Contents

# ?stein2

Computes the eigenvectors corresponding to specified eigenvalues of a real symmetric tridiagonal matrix, using inverse iteration.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
?stein2
function
is a modified LAPACK
function
?stein
. It 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).
Input Parameters
n
The order of the matrix
T
(
n
0)
.
m
The number of eigenvectors to be found
(0
m
n
)
.
d
,
e
,
w
Arrays:
d
, of size
n
. The
n
diagonal elements of the tridiagonal matrix
T
.
e
, of size
n
.
The
(
n
-1)
subdiagonal elements of the tridiagonal matrix
T
, in elements 1 to
n
-1
.
e
[
n
-1]
need not be set.
w
, of size
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
?stebz
with
ORDER
=
'B'
is expected here).
The size of
w
must be at least
max(1,
n
)
.
iblock
Array of size
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,
iblock
[
i
]
= 2, if eigenvalue
w
[
i
]
belongs to the second submatrix, etc. (The output array
iblock
from
?stebz
is expected here).
isplit
Array of size
n
.
The splitting points, at which
T
breaks up into submatrices. The first submatrix consists of rows/columns 1 to
isplit

, the second submatrix consists of rows/columns
isplit

+1 through
isplit

, etc. (The output array
isplit
from
?stebz
is expected here).
orfac
orfac
specifies which eigenvectors should be orthogonalized. Eigenvectors that correspond to eigenvalues which are within
orfac
*
||T||
of each other are to be orthogonalized.
ldz
The leading dimension of the output array
z
;
ldz
max(1,
n
)
.
work
Workspace array of size 5
n
.
iwork
Workspace array of size
n
.
Output Parameters
z
Array of size
ldz
*
m
.
The computed eigenvectors. The eigenvector associated with the eigenvalue
w
[
i
]
is stored in the
(
i
+1)
-th column of
the matrix
Z
represented by
z
,
i
=0, ...,
m
-1
. Any vector that fails to converge is set to its current iterate after
maxits
iterations.
ifail
Array of size
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 the array
ifail
.
info
info
= 0
, the exit is successful.
info
< 0
: if
info
=
-i
, the
i
info
> 0
: if
info
=
i
, then
i
eigenvectors failed to converge in
maxits
iterations. Their indices are stored in the array
ifail
.

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.