chseqr man page on Scientific

Man page or keyword search:  
man Server   26626 pages
apropos Keyword Search (all sections)
Output format
Scientific logo
[printable version]

CHSEQR(1)	      LAPACK driver routine (version 3.2)	     CHSEQR(1)

NAME
       CHSEQR  - CHSEQR compute the eigenvalues of a Hessenberg matrix H  and,
       optionally, the matrices T and Z from the Schur decomposition  H = Z  T
       Z**H, where T is an upper triangular matrix (the	 Schur form), and Z is
       the unitary matrix of Schur vectors

SYNOPSIS
       SUBROUTINE CHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, W,  Z,  LDZ,	 WORK,
			  LWORK, INFO )

	   INTEGER	  IHI, ILO, INFO, LDH, LDZ, LWORK, N

	   CHARACTER	  COMPZ, JOB

	   COMPLEX	  H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * )

PURPOSE
	  CHSEQR computes the eigenvalues of a Hessenberg matrix H
	  and, optionally, the matrices T and Z from the Schur decomposition
	  H = Z T Z**H, where T is an upper triangular matrix (the
	  Schur form), and Z is the unitary matrix of Schur vectors.
	  Optionally Z may be postmultiplied into an input unitary
	  matrix Q so that this routine can give the Schur factorization
	  of a matrix A which has been reduced to the Hessenberg form H
	  by the unitary matrix Q:  A = Q*H*Q**H = (QZ)*H*(QZ)**H.

ARGUMENTS
       JOB   (input) CHARACTER*1
	     = 'E':  compute eigenvalues only;
	     =	'S':  compute eigenvalues and the Schur form T.	 COMPZ (input)
	     CHARACTER*1
	     = 'N':  no Schur vectors are computed;
	     = 'I':  Z is initialized to the unit matrix and the matrix	 Z  of
	     Schur vectors of H is returned; = 'V':  Z must contain an unitary
	     matrix Q on entry, and the product Q*Z is returned.

       N     (input) INTEGER
	     The order of the matrix H.	 N .GE. 0.

       ILO   (input) INTEGER
	     IHI   (input) INTEGER It is assumed that H is already upper  tri‐
	     angular  in rows and columns 1:ILO-1 and IHI+1:N. ILO and IHI are
	     normally set by a previous call to CGEBAL,	 and  then  passed  to
	     CGEHRD  when the matrix output by CGEBAL is reduced to Hessenberg
	     form. Otherwise ILO and IHI should be set	to  1  and  N  respec‐
	     tively.   If  N.GT.0,  then 1.LE.ILO.LE.IHI.LE.N.	If N = 0, then
	     ILO = 1 and IHI = 0.

       H     (input/output) COMPLEX array, dimension (LDH,N)
	     On entry, the upper Hessenberg matrix H.  On exit, if  INFO  =  0
	     and  JOB = 'S', H contains the upper triangular matrix T from the
	     Schur decomposition (the Schur form). If INFO = 0 and JOB =  'E',
	     the  contents of H are unspecified on exit.  (The output value of
	     H when INFO.GT.0 is given under the description of	 INFO  below.)
	     Unlike earlier versions of CHSEQR, this subroutine may explicitly
	     H(i,j) = 0 for i.GT.j and j = 1, 2,  ...  ILO-1  or  j  =	IHI+1,
	     IHI+2, ... N.

       LDH   (input) INTEGER
	     The leading dimension of the array H. LDH .GE. max(1,N).

       W	(output) COMPLEX array, dimension (N)
		The  computed  eigenvalues.  If JOB = 'S', the eigenvalues are
		stored in the same order as on the diagonal of the Schur  form
		returned in H, with W(i) = H(i,i).

       Z     (input/output) COMPLEX array, dimension (LDZ,N)
	     If	 COMPZ = 'N', Z is not referenced.  If COMPZ = 'I', on entry Z
	     need not be set and on exit, if INFO = 0, Z contains the  unitary
	     matrix  Z	of the Schur vectors of H.  If COMPZ = 'V', on entry Z
	     must contain an N-by-N matrix Q, which is assumed to be equal  to
	     the  unit	matrix except for the submatrix Z(ILO:IHI,ILO:IHI). On
	     exit, if INFO = 0, Z contains Q*Z.	 Normally  Q  is  the  unitary
	     matrix  generated by CUNGHR after the call to CGEHRD which formed
	     the Hessenberg matrix H. (The output value of Z when INFO.GT.0 is
	     given under the description of INFO below.)

       LDZ   (input) INTEGER
	     The  leading dimension of the array Z.  if COMPZ = 'I' or COMPZ =
	     'V', then LDZ.GE.MAX(1,N).	 Otherwize, LDZ.GE.1.

       WORK  (workspace/output) COMPLEX array, dimension (LWORK)
	     On exit, if INFO = 0, WORK(1) returns an estimate of the  optimal
	     value  for	 LWORK.	  LWORK	 (input)  INTEGER The dimension of the
	     array WORK.  LWORK .GE. max(1,N) is sufficient and delivers  very
	     good  and sometimes optimal performance.  However, LWORK as large
	     as 11*N may be required for  optimal  performance.	  A  workspace
	     query is recommended to determine the optimal workspace size.  If
	     LWORK = -1, then CHSEQR does a workspace query.   In  this	 case,
	     CHSEQR  checks  the  input	 parameters  and estimates the optimal
	     workspace size for the given values of N, ILO and IHI.  The esti‐
	     mate  is  returned in WORK(1).  No error message related to LWORK
	     is issued by XERBLA.  Neither H nor Z are accessed.

       INFO  (output) INTEGER
	     =	0:  successful exit
	     value
	     the eigenvalues.  Elements 1:ilo-1 and i+1:n of WR and WI contain
	     those  eigenvalues which have been successfully computed.	(Fail‐
	     ures are rare.)  If INFO .GT. 0 and JOB = 'E', then on exit,  the
	     remaining	unconverged  eigenvalues  are the eigen- values of the
	     upper Hessenberg matrix rows and columns ILO through INFO of  the
	     final,  output  value of H.  If INFO .GT. 0 and JOB   = 'S', then
	     on exit

       (*)  (initial value of H)*U  = U*(final value of H)
	    where U is a unitary matrix.  The final value of  H is upper  Hes‐
	    senberg and triangular in rows and columns INFO+1 through IHI.  If
	    INFO .GT. 0 and COMPZ = 'V', then on exit (final value  of	Z)   =
	    (initial  value  of	 Z)*U  where  U	 is  the unitary matrix in (*)
	    (regard- less of the value of JOB.)	 If INFO .GT. 0	 and  COMPZ  =
	    'I',  then	on exit (final value of Z)  = U where U is the unitary
	    matrix in (*) (regard- less of the value of JOB.)  If INFO .GT.  0
	    and COMPZ = 'N', then Z is not accessed.

 LAPACK driver routine (version 3November 2008			     CHSEQR(1)
[top]

List of man pages available for Scientific

Copyright (c) for man pages and the logo by the respective OS vendor.

For those who want to learn more, the polarhome community provides shell access and support.

[legal] [privacy] [GNU] [policy] [cookies] [netiquette] [sponsors] [FAQ]
Tweet
Polarhome, production since 1999.
Member of Polarhome portal.
Based on Fawad Halim's script.
....................................................................
Vote for polarhome
Free Shell Accounts :: the biggest list on the net