FflasFfpack
Namespaces | Constant Groups | Functions
ffpack.h File Reference

Set of elimination based routines for dense linear algebra. More...

#include "fflas-ffpack/fflas/fflas.h"
#include <list>
#include <vector>
#include <iostream>
#include "ffpack_ludivine.inl"
#include "ffpack_minpoly.inl"
#include "ffpack_charpoly_kglu.inl"
#include "ffpack_charpoly_kgfast.inl"
#include "ffpack_charpoly_kgfastgeneralized.inl"
#include "ffpack_charpoly_danilevski.inl"
#include "ffpack_charpoly.inl"
#include "ffpack_krylovelim.inl"
#include "ffpack_frobenius.inl"
#include "ffpack_echelonforms.inl"

Namespaces

 FFPACK
 Finite Field PACK Set of elimination based routines for dense linear algebra.
 

Constant Groups

 FFPACK
 Finite Field PACK Set of elimination based routines for dense linear algebra.
 

Functions

template<class Field >
void applyP (const Field &F, const FFLAS::FFLAS_SIDE Side, const FFLAS::FFLAS_TRANSPOSE Trans, const size_t M, const int ibeg, const int iend, typename Field::Element *A, const size_t lda, const size_t *P)
 Apply a permutation submatrix of P (between ibeg and iend) to a matrix to (iend-ibeg) vectors of size M stored in A (as column for NoTrans and rows for Trans). More...
 
template<class Field >
size_t Rank (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda)
 Computes the rank of the given matrix using a LQUP factorization. More...
 
template<class Field >
bool IsSingular (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda)
 Returns true if the given matrix is singular. More...
 
template<class Field >
Field::Element Det (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda)
 Returns the determinant of the given matrix. More...
 
template<class Field >
void solveLB2 (const Field &F, const FFLAS::FFLAS_SIDE Side, const size_t M, const size_t N, const size_t R, typename Field::Element *L, const size_t ldl, const size_t *Q, typename Field::Element *B, const size_t ldb)
 Solve L X = B in place. More...
 
template<class Field >
void fgetrs (const Field &F, const FFLAS::FFLAS_SIDE Side, const size_t M, const size_t N, const size_t R, typename Field::Element *A, const size_t lda, const size_t *P, const size_t *Q, typename Field::Element *B, const size_t ldb, int *info)
 Solve the system $A X = B$ or $X A = B$. More...
 
template<class Field >
Field::Element * fgetrs (const Field &F, const FFLAS::FFLAS_SIDE Side, const size_t M, const size_t N, const size_t NRHS, const size_t R, typename Field::Element *A, const size_t lda, const size_t *P, const size_t *Q, typename Field::Element *X, const size_t ldx, const typename Field::Element *B, const size_t ldb, int *info)
 Solve the system A X = B or X A = B. More...
 
template<class Field >
size_t fgesv (const Field &F, const FFLAS::FFLAS_SIDE Side, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, typename Field::Element *B, const size_t ldb, int *info)
 Square system solver. More...
 
template<class Field >
size_t fgesv (const Field &F, const FFLAS::FFLAS_SIDE Side, const size_t M, const size_t N, const size_t NRHS, typename Field::Element *A, const size_t lda, typename Field::Element *X, const size_t ldx, const typename Field::Element *B, const size_t ldb, int *info)
 Rectangular system solver. More...
 
template<class Field >
Field::Element * Solve (const Field &F, const size_t M, typename Field::Element *A, const size_t lda, typename Field::Element *x, const int incx, const typename Field::Element *b, const int incb)
 Solve the system Ax=b. More...
 
template<class Field >
size_t NullSpaceBasis (const Field &F, const FFLAS::FFLAS_SIDE Side, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, typename Field::Element *&NS, size_t &ldn, size_t &NSdim)
 Computes a basis of the Left/Right nullspace of the matrix A. More...
 
template<class Field >
size_t RowRankProfile (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *&rkprofile)
 Computes the row rank profile of A. More...
 
template<class Field >
size_t ColumnRankProfile (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *&rkprofile)
 Computes the column rank profile of A. More...
 
template<class Field >
size_t RowRankProfileSubmatrixIndices (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *&rowindices, size_t *&colindices, size_t &R)
 RowRankProfileSubmatrixIndices. More...
 
template<class Field >
size_t ColRankProfileSubmatrixIndices (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *&rowindices, size_t *&colindices, size_t &R)
 Computes the indices of the submatrix r*r X of A whose columns correspond to the column rank profile of A. More...
 
template<class Field >
size_t RowRankProfileSubmatrix (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, typename Field::Element *&X, size_t &R)
 Compute the r*r submatrix X of A, by picking the row rank profile rows of A. More...
 
template<class Field >
size_t ColRankProfileSubmatrix (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, typename Field::Element *&X, size_t &R)
 Compute the $ r\times r$ submatrix X of A, by picking the row rank profile rows of A. More...
 
template<class Field >
Field::Element * LQUPtoInverseOfFullRankMinor (const Field &F, const size_t rank, typename Field::Element *A_factors, const size_t lda, const size_t *QtPointer, typename Field::Element *X, const size_t ldx)
 LQUPtoInverseOfFullRankMinor. More...
 
template<class Field >
size_t TURBO (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Q, const size_t cutoff)
 
template<class Field >
size_t LUdivine (const Field &F, const FFLAS::FFLAS_DIAG Diag, const FFLAS::FFLAS_TRANSPOSE trans, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Qt, const FFPACK_LUDIVINE_TAG LuTag=FfpackLQUP, const size_t cutoff=0)
 Compute the LQUP factorization of the given matrix. More...
 
template<class Field >
size_t LUpdate (const Field &F, const FFLAS::FFLAS_DIAG Diag, const FFLAS::FFLAS_TRANSPOSE trans, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, const size_t R, const size_t K, typename Field::Element *B, const size_t ldb, size_t *P, size_t *Q, const FFPACK::FFPACK_LUDIVINE_TAG LuTag=FFPACK::FfpackLQUP, const size_t cutoff=0)
 LUpdate. More...
 
template<class Field >
size_t LUdivine_small (const Field &F, const FFLAS::FFLAS_DIAG Diag, const FFLAS::FFLAS_TRANSPOSE trans, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Q, const FFPACK_LUDIVINE_TAG LuTag=FfpackLQUP)
 LUdivine small case.
 
template<class Field >
size_t LUdivine_gauss (const Field &F, const FFLAS::FFLAS_DIAG Diag, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Q, const FFPACK_LUDIVINE_TAG LuTag=FfpackLQUP)
 LUdivine gauss.
 
template<class Field >
void ftrtri (const Field &F, const FFLAS::FFLAS_UPLO Uplo, const FFLAS::FFLAS_DIAG Diag, const size_t N, typename Field::Element *A, const size_t lda)
 Compute the inverse of a triangular matrix. More...
 
template<class Field >
void ftrtrm (const Field &F, const FFLAS::FFLAS_DIAG diag, const size_t N, typename Field::Element *A, const size_t lda)
 Compute the product UL. More...
 
template<class Field >
size_t ColumnEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Qt, bool transform=true)
 Compute the Column Echelon form of the input matrix in-place. More...
 
template<class Field >
size_t RowEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Qt, const bool transform=false)
 Compute the Row Echelon form of the input matrix in-place. More...
 
template<class Field >
size_t ReducedColumnEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Qt, const bool transform=true)
 Compute the Reduced Column Echelon form of the input matrix in-place. More...
 
template<class Field >
size_t ReducedRowEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Qt, const bool transform=true)
 Compute the Reduced Row Echelon form of the input matrix in-place. More...
 
template<class Field >
size_t ReducedRowEchelonForm2 (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Qt, const bool transform=true)
 Variant by the block recursive algorithm. More...
 
template<class Field >
size_t REF (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, const size_t colbeg, const size_t rowbeg, const size_t colsize, size_t *Qt, size_t *P)
 REF. More...
 
template<class Field >
Field::Element * Invert (const Field &F, const size_t M, typename Field::Element *A, const size_t lda, int &nullity)
 Invert the given matrix in place or computes its nullity if it is singular. More...
 
template<class Field >
Field::Element * Invert (const Field &F, const size_t M, const typename Field::Element *A, const size_t lda, typename Field::Element *X, const size_t ldx, int &nullity)
 Invert the given matrix in place or computes its nullity if it is singular. More...
 
template<class Field >
Field::Element * Invert2 (const Field &F, const size_t M, typename Field::Element *A, const size_t lda, typename Field::Element *X, const size_t ldx, int &nullity)
 Invert the given matrix or computes its nullity if it is singular. More...
 
template<class Field , class Polynomial >
std::list< Polynomial > & CharPoly (const Field &F, std::list< Polynomial > &charp, const size_t N, typename Field::Element *A, const size_t lda, const FFPACK_CHARPOLY_TAG CharpTag=FfpackArithProg)
 Compute the characteristic polynomial of A using Krylov Method, and LUP factorization of the Krylov matrix.
 
template<class Field , class Polynomial >
Polynomial & MinPoly (const Field &F, Polynomial &minP, const size_t N, const typename Field::Element *A, const size_t lda, typename Field::Element *X, const size_t ldx, size_t *P, const FFPACK::FFPACK_MINPOLY_TAG MinTag=FFPACK::FfpackDense, const size_t kg_mc=0, const size_t kg_mb=0, const size_t kg_j=0)
 Compute the minimal polynomial. More...
 
template<class Field >
void solveLB (const Field &F, const FFLAS::FFLAS_SIDE Side, const size_t M, const size_t N, const size_t R, typename Field::Element *L, const size_t ldl, const size_t *Q, typename Field::Element *B, const size_t ldb)
 Solve L X = B or X L = B in place. More...
 
template<class Field , class Polynomial >
std::list< Polynomial > & CharpolyArithProg (const Field &F, std::list< Polynomial > &frobeniusForm, const size_t N, typename Field::Element *A, const size_t lda, const size_t c)
 

Detailed Description

Set of elimination based routines for dense linear algebra.

Matrices are supposed over finite prime field of characteristic less than 2^26.