larfg(3) Library Functions Manual larfg(3)

larfg - larfg: generate Householder reflector


subroutine clarfg (n, alpha, x, incx, tau)
CLARFG generates an elementary reflector (Householder matrix). subroutine dlarfg (n, alpha, x, incx, tau)
DLARFG generates an elementary reflector (Householder matrix). subroutine slarfg (n, alpha, x, incx, tau)
SLARFG generates an elementary reflector (Householder matrix). subroutine zlarfg (n, alpha, x, incx, tau)
ZLARFG generates an elementary reflector (Householder matrix).

CLARFG generates an elementary reflector (Householder matrix).

Purpose:

 CLARFG generates a complex elementary reflector H of order n, such
 that
       H**H * ( alpha ) = ( beta ),   H**H * H = I.
              (   x   )   (   0  )
 where alpha and beta are scalars, with beta real, and x is an
 (n-1)-element complex vector. H is represented in the form
       H = I - tau * ( 1 ) * ( 1 v**H ) ,
                     ( v )
 where tau is a complex scalar and v is a complex (n-1)-element
 vector. Note that H is not hermitian.
 If the elements of x are all zero and alpha is real, then tau = 0
 and H is taken to be the unit matrix.
 Otherwise  1 <= real(tau) <= 2  and  abs(tau-1) <= 1 .

Parameters

N 
          N is INTEGER
          The order of the elementary reflector.

ALPHA

          ALPHA is COMPLEX
          On entry, the value alpha.
          On exit, it is overwritten with the value beta.

X

          X is COMPLEX array, dimension
                         (1+(N-2)*abs(INCX))
          On entry, the vector x.
          On exit, it is overwritten with the vector v.

INCX

          INCX is INTEGER
          The increment between elements of X. INCX > 0.

TAU

          TAU is COMPLEX
          The value tau.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 105 of file clarfg.f.

DLARFG generates an elementary reflector (Householder matrix).

Purpose:

 DLARFG generates a real elementary reflector H of order n, such
 that
       H * ( alpha ) = ( beta ),   H**T * H = I.
           (   x   )   (   0  )
 where alpha and beta are scalars, and x is an (n-1)-element real
 vector. H is represented in the form
       H = I - tau * ( 1 ) * ( 1 v**T ) ,
                     ( v )
 where tau is a real scalar and v is a real (n-1)-element
 vector.
 If the elements of x are all zero, then tau = 0 and H is taken to be
 the unit matrix.
 Otherwise  1 <= tau <= 2.

Parameters

N 
          N is INTEGER
          The order of the elementary reflector.

ALPHA

          ALPHA is DOUBLE PRECISION
          On entry, the value alpha.
          On exit, it is overwritten with the value beta.

X

          X is DOUBLE PRECISION array, dimension
                         (1+(N-2)*abs(INCX))
          On entry, the vector x.
          On exit, it is overwritten with the vector v.

INCX

          INCX is INTEGER
          The increment between elements of X. INCX > 0.

TAU

          TAU is DOUBLE PRECISION
          The value tau.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 105 of file dlarfg.f.

SLARFG generates an elementary reflector (Householder matrix).

Purpose:

 SLARFG generates a real elementary reflector H of order n, such
 that
       H * ( alpha ) = ( beta ),   H**T * H = I.
           (   x   )   (   0  )
 where alpha and beta are scalars, and x is an (n-1)-element real
 vector. H is represented in the form
       H = I - tau * ( 1 ) * ( 1 v**T ) ,
                     ( v )
 where tau is a real scalar and v is a real (n-1)-element
 vector.
 If the elements of x are all zero, then tau = 0 and H is taken to be
 the unit matrix.
 Otherwise  1 <= tau <= 2.

Parameters

N 
          N is INTEGER
          The order of the elementary reflector.

ALPHA

          ALPHA is REAL
          On entry, the value alpha.
          On exit, it is overwritten with the value beta.

X

          X is REAL array, dimension
                         (1+(N-2)*abs(INCX))
          On entry, the vector x.
          On exit, it is overwritten with the vector v.

INCX

          INCX is INTEGER
          The increment between elements of X. INCX > 0.

TAU

          TAU is REAL
          The value tau.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 105 of file slarfg.f.

ZLARFG generates an elementary reflector (Householder matrix).

Purpose:

 ZLARFG generates a complex elementary reflector H of order n, such
 that
       H**H * ( alpha ) = ( beta ),   H**H * H = I.
              (   x   )   (   0  )
 where alpha and beta are scalars, with beta real, and x is an
 (n-1)-element complex vector. H is represented in the form
       H = I - tau * ( 1 ) * ( 1 v**H ) ,
                     ( v )
 where tau is a complex scalar and v is a complex (n-1)-element
 vector. Note that H is not hermitian.
 If the elements of x are all zero and alpha is real, then tau = 0
 and H is taken to be the unit matrix.
 Otherwise  1 <= real(tau) <= 2  and  abs(tau-1) <= 1 .

Parameters

N 
          N is INTEGER
          The order of the elementary reflector.

ALPHA

          ALPHA is COMPLEX*16
          On entry, the value alpha.
          On exit, it is overwritten with the value beta.

X

          X is COMPLEX*16 array, dimension
                         (1+(N-2)*abs(INCX))
          On entry, the vector x.
          On exit, it is overwritten with the vector v.

INCX

          INCX is INTEGER
          The increment between elements of X. INCX > 0.

TAU

          TAU is COMPLEX*16
          The value tau.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 105 of file zlarfg.f.

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