Developer Reference

  • 0.10
  • 10/21/2020
  • Public Content
Contents

?sygv

Computes all eigenvalues and, optionally, eigenvectors of a real generalized symmetric definite eigenproblem.

Syntax

lapack_int
LAPACKE_ssygv
(
int
matrix_layout
,
lapack_int
itype
,
char
jobz
,
char
uplo
,
lapack_int
n
,
float
*
a
,
lapack_int
lda
,
float
*
b
,
lapack_int
ldb
,
float
*
w
);
lapack_int
LAPACKE_dsygv
(
int
matrix_layout
,
lapack_int
itype
,
char
jobz
,
char
uplo
,
lapack_int
n
,
double
*
a
,
lapack_int
lda
,
double
*
b
,
lapack_int
ldb
,
double
*
w
);
Include Files
  • mkl.h
Description
The routine computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-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 symmetric 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 symmetric matrix
A
, as specified by
uplo
.
b
(size at least max(1,
ldb
*
n
))
contains the upper or lower triangle of the symmetric 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
T
*
B
*
Z
= I
;
if
itype
= 3
,
Z
T
*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
T
*U
or
B
=
L*
L
T
.
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
,
spotrf
/
dpotrf
or
ssyev
/
dsyev
returned an error code:
If
info
=
i
n
,
ssyev
/
dsyev
failed to converge, and
i
off-diagonal elements of an intermediate tridiagonal did 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
could not be completed and no eigenvalues or eigenvectors were 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