linbox
Functions
Solvers

Functions

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. More...
 
template<class Blackbox , class Vector >
ReturnStatus solveNonsingular (const Blackbox &A, Vector &x, const Vector &b, bool useRandIter=false)
 Solve a nonsingular system Ax=b. More...
 
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. More...
 
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. More...
 
template<class Blackbox , class Vector >
ReturnStatus findNullspaceElement (Vector &x, const Blackbox &A)
 Get a random element of the right nullspace of A. More...
 
template<class Blackbox , class Vector >
bool certifyInconsistency (Vector &u, const Blackbox &A, const Vector &b)
 Get a certificate u that the given system $Ax=b$ is inconsistent, if one can be found. More...
 

Detailed Description

Function Documentation

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.

Parameters
ABlack box of linear system
xVector in which to store solution
bRight-hand side of system
uVector in which to store certificate of inconsistency
Returns
Reference to solution vector
ReturnStatus solveNonsingular ( const Blackbox &  A,
Vector x,
const Vector b,
bool  useRandIter = false 
)

Solve a nonsingular system Ax=b.

This is a "Las Vegas" method, which makes use of randomization. It attempts to certify that the system solution is correct. It will only make one attempt to solve the system before giving up.

Parameters
ABlack box of linear system
xVector in which to store solution
bRight-hand side of system
useRandItertrue if solveNonsingular should use a random iterator for the Krylov sequence computation; false if it should use the right-hand side
Returns
Reference to solution vector
ReturnStatus solveSingular ( const Blackbox &  A,
Vector x,
const Vector b,
Vector u,
unsigned long  r 
)

Solve a general singular linear system.

Parameters
ABlack box of linear system
xVector in which to store solution
bRight-hand side of system
uVector into which certificate of inconsistency will be stored
rRank of A
Returns
Return status
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.

Parameters
ABlack box of linear system
xVector in which to store solution
bRight-hand side of system
rRank of A
PLeft preconditioner (NULL if none needed)
QRight preconditioner (NULL if none needed)
Returns
Return status
ReturnStatus findNullspaceElement ( Vector x,
const Blackbox &  A 
)

Get a random element of the right nullspace of A.

Parameters
xVector in which to store nullspace element
ABlack box of which to find nullspace element
bool certifyInconsistency ( Vector u,
const Blackbox &  A,
const Vector b 
)

Get a certificate u that the given system $Ax=b$ is inconsistent, if one can be found.

Parameters
uVector in which to store certificate
ABlackbox for the linear system
bRight-hand side for the linear system
Returns
true if a certificate can be found in one iteration; u is filled in with that certificate; and false otherwise