Developer Reference

Contents

?heevx

Computes selected eigenvalues and, optionally, eigenvectors of a Hermitian matrix.

Syntax

lapack_int LAPACKE_cheevx
(
int
matrix_layout
,
char
jobz
,
char
range
,
char
uplo
,
lapack_int
n
,
lapack_complex_float*
a
,
lapack_int
lda
,
float
vl
,
float
vu
,
lapack_int
il
,
lapack_int
iu
,
float
abstol
,
lapack_int*
m
,
float*
w
,
lapack_complex_float*
z
,
lapack_int
ldz
,
lapack_int*
ifail
);
lapack_int LAPACKE_zheevx
(
int
matrix_layout
,
char
jobz
,
char
range
,
char
uplo
,
lapack_int
n
,
lapack_complex_double*
a
,
lapack_int
lda
,
double
vl
,
double
vu
,
lapack_int
il
,
lapack_int
iu
,
double
abstol
,
lapack_int*
m
,
double*
w
,
lapack_complex_double*
z
,
lapack_int
ldz
,
lapack_int*
ifail
);
Include Files
  • mkl.h
Description
The routine computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
A
. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.
Note that for most cases of complex Hermetian eigenvalue problems the default choice should be heevr function as its underlying algorithm is faster and uses less workspace.
?heevx
is faster for a few selected 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
jobz
=
'N'
, then only eigenvalues are computed.
If
jobz
=
'V'
, then eigenvalues and eigenvectors are computed.
range
Must be
'A'
,
'V'
, or
'I'
.
If
range
=
'A'
, all eigenvalues will be found.
If
range
=
'V'
, all eigenvalues in the half-open interval (
vl
,
vu
] will be found.
If
range
=
'I'
, the eigenvalues with indices
il
through
iu
will be found.
uplo
Must be
'U'
or
'L'
.
If
uplo
=
'U'
,
a
stores the upper triangular part of
A
.
If
uplo
=
'L'
,
a
stores the lower triangular part of
A
.
n
The order of the matrix
A
(
n
≥ 0
).
a
a
(size max(1,
lda
*
n
))
is an array containing either upper or lower triangular part of the Hermitian matrix
A
, as specified by
uplo
.
lda
The leading dimension of the array
a
. Must be at least max(1,
n
).
vl
,
vu
If
range
=
'V'
, the lower and upper bounds of the interval to be searched for eigenvalues;
vl
vu
. Not referenced if
range
=
'A'
or
'I'
.
il
,
iu
If
range
=
'I'
, the indices of the smallest and largest eigenvalues to be returned. Constraints:
1
il
iu
n
, if
n
> 0
;
il
= 1 and
iu
= 0
, if
n
= 0
. Not referenced if
range
=
'A'
or
'V'
.
abstol
ldz
The leading dimension of the output array
z
;
ldz
1
.
If
jobz
=
'V'
, then
ldz
max(1,
n
)
for column major layout and
lda
max(1,
m
) for row major layout
.
Output Parameters
a
On exit, the lower triangle (if
uplo
=
'L'
) or the upper triangle (if
uplo
=
'U'
) of
A
, including the diagonal, is overwritten.
m
The total number of eigenvalues found; 0
m
n
.
If
range
=
'A'
,
m
=
n
, and if
range
=
'I'
,
m
=
iu
-
il
+
1
.
w
Array, size max(1,
n
). The first
m
elements contain the selected eigenvalues of the matrix
A
in ascending order.
z
Array
z
(size max(1,
ldz
*
m
) for column major layout and max(1,
ldz
*
n
) for row major layout)
contains eigenvectors.
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).
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.
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
, then
ifail
contains the indices of the eigenvectors that failed to converge.
If
jobz
=
'V'
, 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
*||
T
||
will be used in its place, where
||
T
||
is the 1-norm of the tridiagonal matrix obtained by reducing
A
to tridiagonal form. Eigenvalues will be 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, try setting
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