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*> \brief \b ZLARFY
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZLARFY( UPLO, N, V, INCV, TAU, C, LDC, WORK )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER INCV, LDC, N
* COMPLEX*16 TAU
* ..
* .. Array Arguments ..
* COMPLEX*16 C( LDC, * ), V( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZLARFY applies an elementary reflector, or Householder matrix, H,
*> to an n x n Hermitian matrix C, from both the left and the right.
*>
*> H is represented in the form
*>
*> H = I - tau * v * v'
*>
*> where tau is a scalar and v is a vector.
*>
*> If tau is zero, then H is taken to be the unit matrix.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> Specifies whether the upper or lower triangular part of the
*> Hermitian matrix C is stored.
*> = 'U': Upper triangle
*> = 'L': Lower triangle
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of rows and columns of the matrix C. N >= 0.
*> \endverbatim
*>
*> \param[in] V
*> \verbatim
*> V is COMPLEX*16 array, dimension
*> (1 + (N-1)*abs(INCV))
*> The vector v as described above.
*> \endverbatim
*>
*> \param[in] INCV
*> \verbatim
*> INCV is INTEGER
*> The increment between successive elements of v. INCV must
*> not be zero.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is COMPLEX*16
*> The value tau as described above.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is COMPLEX*16 array, dimension (LDC, N)
*> On entry, the matrix C.
*> On exit, C is overwritten by H * C * H'.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*> LDC is INTEGER
*> The leading dimension of the array C. LDC >= max( 1, N ).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (N)
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complex16_eig
*
* =====================================================================
SUBROUTINE ZLARFY( UPLO, N, V, INCV, TAU, C, LDC, WORK )
*
* -- LAPACK test 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 ..
CHARACTER UPLO
INTEGER INCV, LDC, N
COMPLEX*16 TAU
* ..
* .. Array Arguments ..
COMPLEX*16 C( LDC, * ), V( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX*16 ONE, ZERO, HALF
PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
$ ZERO = ( 0.0D+0, 0.0D+0 ),
$ HALF = ( 0.5D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
COMPLEX*16 ALPHA
* ..
* .. External Subroutines ..
EXTERNAL ZAXPY, ZHEMV, ZHER2
* ..
* .. External Functions ..
COMPLEX*16 ZDOTC
EXTERNAL ZDOTC
* ..
* .. Executable Statements ..
*
IF( TAU.EQ.ZERO )
$ RETURN
*
* Form w:= C * v
*
CALL ZHEMV( UPLO, N, ONE, C, LDC, V, INCV, ZERO, WORK, 1 )
*
ALPHA = -HALF*TAU*ZDOTC( N, WORK, 1, V, INCV )
CALL ZAXPY( N, ALPHA, V, INCV, WORK, 1 )
*
* C := C - v * w' - w * v'
*
CALL ZHER2( UPLO, N, -TAU, V, INCV, WORK, 1, C, LDC )
*
RETURN
*
* End of ZLARFY
*
END
|
