clarfy()

subroutine clarfy	(	character	UPLO,
		integer	N,
		complex, dimension( * )	V,
		integer	INCV,
		complex	TAU,
		complex, dimension( ldc, * )	C,
		integer	LDC,
		complex, dimension( * )	WORK
	)

CLARFY

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.

Parameters

[in]	UPLO	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
[in]	N	N is INTEGER The number of rows and columns of the matrix C. N >= 0.
[in]	V	V is COMPLEX array, dimension (1 + (N-1)*abs(INCV)) The vector v as described above.
[in]	INCV	INCV is INTEGER The increment between successive elements of v. INCV must not be zero.
[in]	TAU	TAU is COMPLEX The value tau as described above.
[in,out]	C	C is COMPLEX array, dimension (LDC, N) On entry, the matrix C. On exit, C is overwritten by H * C * H'.
[in]	LDC	LDC is INTEGER The leading dimension of the array C. LDC >= max( 1, N ).
[out]	WORK	WORK is COMPLEX array, dimension (N)

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

December 2016

Definition at line 110 of file clarfy.f.

*
*  -- 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            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
*

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