CODEWITHSUNDEEP
matlabvectorization
phdstudent
phdstudent

Reputation: 1144

Vectorize loop to increase efficiency

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

Upvotes: 2

Views: 113

Answers (1)

Divakar
Divakar

Reputation: 221564

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!!

Upvotes: 3

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