?ptrfs
?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 with a symmetric (Hermitian) positive definite tridiagonal matrix
A*X
= B
A
, with multiple right-hand sides. For each computed solution vector x
, the routine computes the component-wise backward errorβ
. This error is the smallest relative perturbation in elements of A
and b
such that x
is the exact solution of the perturbed system:|| |, || |
such that δ
a
i
j
≤
β
|a
i
j
δ
b
i
≤
β
|b
i
(
.A
+ δ
A
)x
= (b
+ δ
b
)Finally, the routine estimates the component-wise forward error in the computed solution is the exact solution).
||||/||
(here x
- x
e
∞
x
||∞
x
e
Before calling this routine:
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 matrixAis stored and howAis factored:If, the arrayuplo='U'estores the superdiagonal ofA, andAis factored as.UH*D*UIf, the arrayuplo='L'estores the subdiagonal ofA, andAis factored as.L*D*LH
- n
- The order of the matrixA;n≥0.
- nrhs
- The number of right-hand sides;nrhs≥0.
- d
- The arrayd(sizen) contains thendiagonal elements of the tridiagonal matrixA.
- df
- The arraydf(sizen) contains thendiagonal elements of the diagonal matrixDfrom the factorization ofAas computed by?pttrf.
- e,ef,b,x
- The arraye(sizen-1) contains the (n- 1) off-diagonal elements of the tridiagonal matrixA(seeuplo).The arrayef(sizen-1) contains the (n- 1) off-diagonal elements of the unit bidiagonal factorUorLfrom the factorization computed by?pttrf(seeuplo).The arraybof size max(1,ldb*nrhs) for column major layout and max(1,ldb*n) for row major layout contains the matrixBwhose columns are the right-hand sides for the systems of equations.The arrayxof size max(1,ldx*nrhs) for column major layout and max(1,ldx*n) for row major layout contains the solution matrixXas computed by?pttrs.
- ldb
- The leading dimension ofb;.ldb≥max(1,n) for column major layout andldb≥nrhsfor row major layout
- ldx
- The leading dimension ofx;.ldx≥max(1,n) for column major layout andldx≥nrhsfor row major layout
Output Parameters
- x
- The refined solution matrixX.
- ferr,berr
- Arrays, size at leastmax(1,. Contain the component-wise forward and backward errors, respectively, for each solution vector.nrhs)
Return Values
This function returns a value
info
.If , the execution is successful.
info
= 0If
info
= -i
, parameter i
had an illegal value.