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LABlockLanczosSolver Class Template Reference

#include <la-block-lanczos.h>

List of all members.

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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.

Public Types
typedef Field::Element	Element
Public Methods
	LABlockLanczosSolver (const Field &F, const SolverTraits< BlockLanczosTraits > &traits)
	LABlockLanczosSolver (const Field &F, const SolverTraits< 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)
Friends
class	BasisTransformation

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Member Typedef Documentation

typedef Field::Element Element

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Constructor & Destructor Documentation

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

Constructor Parameters: F  Field over which to operate traits  @ref{SolverTraits} structure describing user options for the solver

LABlockLanczosSolver (  const Field &    F, const SolverTraits< BlockLanczosTraits > &    traits, typename Field::RandIter    r )  [inline]

Constructor with a random iterator Parameters: F  Field over which to operate traits  @ref{SolverTraits} structure describing user options for the solver r  Random iterator to use for randomization

~LABlockLanczosSolver (    )

Destructor

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Member Function Documentation

unsigned int rank (  const Blackbox &    A )

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

unsigned int sampleNullspace (  const Blackbox &    A, Matrix1 &    x )

Sample uniformly from the (right) nullspace of A Parameters: A  Black box for the matrix A x  Matrix into whose columns to store nullspace elements Returns: Number of nullspace vectors found

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: A  Black box for the matrix A x  Vector in which to store solution b  Right-hand side of system Returns: True on success; false on failure

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Friends And Related Function Documentation

friend class BasisTransformation [friend]

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