sgsvj1 - processor for the routine sgesvj, apply Jacobi rotations targeting only particular pivots
SUBROUTINE SGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) REAL EPS, SFMIN, TOL INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP REAL A(LDA,*), D(N),SVA(N), V(LDV,*), WORK(LWORK) SUBROUTINE SGSVJ1_64( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) REAL EPS, SFMIN, TOL INTEGER*8 INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP REAL A(LDA,*), D(N), SVA(N), V(LDV,*), WORK(LWORK) F95 INTERFACE SUBROUTINE GSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) REAL, DIMENSION(:,:) :: A, V INTEGER :: M, N, N1, LDA, MV, LDV, SFMIN, NSWEEP, LWORK, INFO CHARACTER(LEN=1) :: JOBV REAL, DIMENSION(:) :: D, SVA, WORK REAL :: TOL, EPS, SFMIN SUBROUTINE GSVJ1_64( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) REAL, DIMENSION(:,:) :: A, V INTEGER(8) :: M, N, N1, LDA, MV, LDV, NSWEEP, LWORK, INFO CHARACTER(LEN=1) :: JOBV REAL, DIMENSION(:) :: D, SVA, WORK REAL :: TOL, EPS, SFMIN C INTERFACE #include <sunperf.h> void sgsvj1 (char jobv, int m, int n, int n1, float *a, int lda, float *d, float *sva, int mv, float *v, int ldv, float eps, float sfmin, float tol, int nsweep, int *info); void sgsvj1_64 (char jobv, long m, long n, long n1, float *a, long lda, float *d, float *sva, long mv, float *v, long ldv, float eps, float sfmin, float tol, long nsweep, long *info);
Oracle Solaris Studio Performance Library sgsvj1(3P)
NAME
sgsvj1 - pre-processor for the routine sgesvj, apply Jacobi rotations
targeting only particular pivots
SYNOPSIS
SUBROUTINE SGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, EPS,
SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
REAL EPS, SFMIN, TOL
INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP
REAL A(LDA,*), D(N),SVA(N), V(LDV,*), WORK(LWORK)
SUBROUTINE SGSVJ1_64( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, EPS,
SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
REAL EPS, SFMIN, TOL
INTEGER*8 INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP
REAL A(LDA,*), D(N), SVA(N), V(LDV,*), WORK(LWORK)
F95 INTERFACE
SUBROUTINE GSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, EPS,
SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
REAL, DIMENSION(:,:) :: A, V
INTEGER :: M, N, N1, LDA, MV, LDV, SFMIN, NSWEEP, LWORK, INFO
CHARACTER(LEN=1) :: JOBV
REAL, DIMENSION(:) :: D, SVA, WORK
REAL :: TOL, EPS, SFMIN
SUBROUTINE GSVJ1_64( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, EPS,
SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
REAL, DIMENSION(:,:) :: A, V
INTEGER(8) :: M, N, N1, LDA, MV, LDV, NSWEEP, LWORK, INFO
CHARACTER(LEN=1) :: JOBV
REAL, DIMENSION(:) :: D, SVA, WORK
REAL :: TOL, EPS, SFMIN
C INTERFACE
#include <sunperf.h>
void sgsvj1 (char jobv, int m, int n, int n1, float *a, int lda, float
*d, float *sva, int mv, float *v, int ldv, float eps, float
sfmin, float tol, int nsweep, int *info);
void sgsvj1_64 (char jobv, long m, long n, long n1, float *a, long lda,
float *d, float *sva, long mv, float *v, long ldv, float eps,
float sfmin, float tol, long nsweep, long *info);
PURPOSE
sgsvj1 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 targets only particular pivots and it does not check convergence
(stopping criterion). Few tunning parameters (marked by [TP]) are
available for the implementer.
Further Details ~~~~~~~~~~~~~~~ SGSVJ1 applies few sweeps of Jacobi
rotations in the column space of the input M-by-N matrix A. The pivot
pairs are taken from the (1,2) off-diagonal block in the corresponding
N-by-N Gram matrix A^T * A. The block-entries (tiles) of the (1,2) off-
diagonal block are marked by the [x]'s in the following scheme:
| * * * [x] [x] [x]| | * * * [x] [x] [x]| Row-cycling in the
nblr-by-nblc [x] blocks. | * * * [x] [x] [x]| Row-cyclic pivoting
inside each [x] block. |[x] [x] [x] * * * |
In terms of the columns of A, the first N1 columns are rotated
'against' the remaining N-N1 columns, trying to increase the angle
between the corresponding subspaces. The off-diagonal block is N1-by(N-
N1) and it is tiled using quadratic tiles of side KBL. Here, KBL is a
tunning parmeter. The number of sweeps is given in NSWEEP and the
orthogonality threshold is given in TOL.
ARGUMENTS
JOBV (input)
JOBV is 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)
M is INTEGER
The number of rows of the input matrix A. M >= 0.
N (input)
N is INTEGER
The number of columns of the input matrix A.
M >= N >= 0.
N1 (input)
N1 is INTEGER
N1 specifies the 2 x 2 block partition, the first N1 columns
are
rotated 'against' the remaining N-N1 columns of A.
A (input/output)
A is 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 N1, D, TOL and NSWEEP.)
LDA (input)
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
D (input/output)
D is 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 N1, A, TOL and NSWEEP.)
SVA (input/output)
SVA is 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)
MV is 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)
V is 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)
LDV is INTEGER
The leading dimension of the array V, LDV >= 1.
If JOBV = 'V', LDV .GE. N.
If JOBV = 'A', LDV .GE. MV.
EPS (input)
EPS is REAL
EPS = SLAMCH('Epsilon')
SFMIN (input)
SFMIN is REAL
SFMIN = SLAMCH('Safe Minimum')
TOL (input)
TOL is 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)
NSWEEP is INTEGER
NSWEEP is the number of sweeps of Jacobi rotations to be
performed.
WORK (output)
WORK is REAL array, dimension LWORK.
LWORK (input)
LWORK is INTEGER
LWORK is the dimension of WORK. LWORK .GE. M.
INFO (output)
INFO is INTEGER
= 0 : successful exit.
< 0 : if INFO = -i, then the i-th argument had an illegal
value
7 Nov 2015 sgsvj1(3P)