arrays - matlab: Addressing multiple rows in multidimensional array

Question

Suppose that "r" is a multidimensional array of size [N, N, M] and "tab" is a table of size [N] with values 1..N (e.g. take "tab=randperm(N)"). I'm looking for efficient way to do the following:

    c = ones(M, 1);
    for k=1:N
        c = c .* squeeze(r(tab(k),k,:));
    end

I'd like to do that in matrix notation, using prod, but didn't find a solution, as "r(tab(1:N),1:N,:)" returns an NxNxM matrix rather than N rows.

Any suggestions?

Answer 1

sub2ind跨维度 1、2使用；bsxfun沿维度 3 复制；然后prod：

c = prod(r(bsxfun(@plus, sub2ind([N N], tab, 1:N).', (0:M-1)*N^2))).';

Answer 2

%% example data
M=3;
N=4;
r=rand(N,N,M);
tab=randperm(N);

%% original code    

c = ones(M, 1);
for k=1:N
    c = c .* squeeze(r(tab(k),k,:));
end

%% Code is equivalent to:

% rh=r(tab,:,:);
% c2 = ones(M, 1);
% for k=1:N
%     c2 = c2 .* squeeze(rh(k,k,:));
% end
% assert(all(c2==c));

%% second solution: Use sub2ind to index
rh=r(tab,:,:);

ix=sub2ind(size(rh),ceil(1/M:1/M:N),ceil(1/M:1/M:N),repmat(1:M,1,N));
rh2=rh(ix);
rh3=reshape(rh2,M,N);
c3=prod(rh3,2);
assert(all(c3==c));