Block Lanczos iteration. More...
#include <mg-block-lanczos.h>
Public Member Functions | |
| MGBlockLanczosSolver (const Field &F, const Method::BlockLanczos &traits) | |
| Constructor. More... | |
| MGBlockLanczosSolver (const Field &F, const Method::BlockLanczos &traits, typename Field::RandIter r) | |
| Constructor with a random iterator. More... | |
| 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... | |
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]
|
inline |
Constructor.
- Parameters
-
F Field over which to operate traits SolverTraits structure describing user options for the solver
◆ MGBlockLanczosSolver() [2/2]
|
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()
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()
|
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
The documentation for this class was generated from the following files:
- mg-block-lanczos.h
- mg-block-lanczos.inl
