NAME

       dormbr.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dormbr (VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
           DORMBR

Function/Subroutine Documentation

   subroutine dormbr (character VECT, character SIDE, character TRANS, integer M, integer N,
       integer K, double precision, dimension( lda, * ) A, integer LDA, double precision,
       dimension( * ) TAU, double precision, dimension( ldc, * ) C, integer LDC, double
       precision, dimension( * ) WORK, integer LWORK, integer INFO)
       DORMBR

       Purpose:

            If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C
            with
                            SIDE = 'L'     SIDE = 'R'
            TRANS = 'N':      Q * C          C * Q
            TRANS = 'T':      Q**T * C       C * Q**T

            If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C
            with
                            SIDE = 'L'     SIDE = 'R'
            TRANS = 'N':      P * C          C * P
            TRANS = 'T':      P**T * C       C * P**T

            Here Q and P**T are the orthogonal matrices determined by DGEBRD 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) and G(i)
            respectively.

            Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
            order of the orthogonal matrix Q or P**T that is applied.

            If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
            if nq >= k, Q = H(1) H(2) . . . H(k);
            if nq < k, Q = H(1) H(2) . . . H(nq-1).

            If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
            if k < nq, P = G(1) G(2) . . . G(k);
            if k >= nq, P = G(1) G(2) . . . G(nq-1).

       Parameters:
           VECT

                     VECT is CHARACTER*1
                     = 'Q': apply Q or Q**T;
                     = 'P': apply P or P**T.

           SIDE

                     SIDE is CHARACTER*1
                     = 'L': apply Q, Q**T, P or P**T from the Left;
                     = 'R': apply Q, Q**T, P or P**T from the Right.

           TRANS

                     TRANS is CHARACTER*1
                     = 'N':  No transpose, apply Q  or P;
                     = 'T':  Transpose, apply Q**T or P**T.

           M

                     M is INTEGER
                     The number of rows of the matrix C. M >= 0.

           N

                     N is INTEGER
                     The number of columns of the matrix C. N >= 0.

           K

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

           A

                     A is DOUBLE PRECISION array, dimension
                                           (LDA,min(nq,K)) if VECT = 'Q'
                                           (LDA,nq)        if VECT = 'P'
                     The vectors which define the elementary reflectors H(i) and
                     G(i), whose products determine the matrices Q and P, as
                     returned by DGEBRD.

           LDA

                     LDA is INTEGER
                     The leading dimension of the array A.
                     If VECT = 'Q', LDA >= max(1,nq);
                     if VECT = 'P', LDA >= max(1,min(nq,K)).

           TAU

                     TAU is DOUBLE PRECISION array, dimension (min(nq,K))
                     TAU(i) must contain the scalar factor of the elementary
                     reflector H(i) or G(i) which determines Q or P, as returned
                     by DGEBRD in the array argument TAUQ or TAUP.

           C

                     C is DOUBLE PRECISION array, dimension (LDC,N)
                     On entry, the M-by-N matrix C.
                     On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q
                     or P*C or P**T*C or C*P or C*P**T.

           LDC

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

           WORK

                     WORK is DOUBLE PRECISION 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.
                     If SIDE = 'L', LWORK >= max(1,N);
                     if SIDE = 'R', LWORK >= max(1,M).
                     For optimum performance LWORK >= N*NB if SIDE = 'L', and
                     LWORK >= M*NB if SIDE = 'R', 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:
           November 2011

Author

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