how to vectorize these "for loop"?

clear all;
close all; 
clc;
i=1;
for k=1:0.5:10;
    for a=1:0.5:10;
        for b= 1:0.5:10;
            num(i,:)=[ k k*a];
            den(i,:)=[1 b 0];
            i=i+1; 
        end
    end
end

[EDITED, Jan, Code formatted]

Answer 1

[Andrei Bobrov]

My "ruble".

[b,a,k] = ndgrid(1:.5:10);
n = numel(k);
num1 = [k(:),k(:).*a(:)];
den1 = [ones(n,1), b(:), zeros(n,1)];

[Jan]

+1: This looks nice and clean. It is just 0.008 sec slower (for 100 iterations!) than the fastest solution I've found, but expanding, debugging and maintaining this nicer code will save at least minutes.

30% faster with explicite pre-allocation:

[b,a,k]  = ndgrid(1:.5:10);
n        = numel(k);
num      = zeros(n, 2);
num(:,1) = k(:);
num(:,2) = k(:) .* a(:);
den      = zeros(n, 3);
den(:,1) = 1;
den(:,2) = b(:);

But again: less nice and more prone to typos.

[nelson]

thanks....

Answer 2

[Jan]

The loops are not the main problem here, but the missing pre-allocation.

n   = 19^3;
num = zeros(n, 2);   % <-- Inserted
den = zeros(n, 3);   % <-- Inserted
i = 1;
for k = 1:0.5:10
  for a = 1:0.5:10
      for b = 1:0.5:10
          num(i, :) = [k, k*a];
          den(i, :) = [1, b, 0];
          i         = i + 1; 
      end
  end
end

Now take a look in the data: all den(:, 1) are 1, all den(:, 3) are 0, and the 2nd component is a repeated 1:0.5:10. This can be abbreviated:

v   = 1:0.5:10;
n   = length(v);
den = zeros(n^3, 3);
den(:, 1) = 1;
den(:, 2) = repmat(v, 1, n^2);

For num:

num       = zeros(n^3, 2);
num(:, 1) = repelem(v.', n^2, 1);    % REPELEM in >= R2015a
tmp       = repelem(v.', n, 1) * v;  % Auto-Expand in >= R2016b
num(:, 2) = tmp(:);

For older Matlab versions:

num       = zeros(n^3, 2);
num(:, 1) = reshape(repmat(v, n^2, 1), [], 1);
tmp1      = repmat(v, n, 1);
tmp2      = bsxfun(@times, tmp1(:), v);
num(:, 2) = tmp2(:);

Some timings (R2016b/64, Win7, Core2Duo):

tic; for k = 1:100, [d,n] = Untitled; end; toc
Elapsed time is 12.222231 seconds.    % Original
Elapsed time is  0.779765 seconds.    % Original with pre-allocation !!!
Elapsed time is  0.012142 seconds.    % Vectorized >= 2016b
Elapsed time is  0.013797 seconds.    % Vectorized <= 2015a
Elapsed time is  0.020055 seconds.    % Andrei's solution

Pre-allocation yields a speed gain of factor 16, the vectorization a factor of 1000. Nice!

[nelson]

numerator is not match..

[Andrei Bobrov]

+1 Good work.

[Jan]

@nelson: Please try it again. I've fixed some typos since the first posting. I get:

v = 1:0.5:10;
n = length(v);

i=1;
for k=v, for a=v, for b=v
   num(i,:)=[ k k*a];
   i=i+1; 
end, end, end

num2       = zeros(n^3, 2);
num2(:, 1) = repelem(v.', n^2, 1);    % >= R2015a
tmp        = repelem(v.', n, 1) * v;  % >= R2016b
num2(:, 2) = tmp(:);

isequal(num, num2)  %   1: okay