BlockLanczosSolver Class Template Reference

#include <block-lanczos.h>

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Detailed Description

template<class Field, class Matrix = DenseMatrixBase<typename Field::Element>>
class LinBox::BlockLanczosSolver< 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 $n N$ matrix $V$ or, equivalently, to $N$ vectors $v_1, , v_N$ Scalars in the original iteration become $N N$ 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.

Public Types
typedef Field::Element	Element
Public Member Functions
	BlockLanczosSolver (const Field &F, const SolverTraits< BlockLanczosTraits > &traits)
	BlockLanczosSolver (const Field &F, const SolverTraits< BlockLanczosTraits > &traits, typename Field::RandIter r)
template<class Blackbox, class Vector> Vector &	solve (const Blackbox &A, Vector &x, const Vector &b)
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

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Member Typedef Documentation

typedef Field::Element Element

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Constructor & Destructor Documentation

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

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

BlockLanczosSolver (  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  {SolverTraits} structure describing user options for the solver r  Random iterator to use for randomization

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Member Function Documentation

Vector& 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. 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: Reference to solution vector

bool isAlmostIdentity (  const Matrix1 &  M  )  const [protected]

bool test_compute_Winv_S_mul (  int  n  )  const [protected]

bool test_compute_Winv_S_mulin (  int  n  )  const [protected]

bool test_mul_SST (  int  n  )  const [protected]

bool test_mul_ABSST (  int  n  )  const [protected]

bool test_mulTranspose (  int  m, int  n )  const [protected]

bool test_mulTranspose_ABSST (  int  n  )  const [protected]

bool test_mulin_ABSST (  int  n  )  const [protected]

bool test_addin_ABSST (  int  n  )  const [protected]

bool runSelfCheck (   )  const

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