Contents

# ?hegv

Computes all eigenvalues and, optionally, eigenvectors of a complex generalized Hermitian positive-definite eigenproblem.

## Syntax

Include Files
• mkl.h
Description
The routine computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian positive-definite eigenproblem, of the form
A
*
x
=
λ
*
B
*
x
,
A
*
B
*
x
=
λ
*
x
, or
B
*
A
*
x
=
λ
*
x
.
Here
A
and
B
are assumed to be Hermitian and
B
is also positive definite.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
itype
Must be 1 or 2 or 3. Specifies the problem type to be solved:
if
itype
= 1
, the problem type is
A*x
=
lambda
*
B
*
x
;
if
itype
= 2
, the problem type is
A*B*x
=
lambda
*
x
;
if
itype
= 3
, the problem type is
B
*
A*x
=
lambda
*
x
.
jobz
Must be
'N'
or
'V'
.
If
jobz
=
'N'
, then compute eigenvalues only.
If
jobz
=
'V'
, then compute eigenvalues and eigenvectors.
uplo
Must be
'U'
or
'L'
.
If
uplo
=
'U'
, arrays
a
and
b
store the upper triangles of
A
and
B
;
If
uplo
=
'L'
, arrays
a
and
b
store the lower triangles of
A
and
B
.
n
The order of the matrices
A
and
B
(
n
0
).
a
,
b
Arrays:
a
(size at least max(1,
lda
*
n
))
contains the upper or lower triangle of the Hermitian matrix
A
, as specified by
uplo
.
b
(size at least max(1,
ldb
*
n
))
contains the upper or lower triangle of the Hermitian positive definite matrix
B
, as specified by
uplo
.
lda
a
; at least max(1,
n
).
ldb
b
; at least max(1,
n
).
Output Parameters
a
On exit, if
jobz
=
'V'
, then if
info
= 0
,
a
contains the matrix
Z
of eigenvectors. The eigenvectors are normalized as follows:
if
itype
= 1
or 2,
Z
H
*
B
*
Z
= I
;
if
itype
= 3
,
Z
H
*inv(
B
)*
Z
= I
;
If
jobz
=
'N'
, then on exit the upper triangle (if
uplo
=
'U'
) or the lower triangle (if
uplo
=
'L'
) of
A
, including the diagonal, is destroyed.
b
On exit, if
info
n
, the part of
b
containing the matrix is overwritten by the triangular factor
U
or
L
from the Cholesky factorization
B
=
U
H
*
U
or
B
=
L
*
L
H
.
w
Array, size at least max(1,
n
).
If
info
= 0
, contains the eigenvalues in ascending order.
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
> 0
,
cpotrf
/
zpotrf
or
cheev
/
zheev
return an error code:
If
info
=
i
n
,
cheev
/
zheev
fails to converge, and
i
off-diagonal elements of an intermediate tridiagonal do not converge to zero;
If
info
=
n
+
i
, for
1
i
n
, then the leading minor of order
i
of
B
is not positive-definite. The factorization of
B
can not be completed and no eigenvalues or eigenvectors are computed.

#### 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