gsvj1(3)

NAME
gsvj1 - gsvj1: step in gesvj

SYNOPSIS

  Functions

subroutine cgsvj1 (jobv, m, n, n1, a, lda, d, sva, mv, v, ldv, eps, sfmin, tol, nsweep, work, lwork, info)
CGSVJ1 pre-processor for the routine cgesvj, applies Jacobi rotations targeting only particular pivots.
subroutine dgsvj1 (jobv, m, n, n1, a, lda, d, sva, mv, v, ldv, eps, sfmin, tol, nsweep, work, lwork, info)
DGSVJ1 pre-processor for the routine dgesvj, applies 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)
SGSVJ1 pre-processor for the routine sgesvj, applies Jacobi rotations targeting only particular pivots.
subroutine zgsvj1 (jobv, m, n, n1, a, lda, d, sva, mv, v, ldv, eps, sfmin, tol, nsweep, work, lwork, info)
ZGSVJ1 pre-processor for the routine zgesvj, applies Jacobi rotations targeting only particular pivots.

Detailed Description

Function Documentation

  subroutine cgsvj1 (character*1 jobv, integer m, integer n, integer n1, 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)

CGSVJ1 pre-processor for the routine cgesvj, applies Jacobi rotations targeting only particular pivots.

Purpose:

    !>
    !> CGSVJ1 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 targets only particular pivots and it does not check convergence
    !> (stopping criterion). Few tuning parameters (marked by [TP]) are
    !> available for the implementer.
    !>
    !> Further Details
    !> ~~~~~~~~~~~~~~~
    !> CGSVJ1 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] *  *  * |
    !>    |[x] [x] [x] *  *  * |
    !>    |[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 tuning parameter.
    !> The number of sweeps is given in NSWEEP and the orthogonality threshold
    !> is given in TOL.
    !>

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.
    !>

    N1

    !>          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

    !>          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 * 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

    !>          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 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

    !>          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 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.

Contributor:
    Zlatko Drmac (Zagreb, Croatia)

  subroutine dgsvj1 (character*1 jobv, integer m, integer n, integer n1, 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)

DGSVJ1 pre-processor for the routine dgesvj, applies Jacobi rotations targeting only particular pivots.

Purpose:

    !>
    !> DGSVJ1 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 targets only particular pivots and it does not check convergence
    !> (stopping criterion). Few tuning parameters (marked by [TP]) are
    !> available for the implementer.
    !>
    !> Further Details
    !> ~~~~~~~~~~~~~~~
    !> DGSVJ1 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] *  *  * |
    !>    |[x] [x] [x] *  *  * |
    !>    |[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 tuning parameter.
    !> The number of sweeps is given in NSWEEP and the orthogonality threshold
    !> is given in TOL.
    !>

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.
    !>

    N1

    !>          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

    !>          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 N1, 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 N1, 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.

Contributors:
    Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)

  subroutine sgsvj1 (character*1 jobv, integer m, integer n, integer n1, 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)

SGSVJ1 pre-processor for the routine sgesvj, applies Jacobi rotations targeting only particular pivots.

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 tuning 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] *  *  * |
    !>    |[x] [x] [x] *  *  * |
    !>    |[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 tuning parameter.
    !> The number of sweeps is given in NSWEEP and the orthogonality threshold
    !> is given in TOL.
    !>

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.
    !>

    N1

    !>          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

    !>          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

    !>          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 N1, 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.

Contributors:
    Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)

  subroutine zgsvj1 (character*1 jobv, integer m, integer n, integer n1, 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)

ZGSVJ1 pre-processor for the routine zgesvj, applies Jacobi rotations targeting only particular pivots.

Purpose:

    !>
    !> ZGSVJ1 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 targets only particular pivots and it does not check convergence
    !> (stopping criterion). Few tuning parameters (marked by [TP]) are
    !> available for the implementer.
    !>
    !> Further Details
    !> ~~~~~~~~~~~~~~~
    !> ZGSVJ1 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] *  *  * |
    !>    |[x] [x] [x] *  *  * |
    !>    |[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 tuning parameter.
    !> The number of sweeps is given in NSWEEP and the orthogonality threshold
    !> is given in TOL.
    !>

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.
    !>

    N1

    !>          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

    !>          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 * 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

    !>          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 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

    !>          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 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.

Contributor:
    Zlatko Drmac (Zagreb, Croatia)

Author

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