Matlab - 將矩陣乘以3D矩陣的每個矩陣

Question

我有兩個似乎密切相關的matlab問題。

1. 我要找到最有效的方式（無循環？）乘以一個（A×A）個矩陣與3D矩陣的每一個矩陣（A X A X N）。另外，我想跟蹤這些產品中的每一種。 http://en.wikipedia.org/wiki/Matrix_multiplication#Frobenius_product

   這是frobenius的產品。在下面的蹩腳代碼中，我使用了更高效的二級定義。

2. 我想將一個向量（N x 1）的每個元素乘以一個3d矩陣（A x A x N）的「對應」矩陣。

   function Y_returned = problem_1(X_matrix, weight_matrix) 
   
   % X_matrix is the randn(50, 50, 2000) matrix 
   % weight_matrix is the randn(50, 50) matrix 
   
   [~, ~, number_of_matries] = size(X_matrix); 
   Y_returned = zeros(number_of_matries, 1); 
   for i = 1:number_of_matries 
   %  Y_returned(i) = trace(X_matrix(:,:,i) * weight_matrix'); 
       temp1 = X_matrix(:,:,i)'; 
       temp2 = weight_matrix'; 
       Y_returned(i) = temp1(:)' * temp2(:); 
   end 
   end 
   
   
   function output = problem_2(vector, matrix) 
   
   % matrix is the randn(50, 50, 2000) matrix 
   % vector is the randn(2000, 1) vector 
   
   [n1, n2, number_of_matries] = size(matrix); 
   output = zeros(n1, n2, number_of_matries); 
   for i = 1:number_of_matries 
       output(:, :, i) = vector(i) .* matrix(:, :, i); 
   end 
   output = sum(output, 3); 
   
   end 
   

Answer 1

我假定你的意思逐元素乘法：

1. 使用bsxfun：

   A = 10; 
   N = 4; 
   mat1 = randn(A,A); 
   mat2 = randn(A,A,N); 
   result = bsxfun(@times, mat1, mat2); 
   

2. 使用bsxfun與permute對齊尺寸：

   A = 10; 
   N = 4; 
   vec1 = rand(N,1); 
   mat2 = randn(A,A,N); 
   result = bsxfun(@times, permute(vec1,[2 3 1]), mat2);