!>
!> 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).
!> 

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
!> 

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