!>
!> 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.
!> 

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.
!>
!>          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.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

!>
!>  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.
!>
!>