K Nested For Loops for arbitrary K

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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

Accepted Answer

Bruno Luong
Bruno Luong on 28 Oct 2024
Edited: Bruno Luong on 28 Oct 2024
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.
  2 Comments
Bruno Luong
Bruno Luong on 28 Oct 2024
Moved: Bruno Luong on 29 Oct 2024
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
[-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] [-15 -15 -15 -4] [-15 -15 -15 -3] [-15 -15 -15 -2] [-15 -15 -15 -1] [-15 -15 -15 0] [-15 -15 -15 1] [-15 -15 -15 2] [-15 -15 -15 3] [-15 -15 -15 4] [-15 -15 -15 5] [-15 -15 -15 6] [-15 -15 -15 7] [-15 -15 -15 8] [-15 -15 -15 9] [-15 -15 -15 10] [-15 -15 -15 11] [-15 -15 -15 12] [-15 -15 -15 13] [-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] [-15 -15 -14 2] [-15 -15 -14 3] [-15 -15 -14 4] [-15 -15 -14 5] [-15 -15 -14 6] [-15 -15 -14 7] [-15 -15 -14 8] [-15 -15 -14 9] [-15 -15 -14 10] [-15 -15 -14 11] [-15 -15 -14 12] [-15 -15 -14 13] [-15 -15 -14 14] [-15 -15 -14 15] [-15 -15 -13 -13] [-15 -15 -13 -12] [-15 -15 -13 -11] [-15 -15 -13 -10] [-15 -15 -13 -9] [-15 -15 -13 -8] [-15 -15 -13 -7] [-15 -15 -13 -6] [-15 -15 -13 -5] [-15 -15 -13 -4] [-15 -15 -13 -3] [-15 -15 -13 -2] [-15 -15 -13 -1] [-15 -15 -13 0] [-15 -15 -13 1] [-15 -15 -13 2] [-15 -15 -13 3] [-15 -15 -13 4] [-15 -15 -13 5] [-15 -15 -13 6] [-15 -15 -13 7] [-15 -15 -13 8] [-15 -15 -13 9] [-15 -15 -13 10] [-15 -15 -13 11] [-15 -15 -13 12] [-15 -15 -13 13] [-15 -15 -13 14] [-15 -15 -13 15] [-15 -15 -12 -12] [-15 -15 -12 -11] [-15 -15 -12 -10] [-15 -15 -12 -9] [-15 -15 -12 -8] [-15 -15 -12 -7] [-15 -15 -12 -6] [-15 -15 -12 -5] [-15 -15 -12 -4] [-15 -15 -12 -3] [-15 -15 -12 -2] [-15 -15 -12 -1] [-15 -15 -12 0] [-15 -15 -12 1] [-15 -15 -12 2] [-15 -15 -12 3] [-15 -15 -12 4] [-15 -15 -12 5] [-15 -15 -12 6] [-15 -15 -12 7] [-15 -15 -12 8] [-15 -15 -12 9] [-15 -15 -12 10] [-15 -15 -12 11] [-15 -15 -12 12] [-15 -15 -12 13] [-15 -15 -12 14] [-15 -15 -12 15] [-15 -15 -11 -11] [-15 -15 -11 -10] [-15 -15 -11 -9] [-15 -15 -11 -8] [-15 -15 -11 -7] [-15 -15 -11 -6] [-15 -15 -11 -5] [-15 -15 -11 -4] [-15 -15 -11 -3] [-15 -15 -11 -2] [-15 -15 -11 -1] [-15 -15 -11 0] [-15 -15 -11 1] [-15 -15 -11 2] [-15 -15 -11 3] [-15 -15 -11 4] [-15 -15 -11 5] [-15 -15 -11 6] [-15 -15 -11 7] [-15 -15 -11 8] [-15 -15 -11 9] [-15 -15 -11 10] [-15 -15 -11 11] [-15 -15 -11 12] [-15 -15 -11 13] [-15 -15 -11 14] [-15 -15 -11 15] [-15 -15 -10 -10] [-15 -15 -10 -9] [-15 -15 -10 -8] [-15 -15 -10 -7] [-15 -15 -10 -6] [-15 -15 -10 -5] [-15 -15 -10 -4] [-15 -15 -10 -3] [-15 -15 -10 -2] [-15 -15 -10 -1] [-15 -15 -10 0] [-15 -15 -10 1] [-15 -15 -10 2] [-15 -15 -10 3] [-15 -15 -10 4] [-15 -15 -10 5] [-15 -15 -10 6] [-15 -15 -10 7] [-15 -15 -10 8] [-15 -15 -10 9] [-15 -15 -10 10] [-15 -15 -10 11] [-15 -15 -10 12] [-15 -15 -10 13] [-15 -15 -10 14] [-15 -15 -10 15] [-15 -15 -9 -9] [-15 -15 -9 -8] [-15 -15 -9 -7] [-15 -15 -9 -6] [-15 -15 -9 -5] [-15 -15 -9 -4] [-15 -15 -9 -3] [-15 -15 -9 -2] 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-2] [-15 -15 -3 -1] [-15 -15 -3 0] [-15 -15 -3 1] [-15 -15 -3 2] [-15 -15 -3 3] [-15 -15 -3 4] [-15 -15 -3 5] [-15 -15 -3 6] [-15 -15 -3 7] [-15 -15 -3 8] [-15 -15 -3 9] [-15 -15 -3 10] [-15 -15 -3 11] [-15 -15 -3 12] [-15 -15 -3 13] [-15 -15 -3 14] [-15 -15 -3 15] [-15 -15 -2 -2] [-15 -15 -2 -1] [-15 -15 -2 0] [-15 -15 -2 1] [-15 -15 -2 2] [-15 -15 -2 3] [-15 -15 -2 4] [-15 -15 -2 5] [-15 -15 -2 6] [-15 -15 -2 7] [-15 -15 -2 8] [-15 -15 -2 9] [-15 -15 -2 10] [-15 -15 -2 11] [-15 -15 -2 12] [-15 -15 -2 13] [-15 -15 -2 14] [-15 -15 -2 15] [-15 -15 -1 -1] [-15 -15 -1 0] [-15 -15 -1 1] [-15 -15 -1 2] [-15 -15 -1 3] [-15 -15 -1 4] [-15 -15 -1 5] [-15 -15 -1 6] [-15 -15 -1 7] [-15 -15 -1 8] [-15 -15 -1 9] [-15 -15 -1 10] [-15 -15 -1 11] [-15 -15 -1 12] [-15 -15 -1 13] [-15 -15 -1 14] [-15 -15 -1 15] [-15 -15 0 0] [-15 -15 0 1] [-15 -15 0 2] [-15 -15 0 3] [-15 -15 0 4] [-15 -15 0 5] [-15 -15 0 6] [-15 -15 0 7] [-15 -15 0 8] [-15 -15 0 9] [-15 -15 0 10] [-15 -15 0 11] [-15 -15 0 12] [-15 -15 0 13] [-15 -15 0 14] [-15 -15 0 15] [-15 -15 1 1] [-15 -15 1 2] [-15 -15 1 3] [-15 -15 1 4] [-15 -15 1 5] [-15 -15 1 6] [-15 -15 1 7] [-15 -15 1 8] [-15 -15 1 9] [-15 -15 1 10] [-15 -15 1 11] [-15 -15 1 12] [-15 -15 1 13] [-15 -15 1 14] [-15 -15 1 15] [-15 -15 2 2] [-15 -15 2 3] [-15 -15 2 4] [-15 -15 2 5] [-15 -15 2 6] [-15 -15 2 7] [-15 -15 2 8] [-15 -15 2 9] [-15 -15 2 10] [-15 -15 2 11] [-15 -15 2 12] [-15 -15 2 13] [-15 -15 2 14] [-15 -15 2 15] [-15 -15 3 3] [-15 -15 3 4] [-15 -15 3 5] [-15 -15 3 6] [-15 -15 3 7] [-15 -15 3 8] [-15 -15 3 9] [-15 -15 3 10] [-15 -15 3 11] [-15 -15 3 12] [-15 -15 3 13] [-15 -15 3 14] [-15 -15 3 15] [-15 -15 4 4] [-15 -15 4 5] [-15 -15 4 6] [-15 -15 4 7] [-15 -15 4 8] [-15 -15 4 9] [-15 -15 4 10] [-15 -15 4 11] [-15 -15 4 12] [-15 -15 4 13] [-15 -15 4 14] [-15 -15 4 15] [-15 -15 5 5] [-15 -15 5 6] [-15 -15 5 7] [-15 -15 5 8] [-15 -15 5 9] [-15 -15 5 10] [-15 -15 5 11] [-15 -15 5 12] [-15 -15 5 13] [-15 -15 5 14] [-15 -15 5 15] [-15 -15 6 6] [-15 -15 6 7] [-15 -15 6 8] [-15 -15 6 9] [-15 -15 6 10] [-15 -15 6 11] [-15 -15 6 12] [-15 -15 6 13] [-15 -15 6 14] [-15 -15 6 15] [-15 -15 7 7] [-15 -15 7 8] [-15 -15 7 9] [-15 -15 7 10] [-15 -15 7 11] [-15 -15 7 12] [-15 -15 7 13] [-15 -15 7 14] [-15 -15 7 15] [-15 -15 8 8] [-15 -15 8 9] [-15 -15 8 10] [-15 -15 8 11] [-15 -15 8 12] [-15 -15 8 13] [-15 -15 8 14] [-15 -15 8 15] [-15 -15 9 9] [-15 -15 9 10] [-15 -15 9 11] [-15 -15 9 12] [-15 -15 9 13] [-15 -15 9 14] [-15 -15 9 15] [-15 -15 10 10] [-15 -15 10 11] [-15 -15 10 12] [-15 -15 10 13] [-15 -15 10 14] [-15 -15 10 15] [-15 -15 11 11] [-15 -15 11 12] [-15 -15 11 13] [-15 -15 11 14] [-15 -15 11 15] [-15 -15 12 12] [-15 -15 12 13] [-15 -15 12 14] [-15 -15 12 15] [-15 -15 13 13] [-15 -15 13 14] [-15 -15 13 15] [-15 -15 14 14] [-15 -15 14 15] [-15 -15 15 15] [-15 -14 -14 -14] [-15 -14 -14 -13] [-15 -14 -14 -12] [-15 -14 -14 -11] [-15 -14 -14 -10] [-15 -14 -14 -9] [-15 -14 -14 -8] [-15 -14 -14 -7] [-15 -14 -14 -6] [-15 -14 -14 -5] [-15 -14 -14 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9] [-14 -10 -2 10] [-14 -10 -2 11] [-14 -10 -2 12] [-14 -10 -2 13] [-14 -10 -2 14] [-14 -10 -2 15] [-14 -10 -1 -1] [-14 -10 -1 0] [-14 -10 -1 1] [-14 -10 -1 2] [-14 -10 -1 3] [-14 -10 -1 4] [-14 -10 -1 5] [-14 -10 -1 6] [-14 -10 -1 7] [-14 -10 -1 8] [-14 -10 -1 9] [-14 -10 -1 10] [-14 -10 -1 11] [-14 -10 -1 12] [-14 -10 -1 13] [-14 -10 -1 14] [-14 -10 -1 15] [-14 -10 0 0] [-14 -10 0 1] [-14 -10 0 2] [-14 -10 0 3] [-14 -10 0 4] [-14 -10 0 5] [-14 -10 0 6] [-14 -10 0 7] [-14 -10 0 8] [-14 -10 0 9] [-14 -10 0 10] [-14 -10 0 11] [-14 -10 0 12] [-14 -10 0 13] [-14 -10 0 14] [-14 -10 0 15] [-14 -10 1 1] [-14 -10 1 2] [-14 -10 1 3] [-14 -10 1 4] [-14 -10 1 5] [-14 -10 1 6] [-14 -10 1 7] [-14 -10 1 8] [-14 -10 1 9] [-14 -10 1 10] [-14 -10 1 11] [-14 -10 1 12] [-14 -10 1 13] [-14 -10 1 14] [-14 -10 1 15] [-14 -10 2 2] [-14 -10 2 3] [-14 -10 2 4] [-14 -10 2 5] [-14 -10 2 6] [-14 -10 2 7] [-14 -10 2 8] [-14 -10 2 9] [-14 -10 2 10] [-14 -10 2 11] [-14 -10 2 12] [-14 -10 2 13] [-14 -10 2 14] [-14 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13] [-14 -10 9 14] [-14 -10 9 15] [-14 -10 10 10] [-14 -10 10 11] [-14 -10 10 12] [-14 -10 10 13] [-14 -10 10 14] [-14 -10 10 15] [-14 -10 11 11] [-14 -10 11 12] [-14 -10 11 13] [-14 -10 11 14] [-14 -10 11 15] [-14 -10 12 12] [-14 -10 12 13] [-14 -10 12 14] [-14 -10 12 15] [-14 -10 13 13] [-14 -10 13 14] [-14 -10 13 15] [-14 -10 14 14] [-14 -10 14 15] [-14 -10 15 15] [-14 -9 -9 -9] [-14 -9 -9 -8] [-14 -9 -9 -7] [-14 -9 -9 -6] [-14 -9 -9 -5] [-14 -9 -9 -4] [-14 -9 -9 -3] [-14 -9 -9 -2] [-14 -9 -9 -1] [-14 -9 -9 0] [-14 -9 -9 1] [-14 -9 -9 2] [-14 -9 -9 3] [-14 -9 -9 4] [-14 -9 -9 5] [-14 -9 -9 6] [-14 -9 -9 7] [-14 -9 -9 8] [-14 -9 -9 9] [-14 -9 -9 10] [-14 -9 -9 11] [-14 -9 -9 12] [-14 -9 -9 13] [-14 -9 -9 14] [-14 -9 -9 15] [-14 -9 -8 -8] [-14 -9 -8 -7] [-14 -9 -8 -6] [-14 -9 -8 -5] [-14 -9 -8 -4] [-14 -9 -8 -3] [-14 -9 -8 -2] [-14 -9 -8 -1] [-14 -9 -8 0] [-14 -9 -8 1] [-14 -9 -8 2] [-14 -9 -8 3] [-14 -9 -8 4] [-14 -9 -8 5] [-14 -9 -8 6] [-14 -9 -8 7] [-14 -9 -8 8] [-14 -9 -8 9] [-14 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[-14 -9 -1 8] [-14 -9 -1 9] [-14 -9 -1 10] [-14 -9 -1 11] [-14 -9 -1 12] [-14 -9 -1 13] [-14 -9 -1 14] [-14 -9 -1 15] [-14 -9 0 0] [-14 -9 0 1] [-14 -9 0 2] [-14 -9 0 3] [-14 -9 0 4] [-14 -9 0 5] [-14 -9 0 6] [-14 -9 0 7] [-14 -9 0 8] [-14 -9 0 9] [-14 -9 0 10] [-14 -9 0 11] [-14 -9 0 12] [-14 -9 0 13] [-14 -9 0 14] [-14 -9 0 15] [-14 -9 1 1] [-14 -9 1 2] [-14 -9 1 3] [-14 -9 1 4] [-14 -9 1 5] [-14 -9 1 6] [-14 -9 1 7] [-14 -9 1 8] [-14 -9 1 9] [-14 -9 1 10] [-14 -9 1 11] [-14 -9 1 12] [-14 -9 1 13] [-14 -9 1 14] [-14 -9 1 15] [-14 -9 2 2] [-14 -9 2 3] [-14 -9 2 4] [-14 -9 2 5] [-14 -9 2 6] [-14 -9 2 7] [-14 -9 2 8] [-14 -9 2 9] [-14 -9 2 10] [-14 -9 2 11] [-14 -9 2 12] [-14 -9 2 13] [-14 -9 2 14] [-14 -9 2 15] [-14 -9 3 3] [-14 -9 3 4] [-14 -9 3 5] [-14 -9 3 6] [-14 -9 3 7] [-14 -9 3 8] [-14 -9 3 9] [-14 -9 3 10] [-14 -9 3 11] [-14 -9 3 12] [-14 -9 3 13] [-14 -9 3 14] [-14 -9 3 15] [-14 -9 4 4] [-14 -9 4 5] [-14 -9 4 6] [-14 -9 4 7] [-14 -9 4 8] [-14 -9 4 9] [-14 -9 4 10] [-14 -9 4 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[-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] [-...
Bruno Luong
Bruno Luong on 29 Oct 2024
Moved: Bruno Luong on 29 Oct 2024
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);
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13] [-14 -10 9 14] [-14 -10 9 15] [-14 -10 10 10] [-14 -10 10 11] [-14 -10 10 12] [-14 -10 10 13] [-14 -10 10 14] [-14 -10 10 15] [-14 -10 11 11] [-14 -10 11 12] [-14 -10 11 13] [-14 -10 11 14] [-14 -10 11 15] [-14 -10 12 12] [-14 -10 12 13] [-14 -10 12 14] [-14 -10 12 15] [-14 -10 13 13] [-14 -10 13 14] [-14 -10 13 15] [-14 -10 14 14] [-14 -10 14 15] [-14 -10 15 15] [-14 -9 -9 -9] [-14 -9 -9 -8] [-14 -9 -9 -7] [-14 -9 -9 -6] [-14 -9 -9 -5] [-14 -9 -9 -4] [-14 -9 -9 -3] [-14 -9 -9 -2] [-14 -9 -9 -1] [-14 -9 -9 0] [-14 -9 -9 1] [-14 -9 -9 2] [-14 -9 -9 3] [-14 -9 -9 4] [-14 -9 -9 5] [-14 -9 -9 6] [-14 -9 -9 7] [-14 -9 -9 8] [-14 -9 -9 9] [-14 -9 -9 10] [-14 -9 -9 11] [-14 -9 -9 12] [-14 -9 -9 13] [-14 -9 -9 14] [-14 -9 -9 15] [-14 -9 -8 -8] [-14 -9 -8 -7] [-14 -9 -8 -6] [-14 -9 -8 -5] [-14 -9 -8 -4] [-14 -9 -8 -3] [-14 -9 -8 -2] [-14 -9 -8 -1] [-14 -9 -8 0] [-14 -9 -8 1] [-14 -9 -8 2] [-14 -9 -8 3] [-14 -9 -8 4] [-14 -9 -8 5] [-14 -9 -8 6] [-14 -9 -8 7] [-14 -9 -8 8] [-14 -9 -8 9] [-14 -9 -8 10] [-14 -9 -8 11] [-14 -9 -8 12] [-14 -9 -8 13] [-14 -9 -8 14] [-14 -9 -8 15] [-14 -9 -7 -7] [-14 -9 -7 -6] [-14 -9 -7 -5] [-14 -9 -7 -4] [-14 -9 -7 -3] [-14 -9 -7 -2] [-14 -9 -7 -1] [-14 -9 -7 0] [-14 -9 -7 1] [-14 -9 -7 2] [-14 -9 -7 3] [-14 -9 -7 4] [-14 -9 -7 5] [-14 -9 -7 6] [-14 -9 -7 7] [-14 -9 -7 8] [-14 -9 -7 9] [-14 -9 -7 10] [-14 -9 -7 11] [-14 -9 -7 12] [-14 -9 -7 13] [-14 -9 -7 14] [-14 -9 -7 15] [-14 -9 -6 -6] [-14 -9 -6 -5] [-14 -9 -6 -4] [-14 -9 -6 -3] [-14 -9 -6 -2] [-14 -9 -6 -1] [-14 -9 -6 0] [-14 -9 -6 1] [-14 -9 -6 2] [-14 -9 -6 3] [-14 -9 -6 4] [-14 -9 -6 5] [-14 -9 -6 6] [-14 -9 -6 7] [-14 -9 -6 8] [-14 -9 -6 9] [-14 -9 -6 10] [-14 -9 -6 11] [-14 -9 -6 12] [-14 -9 -6 13] [-14 -9 -6 14] [-14 -9 -6 15] [-14 -9 -5 -5] [-14 -9 -5 -4] [-14 -9 -5 -3] [-14 -9 -5 -2] [-14 -9 -5 -1] [-14 -9 -5 0] [-14 -9 -5 1] [-14 -9 -5 2] [-14 -9 -5 3] [-14 -9 -5 4] [-14 -9 -5 5] [-14 -9 -5 6] [-14 -9 -5 7] [-14 -9 -5 8] [-14 -9 -5 9] [-14 -9 -5 10] [-14 -9 -5 11] [-14 -9 -5 12] [-14 -9 -5 13] [-14 -9 -5 14] [-14 -9 -5 15] [-14 -9 -4 -4] [-14 -9 -4 -3] [-14 -9 -4 -2] [-14 -9 -4 -1] [-14 -9 -4 0] [-14 -9 -4 1] [-14 -9 -4 2] [-14 -9 -4 3] [-14 -9 -4 4] [-14 -9 -4 5] [-14 -9 -4 6] [-14 -9 -4 7] [-14 -9 -4 8] [-14 -9 -4 9] [-14 -9 -4 10] [-14 -9 -4 11] [-14 -9 -4 12] [-14 -9 -4 13] [-14 -9 -4 14] [-14 -9 -4 15] [-14 -9 -3 -3] [-14 -9 -3 -2] [-14 -9 -3 -1] [-14 -9 -3 0] [-14 -9 -3 1] [-14 -9 -3 2] [-14 -9 -3 3] [-14 -9 -3 4] [-14 -9 -3 5] [-14 -9 -3 6] [-14 -9 -3 7] [-14 -9 -3 8] [-14 -9 -3 9] [-14 -9 -3 10] [-14 -9 -3 11] [-14 -9 -3 12] [-14 -9 -3 13] [-14 -9 -3 14] [-14 -9 -3 15] [-14 -9 -2 -2] [-14 -9 -2 -1] [-14 -9 -2 0] [-14 -9 -2 1] [-14 -9 -2 2] [-14 -9 -2 3] [-14 -9 -2 4] [-14 -9 -2 5] [-14 -9 -2 6] [-14 -9 -2 7] [-14 -9 -2 8] [-14 -9 -2 9] [-14 -9 -2 10] [-14 -9 -2 11] [-14 -9 -2 12] [-14 -9 -2 13] [-14 -9 -2 14] [-14 -9 -2 15] [-14 -9 -1 -1] [-14 -9 -1 0] [-14 -9 -1 1] [-14 -9 -1 2] [-14 -9 -1 3] [-14 -9 -1 4] [-14 -9 -1 5] [-14 -9 -1 6] [-14 -9 -1 7] [-14 -9 -1 8] [-14 -9 -1 9] [-14 -9 -1 10] [-14 -9 -1 11] [-14 -9 -1 12] [-14 -9 -1 13] [-14 -9 -1 14] [-14 -9 -1 15] [-14 -9 0 0] [-14 -9 0 1] [-14 -9 0 2] [-14 -9 0 3] [-14 -9 0 4] [-14 -9 0 5] [-14 -9 0 6] [-14 -9 0 7] [-14 -9 0 8] [-14 -9 0 9] [-14 -9 0 10] [-14 -9 0 11] [-14 -9 0 12] [-14 -9 0 13] [-14 -9 0 14] [-14 -9 0 15] [-14 -9 1 1] [-14 -9 1 2] [-14 -9 1 3] [-14 -9 1 4] [-14 -9 1 5] [-14 -9 1 6] [-14 -9 1 7] [-14 -9 1 8] [-14 -9 1 9] [-14 -9 1 10] [-14 -9 1 11] [-14 -9 1 12] [-14 -9 1 13] [-14 -9 1 14] [-14 -9 1 15] [-14 -9 2 2] [-14 -9 2 3] [-14 -9 2 4] [-14 -9 2 5] [-14 -9 2 6] [-14 -9 2 7] [-14 -9 2 8] [-14 -9 2 9] [-14 -9 2 10] [-14 -9 2 11] [-14 -9 2 12] [-14 -9 2 13] [-14 -9 2 14] [-14 -9 2 15] [-14 -9 3 3] [-14 -9 3 4] [-14 -9 3 5] [-14 -9 3 6] [-14 -9 3 7] [-14 -9 3 8] [-14 -9 3 9] [-14 -9 3 10] [-14 -9 3 11] [-14 -9 3 12] [-14 -9 3 13] [-14 -9 3 14] [-14 -9 3 15] [-14 -9 4 4] [-14 -9 4 5] [-14 -9 4 6] [-14 -9 4 7] [-14 -9 4 8] [-14 -9 4 9] [-14 -9 4 10] [-14 -9 4 11] [-14 -9 4 12] [-14 -9 4 13] [-14 -9 4 14] [-14 -9 4 15] [-14 -9 5 5] [-14 -9 5 6] [-14 -9 5 7] [-14 -9 5 8] [-14 -9 5 9] [-14 -9 5 10] [-14 -9 5 11] [-14 -9 5 12] [-14 -9 5 13] [-14 -9 5 14] [-14 -9 5 15] [-14 -9 6 6] [-14 -9 6 7] [-14 -9 6 8] [-14 -9 6 9] [-14 -9 6 10] [-14 -9 6 11] [-14 -9 6 12] [-14 -9 6 13] [-14 -9 6 14] [-14 -9 6 15] [-14 -9 7 7] [-14 -9 7 8] [-14 -9 7 9] [-14 -9 7 10] [-14 -9 7 11] [-14 -9 7 12] [-14 -9 7 13] [-14 -9 7 14] [-14 -9 7 15] [-14 -9 8 8] [-14 -9 8 9] [-14 -9 8 10] [-14 -9 8 11] [-14 -9 8 12] [-14 -9 8 13] [-14 -9 8 14] [-14 -9 8 15] [-14 -9 9 9] [-14 -9 9 10] [-14 -9 9 11] [-14 -9 9 12] [-14 -9 9 13] [-14 -9 9 14] [-14 -9 9 15] [-14 -9 10 10] [-14 -9 10 11] [-14 -9 10 12] [-14 -9 10 13] [-14 -9 10 14] [-14 -9 10 15] [-14 -9 11 11] [-14 -9 11 12] [-14 -9 11 13] [-14 -9 11 14] [-14 -9 11 15] [-14 -9 12 12] [-14 -9 12 13] [-14 -9 12 14] [-14 -9 12 15] [-14 -9 13 13] [-14 -9 13 14] [-14 -9 13 15] [-14 -9 14 14] [-14 -9 14 15] [-14 -9 15 15] [-14 -8 -8 -8] [-14 -8 -8 -7] [-14 -8 -8 -6] [-14 -8 -8 -5] [-14 -8 -8 -4] [-14 -8 -8 -3] [-14 -8 -8 -2] [-14 -8 -8 -1] [-14 -8 -8 0] [-14 -8 -8 1] [-14 -8 -8 2] [-14 -8 -8 3] [-14 -8 -8 4] [-14 -8 -8 5] [-14 -8 -8 6] [-14 -8 -8 7] [-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 -7 -7] [-14 -8 -7 -6] [-14 -8 -7 -5] [-14 -8 -7 -4] [-14 -8 -7 -3] [-14 -8 -7 -2] [-14 -8 -7 -1] [-14 -8 -7 0] [-14 -8 -7 1] [-14 -8 -7 2] [-14 -8 -7 3] [-14 -8 -7 4] [-14 -8 -7 5] [-14 -8 -7 6] [-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 -6 -6] [-14 -8 -6 -5] [-14 -8 -6 -4] [-14 -8 -6 -3] [-14 -8 -6 -2] [-14 -8 -6 -1] [-14 -8 -6 0] [-14 -8 -6 1] [-14 -8 -6 2] [-14 -8 -6 3] [-14 -8 -6 4] [-14 -8 -6 5] [-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 -5 -5] [-14 -8 -5 -4] [-14 -8 -5 -3] [-14 -8 -5 -2] [-14 -8 -5 -1] [-14 -8 -5 0] [-14 -8 -5 1] [-14 -8 -5 2] [-14 -8 -5 3] [-14 -8 -5 4] [-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 -4 -4] [-14 -8 -4 -3] [-14 -8 -4 -2] [-14 -8 -4 -1] [-14 -8 -4 0] [-14 -8 -4 1] [-14 -8 -4 2] [-14 -8 -4 3] [-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 -3 -3] [-14 -8 -3 -2] [-14 -8 -3 -1] [-14 -8 -3 0] [-14 -8 -3 1] [-14 -8 -3 2] [-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 -2 -2] [-14 -8 -2 -1] [-14 -8 -2 0] [-14 -8 -2 1] [-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 -1 -1] [-14 -8 -1 0] [-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 0 0] [-14 -8 0 1] [-14 -8 0 2] [-14 -8 0 3] [-14 -8 0 4] [-14 -8 0 5] [-14 -8 0 6] [-14 -8 0 7] [-14 -8 0 8] [-14 -8 0 9] [-14 -8 0 10] [-14 -8 0 11] [-14 -8 0 12] [-14 -8 0 13] [-14 -8 0 14] [-14 -8 0 15] [-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

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More Answers (2)

Walter Roberson
Walter Roberson on 28 Oct 2024
Edited: Walter Roberson on 28 Oct 2024
  3 Comments
Image Analyst
Image Analyst on 28 Oct 2024
The link just points to this page.
Walter Roberson
Walter Roberson on 28 Oct 2024
Ooops, you are right; I have corrected the URL.

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Torsten
Torsten on 28 Oct 2024
Edited: Torsten on 28 Oct 2024
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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