naginterfaces.library.lapacklin.dtprfs¶
- naginterfaces.library.lapacklin.dtprfs(uplo, trans, diag, n, ap, b, x)[source]¶
dtprfs
returns error bounds for the solution of a real triangular system of linear equations with multiple right-hand sides, or , using packed storage.For full information please refer to the NAG Library document for f07uh
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f07/f07uhf.html
- Parameters
- uplostr, length 1
Specifies whether is upper or lower triangular.
is upper triangular.
is lower triangular.
- transstr, length 1
Indicates the form of the equations.
The equations are of the form .
or
The equations are of the form .
- diagstr, length 1
Indicates whether is a nonunit or unit triangular matrix.
is a nonunit triangular matrix.
is a unit triangular matrix; the diagonal elements are not referenced and are assumed to be .
- nint
, the order of the matrix .
- apfloat, array-like, shape
The triangular matrix , packed by columns.
- bfloat, array-like, shape
The right-hand side matrix .
- xfloat, array-like, shape
The solution matrix , as returned by
dtptrs()
.
- Returns
- ferrfloat, ndarray, shape
contains an estimated error bound for the th solution vector, that is, the th column of , for .
- berrfloat, ndarray, shape
contains the component-wise backward error bound for the th solution vector, that is, the th column of , for .
- Raises
- NagValueError
- (errno )
On entry, error in parameter .
Constraint: or .
- (errno )
On entry, error in parameter .
Constraint: , or .
- (errno )
On entry, error in parameter .
Constraint: or .
- (errno )
On entry, error in parameter .
Constraint: .
- (errno )
On entry, error in parameter .
Constraint: .
- Notes
dtprfs
returns the backward errors and estimated bounds on the forward errors for the solution of a real triangular system of linear equations with multiple right-hand sides or , using packed storage. The function handles each right-hand side vector (stored as a column of the matrix ) independently, so we describe the function ofdtprfs
in terms of a single right-hand side and solution .Given a computed solution , the function computes the component-wise backward error . This is the size of the smallest relative perturbation in each element of and such that is the exact solution of a perturbed system
Then the function estimates a bound for the component-wise forward error in the computed solution, defined by:
where is the true solution.
For details of the method, see the F07 Introduction.
- References
Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore