You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
160 lines
3.9 KiB
160 lines
3.9 KiB
*> \brief \b CLARFY
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE CLARFY( UPLO, N, V, INCV, TAU, C, LDC, WORK )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* CHARACTER UPLO
|
|
* INTEGER INCV, LDC, N
|
|
* COMPLEX TAU
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* COMPLEX C( LDC, * ), V( * ), WORK( * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> CLARFY 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 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
|
|
*> The value tau as described above.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in,out] C
|
|
*> \verbatim
|
|
*> C is COMPLEX 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 array, dimension (N)
|
|
*> \endverbatim
|
|
*
|
|
* Authors:
|
|
* ========
|
|
*
|
|
*> \author Univ. of Tennessee
|
|
*> \author Univ. of California Berkeley
|
|
*> \author Univ. of Colorado Denver
|
|
*> \author NAG Ltd.
|
|
*
|
|
*> \ingroup complex_eig
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE CLARFY( UPLO, N, V, INCV, TAU, C, LDC, WORK )
|
|
*
|
|
* -- LAPACK test routine --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
*
|
|
* .. Scalar Arguments ..
|
|
CHARACTER UPLO
|
|
INTEGER INCV, LDC, N
|
|
COMPLEX TAU
|
|
* ..
|
|
* .. Array Arguments ..
|
|
COMPLEX C( LDC, * ), V( * ), WORK( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
COMPLEX ONE, ZERO, HALF
|
|
PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ),
|
|
$ ZERO = ( 0.0E+0, 0.0E+0 ),
|
|
$ HALF = ( 0.5E+0, 0.0E+0 ) )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
COMPLEX ALPHA
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL CAXPY, CHEMV, CHER2
|
|
* ..
|
|
* .. External Functions ..
|
|
COMPLEX CDOTC
|
|
EXTERNAL CDOTC
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
IF( TAU.EQ.ZERO )
|
|
$ RETURN
|
|
*
|
|
* Form w:= C * v
|
|
*
|
|
CALL CHEMV( UPLO, N, ONE, C, LDC, V, INCV, ZERO, WORK, 1 )
|
|
*
|
|
ALPHA = -HALF*TAU*CDOTC( N, WORK, 1, V, INCV )
|
|
CALL CAXPY( N, ALPHA, V, INCV, WORK, 1 )
|
|
*
|
|
* C := C - v * w' - w * v'
|
|
*
|
|
CALL CHER2( UPLO, N, -TAU, V, INCV, WORK, 1, C, LDC )
|
|
*
|
|
RETURN
|
|
*
|
|
* End of CLARFY
|
|
*
|
|
END
|
|
|