gsvj0(3)

NAME
gsvj0 - 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.

  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.

  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.

  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.

Author

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