SVD examples: incomplete left singular vectors?

0rbital — Tue, 19 Aug 2025 13:02:46 GMT

Dear Sir/Madam,

According to the example of the Singular Value Decomposition (SVD) functions, for instance dgesvd, the left singular vectors, U, should have the dimensions mxm (see snippet below).

The routine computes the singular value decomposition (SVD) of a real m-by-n matrix A, optionally computing the left and/or right singular vectors. The SVD is written as A = U*SIGMA*VT where SIGMA is an m-by-n matrix which is zero except for its min(m,n) diagonal elements, U is an m-by-m orthogonal matrix and VT (V transposed) is an n-by-n orthogonal matrix.

However, in the results snippet

Left singular vectors (stored columnwise) -0.59 0.26 0.36 0.31 0.23 -0.40 0.24 -0.22 -0.75 -0.36 -0.03 -0.60 -0.45 0.23 -0.31 -0.43 0.24 -0.69 0.33 0.16 -0.47 -0.35 0.39 0.16 -0.52 0.29 0.58 -0.02 0.38 -0.65

the matrix is only printed as mxn.

print_matrix( "Left singular vectors (stored columnwise)", m, n, u, ldu );

Shouldn't the line above be

print_matrix( "Left singular vectors (stored columnwise)", m, m, u, ldu );

Could you please update all SVD examples? Or in case I misunderstood, could you please explain to me why U is printed as mxn?

Kind regards

Re: SVD examples: incomplete left singular vectors?

Fengrui — Wed, 20 Aug 2025 21:37:42 GMT

Good catch! U is mxm. We will correct it.

topic SVD examples: incomplete left singular vectors? in Intel® oneAPI Math Kernel Library

SVD examples: incomplete left singular vectors?

Re: SVD examples: incomplete left singular vectors?