linbox  1
Functions
Solvers

Functions

template<class Blackbox , class Vector >
ReturnStatus solve (const Blackbox &A, Vector &x, const Vector &b, Vector &u)
template<class Blackbox , class Vector >
ReturnStatus solveNonsingular (const Blackbox &A, Vector &x, const Vector &b, bool useRandIter=false)
template<class Blackbox , class Vector >
ReturnStatus solveSingular (const Blackbox &A, Vector &x, const Vector &b, Vector &u, unsigned long r)
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)
template<class Blackbox , class Vector >
ReturnStatus findNullspaceElement (Vector &x, const Blackbox &A)
template<class Blackbox , class Vector >
bool certifyInconsistency (Vector &u, const Blackbox &A, const Vector &b)

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
ABlack box for the linear system
bRight-hand side for the linear system
rRank of A
PLeft preconditioner, if applicable
Returns:
true if a certificate can be found in one iteration; u is filled in with that certificate; and false otherwise