LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ dlarfy()

 subroutine dlarfy ( character UPLO, integer N, double precision, dimension( * ) V, integer INCV, double precision TAU, double precision, dimension( ldc, * ) C, integer LDC, double precision, dimension( * ) WORK )

DLARFY

Purpose:
``` DLARFY applies an elementary reflector, or Householder matrix, H,
to an n x n symmetric 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 symmetric 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 DOUBLE PRECISION 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 DOUBLE PRECISION The value tau as described above.``` [in,out] C ``` C is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N)`
Date
December 2016

Definition at line 110 of file dlarfy.f.

110 *
111 * -- LAPACK test routine (version 3.7.0) --
112 * -- LAPACK is a software package provided by Univ. of Tennessee, --
113 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
114 * December 2016
115 *
116 * .. Scalar Arguments ..
117  CHARACTER uplo
118  INTEGER incv, ldc, n
119  DOUBLE PRECISION tau
120 * ..
121 * .. Array Arguments ..
122  DOUBLE PRECISION c( ldc, * ), v( * ), work( * )
123 * ..
124 *
125 * =====================================================================
126 *
127 * .. Parameters ..
128  DOUBLE PRECISION one, zero, half
129  parameter( one = 1.0d+0, zero = 0.0d+0, half = 0.5d+0 )
130 * ..
131 * .. Local Scalars ..
132  DOUBLE PRECISION alpha
133 * ..
134 * .. External Subroutines ..
135  EXTERNAL daxpy, dsymv, dsyr2
136 * ..
137 * .. External Functions ..
138  DOUBLE PRECISION ddot
139  EXTERNAL ddot
140 * ..
141 * .. Executable Statements ..
142 *
143  IF( tau.EQ.zero )
144  \$ RETURN
145 *
146 * Form w:= C * v
147 *
148  CALL dsymv( uplo, n, one, c, ldc, v, incv, zero, work, 1 )
149 *
150  alpha = -half*tau*ddot( n, work, 1, v, incv )
151  CALL daxpy( n, alpha, v, incv, work, 1 )
152 *
153 * C := C - v * w' - w * v'
154 *
155  CALL dsyr2( uplo, n, -tau, v, incv, work, 1, c, ldc )
156 *
157  RETURN
158 *
159 * End of DLARFY
160 *
double precision function ddot(N, DX, INCX, DY, INCY)
DDOT
Definition: ddot.f:84
subroutine daxpy(N, DA, DX, INCX, DY, INCY)
DAXPY
Definition: daxpy.f:91
subroutine dsyr2(UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA)
DSYR2
Definition: dsyr2.f:149
subroutine dsymv(UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DSYMV
Definition: dsymv.f:154
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