向量化循环以提高效率

Question

我有一个 3 for 循环，如果可能的话，我想对两个内部循环进行向量化。

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

知道如何实现吗？这里 'weig'、'inc' 和 'Rates' 是 (size(datesdaily1) by size(secids,1)) 矩阵，'rhoneutral' 是 (size(secids,1) by size (secids,1)) 矩阵。

我试过了，但我不知道该怎么做...

实际完整代码：

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

是什么让您认为矢量化会提高性能？假设您的变量都是双精度变量，您将需要一台超级计算机对它们进行矢量运算，以便比标量运算更高效。

虽然循环外计算会有用：

precomputed=zeroes(size(datesdaily,1),size(secids,1))
for t=1:size(datesdaily,1)
    for j=1:size(secids,1)
        if inc(t,j)==1 
            precomputed(t,j)=weig1(t,j)*sqrt(Rates(t,j));         
        end
    end
end


for t=1:size(datesdaily,1)
    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+precomputed(t,j)*rhoneutral(i,j);         
                end
            end
            b(t,i)=sqrt(Rates(t,i))*sum/MRates(t,1);
        end
    end    
end

Answer 2

一个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)

基准测试

这里有一个专门针对的基准测试，以解决对vectorization性能的疑虑-

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

运行时间 -

--------------------------- 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.

为更大的数据量发布运行时对于循环的方法来说可能太尴尬了，走的路vectorization!!

向量化循环以提高效率

Vectorize loop to increase efficiency

matlab

vectorization

基准测试