MATLAB: Transform from “for loop” into “matrix” form

for loopmatrix

Hi all,
I have a complicated problem about "for loop" and "matrix", I would like to have some helps from you.
Let's X1 be a vector with length n1, X2 be a vector with length n2, F1 be a N1xn1 matrix, F2 be a N2xn2 matrix, and Q be a N1xN2 matrix. I like compute the matrix Q as follows:
for i1=1:N1
for i2=1:N2
        Q(i1,i2)=Q(i1,i2)+trapz(X2(p2(1):p2(3)),trapz(X1(p1(1):p1(3)),Q(p1(1):p1(3),p2(1):p2(3))...
                                                        .*repmat(F1(i1,p1(1):p1(3))',1,p2(3)-p2(1)+1)).*F2(i2,p2(1):p2(3)));
end
end
where p1 and p2 are index vectors.
This program with "for loop" gives me a good result but takes time. I would like to transform it into "matrix" form to accelerate the computation.
The problem is that the output Q is taken as input in the body of "for loop". If it is not taken as the input, I can transform the above "for loop" as follows:
I=squeeze(trapz(X1(p1(1):p1(3)),repmat(Q(p1(1):p1(3),p2(1):p2(3)),[1 1 N1])...
                                                 .*rot90_3D(rot90_3D(repmat(F1(:,p1(1):p1(3)),[1 1 p2(3)-p2(1)+1]),3,3),1,3)));
Q=Q+squeeze(trapz(X2(p2(1):p2(3)),repmat(I,[1 1 N2]).*rot90_3D(rot90_3D(repmat(F2(:,p2(1):p2(3)),[1 1 N1]),3,3),1,3)));
It works but it is not exactly what I want.
So, do you have any idea to deal with the problem? Thank you in advance for you help.
Tuan

Best Answer

Start with simplifying the loops (Q is pre-allocated, isn't it?!):
p11 = p1(1);
p13 = p1(3);
p21 = p2(1);
p23 = p2(3);
c1 = X2(p21:p23);
c2 = p23 - p21 + 1;
c3 = F2(i2, p21:p23);
c4 = X1(p11:p13);
c5 = repmat(F1(i1, p11:p13)', 1, c2);
for i1=1:N1
  for i2=1:N2
    v = Q(p11:p13, p21:p23);
    Q(i1,i2) = Q(i1,i2) + trapz(c1, trapz(c4, v .* c5) .* c3);
  end
end
Is this faster already?
I guess that the most time is spent in trapz() such that optimizing or vectorizing the loop will not help very much.
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