Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
Contents

?ptrfs

Refines the solution of a system of linear equations with a symmetric (Hermitian) positive-definite tridiagonal coefficient matrix and estimates its error.

Syntax

lapack_int LAPACKE_sptrfs
(
int
matrix_layout
,
lapack_int
n
,
lapack_int
nrhs
,
const float*
d
,
const float*
e
,
const float*
df
,
const float*
ef
,
const float*
b
,
lapack_int
ldb
,
float*
x
,
lapack_int
ldx
,
float*
ferr
,
float*
berr
);
lapack_int LAPACKE_dptrfs
(
int
matrix_layout
,
lapack_int
n
,
lapack_int
nrhs
,
const double*
d
,
const double*
e
,
const double*
df
,
const double*
ef
,
const double*
b
,
lapack_int
ldb
,
double*
x
,
lapack_int
ldx
,
double*
ferr
,
double*
berr
);
lapack_int LAPACKE_cptrfs
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
const float*
d
,
const lapack_complex_float*
e
,
const float*
df
,
const lapack_complex_float*
ef
,
const lapack_complex_float*
b
,
lapack_int
ldb
,
lapack_complex_float*
x
,
lapack_int
ldx
,
float*
ferr
,
float*
berr
);
lapack_int LAPACKE_zptrfs
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
const double*
d
,
const lapack_complex_double*
e
,
const double*
df
,
const lapack_complex_double*
ef
,
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
 with a symmetric (Hermitian) positive definite 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
|
≤
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
    ?pttrf
  • call the solver routine
    ?pttrs
    .
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
uplo
Used for complex flavors only. Must be
'U'
 or
'L'
.
Specifies whether the superdiagonal or the subdiagonal of the tridiagonal matrix
A
 is stored and how
A
 is factored:
If
uplo
 =
'U'
, the array
e
 stores the superdiagonal of
A
, and
A
 is factored as
U
H
*D*U
.
If
uplo
 =
'L'
, the array
e
 stores the subdiagonal of
A
, and
A
 is factored as
L*D*L
H
.
n
The order of the matrix
A
;
n
≥
 0.
nrhs
The number of right-hand sides;
nrhs
≥
 0.
d
The array
d
 (size
n
) contains the
n
 diagonal elements of the tridiagonal matrix
A
.
df
The array
df
 (size
n
) contains the
n
 diagonal elements of the diagonal matrix
D
 from the factorization of
A
 as computed by
?pttrf
.
e
,
ef
,
b
,
x
The array
e
 (size
n
 -1) contains the (
n
 - 1) off-diagonal elements of the tridiagonal matrix
A
 (see
uplo
).
The array
ef
 (size
n
 -1) contains the (
n
 - 1) off-diagonal elements of the unit bidiagonal factor
U
 or
L
 from the factorization computed by
?pttrf
 (see
uplo
).
The array
b
 of size max(1,
ldb
*
nrhs
) for column major layout and max(1,
ldb
*
n
) for row major layout contains the matrix
B
 whose columns are the right-hand sides for the systems of equations.
The array
x
 of size max(1,
ldx
*
nrhs
) for column major layout and max(1,
ldx
*
n
) for row major layout contains the solution matrix
X
 as computed by
?pttrs
.
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
.
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.