Provided by: scalapack-doc_1.5-10_all #### NAME

```       SSTEIN2  - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding
to specified eigenvalues, using inverse iteration

```

#### SYNOPSIS

```       SUBROUTINE SSTEIN2( N, D, E, M, W, IBLOCK, ISPLIT, ORFAC, Z, LDZ, WORK, IWORK, IFAIL, INFO
)

INTEGER         INFO, LDZ, M, N

REAL            ORFAC

INTEGER         IBLOCK( * ), IFAIL( * ), ISPLIT( * ), IWORK( * )

REAL            D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )

```

#### PURPOSE

```       SSTEIN2  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 specified by an  internal
parameter MAXITS (currently set to 5).

```

#### ARGUMENTS

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

D       (input) REAL array, dimension (N)
The n diagonal elements of the tridiagonal matrix T.

E       (input) REAL array, dimension (N)
The  (n-1) subdiagonal elements of the tridiagonal matrix T, 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) REAL 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 SSTEBZ 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 SSTEBZ
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 SSTEBZ  is  expected
here. )

ORFAC   (input) REAL
ORFAC  specifies  which  eigenvectors  should be orthogonalized. Eigenvectors that
correspond to eigenvalues which are within ORFAC*||T|| of each  other  are  to  be
orthogonalized.

Z       (output) REAL array, dimension (LDZ, M)
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) INTEGER
The leading dimension of the array Z.  LDZ >= max(1,N).

WORK    (workspace) REAL 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 illegal 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 iterations performed.

EXTRA   INTEGER, default = 2
The  number  of  iterations  performed  after  norm growth criterion is satisfied,
should be at least 1.
```