The OpenNET Project / Index page

[ новости /+++ | форум | теги | ]

Интерактивная система просмотра системных руководств (man-ов)

 ТемаНаборКатегория 
 
 [Cписок руководств | Печать]

dhseqr (3)
  • >> dhseqr (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         dhseqr - compute the eigenvalues of a real upper  Hessenberg
         matrix  H  and,  optionally,  the  matrices T and Z from the
         Schur decomposition H = Z  T  Z**T,  where  T  is  an  upper
         quasi-triangular  matrix  (the  Schur  form),  and  Z is the
         orthogonal matrix of Schur vectors
    
    SYNOPSIS
         SUBROUTINE DHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, WR,  WI,
                   Z, LDZ, WORK, LWORK, INFO )
    
         CHARACTER COMPZ, JOB
    
         INTEGER IHI, ILO, INFO, LDH, LDZ, LWORK, N
    
         DOUBLE PRECISION H( LDH, * ), WI( * ), WORK( * ), WR(  *  ),
                   Z( LDZ, * )
    
    
    
         #include <sunperf.h>
    
         void dhseqr(char job, char compz, int n, int ilo,  int  ihi,
                   double *h, int ldh, double *wr, double *wi, double
                   *dz, int ldz, int *info);
    
    PURPOSE
         DHSEQR computes the eigenvalues of a real  upper  Hessenberg
         matrix  H  and,  optionally,  the  matrices T and Z from the
         Schur decomposition H = Z  T  Z**T,  where  T  is  an  upper
         quasi-triangular  matrix  (the  Schur  form),  and  Z is the
         orthogonal matrix of Schur vectors.
    
         Optionally Z may be postmultiplied into an input  orthogonal
         matrix Q, so that this routine can give the Schur factoriza-
         tion of a matrix A which has been reduced to the  Hessenberg
         form  H  by  the  orthogonal  matrix  Q:   A  =  Q*H*Q**T  =
         (QZ)*T*(QZ)**T.
    
    
    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  orthogonal  matrix  Q  on
                   entry, and the product Q*Z is returned.
    
         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
                   1:ILO-1 and IHI+1:N. ILO and IHI are normally  set
                   by  a  previous call to DGEBAL, and then passed to
                   SGEHRD when the matrix output by DGEBAL is reduced
                   to  Hessenberg  form. Otherwise ILO and IHI should
                   be set to 1 and N respectively.  1 <= ILO  <=  IHI
                   <= N, if N > 0; ILO=1 and IHI=0, if N=0.
    
         H         (input/output) DOUBLE PRECISION  array,  dimension
                   (LDH,N)
                   On entry, the upper Hessenberg matrix H.  On exit,
                   if   JOB  =  'S',  H  contains  the  upper  quasi-
                   triangular matrix T from the  Schur  decomposition
                   (the   Schur   form);   2-by-2   diagonal   blocks
                   (corresponding  to  complex  conjugate  pairs   of
                   eigenvalues)  are  returned in standard form, with
                   H(i,i) = H(i+1,i+1) and H(i+1,i)*H(i,i+1) < 0.  If
                   JOB  =  'E',  the contents of H are unspecified on
                   exit.
    
         LDH       (input) INTEGER
                   The leading dimension  of  the  array  H.  LDH  >=
                   max(1,N).
    
         WR        (output) DOUBLE PRECISION array, dimension (N)
                   WI      (output) DOUBLE PRECISION array, dimension
                   (N) The real and imaginary parts, respectively, of
                   the computed eigenvalues. If two  eigenvalues  are
                   computed  as  a  complex  conjugate pair, they are
                   stored in consecutive elements of WR and  WI,  say
                   the i-th and (i+1)th, with WI(i) > 0 and WI(i+1) <
                   0. If JOB = 'S', the eigenvalues are stored in the
                   same  order  as  on the diagonal of the Schur form
                   returned  in  H,  with  WR(i)  =  H(i,i)  and,  if
                   H(i:i+1,i:i+1) is a 2-by-2 diagonal block, WI(i) =
                   sqrt(H(i+1,i)*H(i,i+1)) and WI(i+1) = -WI(i).
    
         Z         (input/output) DOUBLE PRECISION  array,  dimension
                   (LDZ,N)
                   If COMPZ = 'N': Z is not referenced.
                   If COMPZ = 'I': on entry, Z need not be  set,  and
                   on exit, Z contains the orthogonal 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 sub-
                   matrix Z(ILO:IHI,ILO:IHI); on exit Z contains Q*Z.
                   Normally Q is the orthogonal matrix  generated  by
                   DORGHR  after  the call to DGEHRD which formed the
                   Hessenberg matrix H.
    
         LDZ       (input) INTEGER
                   The leading dimension of  the  array  Z.   LDZ  >=
                   max(1,N)  if  COMPZ  = 'I' or 'V'; LDZ >= 1 other-
                   wise.
    
         WORK      (workspace) DOUBLE PRECISION array, dimension (N)
    
         LWORK     (input) INTEGER
                   This argument is currently redundant.
    
         INFO      (output) INTEGER
                   = 0:  successful exit
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal value
                   > 0:  if INFO = i, DHSEQR failed to compute all of
                   the  eigenvalues  in  a  total  of  30*(IHI-ILO+1)
                   iterations; elements 1:ilo-1 and i+1:n of  WR  and
                   WI  contain those eigenvalues which have been suc-
                   cessfully computed.
    
    
    
    


    Поиск по тексту MAN-ов: 




    Партнёры:
    PostgresPro
    Inferno Solutions
    Hosting by Hoster.ru
    Хостинг:

    Закладки на сайте
    Проследить за страницей
    Created 1996-2024 by Maxim Chirkov
    Добавить, Поддержать, Вебмастеру