LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ zlarfy()

 subroutine zlarfy ( character uplo, integer n, complex*16, dimension( * ) v, integer incv, complex*16 tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work )

ZLARFY

Purpose:
``` 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.```
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*16 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*16 The value tau as described above.``` [in,out] C ``` C is COMPLEX*16 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*16 array, dimension (N)`

Definition at line 107 of file zlarfy.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*16 TAU
117* ..
118* .. Array Arguments ..
119 COMPLEX*16 C( LDC, * ), V( * ), WORK( * )
120* ..
121*
122* =====================================================================
123*
124* .. Parameters ..
125 COMPLEX*16 ONE, ZERO, HALF
126 parameter( one = ( 1.0d+0, 0.0d+0 ),
127 \$ zero = ( 0.0d+0, 0.0d+0 ),
128 \$ half = ( 0.5d+0, 0.0d+0 ) )
129* ..
130* .. Local Scalars ..
131 COMPLEX*16 ALPHA
132* ..
133* .. External Subroutines ..
134 EXTERNAL zaxpy, zhemv, zher2
135* ..
136* .. External Functions ..
137 COMPLEX*16 ZDOTC
138 EXTERNAL zdotc
139* ..
140* .. Executable Statements ..
141*
142 IF( tau.EQ.zero )
143 \$ RETURN
144*
145* Form w:= C * v
146*
147 CALL zhemv( uplo, n, one, c, ldc, v, incv, zero, work, 1 )
148*
149 alpha = -half*tau*zdotc( n, work, 1, v, incv )
150 CALL zaxpy( n, alpha, v, incv, work, 1 )
151*
152* C := C - v * w' - w * v'
153*
154 CALL zher2( uplo, n, -tau, v, incv, work, 1, c, ldc )
155*
156 RETURN
157*
158* End of ZLARFY
159*
subroutine zaxpy(n, za, zx, incx, zy, incy)
ZAXPY
Definition zaxpy.f:88
complex *16 function zdotc(n, zx, incx, zy, incy)
ZDOTC
Definition zdotc.f:83
subroutine zhemv(uplo, n, alpha, a, lda, x, incx, beta, y, incy)
ZHEMV
Definition zhemv.f:154
subroutine zher2(uplo, n, alpha, x, incx, y, incy, a, lda)
ZHER2
Definition zher2.f:150
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