Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
Contents

?steqr2

Computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method.

Syntax

void
ssteqr2
(
char
*compz
,
MKL_INT
*n
,
float
*d
,
float
*e
,
float
*z
,
MKL_INT
*ldz
,
MKL_INT
*nr
,
float
*work
,
MKL_INT
*info
);
void
dsteqr2
(
char
*compz
,
MKL_INT
*n
,
double
*d
,
double
*e
,
double
*z
,
MKL_INT
*ldz
,
MKL_INT
*nr
,
double
*work
,
MKL_INT
*info
);
Include Files
  • mkl_scalapack.h
Description
The
?steqr2
function
is a modified version of LAPACK
function
?steqr
. The
?steqr2
function
computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method.
?steqr2
 is modified from
?steqr
 to allow each ScaLAPACK process running
?steqr2
 to perform updates on a distributed matrix Q. Proper usage of
?steqr2
 can be gleaned from examination of ScaLAPACK
function
p?syev
.
Input Parameters
compz
Must be
'N'
 or
'I'
.
If
compz
 =
'N'
, the
function
computes eigenvalues only. If
compz
 =
'I'
, the
function
computes the eigenvalues and eigenvectors of the tridiagonal matrix
T
.
z
 must be initialized to the identity matrix by
p?laset
 or
?laset
 prior to entering this
function
.
n
The order of the matrix
T
(
n
≥
 0)
.
d
,
e
,
work
Arrays:
d
 contains the diagonal elements of
T
. The size of
d
 must be at least
max(1,
n
)
.
e
 contains the
(
n
-1)
 subdiagonal elements of
T
. The size of
e
 must be at least
max(1,
n
-1)
.
work
 is a workspace array. The size of
work
 is
max(1, 2
*n
-2)
. If
compz
 =
'N'
, then
work
 is not referenced.
z
(local)
Array of global size
n
*
n
 and of local size
ldz
*
nr
.
If
compz
 =
'V'
, then
z
 contains the orthogonal matrix used in the reduction to tridiagonal form.
ldz
The leading dimension of the array
z
. Constraints:
ldz
≥
 1
,
ldz
≥
 max(1,
n
)
, if eigenvectors are desired.
nr
nr
 =
max(1,
numroc
(
n
,
nb
,
myprow
, 0,
nprocs
))
.
If
compz
 =
'N'
, then
nr
 is not referenced.
Output Parameters
d
On exit, the eigenvalues in ascending order, if
info
 = 0
.
See also
info
.
e
On exit,
e
 has been destroyed.
z
On exit, if
info
 = 0
, then,
if
compz
 =
'V'
,
z
 contains the orthonormal eigenvectors of the original symmetric matrix, and if
compz
 =
'I'
,
z
 contains the orthonormal eigenvectors of the symmetric tridiagonal matrix. If
compz
 =
'N'
, then
z
 is not referenced.
info
info
 = 0
, the exit is successful.
info
 < 0
: if
info
 =
-i
, the
i
-th had an illegal value.
info
>
 0
: the algorithm has failed to find all the eigenvalues in a total of 30
n
 iterations;
if
info
 =
i
, then
i
 elements of
e
 have not converged to zero; on exit,
d
 and
e
 contain the elements of a symmetric tridiagonal matrix, which is orthogonally similar to the original matrix.

Product and Performance Information

1

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