performance - Matlab 中更快的矩阵递归

Question

n x n 矩阵 Y_t 的矩阵递归如下所示:

Y_{t} = A + \sum_{i=1}^{p} B_{i} * Y_{t-i}

给出了A和B。

这是我的尝试，但运行缓慢:

Y = zeros(n,n,T); %Going to fill the 3rd dimension for Y_t, t=1:T
Y(:,:,1:p) = initializingY

for t=(p+1):T
    Y(:,:,t) = A;
    for i=1:p
        Y(:,:,t) = Y(:,:,t) + B(:,:,i)*Y(:,:,t-i);
    end
end

你能想出更有效的方法吗？

Answer 1

你可以用matrix-multiplication终止内部循环经过一些reshaping & permuting，像这样-

Y = zeros(n,n,T);
%// Y(:,:,1:p) = initializingY
for t=(p+1):T
    Br = reshape(B(:,:,1:p),n,[]);
    Yr = reshape(permute(Y(:,:,t-(1:p)),[1 3 2]),[],n);
    Y(:,:,t) = A + Br*Yr;
end