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sstevx (3)
  • >> sstevx (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         sstevx  -  compute  selected  eigenvalues  and,  optionally,
         eigenvectors of a real symmetric tridiagonal matrix A
    
    SYNOPSIS
         SUBROUTINE SSTEVX( JOBZ, RANGE, N, D, E,  VL,  VU,  IL,  IU,
                   ABSTOL, M, W, Z, LDZ, WORK, IWORK, IFAIL, INFO )
    
         CHARACTER JOBZ, RANGE
    
         INTEGER IL, INFO, IU, LDZ, M, N
    
         REAL ABSTOL, VL, VU
    
         INTEGER IFAIL( * ), IWORK( * )
    
         REAL D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )
    
    
    
         #include <sunperf.h>
    
         void sstevx(char jobz, char range, int n,  float  *d,  float
                   *e,  float  vl,  float  vu,  int il, int iu, float
                   abstol, int *m, float *w, float *sz, int ldz,  int
                   *ifail, int *info) ;
    
    PURPOSE
         SSTEVX computes selected eigenvalues and, optionally, eigen-
         vectors  of  a  real symmetric tridiagonal matrix A.  Eigen-
         values and eigenvectors can be selected by specifying either
         a  range  of  values  or  a range of indices for the desired
         eigenvalues.
    
    
    ARGUMENTS
         JOBZ      (input) CHARACTER*1
                   = 'N':  Compute eigenvalues only;
                   = 'V':  Compute eigenvalues and eigenvectors.
    
         RANGE     (input) CHARACTER*1
                   = 'A': all eigenvalues will be found.
                   = 'V': all eigenvalues in the  half-open  interval
                   (VL,VU]  will  be found.  = 'I': the IL-th through
                   IU-th eigenvalues will be found.
    
         N         (input) INTEGER
                   The order of the matrix.  N >= 0.
    
         D         (input/output) REAL array, dimension (N)
                   On entry, the n diagonal elements of the tridiago-
                   nal  matrix  A.  On exit, D may be multiplied by a
                   constant factor chosen to avoid over/underflow  in
                   computing the eigenvalues.
    
         E         (input/output) REAL array, dimension (N)
                   On entry, the (n-1) subdiagonal  elements  of  the
                   tridiagonal  matrix  A  in elements 1 to N-1 of E;
                   E(N) need not be set.  On exit, E  may  be  multi-
                   plied   by  a  constant  factor  chosen  to  avoid
                   over/underflow in computing the eigenvalues.
    
         VL        (input) REAL
                   VU      (input) REAL If RANGE='V', the  lower  and
                   upper  bounds  of  the interval to be searched for
                   eigenvalues. VL < VU.  Not referenced if  RANGE  =
                   'A' or 'I'.
    
         IL        (input) INTEGER
                   IU      (input) INTEGER If RANGE='I', the  indices
                   (in  ascending  order) of the smallest and largest
                   eigenvalues to be returned.  1 <= IL <= IU  <=  N,
                   if  N > 0; IL = 1 and IU = 0 if N = 0.  Not refer-
                   enced if RANGE = 'A' or 'V'.
    
         ABSTOL    (input) REAL
                   The absolute error tolerance for the  eigenvalues.
                   An approximate eigenvalue is accepted as converged
                   when it is determined to lie in an interval  [a,b]
                   of width less than or equal to
    
                   ABSTOL + EPS *   max( |a|,|b| ) ,
    
                   where EPS is the machine precision.  If ABSTOL  is
                   less than or equal to zero, then  EPS*|T|  will be
                   used in its place, where |T| is the 1-norm of  the
                   tridiagonal matrix.
    
                   Eigenvalues will be computed most accurately  when
                   ABSTOL  is  set  to  twice the underflow threshold
                   2*SLAMCH('S'), not zero.  If this routine  returns
                   with INFO>0, indicating that some eigenvectors did
                   not converge, try setting ABSTOL to 2*SLAMCH('S').
    
                   See "Computing Small Singular Values of Bidiagonal
                   Matrices  with Guaranteed High Relative Accuracy,"
                   by Demmel and Kahan, LAPACK Working Note #3.
    
         M         (output) INTEGER
                   The total number of eigenvalues found.  0 <= M  <=
                   N.  If RANGE = 'A', M = N, and if RANGE = 'I', M =
                   IU-IL+1.
    
         W         (output) REAL array, dimension (N)
                   The first M elements contain the  selected  eigen-
                   values in ascending order.
    
         Z         (output) REAL array, dimension (LDZ, max(1,M) )
                   If JOBZ = 'V', then if  INFO  =  0,  the  first  M
                   columns  of Z contain the orthonormal eigenvectors
                   of the matrix  A  corresponding  to  the  selected
                   eigenvalues, with the i-th column of Z holding the
                   eigenvector associated with W(i).  If an eigenvec-
                   tor fails to converge (INFO > 0), then that column
                   of Z contains  the  latest  approximation  to  the
                   eigenvector,  and  the index of the eigenvector is
                   returned in IFAIL.  If JOBZ = 'N', then Z  is  not
                   referenced.   Note:  the  user must ensure that at
                   least max(1,M) columns are supplied in  the  array
                   Z;  if  RANGE  =  'V', the exact value of M is not
                   known in advance and an upper bound must be used.
    
         LDZ       (input) INTEGER
                   The leading dimension of the array Z.  LDZ  >=  1,
                   and if JOBZ = 'V', LDZ >= max(1,N).
    
         WORK      (workspace) REAL array, dimension (5*N)
    
         IWORK     (workspace) INTEGER array, dimension (5*N)
    
         IFAIL     (output) INTEGER array, dimension (N)
                   If JOBZ = 'V', then if INFO = 0, the first M  ele-
                   ments  of IFAIL are zero.  If INFO > 0, then IFAIL
                   contains the  indices  of  the  eigenvectors  that
                   failed  to converge.  If JOBZ = 'N', then IFAIL is
                   not referenced.
    
         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.   Their  indices  are  stored  in  array
                   IFAIL.
    
    
    
    


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