向量化加权和Matlab

问题描述

我试图向量化某个加权总和，但不知道该怎么做.我在下面创建了一个简单的最小工作示例.我猜该解决方案涉及bsxfun或reshape和kronecker产品，但我仍然没有设法使其正常工作.

I was trying to vectorize a certain weighted sum but couldn't figure out how to do it. I have created a simple minimal working example below. I guess the solution involves either bsxfun or reshape and kronecker products but I still have not managed to get it working.

rng(1);
N = 200;
T1 = 5;
T2 = 7;

A = rand(N,T1,T2);
w1 = rand(T1,1);
w2 = rand(T2,1);

B = zeros(N,1);

for i = 1:N
for j1=1:T1
for j2=1:T2
    B(i) = B(i) + w1(j1) * w2(j2) * A(i,j1,j2);
end
end
end

A = B;

推荐答案

您可以使用bsxfun，reshape和permute的组合来完成此操作.

You could use a combination of bsxfun, reshape and permute to accomplish this.

我们首先使用permute将N尺寸移动到A的第3尺寸.然后，我们将w1和w2的转置相乘以创建权重网格.然后，我们可以使用bsxfun在此网格与A的每个切片"之间执行逐元素乘法(@times).然后，我们可以将3D结果整形为M x N，并在第一个维度上求和.

We first use permute to move the N dimension to the 3rd dimension of A. We then multiply w1 and the transpose of w2 to create a grid of weights. We can then use bsxfun to perform element-wise multiplication (@times) between this grid and each "slice" of A. We can then reshape the 3D result into M x N and sum across the first dimension.

B = sum(reshape(bsxfun(@times, w1 * w2.', permute(A, [2 3 1])), [], N)).';

更新

实际上有一种更简单的方法，该方法将使用矩阵乘法为您执行求和.不幸的是，它必须分为

There's actually a simpler approach which would use matrix multiplication to perform the summation for you. It unfortunately has to be broken into

% Create the grid of weights
W = w1 * w2.';

% Perform matrix multiplication between a 2D version of A and the weights
B = reshape(A, N, []) * W(:);

或者您可以使用kron创建扁平化的权重网格:

Or you could use kron to create the flattened grid of weights:

B = reshape(A, N, []) * kron(w2, w1);

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