「克朗」產品的多維版本？

Question

現在我有N維矩陣A由p和用q N維的其它矩陣B。我想有是一個矩陣，說的C尺寸N，通過PQ這樣

C(i,:) = kron(A(i,:), B(i,:)); 

如果N大，環比N行可能需要相當長的時間。所以目前我增強甲乙適當（組合repmat，置換和重塑的使用）由PQ轉N維的每個矩陣，然後通過一些配製Ç像

C = A_aug .* B_aug; 

不限更好的主意？

Answer 1

Checkout的bsxfun + permute + reshape魔法 -

out = reshape(bsxfun(@times,permute(A,[1 3 2]),B),size(A,1),[]) 

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標杆&驗證

標杆碼 -

%// Setup inputs 
N = 200; 
p = 190; 
q = 180; 
A = rand(N,p); 
B = rand(N,q); 

disp('--------------------------------------- Without magic') 
tic 
C = zeros(size(A,1),size(A,2)*size(B,2)); 
for i = 1:size(A,1) 
    C(i,:) = kron(A(i,:), B(i,:)); 
end 
toc 

disp('--------------------------------------- With some magic') 
tic 
out = reshape(bsxfun(@times,permute(A,[1 3 2]),B),size(A,1),[]); 
toc 

error_val = max(abs(C(:)-out(:))) 

輸出 -

--------------------------------------- Without magic 
Elapsed time is 0.524396 seconds. 
--------------------------------------- With some magic 
Elapsed time is 0.055082 seconds. 
error_val = 
    0