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zstein (3)
  • >> zstein (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         zstein - compute the eigenvectors of a real symmetric tridi-
         agonal  matrix  T  corresponding  to  specified eigenvalues,
         using inverse iteration
    
    SYNOPSIS
         SUBROUTINE ZSTEIN( N, D, E, M, W, IBLOCK,  ISPLIT,  Z,  LDZ,
                   WORK, IWORK, IFAIL, INFO )
    
         INTEGER INFO, LDZ, M, N
    
         INTEGER IBLOCK( * ), IFAIL( * ), ISPLIT( * ), IWORK( * )
    
         DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * )
    
         COMPLEX*16 Z( LDZ, * )
    
    
    
         #include <sunperf.h>
    
         void zstein(int n, double *d, double *e, int m,  double  *w,
                   int  *iblock,  int *isplit, doublecomplex *zz, int
                   ldz, int *ifail, int *info) ;
    
    PURPOSE
         ZSTEIN computes the eigenvectors of a real symmetric  tridi-
         agonal  matrix  T  corresponding  to  specified eigenvalues,
         using inverse iteration.
    
         The maximum number of iterations allowed for each  eigenvec-
         tor  is specified by an internal parameter MAXITS (currently
         set to 5).
    
         Although the eigenvectors are real, they  are  stored  in  a
         complex  array,  which may be passed to ZUNMTR or ZUPMTR for
         back
         transformation to the eigenvectors of  a  complex  Hermitian
         matrix which was reduced to tridiagonal form.
    
    
    ARGUMENTS
         N         (input) INTEGER
                   The order of the matrix.  N >= 0.
    
         D         (input) DOUBLE PRECISION array, dimension (N)
                   The n diagonal elements of the tridiagonal  matrix
                   T.
    
         E         (input) DOUBLE PRECISION array, dimension (N)
                   The (n-1) subdiagonal elements of the  tridiagonal
                   matrix  T,  stored in elements 1 to N-1; E(N) need
                   not be set.
    
         M         (input) INTEGER
                   The number of eigenvectors to be found.  0 <= M <=
                   N.
    
         W         (input) DOUBLE PRECISION array, dimension (N)
                   The first M elements of W contain the  eigenvalues
                   for  which  eigenvectors  are to be computed.  The
                   eigenvalues should be grouped by  split-off  block
                   and  ordered  from  smallest to largest within the
                   block.  ( The output  array  W  from  DSTEBZ  with
                   ORDER = 'B' is expected here. )
    
         IBLOCK    (input) INTEGER array, dimension (N)
                   The  submatrix   indices   associated   with   the
                   corresponding  eigenvalues  in  W;  IBLOCK(i)=1 if
                   eigenvalue W(i) belongs  to  the  first  submatrix
                   from  the  top,  =2  if W(i) belongs to the second
                   submatrix, etc.  ( The output  array  IBLOCK  from
                   DSTEBZ is expected here. )
    
         ISPLIT    (input) INTEGER array, dimension (N)
                   The splitting points, at which T  breaks  up  into
                   submatrices.   The  first  submatrix  consists  of
                   rows/columns 1 to  ISPLIT(  1  ),  the  second  of
                   rows/columns  ISPLIT(  1  )+1 through ISPLIT( 2 ),
                   etc.  ( The output array  ISPLIT  from  DSTEBZ  is
                   expected here. )
    
         Z         (output) COMPLEX*16 array, dimension (LDZ, M)
                   The computed eigenvectors.  The eigenvector  asso-
                   ciated  with  the eigenvalue W(i) is stored in the
                   i-th column of Z.  Any vector which fails to  con-
                   verge  is  set to its current iterate after MAXITS
                   iterations.  The imaginary parts of the  eigenvec-
                   tors are set to zero.
    
         LDZ       (input) INTEGER
                   The leading dimension of  the  array  Z.   LDZ  >=
                   max(1,N).
    
         WORK      (workspace)  DOUBLE  PRECISION  array,   dimension
                   (5*N)
    
         IWORK     (workspace) INTEGER array, dimension (N)
    
         IFAIL     (output) INTEGER array, dimension (M)
                   On normal exit, all elements of  IFAIL  are  zero.
                   If one or more eigenvectors fail to converge after
                   MAXITS iterations, then their indices  are  stored
                   in array IFAIL.
    
         INFO      (output) INTEGER
                   = 0: successful exit
                   < 0: if INFO = -i, the i-th argument had an  ille-
                   gal value
                   > 0: if INFO = i, then i  eigenvectors  failed  to
                   converge  in MAXITS iterations.  Their indices are
                   stored in array IFAIL.
    
    PARAMETERS
         MAXITS  INTEGER, default = 5 The maximum  number  of  itera-
                   tions performed.
    
         EXTRA   INTEGER, default = 2 The number of  iterations  per-
                   formed  after  norm growth criterion is satisfied,
                   should be at least 1.
    
    
    
    


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