**LA_GESVD** and **LA_GESDD** compute the singular values and,
optionally, the left and/or right singular vectors from the
singular value decomposition () of a real or complex matrix .
The of is written

where is an matrix which is zero except for its diagonal elements, is an orthogonal (unitary) matrix, and is an orthogonal (unitary) matrix. The diagonal elements of , i.e., the values

are the singular values of ; they are real and non-negative, and are returned in descending order. The first columns of and are the left and right singular vectors of , respectively.

Note: The routine returns , not .