SRC/sggsvp3.f(3)

NAME
SRC/sggsvp3.f

SYNOPSIS

  Functions/Subroutines
subroutine sggsvp3 (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)
SGGSVP3

Function/Subroutine Documentation

  subroutine sggsvp3 (character jobu, character jobv, character jobq, integer m, integer p, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real tola, real tolb, integer k, integer l, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldv, * ) v, integer ldv, real, dimension( ldq, * ) q, integer ldq, integer, dimension( * ) iwork, real, dimension( * ) tau, real, dimension( * ) work, integer lwork, integer info)

SGGSVP3

Purpose:

    !>
    !> SGGSVP3 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
    !> SGGSVD3.
    !>

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 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(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 SGEQP3 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.
    !>
    !>  SGGSVP3 replaces the deprecated subroutine SGGSVP.
    !>
    !>

Definition at line 269 of file sggsvp3.f.

Author

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