在有條件的巨大矩陣上計數平均值

Question

以下MATLAB代碼在10^5方陣A上永遠運行。但是，它在10^3方陣上運行幾秒鐘。有什麼方法可以加速嗎？

function [meanNV]=calcMeanNV_k(A,V,d) 
%A: input matrix (n x n) 
%V: eigenvectors of k-th largest eigenvalues (n x 1) 
%d: degrees of each node (n x 1) 
%meanNV: mean of neighbors vectors (n x 1) 
m=size(A,2); 
meanNV=zeros(113336); 
for i=1:m 
    sumNode = 0; 
    for j=1:m 
     if A(i,j)==1 
      sumNode=sumNode+V(j); 
     end 
    end 
    [meanNV(i)]=sumNode/d(i); 
end 

Answer 1

簡單地說，對於每一行中A，你確定是非零和使用這些指標來總結在相應的位置在V並通過d相應的條目劃分的位置。

首先使用find確定非零行和列的位置，然後組的所有使用accumarray和功能他們共同排列位置的應用上accumarray只會所有指數總結了一旦索引V。

像這樣的東西可以工作：

function [meanNV]=calcMeanNV_k1(A,V,d) 
%A: input matrix (n x n) 
%V: eigenvectors of k-th largest eigenvalues (n x 1) 
%d: degrees of each node (n x 1) 
%meanNV: mean of neighbors vectors (n x 1) 

m=size(A,2); 
[row,col] = find(A); % Find non-zero entries in A 
meanNV = accumarray(row, col, [m 1], @(x) sum(V(x))) ./ d; % Compute desired result 

end 

Answer 2

這是什麼在起作用：

function [meanNV]=calcMeanNV_k1(A,V,d) 
%A: input matrix (n x n) 
%V: eigenvectors of k-th largest eigenvalues (n x 1) 
%d: degrees of each node (n x 1) 
%meanNV: mean of neighbors vectors (n x 1) 
tic 
m=size(A,2); 
meanNV=zeros(m,1); 
idx = A == 1; 
for k = 1:m 
    meanNV = sum(V(idx(k,:))); 
end 
meanNV = meanNV./d; 
toc