naginterfaces.library.linsys.real_tridiag_fac_solve¶
- naginterfaces.library.linsys.real_tridiag_fac_solve(job, a, b, c, d, ipiv, y, tol)[source]¶
real_tridiag_fac_solve
solves a system of tridiagonal equations following the factorization bymatop.real_gen_tridiag_lu
. This function is intended for applications such as inverse iteration as well as straightforward linear equation applications.For full information please refer to the NAG Library document for f04le
https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/f04/f04lef.html
- Parameters
- jobint
Must specify the equations to be solved.
The equations are to be solved, but diagonal elements of are not to be perturbed.
The equations are to be solved and, if overflow would otherwise occur, diagonal elements of are to be perturbed. See argument .
The equations are to be solved, but diagonal elements of are not to be perturbed.
The equations are to be solved and, if overflow would otherwise occur, diagonal elements of are to be perturbed. See argument .
The equations are to be solved, but diagonal elements of are not to be perturbed.
The equations are to be solved and, if overflow would otherwise occur, diagonal elements of are to be perturbed. See argument .
- afloat, array-like, shape
The diagonal elements of as returned by
real_tridiag_fac_solve
.- bfloat, array-like, shape
The elements of the first superdiagonal of as returned by
real_tridiag_fac_solve
.- cfloat, array-like, shape
The subdiagonal elements of as returned by
real_tridiag_fac_solve
.- dfloat, array-like, shape
The elements of the second superdiagonal of as returned by
real_tridiag_fac_solve
.- ipivint, array-like, shape
Details of the matrix as returned by
matop.real_gen_tridiag_lu
.- yfloat, array-like, shape
The right-hand side vector .
- tolfloat
The minimum perturbation to be made to very small diagonal elements of . is only referenced when is negative. should normally be chosen as about , where is the machine precision, but if is supplied as non-positive, it is reset to .
- Returns
- yfloat, ndarray, shape
is overwritten by the solution vector .
- tolfloat
If on entry is non-positive, it is reset as just described. Otherwise is unchanged.
- Raises
- NagValueError
- (errno )
Overflow would occur computing the element in the solution. .
- (errno )
On entry, .
Constraint: and and .
- (errno )
On entry, .
Constraint: .
- Notes
No equivalent traditional C interface for this routine exists in the NAG Library.
Following the factorization of the tridiagonal matrix as
by
matop.real_gen_tridiag_lu
,real_tridiag_fac_solve
may be used to solve any of the equationsfor , the choice of equation being controlled by the argument . In each case there is an option to perturb zero or very small diagonal elements of , this option being intended for use in applications such as inverse iteration.
- References
Wilkinson, J H, 1965, The Algebraic Eigenvalue Problem, Oxford University Press, Oxford
Wilkinson, J H and Reinsch, C, 1971, Handbook for Automatic Computation II, Linear Algebra, Springer–Verlag