LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ 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)`

Definition at line 107 of file clarfy.f.

108*
109* -- LAPACK test routine --
110* -- LAPACK is a software package provided by Univ. of Tennessee, --
111* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
112*
113* .. Scalar Arguments ..
114 CHARACTER UPLO
115 INTEGER INCV, LDC, N
116 COMPLEX TAU
117* ..
118* .. Array Arguments ..
119 COMPLEX C( LDC, * ), V( * ), WORK( * )
120* ..
121*
122* =====================================================================
123*
124* .. Parameters ..
125 COMPLEX ONE, ZERO, HALF
126 parameter( one = ( 1.0e+0, 0.0e+0 ),
127 \$ zero = ( 0.0e+0, 0.0e+0 ),
128 \$ half = ( 0.5e+0, 0.0e+0 ) )
129* ..
130* .. Local Scalars ..
131 COMPLEX ALPHA
132* ..
133* .. External Subroutines ..
134 EXTERNAL caxpy, chemv, cher2
135* ..
136* .. External Functions ..
137 COMPLEX CDOTC
138 EXTERNAL cdotc
139* ..
140* .. Executable Statements ..
141*
142 IF( tau.EQ.zero )
143 \$ RETURN
144*
145* Form w:= C * v
146*
147 CALL chemv( uplo, n, one, c, ldc, v, incv, zero, work, 1 )
148*
149 alpha = -half*tau*cdotc( n, work, 1, v, incv )
150 CALL caxpy( n, alpha, v, incv, work, 1 )
151*
152* C := C - v * w' - w * v'
153*
154 CALL cher2( uplo, n, -tau, v, incv, work, 1, c, ldc )
155*
156 RETURN
157*
158* End of CLARFY
159*
complex function cdotc(N, CX, INCX, CY, INCY)
CDOTC
Definition: cdotc.f:83
subroutine caxpy(N, CA, CX, INCX, CY, INCY)
CAXPY
Definition: caxpy.f:88
subroutine cher2(UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA)
CHER2
Definition: cher2.f:150
subroutine chemv(UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CHEMV
Definition: chemv.f:154
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