Which SVD algorithm implementation is used in MATLAB?

29 views (last 30 days)
Hi,
I am comparing singular value decomposition function [U,S,V] = svd(A) to some C implementations of the algorithm. However, I am getting somewhat different results: for example, columns of the output matrix U are mixed-up, or some output values have different sign, etc.
Does anyone know which SVD algorithm implementation is used in MATLAB?
  4 Comments
Walter Roberson
Walter Roberson on 22 Feb 2022
I am not sure how it is relevant that MKL is copyrighted? LAPACK is copyrighted too, with a modified BSD license.
MKL is probably closed source, but you did not indicate that you needed source access; for everything you have mentioned so far you only need to be able to link against it.

Sign in to comment.

Answers (1)

Steven Lord
Steven Lord on 3 Feb 2022
Keep in mind that the SVD of a matrix is not unique. Quoting from Wikipedia: "Non-degenerate singular values always have unique left- and right-singular vectors, up to multiplication by a unit-phase factor (for the real case up to a sign). Consequently, if all singular values of a square matrix M are non-degenerate and non-zero, then its singular value decomposition is unique, up to multiplication of a column of U by a unit-phase factor and simultaneous multiplication of the corresponding column of V by the same unit-phase factor."
A = magic(5);
[U, S, V] = svd(A);
format longg
check1 = U*S*V' - A
check1 = 5×5
1.0e+00 * 3.5527136788005e-15 -1.4210854715202e-14 -1.93178806284777e-14 2.48689957516035e-14 1.59872115546023e-14 0 -1.77635683940025e-14 -1.4210854715202e-14 2.48689957516035e-14 1.77635683940025e-14 -3.5527136788005e-15 6.21724893790088e-15 1.77635683940025e-14 7.105427357601e-15 7.105427357601e-15 -3.5527136788005e-15 3.19744231092045e-14 1.77635683940025e-14 -1.77635683940025e-14 -8.43769498715119e-15 5.32907051820075e-15 3.5527136788005e-14 1.4210854715202e-14 -2.17603712826531e-14 -1.95399252334028e-14
U2 = -U;
V2 = -V;
check2 = U2*S*V2' - A
check2 = 5×5
1.0e+00 * 3.5527136788005e-15 -1.4210854715202e-14 -1.93178806284777e-14 2.48689957516035e-14 1.59872115546023e-14 0 -1.77635683940025e-14 -1.4210854715202e-14 2.48689957516035e-14 1.77635683940025e-14 -3.5527136788005e-15 6.21724893790088e-15 1.77635683940025e-14 7.105427357601e-15 7.105427357601e-15 -3.5527136788005e-15 3.19744231092045e-14 1.77635683940025e-14 -1.77635683940025e-14 -8.43769498715119e-15 5.32907051820075e-15 3.5527136788005e-14 1.4210854715202e-14 -2.17603712826531e-14 -1.95399252334028e-14
The elements of check1 and check2 both look sufficiently small as to be close enough to 0 to say both (U, S, V) and (U2, S, V2) satisfy the SVD contract. It's possible the columns of the output U aren't "mixed up" they're just a different (correct) answer (when combined with the corresponding V) than you expected.

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!