Create a permutation of elements in the same position

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.

Answer 1

[William Rose]

@Salwa Mostafa,

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.

Answer 2

[Yongjian Feng]

Just 3 for loops.

Answer 3

[DGM]

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]

Thanks for your help. I just forgot to mention that the number of coordinate x , y , z is larger for example 5 coordinates x,y,z,v,w each with dimention two values like x = x_1 x_2. I want to write the function for any number of coordinates

[DGM]

I added an example for that as well.

[Salwa Mostafa]

Thanks so much