sorgbr.f(3)

NAME
sorgbr.f -

SYNOPSIS

  Functions/Subroutines

subroutine sorgbr (VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGBR

Function/Subroutine Documentation

  subroutine sorgbr (characterVECT, integerM, integerN, integerK, real, dimension( lda, * )A, integerLDA, real, dimension( * )TAU, real, dimension( * )WORK, integerLWORK, integerINFO)

SORGBR

Purpose:

     SORGBR generates one of the real orthogonal matrices Q or P**T
     determined by SGEBRD when reducing a real matrix A to bidiagonal
     form: A = Q * B * P**T.  Q and P**T are defined as products of
     elementary reflectors H(i) or G(i) respectively.

     If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
     is of order M:
     if m >= k, Q = H(1) H(2) . . . H(k) and SORGBR returns the first n
     columns of Q, where m >= n >= k;
     if m < k, Q = H(1) H(2) . . . H(m-1) and SORGBR returns Q as an
     M-by-M matrix.

     If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T
     is of order N:
     if k < n, P**T = G(k) . . . G(2) G(1) and SORGBR returns the first m
     rows of P**T, where n >= m >= k;
     if k >= n, P**T = G(n-1) . . . G(2) G(1) and SORGBR returns P**T as
     an N-by-N matrix.

Parameters:
    VECT

              VECT is CHARACTER*1
              Specifies whether the matrix Q or the matrix P**T is
              required, as defined in the transformation applied by SGEBRD:
              = 'Q':  generate Q;
              = 'P':  generate P**T.

    M

              M is INTEGER
              The number of rows of the matrix Q or P**T to be returned.
              M >= 0.

    N

              N is INTEGER
              The number of columns of the matrix Q or P**T to be returned.
              N >= 0.
              If VECT = 'Q', M >= N >= min(M,K);
              if VECT = 'P', N >= M >= min(N,K).

    K

              K is INTEGER
              If VECT = 'Q', the number of columns in the original M-by-K
              matrix reduced by SGEBRD.
              If VECT = 'P', the number of rows in the original K-by-N
              matrix reduced by SGEBRD.
              K >= 0.

    A

              A is REAL array, dimension (LDA,N)
              On entry, the vectors which define the elementary reflectors,
              as returned by SGEBRD.
              On exit, the M-by-N matrix Q or P**T.

    LDA

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

    TAU

              TAU is REAL array, dimension
                                    (min(M,K)) if VECT = 'Q'
                                    (min(N,K)) if VECT = 'P'
              TAU(i) must contain the scalar factor of the elementary
              reflector H(i) or G(i), which determines Q or P**T, as
              returned by SGEBRD in its array argument TAUQ or TAUP.

    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 >= max(1,min(M,N)).
              For optimum performance LWORK >= min(M,N)*NB, where NB
              is the optimal blocksize.

              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.

Date:
    April 2012

Definition at line 158 of file sorgbr.f.

Author

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