Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

?gtrfs

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

Syntax

lapack_int LAPACKE_sgtrfs
(
int
matrix_layout
,
char
trans
,
lapack_int
n
,
lapack_int
nrhs
,
const float*
dl
,
const float*
d
,
const float*
du
,
const float*
dlf
,
const float*
df
,
const float*
duf
,
const float*
du2
,
const lapack_int*
ipiv
,
const float*
b
,
lapack_int
ldb
,
float*
x
,
lapack_int
ldx
,
float*
ferr
,
float*
berr
);
lapack_int LAPACKE_dgtrfs
(
int
matrix_layout
,
char
trans
,
lapack_int
n
,
lapack_int
nrhs
,
const double*
dl
,
const double*
d
,
const double*
du
,
const double*
dlf
,
const double*
df
,
const double*
duf
,
const double*
du2
,
const lapack_int*
ipiv
,
const double*
b
,
lapack_int
ldb
,
double*
x
,
lapack_int
ldx
,
double*
ferr
,
double*
berr
);
lapack_int LAPACKE_cgtrfs
(
int
matrix_layout
,
char
trans
,
lapack_int
n
,
lapack_int
nrhs
,
const lapack_complex_float*
dl
,
const lapack_complex_float*
d
,
const lapack_complex_float*
du
,
const lapack_complex_float*
dlf
,
const lapack_complex_float*
df
,
const lapack_complex_float*
duf
,
const lapack_complex_float*
du2
,
const lapack_int*
ipiv
,
const lapack_complex_float*
b
,
lapack_int
ldb
,
lapack_complex_float*
x
,
lapack_int
ldx
,
float*
ferr
,
float*
berr
);
lapack_int LAPACKE_zgtrfs
(
int
matrix_layout
,
char
trans
,
lapack_int
n
,
lapack_int
nrhs
,
const lapack_complex_double*
dl
,
const lapack_complex_double*
d
,
const lapack_complex_double*
du
,
const lapack_complex_double*
dlf
,
const lapack_complex_double*
df
,
const lapack_complex_double*
duf
,
const lapack_complex_double*
du2
,
const lapack_int*
ipiv
,
const lapack_complex_double*
b
,
lapack_int
ldb
,
lapack_complex_double*
x
,
lapack_int
ldx
,
double*
ferr
,
double*
berr
);
Include Files
  • mkl.h
Description
The routine performs an iterative refinement of the solution to a system of linear equations
A*X
 =
B
 or
A
T
*X
 =
B
 or
A
H
*X
 =
B
 with a tridiagonal 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
|/|
a
i
j
|
≤
β
|
a
i
j
|, |
δ
b
i
|/|
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
    ?gttrf
  • call the solver routine
    ?gttrs
    .
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
trans
Must be
'N'
 or
'T'
 or
'C'
.
Indicates the form of the equations:
If
trans
 =
'N'
, the system has the form
A*X
 =
B
.
If
trans
 =
'T'
, the system has the form
A
T
*X
 =
B
.
If
trans
 =
'C'
, the system has the form
A
H
*X
 =
B
.
n
The order of the matrix
A
;
n
≥
 0.
nrhs
The number of right-hand sides, that is, the number of columns of the matrix
B
;
nrhs
≥
 0.
dl
Array
dl
 of size
n
 -1 contains the subdiagonal elements of
A
.
d
Array
d
 of size
n
 contains the diagonal elements of
A
.
du
Array
du
 of size
n
 -1 contains the superdiagonal elements of
A
.
dlf
Array
dlf
 of size
n
 -1 contains the (
n
 - 1) multipliers that define the matrix
L
 from the
LU
 factorization of
A
 as computed by
?gttrf
.
df
Array
df
 of size
n
 contains the
n
 diagonal elements of the upper triangular matrix
U
 from the
LU
 factorization of
A
.
duf
Array
duf
 of size
n
 -1 contains the (
n
 - 1) elements of the first superdiagonal of
U
.
du2
Array
du2
 of size
n
 -2 contains the (
n
 - 2) elements of the second superdiagonal of
U
.
b
Array
b
 (size max(1,
ldb
*
nrhs
) for column major layout and max(1,
ldb
*
n
) for row major layout) contains the right-hand side matrix
B
.
x
Array
x
 (size max(1,
ldx
*
nrhs
) for column major layout and max(1,
ldx
*
n
) contains the solution matrix
X
, as computed by
?gttrs
.
ldb
The leading dimension of
b
;
ldb
≥
 max(1,
n
) for column major layout and
ldb
≥
nrhs
 for row major layout
.
ldx
The leading dimension of
x
;
ldx
≥
 max(1,
n
) for column major layout and
ldx
≥
nrhs
 for row major layout
.
ipiv
Array, size at least
max(1,
n
)
. The
ipiv
 array, as returned by
?gttrf
.
Output Parameters
x
The refined solution matrix
X
.
ferr
,
berr
Arrays, size at least
max(1,
nrhs
)
. Contain the component-wise forward and backward errors, respectively, for each solution vector.
Return Values
This function returns a value
info
.
If
info
 = 0
, the execution is successful.
If
info
 =
-i
, parameter
i
 had an illegal value.

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.