Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • 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

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