MGBlockLanczosSolver< Field, Matrix > Class Template Reference

Block Lanczos iteration. More...

#include <mg-block-lanczos.h>

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

Detailed Description

template<class Field, class Matrix = BlasMatrix<Field,typename RawVector<typename Field::Element >::Dense>>
class LinBox::MGBlockLanczosSolver< Field, Matrix >

Block Lanczos iteration.

This is a blocked version of the iteration given in LanczosSolver. The essential difference is that, rather than applying the black box $A$ to a single vector during each iteration, the block box is applied to an matrix or, equivalently, to $N$ vectors Scalars in the original iteration become matrices in the blocked version. The resulting iteration is a natural extension of the basic theory of the original Lanczos iteration, c.f. (Montgomery 1995). This has the advantage of more flexible parallelization, and does not break down as often when used over small fields.

Currently, only dense vectors are supported for this iteration, and it is unlikely any other vector archetypes will be supported in the future.

Constructor & Destructor Documentation

MGBlockLanczosSolver() [1/2]

MGBlockLanczosSolver ( 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

MGBlockLanczosSolver() [2/2]

MGBlockLanczosSolver ( 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  )

inline

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.

If the matrix A is nonsymmetric, this method preconditions the matrix A with the preconditioner D_1 A^T D_2 A D_1, where D_1 and D_2 are random nonsingular diagonal matrices. If the matrix A is symmetric, this method preconditions the system with A D, where D is a random diagonal matrix.

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 and false on failure

sampleNullspace()

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

inline

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

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

• mg-block-lanczos.h
• mg-block-lanczos.inl