MATLAB: How to vectorize this code

for loopvectorize

Could you let me know how to vectorize the below for-loop ?
pigrid   = zeros(knum,epnum,sepnum,znum,sznum);
    for ki = 1:knum
        for epi = 1:epnum
           for sepi = 1:sepnum
               for zi = 1:znum
                   for szi = 1:sznum
           pigrid(ki,epi,sepi,zi,szi) = epgrid(epi,sepi)*zgrid(zi,szi)*kgrid(ki)^alpha-f;  
                    end
                end
            end
        end
    end

Best Answer

Creating a fully vectorized version of these nested loops seems either not possible or not practical. Here's a summary of some improvements listed in the comment section under the question.
This simplification still relies on 3 of your 5 loops.
for ki = 1:knum
    for epi = 1:epnum
        for sepi = 1:sepnum
            pigrid(ki,epi,sepi,:,:) = epgrid(epi,sepi)*zgrid(1:znum,1:sznum)*kgrid(ki)^alpha-f;
        end
    end
end
if zgrid(1:znum,1:sznum) == zgrid, then a further simplification would be
for ki = 1:knum
    for epi = 1:epnum
        for sepi = 1:sepnum
            pigrid(ki,epi,sepi,:,:) = epgrid(epi,sepi)*zgrid*kgrid(ki)^alpha-f;
        end
    end
end
@OCDER also recommended moving kgrid(ki)^alpha outside of the loop which would eliminate ~10000 exponential calculations.
Assuming kgrid(1:knum)==kgrid,
kgalpha = kgrid.^alpha;              % or kgrid(1:knum).^alpha
for ki = 1:knum
    for epi = 1:epnum
        for sepi = 1:sepnum
            pigrid(ki,epi,sepi,:,:) = epgrid(epi,sepi)*zgrid*kgalpha(ki)-f;
        end
    end
end
Lastly, you could remove the " -f" to after the loop like this:
kgalpha = kgrid.^alpha;         %or kgrid(1:knum).^alpha
for ki = 1:knum
    for epi = 1:epnum
        for sepi = 1:sepnum
            pigrid(ki,epi,sepi,:,:) = epgrid(epi,sepi)*zgrid*kgalpha(ki);
        end
    end
end
pigrid = pigrid - f;
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