MGBlockLanczosSolver< Field, Matrix > Class Template Reference

Block Lanczos iteration. More...

#include <mg-block-lanczos.h>

Public Types
typedef Field::Element	Element

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.
bool	runSelfCheck () const

Protected Member Functions
template<class Matrix1>
bool	isAlmostIdentity (const Matrix1 &M) const
bool	test_compute_Winv_S_mul (int n) const
bool	test_compute_Winv_S_mulin (int n) const
bool	test_mul_SST (int n) const
bool	test_mul_ABSST (int n) const
bool	test_mulTranspose (int m, int n) const
bool	test_mulTranspose_ABSST (int n) const
bool	test_mulin_ABSST (int n) const
bool	test_addin_ABSST (int n) const

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 \(v\) during each iteration, the block box \(A\) is applied to an \(n\times N\) matrix \(V\) or, equivalently, to $N$ vectors \(v_1, \ldots, v_N\) Scalars in the original iteration become \(N\times N\) 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.

Member Typedef Documentation

Element

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

typedef Field::Element Element

Constructor & Destructor Documentation

MGBlockLanczosSolver() [1/2]

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

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]

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

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()

template<class Field, class Matrix>

template<class Blackbox, class Vector>

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()

template<class Field, class Matrix>

template<class Blackbox, class Matrix1>

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

isAlmostIdentity()

template<class Field, class Matrix>

template<class Matrix1>

bool isAlmostIdentity ( const Matrix1 & M ) const

inlineprotected

test_compute_Winv_S_mul()

template<class Field, class Matrix>

bool test_compute_Winv_S_mul ( int n ) const

inlineprotected

test_compute_Winv_S_mulin()

template<class Field, class Matrix>

bool test_compute_Winv_S_mulin ( int n ) const

inlineprotected

test_mul_SST()

template<class Field, class Matrix>

bool test_mul_SST ( int n ) const

inlineprotected

test_mul_ABSST()

template<class Field, class Matrix>

bool test_mul_ABSST ( int n ) const

inlineprotected

test_mulTranspose()

template<class Field, class Matrix>

bool test_mulTranspose ( int m, int n ) const

inlineprotected

test_mulTranspose_ABSST()

template<class Field, class Matrix>

bool test_mulTranspose_ABSST ( int n ) const

inlineprotected

test_mulin_ABSST()

template<class Field, class Matrix>

bool test_mulin_ABSST ( int n ) const

inlineprotected

test_addin_ABSST()

template<class Field, class Matrix>

bool test_addin_ABSST ( int n ) const

inlineprotected

runSelfCheck()

template<class Field, class Matrix>

bool runSelfCheck ( ) const

inline

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

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