linbox
Data Structures | Modules | Files | Functions
algorithms

The core linear algebra algorithms of LinBox. More...

Data Structures

class  BlackboxContainerSymmetrize< Field, _Blackbox, RandIter >
 Symmetrizing iterator (for rank computations). More...

Modules

 Chinese Remaindering Algorithm
 

Chinese Remaindering (cra) in LinBox.


 Diophantine solvers
 

NO DOC YET.


 Elimination
 

NO DOC YET.


 Lanczos
 

NO DOC YET.


 p-adic lifting for linear system solutions.
 

interface for solving linear system by p-adic lifting technique over the quotient field of a ring.


 Sigma-basis
 

NO DOC YET.


 Wiedemann
 

NO DOC YET.


 Solvers

Files

file  bbcharpoly.h
 

no doc.


file  blackbox-block-container-base.h
 

NO DOC.


file  blackbox-block-container.h
 

no doc.


file  blas-domain.h
 

NO DOC.


file  cra-domain.h
 

Wrapper around OMP/SEQ version of ChineseRemainder.


file  cra-early-multip.h
 

NO DOC.


file  cra-early-single.h
 

NO DOC.


file  cra-full-multip-fixed.h
 

CRA for multi-residues.


file  cra-full-multip.h
 

NO DOC.


file  cra-givrnsfixed.h
 

NO DOC.


file  cra-kaapi.h
 

NO DOC.


file  lifting-container.h
 

Lifting from mod p^n to rationals NO DOC.


file  linbox-tags.h
 

Provides tags for various algorithms/solutions, à la FFLAS.


file  matrix-hom.h
 

Matrix Homomorphism A map function converts a matrix on a field/ring to its natural image in another field/ring.


file  rational-reconstruction.h
 

NO DOC.


file  rational-solver.h
 

Rational solving (Dixon, Wiedemann,...)


file  rns.h
 

Residue Number System tools.


file  rns.inl
 

Residue Number System implementation.


file  smith-form-adaptive.h
 

Implement the adaptive algorithm for Smith form computation.


file  wiedemann.h
 

minpoly computation and Wiedeman solvers.


Functions

template<class Polynomial , class Blackbox >
Polynomial & cia (Polynomial &P, const Blackbox &A, const Method::BlasElimination &M)
 Algorithm computing the integer characteristic polynomial of a dense matrix.

Detailed Description

The core linear algebra algorithms of LinBox.

The codes here implement algorithms for linear algebra problems. The names often reflect the authorship of the central algorithm (Lanczos, Wiedemann, ...). In contrast, the "drivers" in the solutions directory are named for the problem solved (rank, det, ...). Those are generally wrappers of algorithms from this directory. Their purpose is to give a simple and direct user interface and sometimes to provide a solution strategy which is a hybrid of algorithms from this directory.

Algorithm classes and functions generally have the field class as a template parameter. Blackbox algorithms may have a BlackboxMatrix parameter or allow a Blackbox class as template parameter. Elimination codes work over DenseMatrix or SparseMatrix types with varying degrees of substitution among the types possible.


Function Documentation

Polynomial& LinBox::cia ( Polynomial &  P,
const Blackbox &  A,
const Method::BlasElimination &  M 
)

Algorithm computing the integer characteristic polynomial of a dense matrix.

Bibliography:
[Dumas-Pernet-Wan ISSAC05]