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?hegvd

Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian positive-definite eigenproblem using a divide and conquer method.

Syntax

lapack_int LAPACKE_chegvd
(
int
matrix_layout
,
lapack_int
itype
,
char
jobz
,
char
uplo
,
lapack_int
n
,
lapack_complex_float*
a
,
lapack_int
lda
,
lapack_complex_float*
b
,
lapack_int
ldb
,
float*
w
);
lapack_int LAPACKE_zhegvd
(
int
matrix_layout
,
lapack_int
itype
,
char
jobz
,
char
uplo
,
lapack_int
n
,
lapack_complex_double*
a
,
lapack_int
lda
,
lapack_complex_double*
b
,
lapack_int
ldb
,
double*
w
);
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.
It uses a divide and conquer algorithm.
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
The leading dimension of
a
; at least max(1,
n
).
ldb
The leading dimension of
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
=
i
, and
jobz
= 'N'
, then the algorithm failed to converge;
i
off-diagonal elements of an intermediate tridiagonal form did not converge to zero;
if
info
=
i
, and
jobz
= 'V'
, then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns
info
/(
n
+1)
through
mod(
info
,
n
+1)
.
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
could not be completed and no eigenvalues or eigenvectors were computed.

Product and Performance Information

1

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