One big speed improvement you can do is to move the scalar multiplication of Dz outside the loop, but if you don't use a loop, it doesn't really matter.
% Test data for function (i'm using bigger arrays)
Nx = 320;
Nz = 320;
u = zeros(Nx,Nz+1);
ntests = 100; % number of test iterations to average exec time
Dz = rand(Nx+1,Nz+1);
u_z = zeros(Nx,Nz+1);
u_z_2 = zeros(Nx,Nz+1);
g = zeros(Nz+1,1);
% Method 1 - Original Implementation with double for loop
tic
for N = 1:ntests
for j=1:Nx
for ell=0:Nz
g(ell+1) = u(j,ell+1);
end
u_z(j,:) = (2.0)*Dz*g;
end
end
toc/ntests
% Method 2 - Remove one for loop
tic
for N = 1:ntests
for j=1:Nx
g=u(j,:)';
u_z_2(j,:) = (2.0)*Dz*g;
end
end
toc/ntests
immse(u_z,u_z_2) % result is identical
% simplified
tic
for N = 1:ntests
uuu = (2*Dz*u.').';
end
toc/ntests
immse(u_z,uuu) % result is identical
When you're trying to find out how to make things fast, it might matter how you scale the test to emphasize the execution time. Increasing the number of iterations or the size of the inputs may reveal different things. It all depends on what you expect to do.
