Matlab - 将矩阵与 3d 矩阵的每个矩阵相乘 [英] Matlab - Multiplying a matrix with every matrix of a 3d matrix

问题描述

我有两个似乎密切相关的 matlab 问题.

I have two matlab questions that seem closely related.

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，我想对这些产品中的每一个进行跟踪.http://en.wikipedia.org/wiki/Matrix_multiplication#Frobenius_product

这是内部的frobenius产品.在我下面的蹩脚代码中，我使用的是更有效的辅助定义.

This is the inner frobenius product. On the crappy code I have below I'm using its secondary definition which is more efficient.

我想将向量 (N x 1) 的每个元素与其 3d 矩阵 (A x A x N) 的对应"矩阵相乘.

I want to multiply each element of a vector (N x 1) with its "corresponding" matrix of a 3d matrix (A x A x N).

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

推荐答案

我假设你的意思是元素乘法:

I assume you mean element-wise multiplication:

1. 使用bsxfun:

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

使用 bsxfun 和 permute 对齐尺寸:

Use bsxfun with permute to align dimensions:

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

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