gsvj0 - Man Page

gsvj0: step in gesvj

Synopsis

Functions

subroutine cgsvj0 (jobv, m, n, a, lda, d, sva, mv, v, ldv, eps, sfmin, tol, nsweep, work, lwork, info)
CGSVJ0 pre-processor for the routine cgesvj.
subroutine dgsvj0 (jobv, m, n, a, lda, d, sva, mv, v, ldv, eps, sfmin, tol, nsweep, work, lwork, info)
DGSVJ0 pre-processor for the routine dgesvj.
subroutine sgsvj0 (jobv, m, n, a, lda, d, sva, mv, v, ldv, eps, sfmin, tol, nsweep, work, lwork, info)
SGSVJ0 pre-processor for the routine sgesvj.
subroutine zgsvj0 (jobv, m, n, a, lda, d, sva, mv, v, ldv, eps, sfmin, tol, nsweep, work, lwork, info)
ZGSVJ0 pre-processor for the routine zgesvj.

Detailed Description

Function Documentation

subroutine cgsvj0 (character*1 jobv, integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( n ) d, real, dimension( n ) sva, integer mv, complex, dimension( ldv, * ) v, integer ldv, real eps, real sfmin, real tol, integer nsweep, complex, dimension( lwork ) work, integer lwork, integer info)

CGSVJ0 pre-processor for the routine cgesvj.  

Purpose:

 CGSVJ0 is called from CGESVJ as a pre-processor and that is its main
 purpose. It applies Jacobi rotations in the same way as CGESVJ does, but
 it does not check convergence (stopping criterion). Few tuning
 parameters (marked by [TP]) are available for the implementer.
Parameters

JOBV

          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 postmultiplying the N-by-N array V.
                (See the description of V.)
          = 'A': the product of the Jacobi rotations is accumulated
                 by postmultiplying the MV-by-N array V.
                (See the descriptions of MV and V.)
          = 'N': the Jacobi rotations are not accumulated.

M

          M is INTEGER
          The number of rows of the input matrix A.  M >= 0.

N

          N is INTEGER
          The number of columns of the input matrix A.
          M >= N >= 0.

A

          A is COMPLEX array, dimension (LDA,N)
          On entry, M-by-N matrix A, such that A*diag(D) represents
          the input matrix.
          On exit,
          A_onexit * diag(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

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

D

          D is COMPLEX array, dimension (N)
          The array D accumulates the scaling factors from the complex 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

          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 A_onexit*diag(D_onexit).

MV

          MV is INTEGER
          If JOBV = 'A', then MV rows of V are post-multiplied by a
                           sequence of Jacobi rotations.
          If JOBV = 'N',   then MV is not referenced.

V

          V is COMPLEX array, dimension (LDV,N)
          If JOBV = 'V' then N rows of V are post-multiplied by a
                           sequence of Jacobi rotations.
          If JOBV = 'A' then MV rows of V are post-multiplied by a
                           sequence of Jacobi rotations.
          If JOBV = 'N',   then V is not referenced.

LDV

          LDV is INTEGER
          The leading dimension of the array V,  LDV >= 1.
          If JOBV = 'V', LDV >= N.
          If JOBV = 'A', LDV >= MV.

EPS

          EPS is REAL
          EPS = SLAMCH('Epsilon')

SFMIN

          SFMIN is REAL
          SFMIN = SLAMCH('Safe Minimum')

TOL

          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)))) > TOL.

NSWEEP

          NSWEEP is INTEGER
          NSWEEP is the number of sweeps of Jacobi rotations to be
          performed.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          LWORK is the dimension of WORK. LWORK >= M.

INFO

          INFO is INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, then the i-th argument had an illegal value
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

CGSVJ0 is used just to enable CGESVJ to call a simplified version of itself to work on a submatrix of the original matrix.

Contributor:

Zlatko Drmac (Zagreb, Croatia)

Bugs, Examples and Comments:

Please report all bugs and send interesting test examples and comments to drmac@math.hr. Thank you.

Definition at line 216 of file cgsvj0.f.

subroutine dgsvj0 (character*1 jobv, integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( n ) d, double precision, dimension( n ) sva, integer mv, double precision, dimension( ldv, * ) v, integer ldv, double precision eps, double precision sfmin, double precision tol, integer nsweep, double precision, dimension( lwork ) work, integer lwork, integer info)

DGSVJ0 pre-processor for the routine dgesvj.  

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.
Parameters

JOBV

          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 postmultiplying the N-by-N array V.
                (See the description of V.)
          = 'A': the product of the Jacobi rotations is accumulated
                 by postmultiplying the MV-by-N array V.
                (See the descriptions of MV and V.)
          = 'N': the Jacobi rotations are not accumulated.

M

          M is INTEGER
          The number of rows of the input matrix A.  M >= 0.

N

          N is INTEGER
          The number of columns of the input matrix A.
          M >= N >= 0.

A

          A is 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

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

D

          D is 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

          SVA is 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

          MV is INTEGER
          If JOBV = 'A', then MV rows of V are post-multiplied by a
                           sequence of Jacobi rotations.
          If JOBV = 'N',   then MV is not referenced.

V

          V is DOUBLE PRECISION array, dimension (LDV,N)
          If JOBV = 'V' then N rows of V are post-multiplied by a
                           sequence of Jacobi rotations.
          If JOBV = 'A' then MV rows of V are post-multiplied by a
                           sequence of Jacobi rotations.
          If JOBV = 'N',   then V is not referenced.

LDV

          LDV is INTEGER
          The leading dimension of the array V,  LDV >= 1.
          If JOBV = 'V', LDV >= N.
          If JOBV = 'A', LDV >= MV.

EPS

          EPS is DOUBLE PRECISION
          EPS = DLAMCH('Epsilon')

SFMIN

          SFMIN is DOUBLE PRECISION
          SFMIN = DLAMCH('Safe Minimum')

TOL

          TOL is 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)))) > TOL.

NSWEEP

          NSWEEP is INTEGER
          NSWEEP is the number of sweeps of Jacobi rotations to be
          performed.

WORK

          WORK is DOUBLE PRECISION array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          LWORK is the dimension of WORK. LWORK >= M.

INFO

          INFO is INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, then the i-th argument had an illegal value
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

DGSVJ0 is used just to enable DGESVJ 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.

Definition at line 216 of file dgsvj0.f.

subroutine sgsvj0 (character*1 jobv, integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( n ) d, real, dimension( n ) sva, integer mv, real, dimension( ldv, * ) v, integer ldv, real eps, real sfmin, real tol, integer nsweep, real, dimension( lwork ) work, integer lwork, integer info)

SGSVJ0 pre-processor for the routine sgesvj.  

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.
Parameters

JOBV

          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 postmultiplying the N-by-N array V.
                (See the description of V.)
          = 'A': the product of the Jacobi rotations is accumulated
                 by postmultiplying the MV-by-N array V.
                (See the descriptions of MV and V.)
          = 'N': the Jacobi rotations are not accumulated.

M

          M is INTEGER
          The number of rows of the input matrix A.  M >= 0.

N

          N is INTEGER
          The number of columns of the input matrix A.
          M >= N >= 0.

A

          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 D, TOL and NSWEEP.)

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

D

          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 A, TOL and NSWEEP.)

SVA

          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

          MV is INTEGER
          If JOBV = 'A', then MV rows of V are post-multiplied by a
                           sequence of Jacobi rotations.
          If JOBV = 'N',   then MV is not referenced.

V

          V is REAL array, dimension (LDV,N)
          If JOBV = 'V' then N rows of V are post-multiplied by a
                           sequence of Jacobi rotations.
          If JOBV = 'A' then MV rows of V are post-multiplied by a
                           sequence of Jacobi rotations.
          If JOBV = 'N',   then V is not referenced.

LDV

          LDV is INTEGER
          The leading dimension of the array V,  LDV >= 1.
          If JOBV = 'V', LDV >= N.
          If JOBV = 'A', LDV >= MV.

EPS

          EPS is REAL
          EPS = SLAMCH('Epsilon')

SFMIN

          SFMIN is REAL
          SFMIN = SLAMCH('Safe Minimum')

TOL

          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)))) > TOL.

NSWEEP

          NSWEEP is INTEGER
          NSWEEP is the number of sweeps of Jacobi rotations to be
          performed.

WORK

          WORK is REAL array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          LWORK is the dimension of WORK. LWORK >= M.

INFO

          INFO is INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, then the i-th argument had an illegal value
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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.

Definition at line 216 of file sgsvj0.f.

subroutine zgsvj0 (character*1 jobv, integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( n ) d, double precision, dimension( n ) sva, integer mv, complex*16, dimension( ldv, * ) v, integer ldv, double precision eps, double precision sfmin, double precision tol, integer nsweep, complex*16, dimension( lwork ) work, integer lwork, integer info)

ZGSVJ0 pre-processor for the routine zgesvj.  

Purpose:

 ZGSVJ0 is called from ZGESVJ as a pre-processor and that is its main
 purpose. It applies Jacobi rotations in the same way as ZGESVJ does, but
 it does not check convergence (stopping criterion). Few tuning
 parameters (marked by [TP]) are available for the implementer.
Parameters

JOBV

          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 postmultiplying the N-by-N array V.
                (See the description of V.)
          = 'A': the product of the Jacobi rotations is accumulated
                 by postmultiplying the MV-by-N array V.
                (See the descriptions of MV and V.)
          = 'N': the Jacobi rotations are not accumulated.

M

          M is INTEGER
          The number of rows of the input matrix A.  M >= 0.

N

          N is INTEGER
          The number of columns of the input matrix A.
          M >= N >= 0.

A

          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, M-by-N matrix A, such that A*diag(D) represents
          the input matrix.
          On exit,
          A_onexit * diag(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

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

D

          D is COMPLEX*16 array, dimension (N)
          The array D accumulates the scaling factors from the complex 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

          SVA is 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 A_onexit*diag(D_onexit).

MV

          MV is INTEGER
          If JOBV = 'A', then MV rows of V are post-multiplied by a
                           sequence of Jacobi rotations.
          If JOBV = 'N',   then MV is not referenced.

V

          V is COMPLEX*16 array, dimension (LDV,N)
          If JOBV = 'V' then N rows of V are post-multiplied by a
                           sequence of Jacobi rotations.
          If JOBV = 'A' then MV rows of V are post-multiplied by a
                           sequence of Jacobi rotations.
          If JOBV = 'N',   then V is not referenced.

LDV

          LDV is INTEGER
          The leading dimension of the array V,  LDV >= 1.
          If JOBV = 'V', LDV >= N.
          If JOBV = 'A', LDV >= MV.

EPS

          EPS is DOUBLE PRECISION
          EPS = DLAMCH('Epsilon')

SFMIN

          SFMIN is DOUBLE PRECISION
          SFMIN = DLAMCH('Safe Minimum')

TOL

          TOL is 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 ABS(COS(angle(A(:,p),A(:,q)))) > TOL.

NSWEEP

          NSWEEP is INTEGER
          NSWEEP is the number of sweeps of Jacobi rotations to be
          performed.

WORK

          WORK is COMPLEX*16 array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          LWORK is the dimension of WORK. LWORK >= M.

INFO

          INFO is INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, then the i-th argument had an illegal value
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

ZGSVJ0 is used just to enable ZGESVJ to call a simplified version of itself to work on a submatrix of the original matrix.

Contributor: Zlatko Drmac (Zagreb, Croatia)

Bugs, Examples and Comments:

Please report all bugs and send interesting test examples and comments to drmac@math.hr. Thank you.

Definition at line 216 of file zgsvj0.f.

Author

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Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK