cgehd2.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
Page Index
 

NAME

cgehd2.f  

SYNOPSIS


 

Functions/Subroutines


subroutine cgehd2 (N, ILO, IHI, A, LDA, TAU, WORK, INFO)
CGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked algorithm.  

Function/Subroutine Documentation

 

subroutine cgehd2 (integer N, integer ILO, integer IHI, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) TAU, complex, dimension( * ) WORK, integer INFO)

CGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked algorithm.

Purpose:

 CGEHD2 reduces a complex general matrix A to upper Hessenberg form H
 by a unitary similarity transformation:  Q**H * A * Q = H .


 

Parameters:

N

          N is INTEGER
          The order of the matrix A.  N >= 0.


ILO

          ILO is INTEGER


IHI

          IHI is INTEGER

          It is assumed that A is already upper triangular in rows
          and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
          set by a previous call to CGEBAL; otherwise they should be
          set to 1 and N respectively. See Further Details.
          1 <= ILO <= IHI <= max(1,N).


A

          A is COMPLEX array, dimension (LDA,N)
          On entry, the n by n general matrix to be reduced.
          On exit, the upper triangle and the first subdiagonal of A
          are overwritten with the upper Hessenberg matrix H, and the
          elements below the first subdiagonal, with the array TAU,
          represent the unitary matrix Q as a product of elementary
          reflectors. See Further Details.


LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).


TAU

          TAU is COMPLEX array, dimension (N-1)
          The scalar factors of the elementary reflectors (see Further
          Details).


WORK

          WORK is COMPLEX array, dimension (N)


INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value.


 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Further Details:

  The matrix Q is represented as a product of (ihi-ilo) elementary
  reflectors

     Q = H(ilo) H(ilo+1) . . . H(ihi-1).

  Each H(i) has the form

     H(i) = I - tau * v * v**H

  where tau is a complex scalar, and v is a complex vector with
  v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
  exit in A(i+2:ihi,i), and tau in TAU(i).

  The contents of A are illustrated by the following example, with
  n = 7, ilo = 2 and ihi = 6:

  on entry,                        on exit,

  ( a   a   a   a   a   a   a )    (  a   a   h   h   h   h   a )
  (     a   a   a   a   a   a )    (      a   h   h   h   h   a )
  (     a   a   a   a   a   a )    (      h   h   h   h   h   h )
  (     a   a   a   a   a   a )    (      v2  h   h   h   h   h )
  (     a   a   a   a   a   a )    (      v2  v3  h   h   h   h )
  (     a   a   a   a   a   a )    (      v2  v3  v4  h   h   h )
  (                         a )    (                          a )

  where a denotes an element of the original matrix A, h denotes a
  modified element of the upper Hessenberg matrix H, and vi denotes an
  element of the vector defining H(i).


 

Definition at line 151 of file cgehd2.f.  

Author

Generated automatically by Doxygen for LAPACK from the source code.


 

Index

NAME
SYNOPSIS
Functions/Subroutines
Function/Subroutine Documentation
subroutine cgehd2 (integer N, integer ILO, integer IHI, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) TAU, complex, dimension( * ) WORK, integer INFO)
Author