Contents

# ?feast_scsrgv/?feast_hcsrgv

Extended Eigensolver interface for generalized eigenvalue problem with sparse matrices.

## Syntax

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 position of the non-zero elements can be different (CSR coordinates
ib
and
jb
can be different from
ia
and
ja
).
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.
a
Array containing the nonzero elements of either the full matrix
A
or the upper or lower triangular part of the matrix
A
, as specified by
uplo
.
ia
Array of length
n
+ 1, containing indices of elements in the array
a
, such that
ia
[
i
- 1]
is the index in the array
a
of the first non-zero element from the row
i
. The value of the last element
ia
[
n
]
is equal to the number of non-zeros plus one.
ja
Array containing the column indices for each non-zero element of the matrix
A
being represented in the array
a
. Its length is equal to the length of the array
a
.
b
Array of dimension
ldb
by *, contains the nonzero elements of either the full matrix
B
or the upper or lower triangular part of the matrix
B
, as specified by
uplo
.
ib
Array of length
n
+ 1, containing indices of elements in the array
b
, such that
ib
[
i
- 1]
is the index in the array
b
of the first non-zero element from the row
i
. The value of the last element
ib
[
n
]
is equal to the number of non-zeros plus one.
jb
Array containing the column indices for each non-zero element of the matrix
B
being represented in the array
b
. Its length is equal to the length of the array
b
.
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

=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
fpm
On output, the last 64 values correspond to
Intel® oneAPI Math Kernel Library
PARDISO
iparm

to
iparm

(regardless of the value of
fpm

on input).
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

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