DORGRQ(3)      LAPACK routine of NEC Numeric Library Collection      DORGRQ(3)



NAME
       DORGRQ

SYNOPSIS
       SUBROUTINE DORGRQ (M, N, K, A, LDA, TAU, WORK, LWORK, INFO)



PURPOSE
            DORGRQ generates an M-by-N real matrix Q with orthonormal rows,
            which is defined as the last M rows of a product of K elementary
            reflectors of order N

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

            as returned by DGERQF.




ARGUMENTS
           M         (input)
                     M is INTEGER
                     The number of rows of the matrix Q. M >= 0.

           N         (input)
                     N is INTEGER
                     The number of columns of the matrix Q. N >= M.

           K         (input)
                     K is INTEGER
                     The number of elementary reflectors whose product defines the
                     matrix Q. M >= K >= 0.

           A         (input/output)
                     A is DOUBLE PRECISION array, dimension (LDA,N)
                     On entry, the (m-k+i)-th row must contain the vector which
                     defines the elementary reflector H(i), for i = 1,2,...,k, as
                     returned by DGERQF in the last k rows of its array argument
                     A.
                     On exit, the M-by-N matrix Q.

           LDA       (input)
                     LDA is INTEGER
                     The first dimension of the array A. LDA >= max(1,M).

           TAU       (input)
                     TAU is DOUBLE PRECISION array, dimension (K)
                     TAU(i) must contain the scalar factor of the elementary
                     reflector H(i), as returned by DGERQF.

           WORK      (output)
                     WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK     (input)
                     LWORK is INTEGER
                     The dimension of the array WORK. LWORK >= max(1,M).
                     For optimum performance LWORK >= M*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      (output)
                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument has an illegal value



LAPACK routine                  31 October 2017                      DORGRQ(3)