Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

?hbevx

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

Syntax

lapack_int LAPACKE_chbevx
(
int
matrix_layout
,
char
jobz
,
char
range
,
char
uplo
,
lapack_int
n
,
lapack_int
kd
,
lapack_complex_float*
ab
,
lapack_int
ldab
,
lapack_complex_float*
q
,
lapack_int
ldq
,
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_zhbevx
(
int
matrix_layout
,
char
jobz
,
char
range
,
char
uplo
,
lapack_int
n
,
lapack_int
kd
,
lapack_complex_double*
ab
,
lapack_int
ldab
,
lapack_complex_double*
q
,
lapack_int
ldq
,
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 band 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
.
uplo
Must be
'U'
 or
'L'
.
If
uplo
 =
'U'
,
ab
 stores the upper triangular part of
A
.
If
uplo
 =
'L'
,
ab
 stores the lower triangular part of
A
.
n
The order of the matrix
A
 (
n
≥
 0
).
kd
The number of super- or sub-diagonals in
A
(
kd
≥
 0
).
ab
ab
(size at least max(1,
ldab
*
n
) for column major layout and at least max(1,
ldab
*(
kd
 + 1)) for row major layout)
 is an array containing either upper or lower triangular part of the Hermitian matrix
A
 (as specified by
uplo
) in band storage format.
ldab
The leading dimension of
ab
; must be at least
kd
 +1
for column major layout and
n
 for row major layout
.
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
The absolute error tolerance to which each eigenvalue is required.
See
Application notes
 for details on error tolerance.
ldq
,
ldz
The leading dimensions of the output arrays
q
 and
z
, respectively.
Constraints:
ldq
≥
 1,
ldz
≥
 1
;
If
jobz
 =
'V'
, then
ldq
≥
 max
(1,
n
) and
ldz
≥
 max
(1,
n
)
for column major layout and
ldz
≥
 max(1,
m
) for row major layout
.
Output Parameters
q
Array, size
max(1,
ldz
*
n
)
.
If
jobz
 =
'V'
, the
n
-by-
n
 unitary matrix is used in the reduction to tridiagonal form.
If
jobz
 =
'N'
, the array
q
 is not referenced.
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 not known in advance..
w
Array, size at least max(1,
n
). The first
m
 elements contain the selected eigenvalues of the matrix
A
 in ascending order.
z
Array
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.
ab
On exit, this array is overwritten by the values generated during the reduction to tridiagonal form.
If
uplo
 =
'U'
, the first superdiagonal and the diagonal of the tridiagonal matrix
T
 are returned in rows
kd
 and
kd
+1 of
ab
, and if
uplo
 =
'L'
, the diagonal and first subdiagonal of
T
 are returned in the first two rows of
ab
.
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
*||
T
||
1
 will be used in its place, where
T
 is 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