Permutations with repetition of vectors in different matrices

I'd like to know how combine different vector in order to obtain different matrix. I explain it with an exemple. I have four vectors a=[15 30 45]; b=[1 65 8]; c=[70 13 95] and d=[3 61 93]. I want to combine this four vectors in order to obtain 64 matrices (permutations with repetition: 4^3) with three rows or a 3D matrix. M1=[a;a;a] M1=[a;a;b] M1=[a;a;c] M1=[a;a;d] M1=[a;b;a] M1=[a;b;b] M1=[a;b;c] ... Does anyone know if there is a specific function or can anyone help me to create a matlab code in order to do it?

Answer 1

[Guillaume]

A fairly simple way is to put your different vectors into a matrix and use dec2base to generate the 64 different row indices for that matrix:

a = [15 30 45]; 
b = [1 65 8];
c = [70 13 95];
d = [3 61 93];

srcvec = [a; b; c; d];
rowchoices = dec2base(0:4^3-1, 4) - '0' + 1; 
veccomb = cellfun(@(c) srcvec(c, :), num2cell(rowchoices, 2), 'UniformOutput', false);
veccomb = cat(3, veccomb{:})

[Davide Ferrario]

Thanks for your help. If I want to change the number of vector (in my exemple it's equal to 4) for exemple to 8, I have to change only rowchoices in this way: rowchoices = dec2base(0:8^3-1, 8) - '0' + 1; Am I right?

[Guillaume]

Yes, you only have to change rowchoices. However, it will only work for up to 10 vectors. After that dec2bin will start to use letters, so the - '0' to convert the ascii values of '0' to '9' into their respective numbers won't work any more.

With a bit more sophistication, you could get it to work up to 36, which is the maximum base supported by dec2base.

[Davide Ferrario]

Thank you for your support

Answer 2

[Stephen23]

This simple code will generate a matrix with all of the permutations of 3 chosen from 1:4 with replacement:

N = 3;
[Y{N:-1:1}] = ndgrid(1:4);
Y = reshape(cat(N+1,Y{:}),[],N);

>> Y
Y =
   1     1     1
   1     1     2
   1     1     3
   1     1     4
   1     2     1
   1     2     2
   ...
   4     4     1
   4     4     2
   4     4     3
   4     4     4

You can use these as indices to extract the elements from each vector:

X = [a; b; c; d];
Z = cellfun(@(y)X(y,:), num2cell(Y,2), 'UniformOutput', false);
Z = cat(3,Z{:});