dorgtr(3F)

NAME
     DORGTR - generate a real orthogonal matrix Q which is defined as the
     product of n-1 elementary reflectors of order N, as returned by DSYTRD

SYNOPSIS
     SUBROUTINE DORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )

         CHARACTER      UPLO

         INTEGER        INFO, LDA, LWORK, N

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

PURPOSE
     DORGTR generates a real orthogonal matrix Q which is defined as the
     product of n-1 elementary reflectors of order N, as returned by DSYTRD:

     if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),

     if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).


ARGUMENTS
     UPLO    (input) CHARACTER*1
             = 'U': Upper triangle of A contains elementary reflectors from
             DSYTRD; = 'L': Lower triangle of A contains elementary reflectors
             from DSYTRD.

     N       (input) INTEGER
             The order of the matrix Q. N >= 0.

     A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
             On entry, the vectors which define the elementary reflectors, as
             returned by DSYTRD.  On exit, the N-by-N orthogonal matrix Q.

     LDA     (input) INTEGER
             The leading dimension of the array A. LDA >= max(1,N).

     TAU     (input) DOUBLE PRECISION array, dimension (N-1)
             TAU(i) must contain the scalar factor of the elementary reflector
             H(i), as returned by DSYTRD.

     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. LWORK >= max(1,N-1).  For
             optimum performance LWORK >= (N-1)*NB, where NB is the optimal
             blocksize.
     INFO    (output) INTEGER
             = 0:  successful exit
             < 0:  if INFO = -i, the i-th argument had an illegal value