?tprfs
?tprfs
Estimates the error in the solution of a system of linear equations with a packed triangular coefficient matrix.
Syntax
lapack_int LAPACKE_stprfs
(
int
matrix_layout
,
char
uplo
,
char
trans
,
char
diag
,
lapack_int
n
,
lapack_int
nrhs
,
const float*
ap
,
const float*
b
,
lapack_int
ldb
,
const float*
x
,
lapack_int
ldx
,
float*
ferr
,
float*
berr
);
lapack_int LAPACKE_dtprfs
(
int
matrix_layout
,
char
uplo
,
char
trans
,
char
diag
,
lapack_int
n
,
lapack_int
nrhs
,
const double*
ap
,
const double*
b
,
lapack_int
ldb
,
const double*
x
,
lapack_int
ldx
,
double*
ferr
,
double*
berr
);
lapack_int LAPACKE_ctprfs
(
int
matrix_layout
,
char
uplo
,
char
trans
,
char
diag
,
lapack_int
n
,
lapack_int
nrhs
,
const lapack_complex_float*
ap
,
const lapack_complex_float*
b
,
lapack_int
ldb
,
const lapack_complex_float*
x
,
lapack_int
ldx
,
float*
ferr
,
float*
berr
);
lapack_int LAPACKE_ztprfs
(
int
matrix_layout
,
char
uplo
,
char
trans
,
char
diag
,
lapack_int
n
,
lapack_int
nrhs
,
const lapack_complex_double*
ap
,
const lapack_complex_double*
b
,
lapack_int
ldb
,
const lapack_complex_double*
x
,
lapack_int
ldx
,
double*
ferr
,
double*
berr
);
Include Files
- mkl.h
Description
The routine estimates the errors in the solution to a system of linear equations or or
A*X
= B
A
T
*X
= B
A
H
*X
= B
with a packed triangular matrix 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
)The routine also 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, call the solver routine
?tptrs
.Input Parameters
- matrix_layout
- Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
- uplo
- Must be'U'or'L'.Indicates whetherAis upper or lower triangular:If, thenuplo='U'Ais upper triangular.If, thenuplo='L'Ais lower triangular.
- trans
- Must be'N'or'T'or'C'.Indicates the form of the equations:If, the system has the formtrans='N'.A*X=BIf, the system has the formtrans='T'AT*X=B.If, the system has the formtrans='C'AH*X=B.
- diag
- Must be'N'or'U'.If,diag='N'Ais not a unit triangular matrix.If,diag='U'Ais unit triangular: diagonal elements ofAare assumed to be 1 and not referenced in the arrayap.
- n
- The order of the matrixA;n≥0.
- nrhs
- The number of right-hand sides;nrhs≥0.
- ap,b,x
- Arrays:apmax(1,contains the upper or lower triangular matrixn(n+ 1)/2)A, as specified byuplo.bof size max(1,contains the right-hand side matrixldb*nrhs) for column major layout and max(1,ldb*n) for row major layoutB.xof size max(1,contains the solution matrixldx*nrhs) for column major layout and max(1,ldx*n) for row major layoutX.
- ldb
- The leading dimension ofb;.ldb≥max(1,n) for column major layout andldb≥nrhsfor row major layout
- ldx
- The leading dimension ofx;.ldb≥max(1,n) for column major layout andldb≥nrhsfor row major layout
Output Parameters
- 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.Application Notes
The bounds returned in
ferr
are not rigorous, but in practice they almost always overestimate the actual error.A call to this routine involves, for each right-hand side, solving a number of systems of linear equations ; the number of systems is usually 4 or 5 and never more than 11. Each solution requires approximately floating-point operations for real flavors or
A
*x
= b
n
2
4
for complex flavors.n
2