Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 0.9
  • 09/09/2020
  • Public Content
Contents

?feast_sbgv/?feast_hbgv

Extended Eigensolver interface for generalized eigenvalue problem with banded matrices.

Syntax

void
sfeast_sbgv
(
const
char
*
uplo
,
const
MKL_INT
*
n
,
const
MKL_INT
*
kla
,
const
float
*
a
,
const
MKL_INT
*
lda
,
const
MKL_INT
*
klb
,
const
float
*
b
,
const
MKL_INT
*
ldb
,
MKL_INT
*
fpm
,
float
*
epsout
,
MKL_INT
*
loop
,
const
float
*
emin
,
const
float
*
emax
,
MKL_INT
*
m0
,
float
*
e
,
float
*
x
,
MKL_INT
*
m
,
float
*
res
,
MKL_INT
*
info
);
void
dfeast_sbgv
(
const
char
*
uplo
,
const
MKL_INT
*
n
,
const
MKL_INT
*
kla
,
const
double
*
a
,
const
MKL_INT
*
lda
,
const
MKL_INT
*
klb
,
const
double
*
b
,
const
MKL_INT
*
ldb
,
MKL_INT
*
fpm
,
double
*
epsout
,
MKL_INT
*
loop
,
const
double
*
emin
,
const
double
*
emax
,
MKL_INT
*
m0
,
double
*
e
,
double
*
x
,
MKL_INT
*
m
,
double
*
res
,
MKL_INT
*
info
);
void
cfeast_hbgv
(
const
char
*
uplo
,
const
MKL_INT
*
n
,
const
MKL_INT
*
kla
,
const
MKL_Complex8
*
a
,
const
MKL_INT
*
lda
,
const
MKL_INT
*
klb
,
const
MKL_Complex8
*
b
,
const
MKL_INT
*
ldb
,
MKL_INT
*
fpm
,
float
*
epsout
,
MKL_INT
*
loop
,
const
float
*
emin
,
const
float
*
emax
,
MKL_INT
*
m0
,
float
*
e
,
MKL_Complex8
*
x
,
MKL_INT
*
m
,
float
*
res
,
MKL_INT
*
info
);
void
zfeast_hbgv
(
const
char
*
uplo
,
const
MKL_INT
*
n
,
const
MKL_INT
*
kla
,
const
MKL_Complex16
*
a
,
const
MKL_INT
*
lda
,
const
MKL_INT
*
klb
,
const
MKL_Complex16
*
b
,
const
MKL_INT
*
ldb
,
MKL_INT
*
fpm
,
double
*
epsout
,
MKL_INT
*
loop
,
const
double
*
emin
,
const
double
*
emax
,
MKL_INT
*
m0
,
double
*
e
,
MKL_Complex16
*
x
,
MKL_INT
*
m
,
double
*
res
,
MKL_INT
*
info
);
Include Files
  • mkl.h
Description
The routines compute all the eigenvalues and eigenvectors for generalized eigenvalue problems,
Ax
 =
λ
Bx
, within a given search interval.
Both matrices
A
 and
B
 must use the same family of storage format. The bandwidth, however, can be different (
klb
 can be different from
kla
).
Input Parameters
uplo
Must be
'U'
 or
'L'
 or
'F'
 .
If
UPLO
 =
'U'
,
a
 and
b
 store the upper triangular parts of
A
 and
B
 respectively.
If
UPLO
 =
'L'
,
a
 and
b
 store the lower triangular parts of
A
 and
B
 respectively.
If
UPLO
=
'F'
,
a
 and
b
 store the full matrices
A
 and
B
 respectively.
n
Sets the size of the problem.
n
 > 0.
kla
The number of super- or sub-diagonals within the band in
A
 (
kla
≥
 0).
a
Array of dimension
lda
 by
n
, contains either full matrix
A
 or upper or lower triangular part of the matrix
A
, as specified by
uplo
lda
The leading dimension of the array
a
. Must be at least max(1,
n
).
klb
The number of super- or sub-diagonals within the band in
B
 (
klb
≥
 0).
b
Array of dimension
ldb
 by
n
, contains either full matrix
B
 or upper or lower triangular part of the matrix
B
, as specified by
uplo
ldb
The leading dimension of the array
B
. Must be at least max(1,
n
).
fpm
Array, dimension of 128. This array is used to pass various parameters to Extended Eigensolver routines. See Extended Eigensolver Input Parameters for a complete description of the parameters and their default values.
emin
,
emax
The lower and upper bounds of the interval to be searched for eigenvalues;
emin
 ≤
emax.
m0
On entry, specifies the initial guess for subspace dimension to be used,
0 <
m0
≤
n
. Set
m0
 ≥
m
 where
m
 is the total number of eigenvalues located in the interval [
emin
,
emax
]. If the initial guess is wrong, Extended Eigensolver routines return
info
=3.
x
On entry, if
fpm
[4]
=1, the array
x
of size
n
 by
m
 contains a basis of guess subspace where
n
 is the order of the input matrix.
Output Parameters
epsout
On output, contains the relative error on the trace: |
trace
i
 -
trace
i-1
| /max(|
emin
|, |
emax
|)
loop
On output, contains the number of refinement loop executed. Ignored on input.
e
Array of length
m0
. On output, the first
m
 entries of
e
 are eigenvalues found in the interval.
x
On output, the first
m
 columns of
x
 contain the orthonormal eigenvectors corresponding to the computed eigenvalues
e
, with the
i
-th column of
x
 holding the eigenvector associated with
e
[
i
]
.
m
The total number of eigenvalues found in the interval [
emin
,
emax
]: 0 ≤
m
 ≤
m0
.
res
Array of length
m0
. On exit, the first
m
 components contain the relative residual vector:
for
i
=1, 2, …,
m
, and where
m
 is the total number of eigenvalues found in the search interval.
info
If
info
=0, the execution is successful. If
info
 ≠ 0, see Output Eigensolver info Details.

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