如何在Matlab中向量化两个for循环以加快速度

Question

How can I speed up the two for loops below by vectorization in MATLAB? This is a part of an iterative algorithm and I need to do it many times.

Temp1=0;
Temp2=0;

for i=1:m_plus
    for j=1:m_minus
        Temp1=Temp1+(p_m(j,:)-p_p(i,:))';
        Temp2=Temp2+(p_m(j,:)-p_p(i,:))'*(p_m(j,:)-p_p(i,:));
    end
end

Answer 1

Assuming

m_plus = size(p_p,1);
m_minus = size(p_m,1);

then it's easy enough to do Temp1 without loops

Temp1 = (m_plus*sum(p_m)-m_minus*sum(p_p))'

For Temp2 it's easy to get rid of one of the loops,

Temp2 = 0;
for idx = 1:m_plus
    temp = p_m-ones(m_minus,1)*p_p(idx,:); % or could use bsxfun to do this
    Temp2 = Temp2 + temp'*temp;
end

although with a little more thought it may be possible to get rid of this loop too.

Answer 2

Another vectorized approach that is sort of inspired from Phil's smart answer -

t1 = bsxfun(@minus,p_m,permute(p_p,[3 2 1]));
t2 = reshape(permute(t1,[1 3 2]),m_minus*m_plus,[]);
Temp1 = sum(t2)'; %//'
Temp2 = t2'*t2;