On entry: specifies, in the case
$n=m$, whether the routine is permitted to use the transpose of
$A$ for improved efficiency. If the matrix is square then the procedure may use transposed
$A$ if
${A}^{\mathrm{T}}$ seems to be better with respect to convergence. If the matrix is not square,
JOBT is ignored. The decision is based on two values of entropy over the adjoint orbit of
${A}^{\mathrm{T}}A$. See the descriptions of
${\mathbf{WORK}}\left(6\right)$ and
${\mathbf{WORK}}\left(7\right)$.
- ${\mathbf{JOBT}}=\text{'T'}$
- If $n=m$, perform an entropy test and then transpose if the test indicates possibly faster convergence of the Jacobi process if ${A}^{\mathrm{T}}$ is taken as input. If $A$ is replaced with ${A}^{\mathrm{T}}$, then the row pivoting is included automatically.
- ${\mathbf{JOBT}}=\text{'N'}$
- No entropy test and no transposition is performed.
The option
${\mathbf{JOBT}}=\text{'T'}$ can be used to compute only the singular values, or the full SVD (
$U$,
$\Sigma $ and
$V$). In the case where only one set of singular vectors (
$U$ or
$V$) is required, the caller must still provide both
U and
V, as one of the matrices is used as workspace if the matrix
$A$ is transposed. See the descriptions of
U and
V.