D for loops concatenated

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Luca  Fenzi
Luca Fenzi on 17 Oct 2015
Answered: Luca Fenzi on 20 Oct 2015
I would like to generalize the following codes for dimension D=2:
D=2;
dim=factorial(P-1+D)/(factorial(P-1)*factorial(D));
indexes=zeros(dim,D);
s=0;
for i=1:P
for j=1:i
s=s+1;
indexes(s,:)=[i-j,j-1];
end
end
dimension D=3:
D=3;
dim=factorial(P-1+D)/(factorial(P-1)*factorial(D));
indexes=zeros(dim,D);
s=1;
for i=1:P
for j=1:i
for k=1:j
indexes(s,:)=[i-j,j-k,k-1];
s=s+1;
end
end
end
P can be an arbitrary integer (e.g. P=4).
In other words I would like to create D for loops in such a way that the first loop goes from 1 to P (i=1:P) the second loop from 1 to the previous one (j=1:i) the third one from 1 to the second one (h=1:j) etc.
Thank you in advance.

Accepted Answer

Jan
Jan on 17 Oct 2015
D = 3;
dim = factorial(P-1+D)/(factorial(P-1)*factorial(D));
indexes = zeros(dim,D);
v = ones(1, dim);
for s = 1:dim
indexes(s, 1:D-1) = diff(v);
indexes(s, D) = v(D) - 1;
% Update index vector:
found = false;
for k = D:-1:1
v(k) = v(k) + 1;
if k > 1
if v(k) <= v(k - 1)
break; % Exit for k loop
end
v(k) = 1;
end
end
end
Please test and adjust this to your needs. The idea gets clear: Use one loop and a vector of indices, which are incremented according to the rules in each iteration.

More Answers (1)

Luca  Fenzi
Luca Fenzi on 20 Oct 2015
Thank you very much for your answer I adjust it in the following way
P=5;
D =3;
dim = nchoosek(P-1+D,D);
indexes = zeros(dim,D);
v = ones(1,D);
for s = 1:dim
indexes(s, 1:D-1) = -diff(v);
indexes(s, D) = v(D) - 1;
% Update index vector:
for k = D:-1:1
v(k) = v(k) + 1;
if k > 1
if v(k) <= v(k - 1);
break; % Exit for k loop
end
v(k) = 1;
end
end
end
Here I add also an other code for general for-loops concatenated
N=P^D;
indexes=zeros(P,D);
row=zeros(1,D);
for s=1:N
indexes(s,:)=row;
%%Updating
%the alghorithm is counting how many indexes arrived to P-1 (Maximum
%degree)
h=0;
while (h<=D-2)&&(row(h+1)==P-1)
h=h+1;
end
if h>0
row(1:h)=zeros(1,h); %Put zero all the values that were P-1
row(h+1)=row(h+1)+1; % add one to the next index.
end
row(1)=mod(s,P);
end
(Please feel free to comment and improve my codes so I can learn something new =) )

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