Developer Reference

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

?herfs

Refines the solution of a system of linear equations with a complex Hermitian coefficient matrix and estimates its error.

Syntax

call cherfs
(
uplo
,
n
,
nrhs
,
a
,
lda
,
af
,
ldaf
,
ipiv
,
b
,
ldb
,
x
,
ldx
,
ferr
,
berr
,
work
,
rwork
,
info
)
call zherfs
(
uplo
,
n
,
nrhs
,
a
,
lda
,
af
,
ldaf
,
ipiv
,
b
,
ldb
,
x
,
ldx
,
ferr
,
berr
,
work
,
rwork
,
info
)
call herfs
(
a
,
af
,
ipiv
,
b
,
x
[
,
uplo
]
[
,
ferr
]
[
,
berr
]
[
,
info
]
)
Include Files
  • mkl.fi
    ,
    lapack.f90
Description
The routine performs an iterative refinement of the solution to a system of linear equations
A*X
=
B
with a complex Hermitian full-storage matrix
A
, with multiple right-hand sides. For each computed solution vector
x
, the routine computes the component-wise backward error
β
. This error is the smallest relative perturbation in elements of
A
and
b
such that
x
is the exact solution of the perturbed system:
|
δ
a
i
j
|
β
|
a
i
j
|, |
δ
b
i
|
β
|
b
i
|
such that
(
A
+
δ
A
)
x
= (
b
+
δ
b
)
.
Finally, the routine estimates the component-wise forward error in the computed solution
||
x
-
x
e
||
/||
x
||
(here
x
e
is the exact solution).
Before calling this routine:
  • call the factorization routine
    ?hetrf
  • call the solver routine
    ?hetrs
    .
Input Parameters
uplo
CHARACTER*1
.
Must be
'U'