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)
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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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