DGSVJ0
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
DGSVJ0 is called from DGESVJ as a pre-processor and that is its main
purpose. It applies Jacobi rotations in the same way as DGESVJ does, but
it does not check convergence (stopping criterion). Few tuning
parameters (marked by [TP]) are available for the implementer.
Further Details
~~~~~~~~~~~~~~~
DGSVJ0 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 DGESVJ does, but
it does not check convergence (stopping criterion). Few tuning
parameters (marked by [TP]) are available for the implementer.
Further Details
~~~~~~~~~~~~~~~
DGSVJ0 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION
EPS = DLAMCH('Epsilon')
|
| SFMIN |
(input) DOUBLE PRECISION
SFMIN = DLAMCH('Safe Minimum')
|
| TOL |
(input) DOUBLE PRECISION
TOL is the threshold for Jacobi rotations. For a pair
A(:,p), A(:,q) of pivot columns, the Jacobi rotation is applied only if DABS(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) DOUBLE PRECISION 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 |