Is it possible to speed up this code?

Probably the right question should be, how can I speed up this code. All help is much appreciated

N = 100
 x_1 = linspace(0,1,N)
 x_2 = linspace(0,1,N)
 x_3 = linspace(0,1,N)
 x_4 = linspace(0,1,N)
 x_5 = linspace(0,1,N)
 x_6 = linspace(0,1,N)
x_10=.5;x_20=.5;x_30=.5;x_40=.5;x_50=.5;x_60=.5;
objective = zeros(N,N,N,N,N,N);
distance = zeros(N,N,N,N,N,N);
for i = 1:N
for j = 1:N
for k = 1:N
 for ii = 1:N
  for jj = 1:N
   for kk = 1:N
      theta = [x_1(i) x_2(j) x_3(k) x_4(ii) x_5(jj) x_6(kk)];
      objective = relevant_func(theta);
      distance = ( (x_1(i) - x_10)^2 + (x_2(j) - x_20)^2 + (x_3(k) - x_30)^2 + (x_4(ii) - x_40)^2 + (x_5(jj) - x_50)^2 + (x_6(kk) - x_60)^2  )^(1/2);
   end
  end
 end
end
end
end

Not real numbers, just to show the code.

[Doug Hull]

Why are you making a six dimensional matrix with 1,000,000,000,000 elements? Is this really a good idea?

[Jan]

It seems like this code is too much simplified. None of the calculations is stored anywhere, so the loops can be omitted.

Optimizing a simplified code is not meaningful. Better let the profile or some TIC/TOCs identify the bottleneck. If e.g. relevant_func() consumes 96% of the computing time, changing ^(1/2) to sqrt() cannot be a significant improvement.

Answer 1

[Walter Roberson]

Equivalent but faster code:

theta = [1 1 1 1 1 1];
objective = relevant_func(theta);
distance = sqrt( sum((theta - [x_10 x_20 x_30 x_40 x_50 x_60]).^2) );

With no loops.