LABlockLanczosSolver< Field, Matrix > Class Template Reference

Biorthogonalising block Lanczos iteration. More...

#include <la-block-lanczos.h>

Public Member Functions
	LABlockLanczosSolver (const Field &F, const Method::BlockLanczos &traits)
	Constructor. More...
	LABlockLanczosSolver (const Field &F, const Method::BlockLanczos &traits, typename Field::RandIter r)
	Constructor with a random iterator. More...
	~LABlockLanczosSolver ()
	Destructor.
template<class Blackbox , class Vector >
bool	solve (const Blackbox &A, Vector &x, const Vector &b)
	Solve the linear system Ax = b. More...
template<class Blackbox , class Matrix1 >
unsigned int	sampleNullspace (const Blackbox &A, Matrix1 &x)
	Sample uniformly from the (right) nullspace of A. More...
template<class Blackbox >
unsigned int	rank (const Blackbox &A)
	Estimate the rank of A. More...

Detailed Description

template<class Field, class Matrix = BlasMatrix<Field>>
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() [1/2]

LABlockLanczosSolver ( const Field &  F, const Method::BlockLanczos &  traits  )

inline

Constructor.

Parameters

F	Field over which to operate
traits	SolverTraits structure describing user options for the solver

LABlockLanczosSolver() [2/2]

LABlockLanczosSolver ( const Field &  F, const Method::BlockLanczos &  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

Member Function Documentation

solve()

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

sampleNullspace()

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

rank()

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 files:

• la-block-lanczos.h
• la-block-lanczos.inl