larfgp(3) Library Functions Manual larfgp(3)

larfgp - larfgp: generate Householder reflector, beta ≥ 0


subroutine clarfgp (n, alpha, x, incx, tau)
CLARFGP generates an elementary reflector (Householder matrix) with non-negative beta. subroutine dlarfgp (n, alpha, x, incx, tau)
DLARFGP generates an elementary reflector (Householder matrix) with non-negative beta. subroutine slarfgp (n, alpha, x, incx, tau)
SLARFGP generates an elementary reflector (Householder matrix) with non-negative beta. subroutine zlarfgp (n, alpha, x, incx, tau)
ZLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.

CLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.

Purpose:

 CLARFGP 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, beta is real and non-negative, 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.

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 103 of file clarfgp.f.

DLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.

Purpose:

 DLARFGP 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, beta is non-negative, 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.

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 103 of file dlarfgp.f.

SLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.

Purpose:

 SLARFGP 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, beta is non-negative, 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.

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 103 of file slarfgp.f.

ZLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.

Purpose:

 ZLARFGP 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, beta is real and non-negative, 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.

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 103 of file zlarfgp.f.

Generated automatically by Doxygen for LAPACK from the source code.

Version 3.12.0 LAPACK