Developer Reference

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

?trrfs

Estimates the error in the solution of a system of linear equations with a triangular coefficient matrix.

Syntax

call strrfs
(
uplo
,
trans
,
diag
,
n
,
nrhs
,
a
,
lda
,
b
,
ldb
,
x
,
ldx
,
ferr
,
berr
,
work
,
iwork
,
info
)
call dtrrfs
(
uplo
,
trans
,
diag
,
n
,
nrhs
,
a
,
lda
,
b
,
ldb
,
x
,
ldx
,
ferr
,
berr
,
work
,
iwork
,
info
)
call ctrrfs
(
uplo
,
trans
,
diag
,
n
,
nrhs
,
a
,
lda
,
b
,
ldb
,
x
,
ldx
,
ferr
,
berr
,
work
,
rwork
,
info
)
call ztrrfs
(
uplo
,
trans
,
diag
,
n
,
nrhs
,
a
,
lda
,
b
,
ldb
,
x
,
ldx
,
ferr
,
berr
,
work
,
rwork
,
info
)
call trrfs
(
a
,
b
,
x
[
,
uplo
]
[
,
trans
]
[
,
diag
]
[
,
ferr
]
[
,
berr
]
[
,
info
]
)
Include Files
  • mkl.fi
    ,
    lapack.f90
Description
The routine estimates the errors in the solution to a system of linear equations
A*X
=
B
or
A
T
*X
=
B
or
A
H
*X
=
B
with a triangular 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
)
.
The routine also estimates the component-wise forward error in the computed solution
||
x
-
x