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dormqr

 NAME
      DORMQR - overwrite the general real M-by-N matrix C with
      SIDE = 'L' SIDE = 'R' TRANS = 'N'

 SYNOPSIS
      SUBROUTINE DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C,
                         LDC, WORK, LWORK, INFO )

          CHARACTER      SIDE, TRANS

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

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

 PURPOSE
      DORMQR overwrites the general real M-by-N matrix C with
      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'.

 ARGUMENTS
      SIDE    (input) CHARACTER*1
              = 'L': apply Q or Q**T from the Left;
              = 'R': apply Q or Q**T from the Right.

      TRANS   (input) CHARACTER*1
              = 'N':  No transpose, apply Q;
              = 'T':  Transpose, apply Q**T.

      M       (input) INTEGER
              The number of rows of the matrix C. M >= 0.

      N       (input) INTEGER
              The number of columns of the matrix C. N >= 0.

      K       (input) 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       (input) 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.  A is modified by
              the routine but restored on exit.

      LDA     (input) INTEGER
              The leading dimension of the array A.  If SIDE =
              'L', LDA >= max(1,M); if SIDE = 'R', LDA >=
              max(1,N).

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

      C       (input/output) 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     (input) INTEGER
              The leading dimension of the array C. LDC >=
              max(1,M).

      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.  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.

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