Vectorize loop to increase efficiency - matlab

Question

I have a 3 for loops and I would like if possible to vectorize the two inner loops.
for t=1:size(datesdaily1)
for i=1:size(secids,1)
sum=0;
if inc(t,i)==1
for j=1:size(secids,1)
if inc(t,j)==1
sum=sum+weig1(t,j)*sqrt(Rates(t,j))*rhoneutral(i,j);
end
end
b(t,i)=sqrt(Rates(t,i))*sum/MRates(t,1);
end
end
end
Any idea on how to accomplish that? Here 'weig', 'inc' and 'Rates' are (size(datesdaily1) by size(secids,1)) matrixes and 'rhoneutral' is a (size(secids,1) by size(secids,1)) matrix.
I tried but I was not able to figure out how to do it ...
Actual full code:
for t=1:size(datesdaily1)
rho=NaN(size(secids,1),size(secids,1));
aux=datesdaily1(t,1);
windowlenght=252;
index=find(datesdaily==aux);
auxret=dailyret(index-windowlenght+1:index,:);
numerator=0;
denominator=0;
auxret(:,any(isnan(auxret))) = NaN;
rho = corr(auxret, 'rows','pairwise');
rho1 = 1 - rho;
w = weig1(t,:) .* sqrt(Rates(t,:));
x = w.' * w;
y = x .* rho;
z = x .* rho1;
numerator = numerator + nansum(nansum(y));
denominator = denominator + nansum(nansum(z));;
if not(denominator==0)
alpha(t,1)=-(MRates(t,1)-numerator)/denominator;
%Stocks included
inc(t,:)=not(isnan(weig1(t,:).*diag(rho)'.*Rates(t,:)));
rhoneutral=rho-alpha(t,1).*(1-rho);
for i=1:size(secids,1)
sum=0;
if inc(t,i)==1
for j=1:size(secids,1)
if inc(t,j)==1
sum=sum+weig1(t,j)*sqrt(Rates(t,j))*rhoneutral(i,j);
end
end
bet(t,i)=sqrt(Rates(t,i))*sum/MRates(t,1);
end
end
check(t,1)=nansum(weig1(t,:).*bet(t,:));
end
end

Answer 1

One vectorized approach using fast matrix multiplication in MATLAB -
%// Mask of valid calculations
mask = inc==1
%// Store square root of Rates which seem to be used rather than Rates itself
sqRates = sqrt(Rates)
%// Use mask to set invalid positions in weig1 and sqRates to zeros
weig1masked = weig1.*mask
sqRates = sqRates.*mask
%// Perform the sum calculations using matrix multiplication.
%// This is where the magic happens!!
sum_vals = (weig1masked.*sqRates)*rhoneutral' %//'
%// Perform the outermost loop calculations for the final output
b_vect = bsxfun(#rdivide,sum_vals.*sqRates,MRates)
Benchmarking
Here's a benchmark test specially dedicated to #Dmitry Grigoryev for the doubts put on vectorization for performance -
M = 200;
N = 200;
weig1 = rand(M,N);
inc = rand(M,N)>0.5;
Rates = rand(M,N);
rhoneutral = rand(N,N);
MRates = rand(M,1);
disp('--------------------------- With Original Approach')
tic
%// Code from the original approach
toc
disp('--------------------------- With DmitryGrigoryev Approach')
tic
%// Code from the DmitryGrigoryev's solution
toc
disp('--------------------------- With Much-Hated Vectorized Approach')
tic
%// Proposed matrix-multiplication approach in this solution
toc
Runtimes -
--------------------------- With Original Approach
Elapsed time is 0.104084 seconds.
--------------------------- With DmitryGrigoryev Approach
Elapsed time is 3.562170 seconds.
--------------------------- With Much-Hated Vectorized Approach
Elapsed time is 0.002058 seconds.
Posting runtimes for bigger datasizes might just be too embarrasing for loopy approches, way to go vectorization!!