dormqr(3F)

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 elementary 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/output) 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