Matlab - 用矩阵运算替代for循环

Question

我希望用矩阵操作替换for循环。以下是我的代码的最小工作示例：

A = [1,2,3,4,5,6,7,8,9,10];
B= [5,2,3,4,5,1,4,7,4,2];
C = zeros(1,10);
n = length(A);
abMatrix = [1,-1,0;1,-2,1;0,-1,1];
for i=2:n-1
  C(i) = A(i-1:i+1) * abMatrix * B(i-1:i+1)';
end

这个操作是可行的，但我想在一个矩阵操作中完成对于所有i=[2,n-1]的操作。如何去掉for循环？

- Henrik L

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只是好奇：为什么要踩我？ - Luis Mendo

Answer 1

diag + bsxfun based approach -

nA = numel(A); %// Get number of elements in A
ind1 = bsxfun(@plus,[1:3]',0:nA-3); %// sliding indices
mat_mult = A(ind1)'*abMatrix*B(ind1); %// matrix multiplications of the three arrays

C(1,nA)=0 %// pre-allocate for C
C(2:end-1)=mat_mult(1:size(mat_mult,1)+1:end) %//get right values, set at right places

如果你关心代码的紧凑性，这里有一个例子 -

ind1 = bsxfun(@plus,[1:3]',0:numel(A)-3)
C = [0 ; diag(A(ind1)'*abMatrix*B(ind1)) ; 0].'

- Divakar

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哇！只需两行代码，不需要循环！ - Luis Mendo