Hey, Im trying to run this code but the run time is too long. can anyone help me out here plz

This function that I wrote is supposed to take the DCT of the input image. The run time is too much which I expect to be because of number of irritations. The picture that im using has 700*500 pixels. As u can see theres 4 nested for loops which makes the number of irritations to be 700*500*700*500 (almost 10^11). its that realy too many irritation for a computer or is there something wrong with the code? if yes what could it be?

function out_image = dct2(in_image)

s = size(in_image);

in_image = double(in_image);

out_image = zeros(s);

for i = 1:s(1)

for j = 1:s(2)

x = 0;

ci = 1;

cj = 1;

if i == 1

ci = sqrt(2)/2;

end

if j == 1

cj = sqrt(2)/2;

end

for m = 1:s(1)

for n = 1:s(2)

a = cos((((2*(m-1))+1)*(i-1)*pi)/(2*s(1)));

b = cos((((2*(n-1))+1)*(j-1)*pi)/(2*s(2)));

x = x + (a * b * in_image(m,n));

end

end

out_image(i,j) = (2/sqrt(s(1)*s(2)))* ci * cj * x;

end

end

end

Answer 1

[Mohammad Sami]

As a starting point you can vectorize your inner for loops

m = repelem(1:s(1),1,s(2));
n = repmat(1:s(2),1,s(1));
a = cos((((2.*(m-1))+1).*(i-1).*pi)/(2*s(1)));
b = cos((((2.*(n-1))+1).*(j-1).*pi)/(2*s(2)));
ind = sub2ind(size(in_image),m,n);
x = sum(a.*.b.* in_image(ind));