Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3 - 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

SYNOPSIS

       SUBROUTINE DGGSVP( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, TOLA, TOLB, K, L, U, LDU, V,
                          LDV, Q, LDQ, IWORK, TAU, WORK, INFO )

           CHARACTER      JOBQ, JOBU, JOBV

           INTEGER        INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, P

           DOUBLE         PRECISION TOLA, TOLB

           INTEGER        IWORK( * )

           DOUBLE         PRECISION A( LDA, * ), B( LDB, * ), Q( LDQ, * ), TAU( * ), U( LDU, * ),
                          V( LDV, * ), WORK( * )

PURPOSE

       DGGSVP computes orthogonal matrices U, V and Q such that
                        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
        DGGSVD.

ARGUMENTS

        JOBU    (input) CHARACTER*1
                = 'U':  Orthogonal matrix U is computed;
                = 'N':  U is not computed.

        JOBV    (input) CHARACTER*1
                = 'V':  Orthogonal matrix V is computed;
                = 'N':  V is not computed.

        JOBQ    (input) CHARACTER*1
                = 'Q':  Orthogonal matrix Q is computed;
                = 'N':  Q is not computed.

        M       (input) INTEGER
                The number of rows of the matrix A.  M >= 0.

        P       (input) INTEGER
                The number of rows of the matrix B.  P >= 0.

        N       (input) INTEGER
                The number of columns of the matrices A and B.  N >= 0.

        A       (input/output) 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     (input) INTEGER
                The leading dimension of the array A. LDA >= max(1,M).

        B       (input/output) 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     (input) INTEGER
                The leading dimension of the array B. LDB >= max(1,P).

        TOLA    (input) DOUBLE PRECISION
                TOLB    (input) 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       (output) INTEGER
                L       (output) 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       (output) DOUBLE PRECISION array, dimension (LDU,M)
                If JOBU = 'U', U contains the orthogonal matrix U.
                If JOBU = 'N', U is not referenced.

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

        V       (output) DOUBLE PRECISION array, dimension (LDV,P)
                If JOBV = 'V', V contains the orthogonal matrix V.
                If JOBV = 'N', V is not referenced.

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

        Q       (output) DOUBLE PRECISION array, dimension (LDQ,N)
                If JOBQ = 'Q', Q contains the orthogonal matrix Q.
                If JOBQ = 'N', Q is not referenced.

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

        IWORK   (workspace) INTEGER array, dimension (N)

        TAU     (workspace) DOUBLE PRECISION array, dimension (N)

        WORK    (workspace) DOUBLE PRECISION array, dimension (max(3*N,M,P))

        INFO    (output) INTEGER
                = 0:  successful exit
                < 0:  if INFO = -i, the i-th argument had an illegal value.

FURTHER DETAILS

        The subroutine uses LAPACK subroutine DGEQPF 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.

 LAPACK routine (version 3.3.1)             April 2011                            DGGSVP(3lapack)