cgehrd.f man page




subroutine cgehrd (N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO)

Function/Subroutine Documentation

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



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


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


          ILO is INTEGER


          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 <= N, if N > 0; ILO=1 and IHI=0, if N=0.


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


          TAU is COMPLEX array, dimension (N-1)
          The scalar factors of the elementary reflectors (see Further
          Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to


          WORK is COMPLEX array, dimension (LWORK)
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.


          LWORK is INTEGER
          The length of the array WORK.  LWORK >= max(1,N).
          For good performance, LWORK should generally be larger.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.


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

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December 2016

Further Details:

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

     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).

  This file is a slight modification of LAPACK-3.0's DGEHRD
  subroutine incorporating improvements proposed by Quintana-Orti and
  Van de Geijn (2006). (See DLAHR2.)

Definition at line 169 of file cgehrd.f.


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Referenced By

The man page cgehrd(3) is an alias of cgehrd.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK