?feast_sbgv/?feast

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 = λBx

, 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.

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