dorghr.F90 Source File


Source Code

#include "ESMF_LapackBlas.inc"
!> \brief \b DORGHR
!
!  =========== DOCUMENTATION ===========
!
! Online html documentation available at
!            http://www.netlib.org/lapack/explore-html/
!
!> \htmlonly
!> Download DORGHR + dependencies
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!> [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 December 2016
!
!> \ingroup doubleOTHERcomputational
!
!  =====================================================================
      SUBROUTINE DORGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
!
!  -- LAPACK computational routine (version 3.7.0) --
!  -- LAPACK is a software package provided by Univ. of Tennessee,    --
!  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
!     December 2016
!
!     .. 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