z_2;
x_2 y_2 z_2;
x_2 y_1 z_1;
x_2 y_2 z_2; ]
but the coordinates is changing so it can be x,y,z,v,w I want to write it for a general number of coordinates.

William Rose on 15 Feb 2022
I see that you have already done it for 2 pairs of coordinates. Here is a way to do it for N coordinates.
N=3;
x=rand(1,N); y=rand(1,N); z=rand(1,N);
A=zeros(N^3,3); %initialize array
for i=1:N
for j=1:N
for k=1:N
A(N^2*(i-1)+N*(j-1)+k,:)=[x(i),y(j),z(k)];
end
end
end
Try it. Good luck.

Yongjian Feng on 15 Feb 2022
Just 3 for loops.

DGM on 15 Feb 2022
Edited: DGM on 15 Feb 2022
Consider the example:
% input coordinates
x = [1 2];
y = [11 22];
z = [111 222];
% create the index array
m = (dec2bin(0:7,3) == '1') + 1;
% all combinations in order
xyz = [x(m(:,1)); y(m(:,2)); z(m(:,3))].'
xyz = 8×3
1 11 111 1 11 222 1 22 111 1 22 222 2 11 111 2 11 222 2 22 111 2 22 222
Or more generally:
x = [1 2 3];
y = [11 22 33];
z = [111 222 333];
% create the index array
nx = numel(x);
m = repmat((1:nx)',[nx*2 1]);
m = [repelem(m(1:size(m,1)/nx,1),nx) m];
m = [repelem(m(1:size(m,1)/nx,1),nx) m];
% get the combinations like before
xyz = [x(m(:,1)); y(m(:,2)); z(m(:,3))].'
xyz = 18×3
1 11 111 1 11 222 1 11 333 1 22 111 1 22 222 1 22 333 1 33 111 1 33 222 1 33 333 2 11 111
Salwa Mostafa on 15 Feb 2022
Thanks so much