Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 0.9
  • 09/09/2020
  • Public Content
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

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