How to create an N-ary array

Suppose I have K variables, each of which can take the values 1 through N. I want to create a table such that each column corresponds to the Kth variable, and each row corresponds to a particular combination. This table will be N^K entries long and K entries wide. One way to do this would be, for example

[V1 V2 ... VK] = ngrid(1:N,1:N,...,1:N)
    V = [V1 V2 ... VK]

However, this clearly does not generalize nicely to variable N. Is there a simple way to extend this code so it works for different K?

[James Tursa]

How do you have your K variables stored? Hopefully not as named-numbered variables. In a cell array or as columns of a matrix?

[David Cyncynates]

I called them variables just because it makes sense to think of them that way to me, but ultimately I just want to have a N^K by K array with each combination stored in a given row. I suppose I could do this the old-fashioned way, where I create the matrix row by row, but I feel like there aught to be a better way.

[James Tursa]

That doesn't answer my question. How do you have them currently stored?

[David Cyncynates]

They're not stored. I would like it to be stored in an array. To be clear - this is my point of confusion! It feels very cumbersome to make this object in matlab, so I think I am missing something.

[James Tursa]

OK, I will ask it another way. Are the inputs always the exact values 1:N?

[David Cyncynates]

Yes, the only informatino you need to create this array is the values N and K: Basically, each row stores a number written in N symbols.

[David Cyncynates]

Here's an example of what I was trying to write. Perhaps I'll just stick with this:

N = 4;
K = 3;

V = zeros(K,N^K);

ii = 0 : N^K - 1;
for jj = 1 : K
    V(jj,:) = floor((mod(ii,N^jj))/N^(jj-1));
end

[James Tursa]

OK, got it. Looks like you are basically counting in base N with K digits. How large can K and N be? This could easily eat all your memory if they are too large.

Answer 1

[Stephen23]

N = 4;
K = 3;
C = cell(1,K);
[C{:}] = ndgrid(1:N);
M = reshape(cat(K+1,C{:}),[],K)

M = 64×3

1 1 1 2 1 1 3 1 1 4 1 1 1 2 1 2 2 1 3 2 1 4 2 1 1 3 1 2 3 1 3 3 1 4 3 1 1 4 1 2 4 1 3 4 1

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How it works:

https://www.mathworks.com/help/matlab/matlab_prog/comma-separated-lists.html

https://www.mathworks.com/matlabcentral/answers/320713-how-to-operate-on-comma-separated-lists

As James Tursa pointed out, you could quickly run out of memory for large values of K.

[Paul]

Hi Stephen,

I thought this would work, but it throws an error:

N = 4;
K = 3;
try
   T = combinations(struct('a',repmat({1:N},1,K)).a)
catch ME
    ME.message
end

ans = 'Argument number is not valid.'

But this works:

C = repmat({1:N},1,K);
T = combinations(C{:});

Is it not the case that both calls to combinations use the same comma-separated-list on input?

It appears the issue is with a call to inputname in combinations

try
    inputnametest(struct('a',repmat({1:N},1,K)).a)
catch ME
    ME.message
end

nargin = 

ans = 3

varargin = 1×3 cell array
    {[1 2 3 4]}    {[1 2 3 4]}    {[1 2 3 4]}

ans = 'Argument number is not valid.'

Why is 2 not a valid input argument number when nargin == 3?

But this works fine:

inputnametest(C{:})

nargin = 

ans = 3

varargin = 1×3 cell array
    {[1 2 3 4]}    {[1 2 3 4]}    {[1 2 3 4]}

ans =

  0×0 empty char array

function inputnametest(varargin)
disp('nargin = ');nargin
varargin
inputname(2)
end

[Stephen23]

@Paul: that appears to be a bug in how the fun(struct(..).fieldname) syntax is parsed when the function FUN just happens to call INPUTNAME. It seems to not depend on COMBINATIONS in particular as it also occurs with other functions that call INPUTNAME, e.g. TABLE:

S = struct('a',{1,2});
T = table(S.a) % this works (two lines)...

T = 1×2 table
    Var1    Var2
    ____    ____

     1       2  

[X,Y] = ndgrid(struct('a',{1,2}).a) % and this too (no INPUTNAME)...

X = 1

Y = 2

T = table(struct('a',{1,2}).a) % yet this does not.

Error using inputname
Argument number is not valid.

Error in table (line 159)
for i = 1:numVars, varnames{i} = inputname(i); end
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

I reported the bug. My guess is that it has something to do with how the number of input names are identified from a static code analysis, and perhaps has never been updated for this (still relatively new) syntax.

[Paul]

Would you mind posting back here the outcome of the bug report? Thx.

[Stephen23]

@Paul: TMW confirmed that it is a bug, which apparently arose due to changes made in R2020b. It will get fixed in a future release.

Answer 2

[Bruno Luong]

N=3
K=5
[~,A] = ismember(dec2base(0:N^K-1,N),['0':'9' 'A':'Z']);
A = A-1