364 lines
11 KiB
Fortran
364 lines
11 KiB
Fortran
*> \brief \b ZLAGGE
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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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* Definition:
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* ===========
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*
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* SUBROUTINE ZLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, KL, KU, LDA, M, N
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* ..
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* .. Array Arguments ..
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* INTEGER ISEED( 4 )
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* DOUBLE PRECISION D( * )
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* COMPLEX*16 A( LDA, * ), 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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*> ZLAGGE generates a complex general m by n matrix A, by pre- and post-
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*> multiplying a real diagonal matrix D with random unitary matrices:
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*> A = U*D*V. The lower and upper bandwidths may then be reduced to
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*> kl and ku by additional unitary transformations.
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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] M
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*> \verbatim
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*> M is INTEGER
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*> The number of rows of the matrix A. M >= 0.
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*> \endverbatim
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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 number of columns of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] KL
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*> \verbatim
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*> KL is INTEGER
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*> The number of nonzero subdiagonals within the band of A.
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*> 0 <= KL <= M-1.
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*> \endverbatim
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*>
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*> \param[in] KU
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*> \verbatim
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*> KU is INTEGER
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*> The number of nonzero superdiagonals within the band of A.
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*> 0 <= KU <= N-1.
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*> \endverbatim
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*>
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*> \param[in] D
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*> \verbatim
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*> D is DOUBLE PRECISION array, dimension (min(M,N))
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*> The diagonal elements of the diagonal matrix D.
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*> \endverbatim
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*>
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*> \param[out] A
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*> \verbatim
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*> A is COMPLEX*16 array, dimension (LDA,N)
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*> The generated m by n matrix A.
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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 >= M.
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*> \endverbatim
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*>
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*> \param[in,out] ISEED
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*> \verbatim
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*> ISEED is INTEGER array, dimension (4)
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*> On entry, the seed of the random number generator; the array
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*> elements must be between 0 and 4095, and ISEED(4) must be
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*> odd.
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*> On exit, the seed is updated.
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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 (M+N)
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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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*> \date November 2011
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*
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*> \ingroup complex16_matgen
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*
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* =====================================================================
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SUBROUTINE ZLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO )
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*
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* -- LAPACK auxiliary routine (version 3.4.0) --
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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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* November 2011
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*
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* .. Scalar Arguments ..
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INTEGER INFO, KL, KU, LDA, M, N
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* ..
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* .. Array Arguments ..
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INTEGER ISEED( 4 )
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DOUBLE PRECISION D( * )
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COMPLEX*16 A( LDA, * ), 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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INTEGER I, J
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DOUBLE PRECISION WN
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COMPLEX*16 TAU, WA, WB
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, ZGEMV, ZGERC, ZLACGV, ZLARNV, ZSCAL
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, DBLE, MAX, MIN
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DZNRM2
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EXTERNAL DZNRM2
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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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IF( M.LT.0 ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( KL.LT.0 .OR. KL.GT.M-1 ) THEN
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INFO = -3
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ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN
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INFO = -4
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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INFO = -7
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END IF
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IF( INFO.LT.0 ) THEN
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CALL XERBLA( 'ZLAGGE', -INFO )
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RETURN
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END IF
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*
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* initialize A to diagonal matrix
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*
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DO 20 J = 1, N
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DO 10 I = 1, M
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A( I, J ) = ZERO
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10 CONTINUE
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20 CONTINUE
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DO 30 I = 1, MIN( M, N )
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A( I, I ) = D( I )
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30 CONTINUE
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*
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* pre- and post-multiply A by random unitary matrices
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*
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DO 40 I = MIN( M, N ), 1, -1
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IF( I.LT.M ) THEN
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*
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* generate random reflection
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*
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CALL ZLARNV( 3, ISEED, M-I+1, WORK )
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WN = DZNRM2( M-I+1, WORK, 1 )
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WA = ( WN / ABS( WORK( 1 ) ) )*WORK( 1 )
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IF( WN.EQ.ZERO ) THEN
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TAU = ZERO
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ELSE
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WB = WORK( 1 ) + WA
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CALL ZSCAL( M-I, ONE / WB, WORK( 2 ), 1 )
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WORK( 1 ) = ONE
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TAU = DBLE( WB / WA )
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END IF
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*
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* multiply A(i:m,i:n) by random reflection from the left
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*
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CALL ZGEMV( 'Conjugate transpose', M-I+1, N-I+1, ONE,
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$ A( I, I ), LDA, WORK, 1, ZERO, WORK( M+1 ), 1 )
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CALL ZGERC( M-I+1, N-I+1, -TAU, WORK, 1, WORK( M+1 ), 1,
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$ A( I, I ), LDA )
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END IF
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IF( I.LT.N ) THEN
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*
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* generate random reflection
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*
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CALL ZLARNV( 3, ISEED, N-I+1, WORK )
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WN = DZNRM2( N-I+1, WORK, 1 )
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WA = ( WN / ABS( WORK( 1 ) ) )*WORK( 1 )
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IF( WN.EQ.ZERO ) THEN
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TAU = ZERO
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ELSE
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WB = WORK( 1 ) + WA
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CALL ZSCAL( N-I, ONE / WB, WORK( 2 ), 1 )
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WORK( 1 ) = ONE
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TAU = DBLE( WB / WA )
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END IF
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*
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* multiply A(i:m,i:n) by random reflection from the right
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*
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CALL ZGEMV( 'No transpose', M-I+1, N-I+1, ONE, A( I, I ),
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$ LDA, WORK, 1, ZERO, WORK( N+1 ), 1 )
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CALL ZGERC( M-I+1, N-I+1, -TAU, WORK( N+1 ), 1, WORK, 1,
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$ A( I, I ), LDA )
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END IF
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40 CONTINUE
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*
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* Reduce number of subdiagonals to KL and number of superdiagonals
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* to KU
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*
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DO 70 I = 1, MAX( M-1-KL, N-1-KU )
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IF( KL.LE.KU ) THEN
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*
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* annihilate subdiagonal elements first (necessary if KL = 0)
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*
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IF( I.LE.MIN( M-1-KL, N ) ) THEN
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*
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* generate reflection to annihilate A(kl+i+1:m,i)
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*
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WN = DZNRM2( M-KL-I+1, A( KL+I, I ), 1 )
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WA = ( WN / ABS( A( KL+I, I ) ) )*A( KL+I, I )
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IF( WN.EQ.ZERO ) THEN
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TAU = ZERO
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ELSE
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WB = A( KL+I, I ) + WA
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CALL ZSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 )
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A( KL+I, I ) = ONE
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TAU = DBLE( WB / WA )
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END IF
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*
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* apply reflection to A(kl+i:m,i+1:n) from the left
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*
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CALL ZGEMV( 'Conjugate transpose', M-KL-I+1, N-I, ONE,
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$ A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO,
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$ WORK, 1 )
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CALL ZGERC( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK,
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$ 1, A( KL+I, I+1 ), LDA )
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A( KL+I, I ) = -WA
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END IF
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*
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IF( I.LE.MIN( N-1-KU, M ) ) THEN
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*
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* generate reflection to annihilate A(i,ku+i+1:n)
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*
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WN = DZNRM2( N-KU-I+1, A( I, KU+I ), LDA )
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WA = ( WN / ABS( A( I, KU+I ) ) )*A( I, KU+I )
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IF( WN.EQ.ZERO ) THEN
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TAU = ZERO
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ELSE
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WB = A( I, KU+I ) + WA
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CALL ZSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA )
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A( I, KU+I ) = ONE
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TAU = DBLE( WB / WA )
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END IF
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*
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* apply reflection to A(i+1:m,ku+i:n) from the right
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*
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CALL ZLACGV( N-KU-I+1, A( I, KU+I ), LDA )
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CALL ZGEMV( 'No transpose', M-I, N-KU-I+1, ONE,
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$ A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO,
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$ WORK, 1 )
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CALL ZGERC( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ),
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$ LDA, A( I+1, KU+I ), LDA )
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A( I, KU+I ) = -WA
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END IF
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ELSE
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*
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* annihilate superdiagonal elements first (necessary if
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* KU = 0)
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*
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IF( I.LE.MIN( N-1-KU, M ) ) THEN
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*
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* generate reflection to annihilate A(i,ku+i+1:n)
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*
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WN = DZNRM2( N-KU-I+1, A( I, KU+I ), LDA )
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WA = ( WN / ABS( A( I, KU+I ) ) )*A( I, KU+I )
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IF( WN.EQ.ZERO ) THEN
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TAU = ZERO
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ELSE
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WB = A( I, KU+I ) + WA
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CALL ZSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA )
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A( I, KU+I ) = ONE
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TAU = DBLE( WB / WA )
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END IF
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*
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* apply reflection to A(i+1:m,ku+i:n) from the right
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*
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CALL ZLACGV( N-KU-I+1, A( I, KU+I ), LDA )
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CALL ZGEMV( 'No transpose', M-I, N-KU-I+1, ONE,
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$ A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO,
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$ WORK, 1 )
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CALL ZGERC( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ),
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$ LDA, A( I+1, KU+I ), LDA )
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A( I, KU+I ) = -WA
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END IF
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*
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IF( I.LE.MIN( M-1-KL, N ) ) THEN
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*
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* generate reflection to annihilate A(kl+i+1:m,i)
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*
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WN = DZNRM2( M-KL-I+1, A( KL+I, I ), 1 )
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WA = ( WN / ABS( A( KL+I, I ) ) )*A( KL+I, I )
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IF( WN.EQ.ZERO ) THEN
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TAU = ZERO
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ELSE
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WB = A( KL+I, I ) + WA
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CALL ZSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 )
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A( KL+I, I ) = ONE
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TAU = DBLE( WB / WA )
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END IF
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*
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* apply reflection to A(kl+i:m,i+1:n) from the left
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*
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CALL ZGEMV( 'Conjugate transpose', M-KL-I+1, N-I, ONE,
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$ A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO,
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$ WORK, 1 )
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CALL ZGERC( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK,
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$ 1, A( KL+I, I+1 ), LDA )
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A( KL+I, I ) = -WA
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END IF
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END IF
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*
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DO 50 J = KL + I + 1, M
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A( J, I ) = ZERO
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50 CONTINUE
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*
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DO 60 J = KU + I + 1, N
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A( I, J ) = ZERO
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60 CONTINUE
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70 CONTINUE
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RETURN
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*
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* End of ZLAGGE
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*
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END
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