Contents

# ?hbev

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

## Syntax

Include Files
• mkl.h
Description
The routine computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
A
.
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.
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
ab
; must be at least
kd
+1
for column major layout and
n
for row major layout
.
ldz
The leading dimension of the output array
z
.
Constraints:
if
jobz
=
'N'
, then
ldz
1
;
if
jobz
=
'V'
, then
ldz
max(1,
n
) .
Output Parameters
w
Array, size at least max(1,
n
).
If
info
= 0
, contains the eigenvalues in ascending order.
z
Array
z
(size max(1,
ldz
*
n
)
.
If
jobz
=
'V'
, then if
info
= 0
,
z
contains the orthonormal eigenvectors of the matrix
A
, with the
i
-th column of
z
holding the eigenvector associated with
w
[
i
- 1]
.
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(see the description of hbtrd).
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 the algorithm failed to converge;
i
indicates the number of elements of an intermediate tridiagonal form which did not converge to zero.

#### Product and Performance Information

1

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