LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ 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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