Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

?hpgv

Computes all eigenvalues and, optionally, eigenvectors of a complex generalized Hermitian positive-definite eigenproblem with matrices in packed storage.

Syntax

lapack_int LAPACKE_chpgv
(
int
matrix_layout
,
lapack_int
itype
,
char
jobz
,
char
uplo
,
lapack_int
n
,
lapack_complex_float*
ap
,
lapack_complex_float*
bp
,
float*
w
,
lapack_complex_float*
z
,
lapack_int
ldz
);
lapack_int LAPACKE_zhpgv
(
int
matrix_layout
,
lapack_int
itype
,
char
jobz
,
char
uplo
,
lapack_int
n
,
lapack_complex_double*
ap
,
lapack_complex_double*
bp
,
double*
w
,
lapack_complex_double*
z
,
lapack_int
ldz
);
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, stored in packed format, 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
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 Hermitian 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 Hermitian 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
H
*
U
 or
B
 =
L
*
L
H
, in the same storage format as
B
.
w
Array, size at least max(1,
n
).
If
info
 = 0
, contains the eigenvalues in ascending order.
z
Array
z
(size 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
H
*
B
*
Z
 = I
;
if
itype
 = 3
,
Z
H
*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
,
cpptrf
/
zpptrf
 and
chpev
/
zhpev
 returned an error code:
If
info
 =
i
≤
n
,
chpev
/
zhpev
 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.