linbox
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Linear system solvers based on Wiedemann's method. More...
#include <wiedemann.h>
Public Types | |
enum | ReturnStatus |
{ OK, FAILED, SINGULAR, INCONSISTENT, BAD_PRECONDITIONER } | |
Public Member Functions | |
WiedemannSolver (const Field &F, const WiedemannTraits &traits) | |
Constructor. | |
WiedemannSolver (const Field &F, const WiedemannTraits &traits, typename Field::RandIter r) | |
Constructor with a random iterator. | |
template<class Blackbox , class Vector > | |
ReturnStatus | solve (const Blackbox &A, Vector &x, const Vector &b, Vector &u) |
Solve a system Ax=b, giving a random solution if the system is singular and consistent, and a certificate of inconsistency (if specified in traits parameter at construction time) otherwise. | |
template<class Blackbox , class Vector > | |
ReturnStatus | solveNonsingular (const Blackbox &A, Vector &x, const Vector &b, bool useRandIter=false) |
Solve a nonsingular system Ax=b. | |
template<class Blackbox , class Vector > | |
ReturnStatus | solveSingular (const Blackbox &A, Vector &x, const Vector &b, Vector &u, unsigned long r) |
Solve a general singular linear system. | |
template<class Blackbox , class Vector , class Prec1 , class Prec2 > | |
ReturnStatus | findRandomSolution (const Blackbox &A, Vector &x, const Vector &b, size_t r, const Prec1 *P, const Prec2 *Q) |
Get a random solution to a singular system Ax=b of rank r with generic rank profile. | |
template<class Blackbox , class Vector > | |
ReturnStatus | findNullspaceElement (Vector &x, const Blackbox &A) |
Get a random element of the right nullspace of A. | |
template<class Blackbox , class Vector > | |
bool | certifyInconsistency (Vector &u, const Blackbox &A, const Vector &b) |
Get a certificate u that the given system ![]() |
Linear system solvers based on Wiedemann's method.
This class encapsulates all of the functionality for linear system solving with Wiedemann's algorithm. It includes the random solution and random nullspace element of Kaltofen and Saunders (1991), as well as the certificate of inconsistency of Giesbrecht, Lobo, and Saunders (1998).
WiedemannSolver | ( | const Field & | F, |
const WiedemannTraits & | traits | ||
) | [inline] |
Constructor.
F | Field over which to operate |
traits | SolverTraits structure describing user options for the solver |
WiedemannSolver | ( | const Field & | F, |
const WiedemannTraits & | traits, | ||
typename Field::RandIter | r | ||
) | [inline] |
Constructor with a random iterator.
F | Field over which to operate |
traits | SolverTraits structure describing user options for the solver |
r | Random iterator to use for randomization |