.TH "SRC/zgsvj1.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/zgsvj1.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBzgsvj1\fP (jobv, m, n, n1, a, lda, d, sva, mv, v, ldv, eps, sfmin, tol, nsweep, work, lwork, info)"
.br
.RI "\fBZGSVJ1\fP pre-processor for the routine zgesvj, applies Jacobi rotations targeting only particular pivots\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "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)"

.PP
\fBZGSVJ1\fP pre-processor for the routine zgesvj, applies Jacobi rotations targeting only particular pivots\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOBV\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows of the input matrix A\&.  M >= 0\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the input matrix A\&.
!>          M >= N >= 0\&.
!> 
.fi
.PP
.br
\fIN1\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          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\&.)
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,M)\&.
!> 
.fi
.PP
.br
\fID\fP 
.PP
.nf
!>          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\&.)
!> 
.fi
.PP
.br
\fISVA\fP 
.PP
.nf
!>          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)\&.
!> 
.fi
.PP
.br
\fIMV\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIV\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDV\fP 
.PP
.nf
!>          LDV is INTEGER
!>          The leading dimension of the array V,  LDV >= 1\&.
!>          If JOBV = 'V', LDV >= N\&.
!>          If JOBV = 'A', LDV >= MV\&.
!> 
.fi
.PP
.br
\fIEPS\fP 
.PP
.nf
!>          EPS is DOUBLE PRECISION
!>          EPS = DLAMCH('Epsilon')
!> 
.fi
.PP
.br
\fISFMIN\fP 
.PP
.nf
!>          SFMIN is DOUBLE PRECISION
!>          SFMIN = DLAMCH('Safe Minimum')
!> 
.fi
.PP
.br
\fITOL\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fINSWEEP\fP 
.PP
.nf
!>          NSWEEP is INTEGER
!>          NSWEEP is the number of sweeps of Jacobi rotations to be
!>          performed\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX*16 array, dimension (LWORK)
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          LWORK is INTEGER
!>          LWORK is the dimension of WORK\&. LWORK >= M\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit\&.
!>          < 0:  if INFO = -i, then the i-th argument had an illegal value
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
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\fBContributor:\fP
.RS 4
Zlatko Drmac (Zagreb, Croatia) 
.RE
.PP

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Definition at line \fB234\fP of file \fBzgsvj1\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.