Matlab - 将矩阵与 3d 矩阵的每个矩阵相乘

Question

我有两个似乎密切相关的 matlab 问题。

1. 我想找到最有效的方法(无循环？)将 (A x A) 矩阵与 3d 矩阵 (A x A x N) 的每个矩阵相乘。另外，我想追踪每一种产品的踪迹。 http://en.wikipedia.org/wiki/Matrix_multiplication#Frobenius_product

   这是弗罗贝尼乌斯内积。在下面的蹩脚代码中，我使用了更有效的辅助定义。

2. 我想将向量 (N x 1) 的每个元素与其“对应”的 3d 矩阵 (A x A x N) 矩阵相乘。

   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

我假设你的意思是逐元素乘法:

1. 使用bsxfun :

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

2. 将 bsxfun 与 permute 一起使用对齐尺寸:

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