## Developer Reference

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

# ?la_herfsx_extended

Improves the computed solution to a system of linear equations for Hermitian indefinite matrices by performing extra-precise iterative refinement and provides error bounds and backward error estimates for the solution.

## Syntax

Include Files
• mkl.fi
Description
The
?la_herfsx_extended
subroutine improves the computed solution to a system of linear equations by performing extra-precise iterative refinement and provides error bounds and backward error estimates for the solution. The
?herfsx
routine calls
?la_herfsx_extended
to perform iterative refinement.
In addition to normwise error bound, the code provides maximum componentwise error bound, if possible. See comments for
err_bnds_norm
and
err_bnds_comp
for details of the error bounds.
Use
?la_herfsx_extended
to set only the second fields of
err_bnds_norm
and
err_bnds_comp
.
Input Parameters
prec_type
INTEGER
.
Specifies the intermediate precision to be used in refinement. The value is defined by
ilaprec(p)
, where
p
is a
CHARACTER
and:
If
p
=
'S'
: Single.
If
p
=
'D'
: Double.
If
p
=
'I'
: Indigenous.
If
p
=
'X'
,
'E'
: Extra.
uplo
CHARACTER*1
. Must be
'U'
or
'L'
.
Specifies the triangle of A to store:
If
uplo
=
'U'
, the upper triangle of
A
is stored,
If
uplo
=
'L'
, the lower triangle of
A
is stored.
n
INTEGER
. The number of linear equations; the order of the matrix
A
;
n
0.
nrhs
INTEGER
. The number of right-hand sides; the number of columns of the matrix
B
.
a, af
, b
,
y
COMPLEX
for
cla_herfsx_extended
DOUBLE COMPLEX
for
zla_herfsx_extended
.
Arrays:
a
(
lda
,*)
,
af
(
ldaf
,*),
b
(
ldb
,*)
,
y
(
ldy
,*)
.
The array
a
contains the original
n
-by-
n
matrix
A
. The second dimension of
a
must be at least
max(1,
n
)
.
The array
af
contains the block diagonal matrix D and the multipliers used to obtain the factor
U
or
L
as computed by
?hetrf
. The second dimension of
af
must be at least
max(1,
n
)
.
The array
b
contains the right-hand-side of the matrix
B
. The second dimension of