Developer Reference

  • 2020.2
  • 07/15/2020
  • Public Content
Contents

?stevr

Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix using the Relatively Robust Representations.

Syntax

call sstevr
(
jobz
,
range
,
n
,
d
,
e
,
vl
,
vu
,
il
,
iu
,
abstol
,
m
,
w
,
z
,
ldz
,
isuppz
,
work
,
lwork
,
iwork
,
liwork
,
info
)
call dstevr
(
jobz
,
range
,
n
,
d
,
e
,
vl
,
vu
,
il
,
iu
,
abstol
,
m
,
w
,
z
,
ldz
,
isuppz
,
work
,
lwork
,
iwork
,
liwork
,
info
)
call stevr
(
d
,
e
,
w
[
,
z
]
[
,
vl
]
[
,
vu
]
[
,
il
]
[
,
iu
]
[
,
m
]
[
,
isuppz
]
[
,
abstol
]
[
,
info
]
)
Include Files
  • mkl.fi
    ,
    lapack.f90
Description
The routine computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
T
. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.
Whenever possible, the routine calls stemr to compute the eigenspectrum using Relatively Robust Representations. stegr computes eigenvalues by the
dqds
algorithm, while orthogonal eigenvectors are computed from various "good"
L*D*L
T
representations (also known as Relatively Robust Representations). Gram-Schmidt orthogonalization is avoided as far as possible. More specifically, the various steps of the algorithm are as follows. For the i-th unreduced block of
T
:
  1. Compute
    T
    -
    σ
    i
    =
    L
    i
    *D
    i
    *L
    i
    T
    , such that
    L
    i
    *D
    i
    *L
    i
    T
    is a relatively robust representation.
  2. Compute the eigenvalues,
    λ
    j
    , of
    L
    i
    *D
    i
    *L
    i
    T
    to high relative accuracy by the
    dqds
    algorithm.
  3. If there is a cluster of close eigenvalues, "choose"
    σ
    i
    close to the cluster, and go to Step (a).
  4. Given the approximate eigenvalue
    λ
    j
    of
    L
    i
    *D
    i
    *L
    i
    T
    , compute the corresponding eigenvector by forming a rank-revealing twisted factorization.