DORMQR 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


 where Q is a real orthogonal matrix defined as the product of k


 elementary reflectors


       Q = H(1) H(2) . . . H(k)


 as returned by DGEQRF. Q is of order M if SIDE = 'L' and of order N


 if SIDE = 'R'.

SIDE

          SIDE is CHARACTER*1


          = 'L': apply Q or Q**T from the Left;


          = 'R': apply Q or Q**T from the Right.

TRANS

          TRANS is CHARACTER*1


          = 'N':  No transpose, apply Q;


          = 'T':  Transpose, apply Q**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


          The number of elementary reflectors whose product defines


          the matrix Q.


          If SIDE = 'L', M >= K >= 0;


          if SIDE = 'R', N >= K >= 0.

A

          A is DOUBLE PRECISION array, dimension (LDA,K)


          The i-th column must contain the vector which defines the


          elementary reflector H(i), for i = 1,2,...,k, as returned by


          DGEQRF in the first k columns of its array argument A.

LDA

          LDA is INTEGER


          The leading dimension of the array A.


          If SIDE = 'L', LDA >= max(1,M);


          if SIDE = 'R', LDA >= max(1,N).

TAU

          TAU is DOUBLE PRECISION array, dimension (K)


          TAU(i) must contain the scalar factor of the elementary


          reflector H(i), as returned by DGEQRF.

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.

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.

November 2011