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shsein (3)
  • >> shsein (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         shsein - use  inverse  iteration  to  find  specified  right
         and/or left eigenvectors of a real upper Hessenberg matrix H
    
    SYNOPSIS
         SUBROUTINE SHSEIN( SIDE, EIGSRC, INITV, SELECT, N,  H,  LDH,
                   WR,  WI,  VL, LDVL, VR, LDVR, MM, M, WORK, IFAILL,
                   IFAILR, INFO )
    
         CHARACTER EIGSRC, INITV, SIDE
    
         INTEGER INFO, LDH, LDVL, LDVR, M, MM, N
    
         LOGICAL SELECT( * )
    
         INTEGER IFAILL( * ), IFAILR( * )
    
         REAL H( LDH, * ), VL( LDVL, * ), VR( LDVR, *  ),  WI(  *  ),
                   WORK( * ), WR( * )
    
    
    
         #include <sunperf.h>
    
         void shsein(char side, char eigsrc, char initv, int *select,
                   int  n,  float  *h, int ldh, float *wr, float *wi,
                   float * vl, int ldvl, float *vr, int ldvr, int mm,
                   int *m, int *ifaill, int *ifailr, int *info);
    
    PURPOSE
         SHSEIN uses inverse iteration to find specified right and/or
         left eigenvectors of a real upper Hessenberg matrix H.
    
         The right eigenvector x and the left eigenvector  y  of  the
         matrix H corresponding to an eigenvalue w are defined by:
    
                      H * x = w * x,     y**h * H = w * y**h
    
         where y**h denotes the conjugate transpose of the vector y.
    
    
    ARGUMENTS
         SIDE      (input) CHARACTER*1
                   = 'R': compute right eigenvectors only;
                   = 'L': compute left eigenvectors only;
                   = 'B': compute both right and left eigenvectors.
    
         EIGSRC    (input) CHARACTER*1
                   Specifies the source of  eigenvalues  supplied  in
                   (WR,WI):
                   = 'Q': the eigenvalues were  found  using  SHSEQR;
                   thus,  if  H has zero subdiagonal elements, and so
                   is block-triangular, then the j-th eigenvalue  can
                   be  assumed  to be an eigenvalue of the block con-
                   taining the j-th row/column.  This property allows
                   SHSEIN  to  perform  inverse iteration on just one
                   diagonal block.  = 'N': no assumptions are made on
                   the  correspondence between eigenvalues and diago-
                   nal blocks.  In this case, SHSEIN must always per-
                   form inverse iteration using the whole matrix H.
    
         INITV     (input) CHARACTER*1
                   = 'N': no initial vectors are supplied;
                   = 'U': user-supplied initial vectors are stored in
                   the arrays VL and/or VR.
    
         SELECT    (input/output) LOGICAL array, dimension (N)
                   Specifies the  eigenvectors  to  be  computed.  To
                   select  the  real  eigenvector  corresponding to a
                   real eigenvalue WR(j), SELECT(j) must  be  set  to
                   .TRUE..   To   select   the   complex  eigenvector
                   corresponding    to    a    complex     eigenvalue
                   (WR(j),WI(j)),      with     complex     conjugate
                   (WR(j+1),WI(j+1)), either SELECT(j) or SELECT(j+1)
                   or both must be set to
    
         Each eigenvector is normalized so that the element of  larg-
         est  magnitude has magnitude 1; here the magnitude of a com-
         plex number (x,y) is taken to be |x|+|y|.
    
    
    
    


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