## Developer Reference

• 0.9
• 09/09/2020
• Public Content
Contents

# ?stegr

Computes selected eigenvalues and eigenvectors of a real symmetric tridiagonal matrix.

## Syntax

Include Files
• mkl.h
Description
The routine computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
T
.
The spectrum may be computed either completely or partially by specifying either an interval
(
vl
,
vu
]
or a range of indices
il
:
iu
for the desired eigenvalues.
?stegr
is a compatibility wrapper around the improved stemr routine. See its description for further details.
Note that the
abstol
parameter no longer provides any benefit and hence is no longer used.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
jobz
Must be
'N'
or
'V'
.
If
job
=
'N'
, then only eigenvalues are computed.
If
job
=
'V'
, then eigenvalues and eigenvectors are computed.
range
Must be
'A'
or
'V'
or
'I'
.
If
range
=
'A'
, the routine computes all eigenvalues.
If
range
=
'V'
, the routine computes eigenvalues
w
[
i
]
in the half-open interval:
vl
<
w
[
i
]
vu
.
If
range
=
'I'
, the routine computes eigenvalues with indices
il
to
iu
.
n
The order of the matrix
T
(
n
0
).
d
,
e
Arrays:
d
contains the diagonal elements of
T
.
The dimension of
d
must be at least max(1,
n
).
e
contains the subdiagonal elements of
T
in elements 1 to
n
-1;
e
(
n
) need not be set on input, but it is used as a workspace.
The dimension of
e
must be at least max(1,
n
).
vl
,
vu
If
range
=
'V'
, the lower and upper bounds of the interval to be searched for eigenvalues.
Constraint:
vl
<
vu
.
If
range
=
'A'
or
'I'
,
vl
and
vu
are not referenced.
il
,
iu
If
range
=
'I'
, the indices in ascending order of the smallest and largest eigenvalues to be returned.
Constraint:
1
il
iu
n
, if
n
> 0
.
If
range
=
'A'
or
'V'
,
il
and
iu
are not referenced.
abstol
Unused. Was the absolute error tolerance for the eigenvalues/eigenvectors in previous versions.
ldz
The leading dimension of the output array
z
. Constraints:
ldz
1
if
jobz
=
'N'
;
ldz
max(1,
n
)
if
jobz
=
'V'
.
Output Parameters
d
,
e
On exit,
d
and
e
are overwritten.
m
The total number of eigenvalues found,
0
m
n
.
If
range
=
'A'
,
m
=
n
, and if
range
=
'I'
,
m
=
iu
-
il
+1
.
w
Array, size at least max(1,
n
).
The selected eigenvalues in ascending order, stored in
w

to
w
[
m
- 1]
.
z
Array
z
(size max(1,
ldz
*
m
)).
If
jobz
=
'V'
, and if
info
= 0
, the first
m
columns of
z
contain the orthonormal eigenvectors of the matrix
T
corresponding to the selected eigenvalues, with the
i
-th column of
z
holding the eigenvector associated with
w
[
i
- 1]
.
If
jobz
=
'N'
, then
z
is not referenced.
Note: if
range
=
'V'
, the exact value of
m
is not known in advance and an upper bound must be used. Using
n
=
m
is always safe.
isuppz
Array, size at least
(2*max(1,
m
))
.
The support of the eigenvectors in
z
, that is the indices indicating the nonzero elements in
z
. The
i
-th computed eigenvector is nonzero only in elements
isuppz
[2*
i
- 2]
through
isuppz
[2
*i
- 1]
. This is relevant in the case when the matrix is split.
isuppz
is only accessed when
jobz
=
'V'
, and
n
> 0
.
Return Values
This function returns a value
info
.
If
info
=0
, the execution is successful.
If
info
=
-i
, the
i
-th parameter had an illegal value.
If
info
> 0
, an internal error occurred.

#### Product and Performance Information

1

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804