SRC/DEPRECATED/zggsvp.f(3)                            Library Functions Manual

NAME
       SRC/DEPRECATED/zggsvp.f

SYNOPSIS
   Functions/Subroutines
       subroutine zggsvp (jobu, jobv, jobq, m, p, n, a, lda, b, ldb, tola,
           tolb, k, l, u, ldu, v, ldv, q, ldq, iwork, rwork, tau, work, info)
           ZGGSVP

Function/Subroutine Documentation
   subroutine zggsvp (character jobu, character jobv, character jobq, integer
       m, integer p, integer n, complex*16, dimension( lda, * ) a, integer
       lda, complex*16, dimension( ldb, * ) b, integer ldb, double precision
       tola, double precision tolb, integer k, integer l, complex*16,
       dimension( ldu, * ) u, integer ldu, complex*16, dimension( ldv, * ) v,
       integer ldv, complex*16, dimension( ldq, * ) q, integer ldq, integer,
       dimension( * ) iwork, double precision, dimension( * ) rwork,
       complex*16, dimension( * ) tau, complex*16, dimension( * ) work,
       integer info)
       ZGGSVP

       Purpose:


           !>
           !> This routine is deprecated and has been replaced by routine ZGGSVP3.
           !>
           !> ZGGSVP computes unitary matrices U, V and Q such that
           !>
           !>                    N-K-L  K    L
           !>  U**H*A*Q =     K ( 0    A12  A13 )  if M-K-L >= 0;
           !>                 L ( 0     0   A23 )
           !>             M-K-L ( 0     0    0  )
           !>
           !>                  N-K-L  K    L
           !>         =     K ( 0    A12  A13 )  if M-K-L < 0;
           !>             M-K ( 0     0   A23 )
           !>
           !>                  N-K-L  K    L
           !>  V**H*B*Q =   L ( 0     0   B13 )
           !>             P-L ( 0     0    0  )
           !>
           !> where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
           !> upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
           !> otherwise A23 is (M-K)-by-L upper trapezoidal.  K+L = the effective
           !> numerical rank of the (M+P)-by-N matrix (A**H,B**H)**H.
           !>
           !> This decomposition is the preprocessing step for computing the
           !> Generalized Singular Value Decomposition (GSVD), see subroutine
           !> ZGGSVD.
           !>

       Parameters
           JOBU

           !>          JOBU is CHARACTER*1
           !>          = 'U':  Unitary matrix U is computed;
           !>          = 'N':  U is not computed.
           !>

           JOBV

           !>          JOBV is CHARACTER*1
           !>          = 'V':  Unitary matrix V is computed;
           !>          = 'N':  V is not computed.
           !>

           JOBQ

           !>          JOBQ is CHARACTER*1
           !>          = 'Q':  Unitary matrix Q is computed;
           !>          = 'N':  Q is not computed.
           !>

           M

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

           P

           !>          P is INTEGER
           !>          The number of rows of the matrix B.  P >= 0.
           !>

           N

           !>          N is INTEGER
           !>          The number of columns of the matrices A and B.  N >= 0.
           !>

           A

           !>          A is COMPLEX*16 array, dimension (LDA,N)
           !>          On entry, the M-by-N matrix A.
           !>          On exit, A contains the triangular (or trapezoidal) matrix
           !>          described in the Purpose section.
           !>

           LDA

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

           B

           !>          B is COMPLEX*16 array, dimension (LDB,N)
           !>          On entry, the P-by-N matrix B.
           !>          On exit, B contains the triangular matrix described in
           !>          the Purpose section.
           !>

           LDB

           !>          LDB is INTEGER
           !>          The leading dimension of the array B. LDB >= max(1,P).
           !>

           TOLA

           !>          TOLA is DOUBLE PRECISION
           !>

           TOLB

           !>          TOLB is DOUBLE PRECISION
           !>
           !>          TOLA and TOLB are the thresholds to determine the effective
           !>          numerical rank of matrix B and a subblock of A. Generally,
           !>          they are set to
           !>             TOLA = MAX(M,N)*norm(A)*MAZHEPS,
           !>             TOLB = MAX(P,N)*norm(B)*MAZHEPS.
           !>          The size of TOLA and TOLB may affect the size of backward
           !>          errors of the decomposition.
           !>

           K

           !>          K is INTEGER
           !>

           L

           !>          L is INTEGER
           !>
           !>          On exit, K and L specify the dimension of the subblocks
           !>          described in Purpose section.
           !>          K + L = effective numerical rank of (A**H,B**H)**H.
           !>

           U

           !>          U is COMPLEX*16 array, dimension (LDU,M)
           !>          If JOBU = 'U', U contains the unitary matrix U.
           !>          If JOBU = 'N', U is not referenced.
           !>

           LDU

           !>          LDU is INTEGER
           !>          The leading dimension of the array U. LDU >= max(1,M) if
           !>          JOBU = 'U'; LDU >= 1 otherwise.
           !>

           V

           !>          V is COMPLEX*16 array, dimension (LDV,P)
           !>          If JOBV = 'V', V contains the unitary matrix V.
           !>          If JOBV = 'N', V is not referenced.
           !>

           LDV

           !>          LDV is INTEGER
           !>          The leading dimension of the array V. LDV >= max(1,P) if
           !>          JOBV = 'V'; LDV >= 1 otherwise.
           !>

           Q

           !>          Q is COMPLEX*16 array, dimension (LDQ,N)
           !>          If JOBQ = 'Q', Q contains the unitary matrix Q.
           !>          If JOBQ = 'N', Q is not referenced.
           !>

           LDQ

           !>          LDQ is INTEGER
           !>          The leading dimension of the array Q. LDQ >= max(1,N) if
           !>          JOBQ = 'Q'; LDQ >= 1 otherwise.
           !>

           IWORK

           !>          IWORK is INTEGER array, dimension (N)
           !>

           RWORK

           !>          RWORK is DOUBLE PRECISION array, dimension (2*N)
           !>

           TAU

           !>          TAU is COMPLEX*16 array, dimension (N)
           !>

           WORK

           !>          WORK is COMPLEX*16 array, dimension (max(3*N,M,P))
           !>

           INFO

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

       Author
           Univ. of Tennessee


           Univ. of California Berkeley


           Univ. of Colorado Denver


           NAG Ltd.

       Further Details:


           !>
           !>  The subroutine uses LAPACK subroutine ZGEQPF for the QR factorization
           !>  with column pivoting to detect the effective numerical rank of the
           !>  a matrix. It may be replaced by a better rank determination strategy.
           !>

       Definition at line 262 of file zggsvp.f.

Author
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LAPACK                          Version 3.12.0      SRC/DEPRECATED/zggsvp.f(3)