NAME

       cggsvp.f -

SYNOPSIS

   Functions/Subroutines
       subroutine cggsvp (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)
           CGGSVP

Function/Subroutine Documentation

   subroutine cggsvp (characterJOBU, characterJOBV, characterJOBQ, integerM, integerP, integerN,
       complex, dimension( lda, * )A, integerLDA, complex, dimension( ldb, * )B, integerLDB,
       realTOLA, realTOLB, integerK, integerL, complex, dimension( ldu, * )U, integerLDU,
       complex, dimension( ldv, * )V, integerLDV, complex, dimension( ldq, * )Q, integerLDQ,
       integer, dimension( * )IWORK, real, dimension( * )RWORK, complex, dimension( * )TAU,
       complex, dimension( * )WORK, integerINFO)
       CGGSVP

       Purpose:

            CGGSVP 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
            CGGSVD.

       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 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 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**H,B**H)**H.

           U

                     U is COMPLEX 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 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 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 REAL array, dimension (2*N)

           TAU

                     TAU is COMPLEX array, dimension (N)

           WORK

                     WORK is COMPLEX 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.

       Date:
           November 2011

       Further Details:
           The subroutine uses LAPACK subroutine CGEQPF 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 259 of file cggsvp.f.

Author

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