SGSVJ0
This routine is also part of SIGMA (version 1.23, October 23. 2008.)
SIGMA is a library of algorithms for highly accurate algorithms for
computation of SVD, PSVD, QSVD, (H,K)-SVD, and for solution of the
eigenvalue problems Hx = lambda M x, H M x = lambda x with H, M > 0.
SIGMA is a library of algorithms for highly accurate algorithms for
computation of SVD, PSVD, QSVD, (H,K)-SVD, and for solution of the
eigenvalue problems Hx = lambda M x, H M x = lambda x with H, M > 0.
Purpose
SGSVJ0 is called from SGESVJ as a pre-processor and that is its main
purpose. It applies Jacobi rotations in the same way as SGESVJ does, but
it does not check convergence (stopping criterion). Few tuning
parameters (marked by [TP]) are available for the implementer.
Further Details
~~~~~~~~~~~~~~~
SGSVJ0 is used just to enable SGESVJ to call a simplified version of
itself to work on a submatrix of the original matrix.
Contributors
~~~~~~~~~~~~
Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
Bugs, Examples and Comments
~~~~~~~~~~~~~~~~~~~~~~~~~~~
Please report all bugs and send interesting test examples and comments to
drmac@math.hr. Thank you.
purpose. It applies Jacobi rotations in the same way as SGESVJ does, but
it does not check convergence (stopping criterion). Few tuning
parameters (marked by [TP]) are available for the implementer.
Further Details
~~~~~~~~~~~~~~~
SGSVJ0 is used just to enable SGESVJ to call a simplified version of
itself to work on a submatrix of the original matrix.
Contributors
~~~~~~~~~~~~
Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
Bugs, Examples and Comments
~~~~~~~~~~~~~~~~~~~~~~~~~~~
Please report all bugs and send interesting test examples and comments to
drmac@math.hr. Thank you.
Arguments
| JOBV |
(input) CHARACTER*1
Specifies whether the output from this procedure is used
to compute the matrix V: = 'V': the product of the Jacobi rotations is accumulated by postmulyiplying the N-by-N array V. (See the description of V.) = 'A': the product of the Jacobi rotations is accumulated by postmulyiplying the MV-by-N array V. (See the descriptions of MV and V.) = 'N': the Jacobi rotations are not accumulated. |
| M |
(input) INTEGER
The number of rows of the input matrix A. M >= 0.
|
| N |
(input) INTEGER
The number of columns of the input matrix A.
M >= N >= 0. |
| A |
(input/output) REAL array, dimension (LDA,N)
On entry, M-by-N matrix A, such that A*diag(D) represents
the input matrix. On exit, A_onexit * D_onexit represents the input matrix A*diag(D) post-multiplied by a sequence of Jacobi rotations, where the rotation threshold and the total number of sweeps are given in TOL and NSWEEP, respectively. (See the descriptions of D, TOL and NSWEEP.) |
| LDA |
(input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
|
| D |
(input/workspace/output) REAL array, dimension (N)
The array D accumulates the scaling factors from the fast scaled
Jacobi rotations. On entry, A*diag(D) represents the input matrix. On exit, A_onexit*diag(D_onexit) represents the input matrix post-multiplied by a sequence of Jacobi rotations, where the rotation threshold and the total number of sweeps are given in TOL and NSWEEP, respectively. (See the descriptions of A, TOL and NSWEEP.) |
| SVA |
(input/workspace/output) REAL array, dimension (N)
On entry, SVA contains the Euclidean norms of the columns of
the matrix A*diag(D). On exit, SVA contains the Euclidean norms of the columns of the matrix onexit*diag(D_onexit). |
| MV |
(input) INTEGER
If JOBV .EQ. 'A', then MV rows of V are post-multipled by a
sequence of Jacobi rotations. If JOBV = 'N', then MV is not referenced. |
| V |
(input/output) REAL array, dimension (LDV,N)
If JOBV .EQ. 'V' then N rows of V are post-multipled by a
sequence of Jacobi rotations. If JOBV .EQ. 'A' then MV rows of V are post-multipled by a sequence of Jacobi rotations. If JOBV = 'N', then V is not referenced. |
| LDV |
(input) INTEGER
The leading dimension of the array V, LDV >= 1.
If JOBV = 'V', LDV .GE. N. If JOBV = 'A', LDV .GE. MV. |
| EPS |
(input) INTEGER
EPS = SLAMCH('Epsilon')
|
| SFMIN |
(input) INTEGER
SFMIN = SLAMCH('Safe Minimum')
|
| TOL |
(input) REAL
TOL is the threshold for Jacobi rotations. For a pair
A(:,p), A(:,q) of pivot columns, the Jacobi rotation is applied only if ABS(COS(angle(A(:,p),A(:,q)))) .GT. TOL. |
| NSWEEP |
(input) INTEGER
NSWEEP is the number of sweeps of Jacobi rotations to be
performed. |
| WORK |
(workspace) REAL array, dimension LWORK.
|
| LWORK |
(input) INTEGER
LWORK is the dimension of WORK. LWORK .GE. M.
|
| INFO |
(output) INTEGER
= 0 : successful exit.
< 0 : if INFO = -i, then the i-th argument had an illegal value |