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

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Alexander
Alexander 2023-10-20
编辑： Bruno Luong 2023-10-20
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!

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采纳的回答

Matt J
Matt J 2023-10-20
编辑：Matt J 2023-10-20
Ran in:
syms a b
k=4;
[C{k:-1:1}]=ndgrid([a,b]);
result=reshape(cat(k+1,C{:}) ,[],k)
result = 

更多回答（2 个）

Matt J
Matt J 2023-10-20
编辑：Matt J 2023-10-20
Ran in:
Starting with R2023a,
syms a b
k=4;
v=repmat( {[a,b]},1,k);
result=table2array(combinations(v{:}))
result = 
  4 个评论
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Bruno Luong
Bruno Luong 2023-10-20
编辑：Bruno Luong 2023-10-20
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
Alexander 2023-10-20
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.

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Voss
Voss 2023-10-20
Ran in:
syms a b
v = [a b];
n = numel(v);
k = 4;
result = v(dec2base(0:n^k-1,n)-'0'+1)
result = 

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