Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

?hegst

Reduces a complex Hermitian positive-definite generalized eigenvalue problem to the standard form.

Syntax

lapack_int
LAPACKE_chegst
(
int
matrix_layout
,
lapack_int
itype
,
char
uplo
,
lapack_int
n
,
lapack_complex_float
*
a
,
lapack_int
lda
,
const
lapack_complex_float
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_zhegst
(
int
matrix_layout
,
lapack_int
itype
,
char
uplo
,
lapack_int
n
,
lapack_complex_double
*
a
,
lapack_int
lda
,
const
lapack_complex_double
*
b
,
lapack_int
ldb
);
Include Files
  • mkl.h
Description
The routine reduces a complex Hermitian positive-definite generalized eigenvalue problem to standard form.
itype
Problem
Result
1
A
*
x
 =
λ
*
B
*
x
A
 overwritten by
inv(
U
H
)*
A
*inv(
U
)
 or
inv(
L
)*
A
*inv(
L
H
)
2
A
*
B
*
x
 =
λ
*
x
A
 overwritten by
U
*
A
*
U
H
 or
L
H
*
A
*
L
3
B
*
A
*
x
 =
λ
*
x
Before calling this routine, you must call
?potrf
 to compute the Cholesky factorization:
B
 =
U
H
*U
 or
B
 =
L*L
H
.
Input Parameters
itype
Must be 1 or 2 or 3.
If
itype
 = 1
, the generalized eigenproblem is
A*z
 =
lambda
*
B
*
z
for
uplo
 =
'U'
:
C
 = (
U
H
)
-1
*
A
*
U
-1
;
for
uplo
 =
'L'
:
C
 =
L
-1
*
A
*(
L
H
)
-1
.
If
itype
 = 2
, the generalized eigenproblem is
A
*
B
*
z
 =
lambda
*
z
for
uplo
 =
'U'
:
C
 =
U
*
A
*
U
H
;
for
uplo
 =
'L'
:
C
 =
L
H
*
A
*
L
.
If
itype
 = 3
, the generalized eigenproblem is
B*A
*
z
 =
lambda
*
z
for
uplo
 =
'U'
:
C
 =
U
*
A
*
U
H
;
for
uplo
 =
'L'
:
C
 =
L
H
*
A
*
L
.
uplo
Must be
'U'
 or
'L'
.
If
uplo
 =
'U'
, the array
a
 stores the upper triangle of
A
; you must supply
B
 in the factored form
B
 =
U
H
*U
.
If
uplo
 =
'L'
, the array
a
 stores the lower triangle of
A
; you must supply
B
 in the factored form
B
 =
L*L
H
.
n
The order of the matrices
A
 and
B
 (
n
≥
 0
).
a
,
b
Arrays:
a
(size max(1,
lda
*
n
))
 contains the upper or lower triangle of
A
.
b
(size max(1,
ldb
*
n
))
 contains the Cholesky-factored matrix
B
:
B
 =
U
H
*U
 or
B
 =
L*L
H
 (as returned by
?potrf
).
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
The upper or lower triangle of
A
 is overwritten by the upper or lower triangle of
C
, as specified by the arguments
itype
 and
uplo
.
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.
Application Notes
Forming the reduced matrix
C
 is a stable procedure. However, it involves implicit multiplication by
B
-1
 (if
itype
 = 1
) or
B
 (if
itype
 = 2
 or 3). When the routine is used as a step in the computation of eigenvalues and eigenvectors of the original problem, there may be a significant loss of accuracy if
B
 is ill-conditioned with respect to inversion.
The approximate number of floating-point operations is
n
3
.

Product and Performance Information

1

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