K Nested For Loops for arbitrary K

I have a set of K nested "for" loops, where K is a variable. An example of my code for when K=4 is below. Is it possible to implement these nested "for" loops for arbitrary K, for example, by using recursion or a while loop?

K = 4;
phi_deg = -15:15;
N = length(phi_deg);
V = nchoosek(N+K-1,K); % https://math.stackexchange.com/questions/794716/the-number-of-different-ways-to-choose-k-out-of-n-unique-items
mat = zeros(V,K);
idx = 0;
for q1 = 1:N
    for q2 = q1:N
        for q3 = q2:N
            for q4 = q3:N
                idx = idx+1;
                mat(idx,:) = phi_deg([q1,q2,q3,q4]);
            end
        end
    end
end

Answer 1

[Bruno Luong]

No loop or no recursion is needed at all

K = 4;
phi_deg = -15:15;
N = length(phi_deg);

V = nchoosek(N+K-1,K);
mat = zeros(V,K);
idx = 0;
for q1 = 1:N
    for q2 = q1:N
        for q3 = q2:N
            for q4 = q3:N
                idx = idx+1;
                mat(idx,:) = phi_deg([q1,q2,q3,q4]);
            end
        end
    end
end

Q = nchoosek(1:N+K-1,K)-(0:K-1);
mat2 = phi_deg(Q);
isequal(mat,mat2)

ans = logical
   1

You can then loop on the rows of mat2 generated as such if you have to.

[Bruno Luong]

You can use this FEX if your number combinations

% Q = nchoosek(1:N+K-1,K)-(0:K-1)

is too large to fit into memory, e.g. for k >= 10.

(but then you might not have time to process them all)

The template code looks like this

% https://www.mathworks.com/matlabcentral/fileexchange/91060-nchoosek_enum
k = 4;
phi_deg = -15:15;
n = length(phi_deg);
chunksize = 100;
i = 1:chunksize;
norepetition = false;
while true
    if norepetition
        c = nchoosek_enum(n, k, i);
    else
        c = nchoosek_enum(n+k-1, k, i);
        c = c - (0:k-1);
    end
    for r=1:size(c,1)
        q = c(r,:);
        endcomb = any(isnan(q));
        if endcomb
            break
        end
        % do something with cr
        mat_i = phi_deg(q);
        fprintf('%s\n', mat2str(mat_i));
        ...
    end
    if endcomb
        break
    end
    i = i +  chunksize;
end

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[-14 -8 -8 -8]
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[-14 -8 -5 -5]
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[-14 -8 -4 -4]
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[-14 -8 -4 -2]
[-14 -8 -4 -1]
[-14 -8 -4 0]
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[-14 -8 -4 14]
[-14 -8 -4 15]
[-14 -8 -3 -3]
[-14 -8 -3 -2]
[-14 -8 -3 -1]
[-14 -8 -3 0]
[-14 -8 -3 1]
[-14 -8 -3 2]
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[-14 -8 -3 6]
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[-14 -8 -3 12]
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[-14 -8 -3 15]
[-14 -8 -2 -2]
[-14 -8 -2 -1]
[-14 -8 -2 0]
[-14 -8 -2 1]
[-14 -8 -2 2]
[-14 -8 -2 3]
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[-14 -8 -1 -1]
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[-14 -8 0 0]
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[-14 -8 1 1]
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[-14 -8 2 2]
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[-14 -8 2 9]
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[-14 -8 2 15]
[-14 -8 3 3]
[-14 -8 3 4]
[-14 -8 3 5]
[-14 -8 3 6]
[-14 -8 3 7]
[-14 -8 3 8]
[-14 -8 3 9]
[-14 -8 3 10]
[-14 -8 3 11]
[-14 -8 3 12]
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[-14 -8 3 15]
[-14 -8 4 4]
[-14 -8 4 5]
[-14 -8 4 6]
[-14 -8 4 7]
[-14 -8 4 8]
[-14 -8 4 9]
[-14 -8 4 10]
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[-14 -8 5 6]
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[-14 -8 6 15]
[-14 -8 7 7]
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[-14 -8 7 10]
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[-14 -8 7 12]
[-14 -8 7 13]
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[-14 -8 7 15]
[-14 -8 8 8]
[-14 -8 8 9]
[-14 -8 8 10]
[-14 -8 8 11]
[-14 -8 8 12]
[-14 -8 8 13]
[-14 -8 8 14]
[-14 -8 8 15]
[-14 -8 9 9]
[-14 -8 9 10]
[-14 -8 9 11]
[-14 -8 9 12]
[-14 -8 9 13]
[-14 -8 9 14]
[-14 -8 9 15]
[-14 -8 10 10]
[-14 -8 10 11]
[-14 -8 10 12]
[-14 -8 10 13]
[-14 -8 10 14]
[-14 -8 10 15]
[-14 -8 11 11]
[-14 -8 11 12]
[-14 -8 11 13]
[-14 -8 11 14]
[-14 -8 11 15]
[-...

[Bruno Luong]

For completeness here is a recursion code

k = 4;
phi_deg = -15:15;
n = length(phi_deg);
mydata = struct('phi_deg', phi_deg);
RecursLoop(n, k, [], mydata);

[-15 -15 -15 -15]
[-15 -15 -15 -14]
[-15 -15 -15 -13]
[-15 -15 -15 -12]
[-15 -15 -15 -11]
[-15 -15 -15 -10]
[-15 -15 -15 -9]
[-15 -15 -15 -8]
[-15 -15 -15 -7]
[-15 -15 -15 -6]
[-15 -15 -15 -5]
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[-15 -15 -15 -3]
[-15 -15 -15 -2]
[-15 -15 -15 -1]
[-15 -15 -15 0]
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[-15 -15 -15 11]
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[-15 -15 -15 14]
[-15 -15 -15 15]
[-15 -15 -14 -14]
[-15 -15 -14 -13]
[-15 -15 -14 -12]
[-15 -15 -14 -11]
[-15 -15 -14 -10]
[-15 -15 -14 -9]
[-15 -15 -14 -8]
[-15 -15 -14 -7]
[-15 -15 -14 -6]
[-15 -15 -14 -5]
[-15 -15 -14 -4]
[-15 -15 -14 -3]
[-15 -15 -14 -2]
[-15 -15 -14 -1]
[-15 -15 -14 0]
[-15 -15 -14 1]
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[-15 -15 -14 15]
[-15 -15 -13 -13]
[-15 -15 -13 -12]
[-15 -15 -13 -11]
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[-15 -15 -13 -9]
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[-15 -15 -13 -5]
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[-15 -15 -13 0]
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[-15 -15 -12 -12]
[-15 -15 -12 -11]
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[-15 -15 -12 -9]
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[-15 -15 -12 -6]
[-15 -15 -12 -5]
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[-15 -15 -12 -1]
[-15 -15 -12 0]
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[-15 -15 -12 15]
[-15 -15 -11 -11]
[-15 -15 -11 -10]
[-15 -15 -11 -9]
[-15 -15 -11 -8]
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[-15 -15 -11 -6]
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[-15 -15 -11 -4]
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[-15 -15 -11 -1]
[-15 -15 -11 0]
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[-15 -15 -11 11]
[-15 -15 -11 12]
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[-15 -15 -11 15]
[-15 -15 -10 -10]
[-15 -15 -10 -9]
[-15 -15 -10 -8]
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[-15 -15 -10 -5]
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[-15 -15 -10 -1]
[-15 -15 -10 0]
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[-15 -15 -10 14]
[-15 -15 -10 15]
[-15 -15 -9 -9]
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[-15 -15 -9 -7]
[-15 -15 -9 -6]
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[-15 -15 -5 -5]
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[-14 -8 1 1]
[-14 -8 1 2]
[-14 -8 1 3]
[-14 -8 1 4]
[-14 -8 1 5]
[-14 -8 1 6]
[-14 -8 1 7]
[-14 -8 1 8]
[-14 -8 1 9]
[-14 -8 1 10]
[-14 -8 1 11]
[-14 -8 1 12]
[-14 -8 1 13]
[-14 -8 1 14]
[-14 -8 1 15]
[-14 -8 2 2]
[-14 -8 2 3]
[-14 -8 2 4]
[-14 -8 2 5]
[-14 -8 2 6]
[-14 -8 2 7]
[-14 -8 2 8]
[-14 -8 2 9]
[-14 -8 2 10]
[-14 -8 2 11]
[-14 -8 2 12]
[-14 -8 2 13]
[-14 -8 2 14]
[-14 -8 2 15]
[-14 -8 3 3]
[-14 -8 3 4]
[-14 -8 3 5]
[-14 -8 3 6]
[-14 -8 3 7]
[-14 -8 3 8]
[-14 -8 3 9]
[-14 -8 3 10]
[-14 -8 3 11]
[-14 -8 3 12]
[-14 -8 3 13]
[-14 -8 3 14]
[-14 -8 3 15]
[-14 -8 4 4]
[-14 -8 4 5]
[-14 -8 4 6]
[-14 -8 4 7]
[-14 -8 4 8]
[-14 -8 4 9]
[-14 -8 4 10]
[-14 -8 4 11]
[-14 -8 4 12]
[-14 -8 4 13]
[-14 -8 4 14]
[-14 -8 4 15]
[-14 -8 5 5]
[-14 -8 5 6]
[-14 -8 5 7]
[-14 -8 5 8]
[-14 -8 5 9]
[-14 -8 5 10]
[-14 -8 5 11]
[-14 -8 5 12]
[-14 -8 5 13]
[-14 -8 5 14]
[-14 -8 5 15]
[-14 -8 6 6]
[-14 -8 6 7]
[-14 -8 6 8]
[-14 -8 6 9]
[-14 -8 6 10]
[-14 -8 6 11]
[-14 -8 6 12]
[-14 -8 6 13]
[-14 -8 6 14]
[-14 -8 6 15]
[-14 -8 7 7]
[-14 -8 7 8]
[-14 -8 7 9]
[-14 -8 7 10]
[-14 -8 7 11]
[-14 -8 7 12]
[-14 -8 7 13]
[-14 -8 7 14]
[-14 -8 7 15]
[-14 -8 8 8]
[-14 -8 8 9]
[-14 -8 8 10]
[-14 -8 8 11]
[-14 -8 8 12]
[-14 -8 8 13]
[-14 -8 8 14]
[-14 -8 8 15]
[-14 -8 9 9]
[-14 -8 9 10]
[-14 -8 9 11]
[-14 -8 9 12]
[-14 -8 9 13]
[-14 -8 9 14]
[-14 -8 9 15]
[-14 -8 10 10]
[-14 -8 10 11]
[-14 -8 10 12]
[-14 -8 10 13]
[-14 -8 10 14]
[-14 -8 10 15]
[-14 -8 11 11]
[-14 -8 11 12]
[-14 -8 11 13]
[-14 -8 11 14]
[-14 -8 11 15]
[-...

function RecursLoop(n, k, qhead, mydata)
if isempty(qhead)
    jfirst = 1;
else
    jfirst = qhead(end);
end
jlast = n;
q = [qhead, 0]; % dummy last value
j = numel(q);
islastloop = j == k;
for qj = jfirst:jlast
    q(j) = qj;
    if islastloop
        mati = mydata.phi_deg(q);
        fprintf('%s\n', mat2str(mati));
        ... do something with q and mati
    else
        RecursLoop(n, k, q, mydata);
    end
end
end % RecursLoop

Answer 2

[Walter Roberson]

See sample code at https://www.mathworks.com/matlabcentral/answers/357969-using-recursive-function-to-calculate-all-possible-peptide-combinations#answer_282766 for the "odometer" pattern.

[Stuart Rogers]

You linked to my post. Did you mean to link to this post? https://www.mathworks.com/matlabcentral/answers/357969-using-recursive-function-to-calculate-all-possible-peptide-combinations#answer_282766

[Image Analyst]

The link just points to this page.

[Walter Roberson]

Ooops, you are right; I have corrected the URL.

Answer 3

[Torsten]

I'd generate all possible k-tuples out of the n numbers and throw away those that are not monotonic by using the "diff" command:

A = [1 3 5; 3 1 4; 2 2 8];
idx = all(diff(A,1,2)>=0,2)

idx = 3x1 logical array
   1
   0
   1

A(idx,:)

ans = 2×3

1 3 5 2 2 8

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