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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