Developer Reference

  • 2020.2
  • 07/15/2020
  • Public Content
Contents

?larrf

Finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated.

Syntax

call slarrf
(
n
,
d
,
l
,
ld
,
clstrt
,
clend
,
w
,
wgap
,
werr
,
spdiam
,
clgapl
,
clgapr
,
pivmin
,
sigma
,
dplus
,
lplus
,
work
,
info
)
call dlarrf
(
n
,
d
,
l
,
ld
,
clstrt
,
clend
,
w
,
wgap
,
werr
,
spdiam
,
clgapl
,
clgapr
,
pivmin
,
sigma
,
dplus
,
lplus
,
work
,
info
)
Include Files
  • mkl.fi
Description
Given the initial representation
L*D*L
T
and its cluster of close eigenvalues (in a relative measure),
w
(
clstrt
),
w
(
clstrt
+1), ...
w
(
clend
), the routine
?larrf
finds a new relatively robust representation
L*D*L
T
-
σ
i
*
I
=
L
(+)*
D
(+)*
L
(+)
T
such that at least one of the eigenvalues of
L
(+)*
D*
(+)*
L
(+)
T
is relatively isolated.
Input Parameters
n
INTEGER
. The order of the matrix (subblock, if the matrix is splitted).
d
REAL
for
slarrf
DOUBLE PRECISION
for
dlarrf
Array,
DIMENSION
(
n
). The
n
diagonal elements of the diagonal matrix
D
.
l
REAL
for
slarrf
DOUBLE PRECISION
for
dlarrf
Array,
DIMENSION
(
n
-1).
The (
n
-1) subdiagonal elements of the unit bidiagonal matrix
L
.
ld
REAL
for
slarrf
DOUBLE PRECISION
for
dlarrf
Array,
DIMENSION
(
n
-1).
The
n
-1 elements
L
i
*
D
i
.
clstrt
INTEGER
. The index of the first eigenvalue in the cluster.
clend
INTEGER
. The index of the last eigenvalue in the cluster.
w
REAL
for
slarrf
DOUBLE PRECISION
for
dlarrf
Array,
DIMENSION
≥ (
clend
-
clstrt
+1). The eigenvalue approximations of
L*D*L
T
in ascending order.
w
(
clstrt
) through
w
(
clend
) form the cluster of relatively close eigenvalues.
wgap
REAL
for
slarrf
DOUBLE PRECISION
for
dlarrf
Array,