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)

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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.

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Constructor & Destructor Documentation

LABlockLanczosSolver ( const Field &  F, const BlockLanczosTraits &  traits  )

inline

Constructor

Parameters:

F	Field over which to operate
traits	SolverTraits} 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:

F	Field over which to operate
traits	SolverTraits} structure describing user options for the solver
r	Random iterator to use for randomization

~LABlockLanczosSolver

(

)

Destructor

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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:

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

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

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

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

• /build/linbox-TzW5I9/linbox-1.1.6~rc0/linbox/algorithms/la-block-lanczos.h