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160 lines
3.9 KiB
160 lines
3.9 KiB
*> \brief \b ZLARFY
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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 ZLARFY( UPLO, N, V, INCV, TAU, C, LDC, WORK )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER INCV, LDC, N
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* COMPLEX*16 TAU
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* ..
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* .. Array Arguments ..
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* COMPLEX*16 C( LDC, * ), V( * ), 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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*> ZLARFY applies an elementary reflector, or Householder matrix, H,
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*> to an n x n Hermitian matrix C, from both the left and the right.
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*>
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*> H is represented in the form
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*>
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*> H = I - tau * v * v'
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*>
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*> where tau is a scalar and v is a vector.
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*>
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*> If tau is zero, then H is taken to be the unit matrix.
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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] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> Specifies whether the upper or lower triangular part of the
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*> Hermitian matrix C is stored.
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*> = 'U': Upper triangle
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*> = 'L': Lower triangle
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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 rows and columns of the matrix C. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] V
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*> \verbatim
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*> V is COMPLEX*16 array, dimension
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*> (1 + (N-1)*abs(INCV))
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*> The vector v as described above.
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*> \endverbatim
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*>
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*> \param[in] INCV
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*> \verbatim
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*> INCV is INTEGER
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*> The increment between successive elements of v. INCV must
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*> not be zero.
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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
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*> The value tau as described above.
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*> \endverbatim
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*>
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*> \param[in,out] C
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*> \verbatim
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*> C is COMPLEX*16 array, dimension (LDC, N)
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*> On entry, the matrix C.
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*> On exit, C is overwritten by H * C * H'.
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*> \endverbatim
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*>
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*> \param[in] LDC
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*> \verbatim
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*> LDC is INTEGER
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*> The leading dimension of the array C. LDC >= max( 1, N ).
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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 (N)
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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 complex16OTHERauxiliary
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*
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* =====================================================================
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SUBROUTINE ZLARFY( UPLO, N, V, INCV, TAU, C, LDC, WORK )
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*
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* -- LAPACK test 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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CHARACTER UPLO
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INTEGER INCV, LDC, N
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COMPLEX*16 TAU
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* ..
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* .. Array Arguments ..
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COMPLEX*16 C( LDC, * ), V( * ), 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 ONE, ZERO, HALF
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PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
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$ ZERO = ( 0.0D+0, 0.0D+0 ),
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$ HALF = ( 0.5D+0, 0.0D+0 ) )
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* ..
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* .. Local Scalars ..
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COMPLEX*16 ALPHA
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* ..
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* .. External Subroutines ..
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EXTERNAL ZAXPY, ZHEMV, ZHER2
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* ..
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* .. External Functions ..
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COMPLEX*16 ZDOTC
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EXTERNAL ZDOTC
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* ..
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* .. Executable Statements ..
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*
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IF( TAU.EQ.ZERO )
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$ RETURN
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*
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* Form w:= C * v
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*
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CALL ZHEMV( UPLO, N, ONE, C, LDC, V, INCV, ZERO, WORK, 1 )
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*
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ALPHA = -HALF*TAU*ZDOTC( N, WORK, 1, V, INCV )
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CALL ZAXPY( N, ALPHA, V, INCV, WORK, 1 )
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*
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* C := C - v * w' - w * v'
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*
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CALL ZHER2( UPLO, N, -TAU, V, INCV, WORK, 1, C, LDC )
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*
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RETURN
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*
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* End of ZLARFY
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*
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END
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