SRC/dggsvp3.f(3)           Library Functions Manual           SRC/dggsvp3.f(3)

NAME
       SRC/dggsvp3.f

SYNOPSIS
   Functions/Subroutines
       subroutine dggsvp3 (jobu, jobv, jobq, m, p, n, a, lda, b, ldb, tola,
           tolb, k, l, u, ldu, v, ldv, q, ldq, iwork, tau, work, lwork, info)
           DGGSVP3

Function/Subroutine Documentation
   subroutine dggsvp3 (character jobu, character jobv, character jobq, integer
       m, integer p, integer n, double precision, dimension( lda, * ) a,
       integer lda, double precision, dimension( ldb, * ) b, integer ldb,
       double precision tola, double precision tolb, integer k, integer l,
       double precision, dimension( ldu, * ) u, integer ldu, double precision,
       dimension( ldv, * ) v, integer ldv, double precision, dimension( ldq, *
       ) q, integer ldq, integer, dimension( * ) iwork, double precision,
       dimension( * ) tau, double precision, dimension( * ) work, integer
       lwork, integer info)
       DGGSVP3

       Purpose:


           !>
           !> DGGSVP3 computes orthogonal matrices U, V and Q such that
           !>
           !>                    N-K-L  K    L
           !>  U**T*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**T*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**T,B**T)**T.
           !>
           !> This decomposition is the preprocessing step for computing the
           !> Generalized Singular Value Decomposition (GSVD), see subroutine
           !> DGGSVD3.
           !>

       Parameters
           JOBU

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

           JOBV

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

           JOBQ

           !>          JOBQ is CHARACTER*1
           !>          = 'Q':  Orthogonal 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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)*MACHEPS,
           !>             TOLB = MAX(P,N)*norm(B)*MACHEPS.
           !>          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**T,B**T)**T.
           !>

           U

           !>          U is DOUBLE PRECISION array, dimension (LDU,M)
           !>          If JOBU = 'U', U contains the orthogonal 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 DOUBLE PRECISION array, dimension (LDV,P)
           !>          If JOBV = 'V', V contains the orthogonal 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 DOUBLE PRECISION array, dimension (LDQ,N)
           !>          If JOBQ = 'Q', Q contains the orthogonal 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)
           !>

           TAU

           !>          TAU is DOUBLE PRECISION array, dimension (N)
           !>

           WORK

           !>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
           !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
           !>

           LWORK

           !>          LWORK is INTEGER
           !>          The dimension of the array WORK. LWORK >= 1.
           !>
           !>          If LWORK = -1, then a workspace query is assumed; the routine
           !>          only calculates the optimal size of the WORK array, returns
           !>          this value as the first entry of the WORK array, and no error
           !>          message related to LWORK is issued by XERBLA.
           !>

           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 DGEQP3 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.
           !>
           !>  DGGSVP3 replaces the deprecated subroutine DGGSVP.
           !>
           !>

       Definition at line 269 of file dggsvp3.f.

Author
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LAPACK                          Version 3.12.0                SRC/dggsvp3.f(3)