Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

?stevx

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

Syntax

lapack_int
LAPACKE_sstevx
(
int
matrix_layout
,
char
jobz
,
char
range
,
lapack_int
n
,
float
*
d
,
float
*
e
,
float
vl
,
float
vu
,
lapack_int
il
,
lapack_int
iu
,
float
abstol
,
lapack_int
*
m
,
float
*
w
,
float
*
z
,
lapack_int
ldz
,
lapack_int
*
ifail
);
lapack_int
LAPACKE_dstevx
(
int
matrix_layout
,
char
jobz
,
char
range
,
lapack_int
n
,
double
*
d
,
double
*
e
,
double
vl
,
double
vu
,
lapack_int
il
,
lapack_int
iu
,
double
abstol
,
lapack_int
*
m
,
double
*
w
,
double
*
z
,
lapack_int
ldz
,
lapack_int
*
ifail
);
Include Files
  • mkl.h
Description
The routine computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
A
. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.
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
A
 (
n
≥
 0
).
d
,
e
Arrays:
d
 contains the
n
 diagonal elements of the tridiagonal matrix
A
.
The dimension of
d
 must be at least max(1,
n
).
e
 contains the
n
-1 subdiagonal elements of
A
.
The dimension of
e
 must be at least max(1,
n
-1). The
n
-th element of this array is used as workspace.
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
;
il
=1
 and
iu
=0
 if
n
 = 0
.
If
range
 =
'A'
 or
'V'
,
il
 and
iu
 are not referenced.
abstol
ldz
The leading dimensions of the output array
z
;
ldz
≥
 1
. If
jobz
 =
'V'
, then
ldz
≥
 max
(1,
n
)
for column major layout and
ldz
≥
 max(1,
m
) for row major layout
.
Output Parameters
m
The total number of eigenvalues found,
0
≤
m
≤
n
.
If
range
 =
'A'
,
m
 =
n
, if
range
 =
'I'
,
m
 =
iu
-
il
+1
, and if
range
 =
'V'
 the exact value of
m
 is unknown.
w
,
z
Arrays:
w
, size at least max(1,
n
).
The first
m
 elements of
w
 contain the selected eigenvalues of the matrix
A
 in ascending order.
z
(size at least max(1,
ldz
*
m
) for column major layout and max(1,
ldz
*
n
) for row major layout)
 .
If
jobz
 =
'V'
, then if
info
 = 0
, the first
m
 columns of
z
 contain the orthonormal eigenvectors of the matrix
A
 corresponding to the selected eigenvalues, with the
i
-th column of
z
 holding the eigenvector associated with
w
[
i
 - 1]
.
If an eigenvector fails to converge, then that column of
z
 contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in
ifail
.
If
jobz
 =
'N'
, then
z
 is not referenced.
d
,
e
On exit, these arrays may be multiplied by a constant factor chosen to avoid overflow or underflow in computing the eigenvalues.
ifail
Array, size at least max(1,
n
).
If
jobz
 =
'V'
, then if
info
 = 0
, the first
m
 elements of
ifail
 are zero; if
info
 > 0
, the
ifail
 contains the indices of the eigenvectors that failed to converge.
If
jobz
 =
'N'
, then
ifail
 is not referenced.
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
 =
i
, then
i
 eigenvectors failed to converge; their indices are stored in the array
ifail
.
Application Notes
An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to
abstol
+
ε
*max(|a|,|b|)
, where
ε
 is the machine precision.
If
abstol
 is less than or equal to zero, then
ε
*|
A
|
1
 is used instead. Eigenvalues are computed most accurately when
abstol
 is set to twice the underflow threshold 2*
?lamch
('S'), not zero.
If this routine returns with
info
 > 0
, indicating that some eigenvectors did not converge, set
abstol
 to 2*
?lamch
('S').

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