LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ slarfy()

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

SLARFY

Purpose:
 SLARFY 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 REAL 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 REAL
          The value tau as described above.
[in,out]C
          C is REAL 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 REAL array, dimension (N)
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 107 of file slarfy.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 REAL TAU
117* ..
118* .. Array Arguments ..
119 REAL C( LDC, * ), V( * ), WORK( * )
120* ..
121*
122* =====================================================================
123*
124* .. Parameters ..
125 REAL ONE, ZERO, HALF
126 parameter( one = 1.0e+0, zero = 0.0e+0, half = 0.5e+0 )
127* ..
128* .. Local Scalars ..
129 REAL ALPHA
130* ..
131* .. External Subroutines ..
132 EXTERNAL saxpy, ssymv, ssyr2
133* ..
134* .. External Functions ..
135 REAL SDOT
136 EXTERNAL sdot
137* ..
138* .. Executable Statements ..
139*
140 IF( tau.EQ.zero )
141 $ RETURN
142*
143* Form w:= C * v
144*
145 CALL ssymv( uplo, n, one, c, ldc, v, incv, zero, work, 1 )
146*
147 alpha = -half*tau*sdot( n, work, 1, v, incv )
148 CALL saxpy( n, alpha, v, incv, work, 1 )
149*
150* C := C - v * w' - w * v'
151*
152 CALL ssyr2( uplo, n, -tau, v, incv, work, 1, c, ldc )
153*
154 RETURN
155*
156* End of SLARFY
157*
real function sdot(N, SX, INCX, SY, INCY)
SDOT
Definition: sdot.f:82
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:89
subroutine ssymv(UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SSYMV
Definition: ssymv.f:152
subroutine ssyr2(UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA)
SSYR2
Definition: ssyr2.f:147
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