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239 lines
6.4 KiB
239 lines
6.4 KiB
2 years ago
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*> \brief \b ZUNGHR
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download ZUNGHR + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zunghr.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zunghr.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zunghr.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE ZUNGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER IHI, ILO, INFO, LDA, LWORK, N
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* ..
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* .. Array Arguments ..
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* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> ZUNGHR generates a complex unitary matrix Q which is defined as the
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*> product of IHI-ILO elementary reflectors of order N, as returned by
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*> ZGEHRD:
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*>
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*> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the matrix Q. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] ILO
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*> \verbatim
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*> ILO is INTEGER
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*> \endverbatim
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*>
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*> \param[in] IHI
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*> \verbatim
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*> IHI is INTEGER
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*>
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*> ILO and IHI must have the same values as in the previous call
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*> of ZGEHRD. Q is equal to the unit matrix except in the
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*> submatrix Q(ilo+1:ihi,ilo+1:ihi).
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*> 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
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*> \endverbatim
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*>
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*> \param[in,out] A
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*> \verbatim
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*> A is COMPLEX*16 array, dimension (LDA,N)
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*> On entry, the vectors which define the elementary reflectors,
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*> as returned by ZGEHRD.
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*> On exit, the N-by-N unitary matrix Q.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in] TAU
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*> \verbatim
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*> TAU is COMPLEX*16 array, dimension (N-1)
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*> TAU(i) must contain the scalar factor of the elementary
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*> reflector H(i), as returned by ZGEHRD.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
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*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The dimension of the array WORK. LWORK >= IHI-ILO.
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*> For optimum performance LWORK >= (IHI-ILO)*NB, where NB is
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*> the optimal blocksize.
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*>
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*> If LWORK = -1, then a workspace query is assumed; the routine
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*> only calculates the optimal size of the WORK array, returns
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*> this value as the first entry of the WORK array, and no error
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*> message related to LWORK is issued by XERBLA.
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument had an illegal value
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup complex16OTHERcomputational
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*
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* =====================================================================
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SUBROUTINE ZUNGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
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*
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* -- LAPACK computational routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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INTEGER IHI, ILO, INFO, LDA, LWORK, N
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* ..
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* .. Array Arguments ..
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COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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COMPLEX*16 ZERO, ONE
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PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ),
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$ ONE = ( 1.0D+0, 0.0D+0 ) )
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* ..
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* .. Local Scalars ..
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LOGICAL LQUERY
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INTEGER I, IINFO, J, LWKOPT, NB, NH
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, ZUNGQR
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* ..
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* .. External Functions ..
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INTEGER ILAENV
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EXTERNAL ILAENV
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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* Test the input arguments
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*
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INFO = 0
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NH = IHI - ILO
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LQUERY = ( LWORK.EQ.-1 )
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IF( N.LT.0 ) THEN
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INFO = -1
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ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN
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INFO = -2
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ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN
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INFO = -3
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -5
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ELSE IF( LWORK.LT.MAX( 1, NH ) .AND. .NOT.LQUERY ) THEN
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INFO = -8
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END IF
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*
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IF( INFO.EQ.0 ) THEN
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NB = ILAENV( 1, 'ZUNGQR', ' ', NH, NH, NH, -1 )
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LWKOPT = MAX( 1, NH )*NB
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WORK( 1 ) = LWKOPT
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END IF
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'ZUNGHR', -INFO )
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RETURN
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ELSE IF( LQUERY ) THEN
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 ) THEN
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WORK( 1 ) = 1
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RETURN
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END IF
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*
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* Shift the vectors which define the elementary reflectors one
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* column to the right, and set the first ilo and the last n-ihi
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* rows and columns to those of the unit matrix
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*
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DO 40 J = IHI, ILO + 1, -1
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DO 10 I = 1, J - 1
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A( I, J ) = ZERO
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10 CONTINUE
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DO 20 I = J + 1, IHI
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A( I, J ) = A( I, J-1 )
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20 CONTINUE
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DO 30 I = IHI + 1, N
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A( I, J ) = ZERO
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30 CONTINUE
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40 CONTINUE
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DO 60 J = 1, ILO
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DO 50 I = 1, N
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A( I, J ) = ZERO
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50 CONTINUE
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A( J, J ) = ONE
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60 CONTINUE
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DO 80 J = IHI + 1, N
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DO 70 I = 1, N
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A( I, J ) = ZERO
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70 CONTINUE
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A( J, J ) = ONE
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80 CONTINUE
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*
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IF( NH.GT.0 ) THEN
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*
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* Generate Q(ilo+1:ihi,ilo+1:ihi)
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*
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CALL ZUNGQR( NH, NH, NH, A( ILO+1, ILO+1 ), LDA, TAU( ILO ),
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$ WORK, LWORK, IINFO )
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END IF
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WORK( 1 ) = LWKOPT
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RETURN
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*
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* End of ZUNGHR
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*
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END
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