sggsvp.f(3)

NAME
sggsvp.f -

SYNOPSIS

  Functions/Subroutines
subroutine sggsvp (JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ, IWORK, TAU, WORK, INFO)
SGGSVP

Function/Subroutine Documentation

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

SGGSVP

Purpose:

     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.

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(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 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.

Definition at line 253 of file sggsvp.f.

Author

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