linbox  1
Public Member Functions
LABlockLanczosSolver< Field, Matrix > Class Template Reference

#include <la-block-lanczos.h>

List of all members.

Public Member Functions

 LABlockLanczosSolver (const Field &F, const BlockLanczosTraits &traits)
 LABlockLanczosSolver (const Field &F, const BlockLanczosTraits &traits, typename Field::RandIter r)
 ~LABlockLanczosSolver ()
template<class Blackbox , class Vector >
bool solve (const Blackbox &A, Vector &x, const Vector &b)
template<class Blackbox , class Matrix1 >
unsigned int sampleNullspace (const Blackbox &A, Matrix1 &x)
template<class Blackbox >
unsigned int rank (const Blackbox &A)

Detailed Description

template<class Field, class Matrix = DenseMatrixBase<typename Field::Element>>
class LinBox::LABlockLanczosSolver< Field, Matrix >

Biorthogonalising block Lanczos iteration

This is a biorthogonalising variant of Montgomery's block Lanczos iteration. The goal is to avoid having to symmetrise the input matrix by constructing two sequences of block vectors that have mutual orthogonality properties. This algorithm was proposed by Bradford Hovinen.


Constructor & Destructor Documentation

LABlockLanczosSolver ( const Field F,
const BlockLanczosTraits &  traits 
) [inline]

Constructor

Parameters:
FField over which to operate
traitsSolverTraits} structure describing user options for the solver
LABlockLanczosSolver ( const Field F,
const BlockLanczosTraits &  traits,
typename Field::RandIter  r 
) [inline]

Constructor with a random iterator

Parameters:
FField over which to operate
traitsSolverTraits} structure describing user options for the solver
rRandom iterator to use for randomization

Destructor


Member Function Documentation

bool solve ( const Blackbox &  A,
Vector &  x,
const Vector &  b 
)

Solve the linear system Ax = b.

If the system is nonsingular, this method computes the unique solution to the system Ax = b. If the system is singular, it computes a random solution.

Parameters:
ABlack box for the matrix A
xVector in which to store solution
bRight-hand side of system
Returns:
True on success; false on failure
unsigned int sampleNullspace ( const Blackbox &  A,
Matrix1 &  x 
)

Sample uniformly from the (right) nullspace of A

Parameters:
ABlack box for the matrix A
xMatrix into whose columns to store nullspace elements
Returns:
Number of nullspace vectors found
unsigned int rank ( const Blackbox &  A)

Estimate the rank of A

Parameters:
ABlack box for the matrix A
Returns:
Lower bound on the rank of A

The documentation for this class was generated from the following file: