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SUBROUTINE CLARFY( UPLO, N, V, INCV, TAU, C, LDC, WORK )
*
* -- LAPACK auxiliary test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INCV, LDC, N
COMPLEX TAU
* ..
* .. Array Arguments ..
COMPLEX C( LDC, * ), V( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* 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.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* Specifies whether the upper or lower triangular part of the
* Hermitian matrix C is stored.
* = 'U': Upper triangle
* = 'L': Lower triangle
*
* N (input) INTEGER
* The number of rows and columns of the matrix C. N >= 0.
*
* V (input) COMPLEX array, dimension
* (1 + (N-1)*abs(INCV))
* The vector v as described above.
*
* INCV (input) INTEGER
* The increment between successive elements of v. INCV must
* not be zero.
*
* TAU (input) COMPLEX
* The value tau as described above.
*
* C (input/output) COMPLEX array, dimension (LDC, N)
* On entry, the matrix C.
* On exit, C is overwritten by H * C * H'.
*
* LDC (input) INTEGER
* The leading dimension of the array C. LDC >= max( 1, N ).
*
* WORK (workspace) COMPLEX array, dimension (N)
*
* =====================================================================
*
* .. 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
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