How to find angle between 2 3D vectors?

Hello, I have 2 sets of 3D data and I want to find out the angle between the two after dimensionality reduction. I have written the following code but the accurate angle is not showing.

z2 and z3 are the two mesh grids generated from the 3D data.

[V2,D2]=eigs(z2);
 P2=svd(V2);
[V1,D1] = eigs(z3);
V1=sort(V1,'descend');
P1=svd(V1);           
angle = atan2(norm(cross(P1,P2)), dot(P1,P2))

Can anybody help me in this regard? Thanks in advance, Ampi.

[Matt J]

Give us an example of P1(:,i) and P2(:,i) whose angle calculation doesn't look correct.

[Roger Stafford]

If P1 and P2 are three-element vectors, your formula for the 3D inner angle between them is correct. However I have questions about the preceding code. For example, if you use the non-negative singular values coming from 'svd' for P1 and P2 element values, that restricts your angle to the range 0 to pi/2 radians (0 to 90 degrees). How do you justify that? What are the sizes of z2 and z3? If they are other than 3-by-3, you will have something other than three eigenvectors in V2 and V1 and consequently other than three singular values in both P2 and P1 vectors.

[Kamal]

Dear Roger, I have one question about the princomp function. Can you help me?

Answer 1

[Youssef Khmou]

hi,

is it atan or cos^-1 (acos) because the scalat product is :

 V.U=||U||.||V||.cos(U^V);