dorghr.f

Go to the documentation of this file.

*> \brief \b DORGHR
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*> \htmlonly
*> Download DORGHR + dependencies 
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorghr.f"> 
*> [TGZ]</a> 
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorghr.f"> 
*> [ZIP]</a> 
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorghr.f"> 
*> [TXT]</a>
*> \endhtmlonly 
*
*  Definition:
*  ===========
*
*       SUBROUTINE DORGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
* 
*       .. Scalar Arguments ..
*       INTEGER            IHI, ILO, INFO, LDA, LWORK, N
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> 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).
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix Q. N >= 0.
*> \endverbatim
*>
*> \param[in] ILO
*> \verbatim
*>          ILO is INTEGER
*> \endverbatim
*>
*> \param[in] IHI
*> \verbatim
*>          IHI is 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.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*>          TAU is DOUBLE PRECISION array, dimension (N-1)
*>          TAU(i) must contain the scalar factor of the elementary
*>          reflector H(i), as returned by DGEHRD.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*>          LWORK is INTEGER
*>          The dimension of the array WORK. LWORK >= IHI-ILO.
*>          For optimum performance LWORK >= (IHI-ILO)*NB, where NB is
*>          the optimal blocksize.
*>
*>          If LWORK = -1, then a workspace query is assumed; the routine
*>          only calculates the optimal size of the WORK array, returns
*>          this value as the first entry of the WORK array, and no error
*>          message related to LWORK is issued by XERBLA.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0:  successful exit
*>          < 0:  if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date November 2011
*
*> \ingroup doubleOTHERcomputational
*
*  =====================================================================
      SUBROUTINE dorghr( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
*
*  -- LAPACK computational routine (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      INTEGER            ihi, ilo, info, lda, lwork, n
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   a( lda, * ), tau( * ), work( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   zero, one
      parameter( zero = 0.0d+0, one = 1.0d+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            lquery
      INTEGER            i, iinfo, j, lwkopt, nb, nh
*     ..
*     .. External Subroutines ..
      EXTERNAL           dorgqr, xerbla
*     ..
*     .. External Functions ..
      INTEGER            ilaenv
      EXTERNAL           ilaenv
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      info = 0
      nh = ihi - ilo
      lquery = ( lwork.EQ.-1 )
      IF( n.LT.0 ) THEN
         info = -1
      ELSE IF( ilo.LT.1 .OR. ilo.GT.max( 1, n ) ) THEN
         info = -2
      ELSE IF( ihi.LT.min( ilo, n ) .OR. ihi.GT.n ) THEN
         info = -3
      ELSE IF( lda.LT.max( 1, n ) ) THEN
         info = -5
      ELSE IF( lwork.LT.max( 1, nh ) .AND. .NOT.lquery ) THEN
         info = -8
      END IF
*
      IF( info.EQ.0 ) THEN
         nb = ilaenv( 1, 'DORGQR', ' ', nh, nh, nh, -1 )
         lwkopt = max( 1, nh )*nb
         work( 1 ) = lwkopt
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DORGHR', -info )
         return
      ELSE IF( lquery ) THEN
         return
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 ) THEN
         work( 1 ) = 1
         return
      END IF
*
*     Shift the vectors which define the elementary reflectors one
*     column to the right, and set the first ilo and the last n-ihi
*     rows and columns to those of the unit matrix
*
      DO 40 j = ihi, ilo + 1, -1
         DO 10 i = 1, j - 1
            a( i, j ) = zero
   10    continue
         DO 20 i = j + 1, ihi
            a( i, j ) = a( i, j-1 )
   20    continue
         DO 30 i = ihi + 1, n
            a( i, j ) = zero
   30    continue
   40 continue
      DO 60 j = 1, ilo
         DO 50 i = 1, n
            a( i, j ) = zero
   50    continue
         a( j, j ) = one
   60 continue
      DO 80 j = ihi + 1, n
         DO 70 i = 1, n
            a( i, j ) = zero
   70    continue
         a( j, j ) = one
   80 continue
*
      IF( nh.GT.0 ) THEN
*
*        Generate Q(ilo+1:ihi,ilo+1:ihi)
*
         CALL dorgqr( nh, nh, nh, a( ilo+1, ilo+1 ), lda, tau( ilo ),
     $                work, lwork, iinfo )
      END IF
      work( 1 ) = lwkopt
      return
*
*     End of DORGHR
*
      END