how to vectorize these "for loop" ?

clc;
clear all;
close all;
i=1;
for k=1:1:10;
    for a=1:1:10;
        for b= 1:1:10;
            for c=1:1:10;
                nump(i,:)=[k a*k];
                denmp(i,:)=[1 b+c b*c];
                 i=i+1;
            end
        end
    end
end

[Christos Saragiotis]

If the only reason you want to vectorize is speed and k, b have the same range (i.e. from 1 to 10) and likewise a, c have the same range you can take advantage of this and make this quadruple for-loop a double one.

The following implementation is about 40 times faster than the posted one on my machine:

N  = 10; % nb, nk
M  = 10; % na, nc
NM = N*M;

Num = zeros(NM,2);
Den = zeros(NM,3);
k = 1;
for n = 1:N;
    for m = 1:M;
        Num(k,:) = [n n*m];
        Den(k,:) = [1 n+m n*m];
        k = k+1;
    end
end

Denmp = repmat(Den,NM,1);

Num   = reshape(Num,  1,NM,2);
Nump  = repmat (Num,  NM,1,1);
Nump  = reshape(Nump, NM*NM,2);

Answer 1

[fbaillon]

If you want to vectorize your problem, you can write something like this:

    n=10;
    m=n*n;
  %
    A=repmat(1:n,n*m,1);
    B=repmat(1:n,m,n) ;
    C=repmat((1:n),n*m,1);
    nump=[A(:)  B(:).*C(:)];
  %
    B=repmat(1:n,n,1)+repmat((1:n)',1,n);
    C=repmat(1:n,n,1).*repmat((1:n)',1,n);
    denmp=[ones(m*m,1) repmat(B(:),m,1)  repmat(C(:),m,1)];

Maybe we can make it even faster...

Fabien Baillon.

[Jan]

Since Matlab 2016b you can replace e.g.

C = repmat(1:n,n,1).*repmat((1:n)',1,n);

by

C = (1:n) .* (1:n)';

In older versions:

C = bsxfun(@times, 1:n, (1:n).');

Answer 2

[Andrei Bobrov]

[c,b,a,k] = ndgrid(1:10);
nump = [k(:), a(:).*k(:)];
denmp = [ones(numel(k),1), b(:)+c(:), b(:).*c(:)];

[KL]

Great one, voted! I need to get myself comfortable with ndgrid

Answer 3

[KL]

c = 1:10;
c1 = reshape(repmat(c,1000,1),[10000,1]);
c2 = reshape(repmat(c,100,10),[10000,1]);
nump1 = [c1, c1.*c2];
dc2 = repmat(cell2mat(arrayfun(@(a,b) a:b, 2:11,11:20, 'UniformOutput', false)),1,100)';
dc3 = repmat(cell2mat(arrayfun(@(a,b,s) a:s:b, c,10:10:100,c, 'UniformOutput', false)),1,100)';
denmp1 = [ones(10000,1), dc2, dc3];

isequal(nump,nump1)
isequal(denmp,denmp1)