Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
Contents

?sbgv

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

Syntax

lapack_int
LAPACKE_ssbgv
(
int
matrix_layout
,
char
jobz
,
char
uplo
,
lapack_int
n
,
lapack_int
ka
,
lapack_int
kb
,
float
*
ab
,
lapack_int
ldab
,
float
*
bb
,
lapack_int
ldbb
,
float
*
w
,
float
*
z
,
lapack_int
ldz
);
lapack_int
LAPACKE_dsbgv
(
int
matrix_layout
,
char
jobz
,
char
uplo
,
lapack_int
n
,
lapack_int
ka
,
lapack_int
kb
,
double
*
ab
,
lapack_int
ldab
,
double
*
bb
,
lapack_int
ldbb
,
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 banded eigenproblem, of the form
A
*
x
 =
λ
*
B
*
x
. Here
A
 and
B
 are assumed to be symmetric and banded, 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
).
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
ab
 and
bb
 store the upper triangles of
A
 and
B
;
If
uplo
 =
'L'
, arrays
ab
 and
bb
 store the lower triangles of
A
 and
B
.
n
The order of the matrices
A
 and
B
 (
n
≥
 0
).
ka
The number of super- or sub-diagonals in
A
(
ka
≥
 0
).
kb
The number of super- or sub-diagonals in
B
 (
kb
≥
 0).
ab
,
bb
Arrays:
ab
(size at least max(1,
ldab
*
n
) for column major layout and max(1,
ldab
*(
ka
 + 1)) for row major layout)
 is an array containing either upper or lower triangular part of the symmetric matrix
A
 (as specified by
uplo
) in band storage format.
bb
(size at least max(1,
ldbb
*
n
) for column major layout and max(1,
ldbb
*(
kb
 + 1)) for row major layout)
 is an array containing either upper or lower triangular part of the symmetric matrix
B
 (as specified by
uplo
) in band storage format.
ldab
The leading dimension of the array
ab
; must be at least
ka
+1
for column major layout and at least max(1,
n
) for row major layout
 .
ldbb
The leading dimension of the array
bb
; must be at least
kb
+1
for column major layout and at least max(1,
n
) for row major layout
.
ldz
The leading dimension of the output array
z
;
ldz
≥
 1
. If
jobz
 =
'V'
,
ldz
≥
 max(1,
n
)
.
Output Parameters
ab
On exit, the contents of
ab
 are overwritten.
bb
On exit, contains the factor
S
 from the split Cholesky factorization
B
 =
S
T
*S
, as returned by pbstf/pbstf.
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, with the
i
-th column of
z
 holding the eigenvector associated with
w
(
i
). The eigenvectors are normalized so that
Z
T
*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
, and
if
i
≤
n
, the algorithm 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 pbstf/pbstf returned
info
 =
i
 and
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.