The core linear algebra algorithms of LinBox. More...
Collaboration diagram for algorithms:
Modules | |
| Chinese Remaindering Algorithm | |
Chinese Remaindering (cra) in LinBox. | |
| Diophantine solvers | |
| NO DOC YET. | |
| Elimination | |
| NO DOC YET. | |
| Gauss | |
| NO DOC YET. | |
| IML | |
| NO DOC YET. | |
| Lanczos | |
| NO DOC YET. | |
| Lattice reductions | |
| Lattice reduction (LLL) in LinBox. | |
| Blas3 | |
| BLAS level 3 (matrix-matrix) operations. | |
| 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 | cra-builder-early-multip.h |
| NO DOC. | |
| file | cra-builder-full-multip-fixed.h |
| CRA for multi-residues. | |
| file | cra-builder-full-multip.h |
| NO DOC. | |
| file | cra-builder-single.h |
| Chinese remaindering of a single value. | |
| file | cra-domain.h |
| Wrapper around OMP/SEQ version of ChineseRemainder. | |
| file | cra-givrnsfixed.h |
| NO DOC. | |
| file | cra-kaapi.h |
| NO DOC. | |
| file | lattice.h |
| LLL reductionThis is an interface to NTL/FPLLL. | |
| file | lifting-container.h |
Lifting from mod p^n to rationals NO DOC. | |
| 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 | matrix-rank.h |
| Computes the rank of a matrix by Gaussian Elimination, in place. | |
| 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 | short-vector.h |
| NO DOCNO DOC. | |
| file | smith-form-adaptive.h |
| Implement the adaptive algorithm for Smith form computation. | |
| file | wiedemann.h |
| minpoly computation and Wiedeman solvers. | |
| file | blackbox-block-container.h |
| no doc. | |
| file | linbox-tags.h |
Provides tags for various algorithms/solutions, à la FFLAS. | |
Data Structures | |
| class | BlackboxContainerSymmetrize< Field, _Blackbox, RandIter > |
| Symmetrizing iterator (for rank computations). More... | |
Functions | |
| template<class Polynomial , class Blackbox > | |
| Polynomial & | cia (Polynomial &P, const Blackbox &A, const Method::DenseElimination &M) |
| Algorithm computing the integer characteristic polynomial of a dense matrix. More... | |
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
◆ cia()
| Polynomial& LinBox::cia | ( | Polynomial & | P, |
| const Blackbox & | A, | ||
| const Method::DenseElimination & | M | ||
| ) |
Algorithm computing the integer characteristic polynomial of a dense matrix.
- Bibliography:
- [Dumas-Pernet-Wan ISSAC05]
