zgehrd.f man page

zgehrd.f —

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine zgehrd (integer N, integer ILO, integer IHI, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( * ) TAU, complex*16, dimension( * ) WORK, integer LWORK, integer INFO)

ZGEHRD  

Purpose:

 ZGEHRD reduces a complex general matrix A to upper Hessenberg form H by
 an 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 ZGEBAL; 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

          A is COMPLEX*16 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*16 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
          zero.

WORK

          WORK is COMPLEX*16 array, dimension (LWORK)
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

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

          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).

  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 zgehrd.f.

Author

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Referenced By

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

Sat Jun 24 2017 Version 3.7.1 LAPACK