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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NAG Ltd.

December 2016