Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

?stein2

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

Syntax

void
sstein2
(
MKL_INT
*n
,
float
*d
,
float
*e
,
MKL_INT
*m
,
float
*w
,
MKL_INT
*iblock
,
MKL_INT
*isplit
,
float
*orfac
,
float
*z
,
MKL_INT
*ldz
,
float
*work
,
MKL_INT
*iwork
,
MKL_INT
*ifail
,
MKL_INT
*info
);
void
dstein2
(
MKL_INT
*n
,
double
*d
,
double
*e
,
MKL_INT
*m
,
double
*w
,
MKL_INT
*iblock
,
MKL_INT
*isplit
,
double
*orfac
,
double
*z
,
MKL_INT
*ldz
,
double
*work
,
MKL_INT
*iwork
,
MKL_INT
*ifail
,
MKL_INT
*info
);
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
[0]
, the second submatrix consists of rows/columns
isplit
[0]
+1 through
isplit
[1]
, 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
-th had an illegal value.
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.