sstein (3p)

Name

sstein - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse itera- tion

Synopsis

SUBROUTINE SSTEIN(N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, IWORK,
IFAIL, INFO)

INTEGER N, M, LDZ, INFO
INTEGER IBLOCK(*), ISPLIT(*), IWORK(*), IFAIL(*)
REAL D(*), E(*), W(*), Z(LDZ,*), WORK(*)

SUBROUTINE SSTEIN_64(N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK,
IWORK, IFAIL, INFO)

INTEGER*8 N, M, LDZ, INFO
INTEGER*8 IBLOCK(*), ISPLIT(*), IWORK(*), IFAIL(*)
REAL D(*), E(*), W(*), Z(LDZ,*), WORK(*)




F95 INTERFACE
SUBROUTINE STEIN(N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK,
IWORK, IFAIL, INFO)

INTEGER :: N, M, LDZ, INFO
INTEGER, DIMENSION(:) :: IBLOCK, ISPLIT, IWORK, IFAIL
REAL, DIMENSION(:) :: D, E, W, WORK
REAL, DIMENSION(:,:) :: Z

SUBROUTINE STEIN_64(N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK,
IWORK, IFAIL, INFO)

INTEGER(8) :: N, M, LDZ, INFO
INTEGER(8), DIMENSION(:) :: IBLOCK, ISPLIT, IWORK, IFAIL
REAL, DIMENSION(:) :: D, E, W, WORK
REAL, DIMENSION(:,:) :: Z




C INTERFACE
#include <sunperf.h>

void  sstein(int  n,  float *d, float *e, int m, float *w, int *iblock,
int *isplit, float *z, int ldz, int *ifail, int *info);

void sstein_64(long n, float *d, float  *e,  long  m,  float  *w,  long
*iblock,  long *isplit, float *z, long ldz, long *ifail, long
*info);

Description

Oracle Solaris Studio Performance Library                           sstein(3P)



NAME
       sstein  -  compute  the  eigenvectors  of  a real symmetric tridiagonal
       matrix T corresponding to specified eigenvalues, using  inverse  itera-
       tion


SYNOPSIS
       SUBROUTINE SSTEIN(N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, IWORK,
             IFAIL, INFO)

       INTEGER N, M, LDZ, INFO
       INTEGER IBLOCK(*), ISPLIT(*), IWORK(*), IFAIL(*)
       REAL D(*), E(*), W(*), Z(LDZ,*), WORK(*)

       SUBROUTINE SSTEIN_64(N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK,
             IWORK, IFAIL, INFO)

       INTEGER*8 N, M, LDZ, INFO
       INTEGER*8 IBLOCK(*), ISPLIT(*), IWORK(*), IFAIL(*)
       REAL D(*), E(*), W(*), Z(LDZ,*), WORK(*)




   F95 INTERFACE
       SUBROUTINE STEIN(N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK,
              IWORK, IFAIL, INFO)

       INTEGER :: N, M, LDZ, INFO
       INTEGER, DIMENSION(:) :: IBLOCK, ISPLIT, IWORK, IFAIL
       REAL, DIMENSION(:) :: D, E, W, WORK
       REAL, DIMENSION(:,:) :: Z

       SUBROUTINE STEIN_64(N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK,
              IWORK, IFAIL, INFO)

       INTEGER(8) :: N, M, LDZ, INFO
       INTEGER(8), DIMENSION(:) :: IBLOCK, ISPLIT, IWORK, IFAIL
       REAL, DIMENSION(:) :: D, E, W, WORK
       REAL, DIMENSION(:,:) :: Z




   C INTERFACE
       #include <sunperf.h>

       void  sstein(int  n,  float *d, float *e, int m, float *w, int *iblock,
                 int *isplit, float *z, int ldz, int *ifail, int *info);

       void sstein_64(long n, float *d, float  *e,  long  m,  float  *w,  long
                 *iblock,  long *isplit, float *z, long ldz, long *ifail, long
                 *info);



PURPOSE
       sstein computes the eigenvectors of a real symmetric tridiagonal matrix
       T corresponding to specified eigenvalues, using inverse iteration.

       The maximum number of iterations allowed for each eigenvector is speci-
       fied by an internal parameter MAXITS (currently set to 5).


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


       D (input) The n diagonal elements of the tridiagonal matrix T.


       E (input) The (n-1) subdiagonal elements of the tridiagonal  matrix  T,
                 in elements 1 to N-1.  E(N) need not be set.


       M (input) The number of eigenvectors to be found.  0 <= M <= N.


       W (input) 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  SSTEBZ
                 with ORDER = 'B' is expected here. )


       IBLOCK (input)
                 The  submatrix  indices associated with the corresponding ei-
                 genvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to the
                 first  submatrix from the top, =2 if W(i) belongs to the sec-
                 ond submatrix, etc.  ( The output array IBLOCK from SSTEBZ is
                 expected here. )


       ISPLIT (input)
                 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  SSTEBZ  is  expected
                 here. )


       Z (output)
                 The  computed  eigenvectors.  The eigenvector associated with
                 the eigenvalue W(i) is stored in the i-th column of  Z.   Any
                 vector  which fails to converge is set to its current iterate
                 after MAXITS iterations.


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


       WORK (workspace)
                 dimension(5*N)

       IWORK (workspace)
                 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)
                 = 0: successful exit.
                 < 0: if INFO = -i, the i-th argument had an illegal value
                 > 0: if INFO = i, then i eigenvectors failed to  converge  in
                 MAXITS  iterations.  Their indices are stored in array IFAIL.




                                  7 Nov 2015                        sstein(3P)