!>
!> This routine is deprecated and has been replaced by routine SGGSVP3.
!>
!> SGGSVP 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
!> SGGSVD.
!> 

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 REAL 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 REAL 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 REAL
!> 

TOLB

!>          TOLB is REAL
!>
!>          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 REAL 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 REAL 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 REAL 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 REAL array, dimension (N)
!> 

WORK

!>          WORK is REAL 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.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

The subroutine uses LAPACK subroutine SGEQPF 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.