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?spgvd

Computes all eigenvalues and, optionally, eigenvectors of a real generalized symmetric definite eigenproblem with matrices in packed storage using a divide and conquer method.

Syntax

lapack_int
LAPACKE_sspgvd
(
int
matrix_layout
,
lapack_int
itype
,
char
jobz
,
char
uplo
,
lapack_int
n
,
float
*
ap
,
float
*
bp
,
float
*
w
,
float
*
z
,
lapack_int
ldz
);
lapack_int
LAPACKE_dspgvd
(
int
matrix_layout
,
lapack_int
itype
,
char
jobz
,
char
uplo
,
lapack_int
n
,
double
*
ap
,
double
*
bp
,
double
*
w
,
double
*
z
,
lapack_int
ldz
);
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, stored in packed format, and
B
is also positive definite.
If eigenvectors are desired, 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
ap
and
bp
store the upper triangles of
A
and
B
;
If
uplo
=
'L'
, arrays
ap
and
bp
store the lower triangles of
A
and
B
.
n
The order of the matrices
A
and
B
(
n
0
).
ap
,
bp
Arrays:
ap
contains the packed upper or lower triangle of the symmetric matrix
A
, as specified by
uplo
.
The dimension of
ap
must be at least max(1,
n
*(
n
+1)/2).
bp
contains the packed upper or lower triangle of the symmetric matrix
B
, as specified by
uplo
.
The dimension of
bp
must be at least max(1,
n
*(
n
+1)/2).
ldz
The leading dimension of the output array
z
;
ldz
1
. If
jobz
=
'V'
,
ldz
max(1,
n
)
.
Output Parameters
ap
On exit, the contents of
ap
are overwritten.
bp
On exit, contains the triangular factor
U
or
L
from the Cholesky factorization
B
=
U
T
*U
or
B
=
L*
L
T
, in the same storage format as
B
.
w
,
z
Arrays:
w
, size at least max(1,
n
).
If
info
= 0
, contains the eigenvalues in ascending order.
z
(size at least max(1,
ldz
*
n
))
.
If
jobz
=
'V'
, then if
info
= 0
,
z
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
z
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
> 0
,
spptrf
/
dpptrf
and
sspevd
/
dspevd
returned an error code:
If
info
=
i
n
,
sspevd
/
dspevd
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

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