DORGHR (3lapack)

generate a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by DGEHRD

SYNOPSIS

  SUBROUTINE DORGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )

      INTEGER        IHI, ILO, INFO, LDA, LWORK, N

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

PURPOSE

  DORGHR generates a real orthogonal matrix Q which is defined as the product
  of IHI-ILO elementary reflectors of order N, as returned by DGEHRD:

  Q = H(ilo) H(ilo+1) . . . H(ihi-1).

ARGUMENTS

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

  ILO     (input) INTEGER
          IHI     (input) INTEGER ILO and IHI must have the same values as in
          the previous call of DGEHRD. Q is equal to the unit matrix except
          in the submatrix Q(ilo+1:ihi,ilo+1:ihi).  1 <= ILO <= IHI <= N, if
          N > 0; ILO=1 and IHI=0, if N=0.

  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the vectors which define the elementary reflectors, as
          returned by DGEHRD.  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 DGEHRD.

  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 >= IHI-ILO.  For optimum
          performance LWORK >= (IHI-ILO)*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