Given vector with N entries, generate all combinations with K entries such that K > N, vector entries can repeat

I'm writing a script to work some ideas I had with eigenvalues in a triangular matrix, and part of that is generating all the possible permutations of the eigenvalues in an arbitrarily sized matrix. To do this I want to generate vectors I can feed into the diag(v) function where v is composed solely of 1x1 symbolic variables.

For example: I have 2 symbolc variables a and b, that I want to feed into a 4x4 matrix so that I get all combinations of a and b across the main diagonal. This would create a matrix (or a set of vectors) that looks something like:

[a a a a

a a a b

a a b a

a b a a

a a b b

a b a b

a b b a

a b b b

b b b b

b b b a

b b a b

b a b b

b b a a

b a b a

b a a b

b a a a]

which I'll then be able to iterate over to feed into diag.

Thanks!

Answer 1

[Matt J]

syms a b
k=4;

[C{k:-1:1}]=ndgrid([a,b]);

result=reshape(cat(k+1,C{:})  ,[],k)

result = 

Answer 2

[Matt J]

Starting with R2023a,

syms a b
k=4;

v=repmat( {[a,b]},1,k);

result=table2array(combinations(v{:}))

result = 

[Bruno Luong]

I just wonder why they design combinations to return table instead of standard array.

I don't use it for this reason. Oh well.

[Matt J]

So that you can have combinations of mixed data types, as in this example,

A1 = [0 1; 2 3];
A2 = ["a" "b" "c"];
A3 = categorical(["x" "y"]);
T = combinations(A1,A2,A3)

T = 24×3 table
    A1    A2     A3
    __    ___    __

    0     "a"    x 
    0     "a"    y 
    0     "b"    x 
    0     "b"    y 
    0     "c"    x 
    0     "c"    y 
    2     "a"    x 
    2     "a"    y 
    2     "b"    x 
    2     "b"    y 
    2     "c"    x 
    2     "c"    y 
    1     "a"    x 
    1     "a"    y 
    1     "b"    x 
    1     "b"    y 

[Bruno Luong]

I prefer cell array for mixed data types (would not know if I ever use that use case), array on pure numerical data.

At least I want an option to do it. Table is NOT a serious computing data types in my opinion. Nobody really knows the internal structure and complexity of accessing data (what I know is row access is poor). I would not use it in any program excepted for importing data, and final reprentation for user interface.

[Alexander]

Thanks for the two answers, I had to use your other one because I'm on R2022a (student, don't feel like continuously paying for updates) but Bruno does bring up a good point about the table datatype not being the best for serious computing.

Answer 3

[Voss]

syms a b

v = [a b];
n = numel(v);
k = 4;

result = v(dec2base(0:n^k-1,n)-'0'+1)

result =