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dorgrq

 NAME
      DORGRQ - generate an M-by-N real matrix Q with orthonormal
      rows,

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

          INTEGER        INFO, K, LDA, LWORK, M, N

          DOUBLE         PRECISION A( LDA, * ), TAU( * ), WORK(
                         LWORK )

 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) INTEGER
              The number of rows of the matrix Q. M >= 0.

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

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

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

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

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

      LWORK   (input) INTEGER

              The dimension of the array WORK. LWORK >= max(1,M).
              For optimum performance LWORK >= M*NB, where NB is
              the optimal blocksize.

      INFO    (output) INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument has an illegal
              value