Developer Reference

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

?hpgvd

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

Syntax

lapack_int LAPACKE_chpgvd
(
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_zhpgvd
(
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.
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 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 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
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
chpevd
/
zhpevd
returned an error code:
If
info
=
i
n
,
chpevd
/
zhpevd
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