Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 0.9
  • 09/09/2020
  • 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

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804