clahqr man page on Scientific

Printed from http://www.polarhome.com/service/man/?qf=clahqr&af=0&tf=2&of=Scientific

CLAHQR(1)	    LAPACK auxiliary routine (version 3.2)	     CLAHQR(1)

NAME
       CLAHQR  -  CLAHQR i an auxiliary routine called by CHSEQR to update the
       eigenvalues and Schur decomposition  already  computed  by  CHSEQR,  by
       dealing with the Hessenberg submatrix in rows and columns ILO to	 IHI

SYNOPSIS
       SUBROUTINE CLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, IHIZ, Z,
			  LDZ, INFO )

	   INTEGER	  IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N

	   LOGICAL	  WANTT, WANTZ

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

PURPOSE
	  CLAHQR is an auxiliary routine called by CHSEQR to update the
	  eigenvalues and Schur decomposition already computed by CHSEQR, by
	  dealing with the Hessenberg submatrix in rows and columns ILO to
	  IHI.

ARGUMENTS
       WANTT   (input) LOGICAL
	       = .TRUE. : the full Schur form T is required;
	       = .FALSE.: only eigenvalues are required.

       WANTZ   (input) LOGICAL
	       = .TRUE. : the matrix of Schur vectors Z is required;
	       = .FALSE.: Schur vectors are not required.

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

       ILO     (input) INTEGER
	       IHI     (input) INTEGER It is assumed that H is	already	 upper
	       triangular in rows and columns IHI+1:N, and that H(ILO,ILO-1) =
	       0 (unless ILO = 1).  CLAHQR works primarily with the Hessenberg
	       submatrix in rows and columns ILO to IHI, but applies transfor‐
	       mations to  all	of  H  if  WANTT  is  .TRUE..	1  <=  ILO  <=
	       max(1,IHI); IHI <= N.

       H       (input/output) COMPLEX array, dimension (LDH,N)
	       On  entry,  the upper Hessenberg matrix H.  On exit, if INFO is
	       zero and if WANTT is .TRUE., then H is upper triangular in rows
	       and  columns ILO:IHI.  If INFO is zero and if WANTT is .FALSE.,
	       then the contents of H are unspecified  on  exit.   The	output
	       state  of H in case INF is positive is below under the descrip‐
	       tion of INFO.

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

       W       (output) COMPLEX array, dimension (N)
	       The computed eigenvalues ILO to IHI are stored  in  the	corre‐
	       sponding elements of W. If WANTT is .TRUE., 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).

       ILOZ    (input) INTEGER
	       IHIZ	(input)	 INTEGER Specify the rows of Z to which trans‐
	       formations must be applied if WANTZ is .TRUE..  1  <=  ILOZ  <=
	       ILO; IHI <= IHIZ <= N.

       Z       (input/output) COMPLEX array, dimension (LDZ,N)
	       If  WANTZ is .TRUE., on entry Z must contain the current matrix
	       Z of transformations accumulated by CHSEQR, and on exit	Z  has
	       been updated; transformations are applied only to the submatrix
	       Z(ILOZ:IHIZ,ILO:IHI).  If WANTZ is .FALSE.,  Z  is  not	refer‐
	       enced.

       LDZ     (input) INTEGER
	       The leading dimension of the array Z. LDZ >= max(1,N).

       INFO    (output) INTEGER
	       =   0: successful exit
	       eigenvalues  ILO	 to IHI in a total of 30 iterations per eigen‐
	       value; elements i+1:ihi of W contain  those  eigenvalues	 which
	       have  been  successfully computed.  If INFO .GT. 0 and WANTT is
	       .FALSE., then on exit, the  remaining  unconverged  eigenvalues
	       are  the	 eigenvalues  of  the upper Hessenberg matrix rows and
	       columns ILO thorugh INFO of the final, output value of  H.   If
	       INFO  .GT.  0 and WANTT is .TRUE., then on exit (*)	 (ini‐
	       tial value of H)*U  = U*(final  value  of  H)  where  U	is  an
	       orthognal  matrix.     The final value of H is upper Hessenberg
	       and triangular in rows and columns INFO+1 through IHI.  If INFO
	       .GT.  0 and WANTZ is .TRUE., then on exit (final value of Z)  =
	       (initial value of Z)*U where U is the orthogonal matrix in  (*)
	       (regardless of the value of WANTT.)

FURTHER DETAILS
	  02-96 Based on modifications by
	  David Day, Sandia National Laboratory, USA
	  12-04 Further modifications by
	  Ralph Byers, University of Kansas, USA
	  This is a modified version of CLAHQR from LAPACK version 3.0.
	  It is (1) more robust against overflow and underflow and
	  (2) adopts the more conservative Ahues & Tisseur stopping
	  criterion (LAWN 122, 1997).

 LAPACK auxiliary routine (versioNovember 2008			     CLAHQR(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