#include "ESMF_LapackBlas.inc" !> \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 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