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

#include "givaro/givpoly1.h"
#include <fflas-ffpack/fflas-ffpack-config.h>
#include "fflas-ffpack/fflas/fflas.h"
#include "fflas-ffpack/fflas/fflas_helpers.inl"
#include <list>
#include <vector>
#include <iostream>
#include <algorithm>
#include "fflas-ffpack/checkers/checkers_ffpack.h"
#include "ffpack_fgesv.inl"
#include "ffpack_fgetrs.inl"
#include "fflas-ffpack/checkers/checkers_ffpack.inl"
#include "ffpack_pluq.inl"
#include "ffpack_pluq_mp.inl"
#include "ffpack_ppluq.inl"
#include "ffpack_ludivine.inl"
#include "ffpack_ludivine_mp.inl"
#include "ffpack_echelonforms.inl"
#include "ffpack_fsytrf.inl"
#include "ffpack_invert.inl"
#include "ffpack_ftrtr.inl"
#include "ffpack_ftrstr.inl"
#include "ffpack_ftrssyr2k.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_frobenius.inl"
#include "ffpack_minpoly.inl"
#include "ffpack_krylovelim.inl"
#include "ffpack_permutation.inl"
#include "ffpack_rankprofiles.inl"
#include "ffpack_det_mp.inl"
#include "ffpack_bruhatgen.inl"
#include "ffpack.inl"

Data Structures
class	CharpolyFailed

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

namespace	FFPACK::Protected

Macros
#define	__FFLASFFPACK_FTRSTR_THRESHOLD 64

#define	__FFLASFFPACK_FTRSSYR2K_THRESHOLD 64

Functions
void	LAPACKPerm2MathPerm (size_t MathP, const size_t LapackP, const size_t N)
	Conversion of a permutation from LAPACK format to Math format. More...

void	MathPerm2LAPACKPerm (size_t LapackP, const size_t MathP, const size_t N)
	Conversion of a permutation from Maths format to LAPACK format. More...

template<class Field >
void	applyP (const Field &F, const FFLAS::FFLAS_SIDE Side, const FFLAS::FFLAS_TRANSPOSE Trans, const size_t M, const size_t ibeg, const size_t iend, typename Field::Element_ptr A, const size_t lda, const size_t *P)
	Computes P1 x Diag (I_R, P2) where P1 is a LAPACK and P2 a LAPACK permutation and store the result in P1 as a LAPACK permutation. More...

template<class Field >
void	applyP (const Field &F, const FFLAS::FFLAS_SIDE Side, const FFLAS::FFLAS_TRANSPOSE Trans, const size_t m, const size_t ibeg, const size_t iend, typename Field::Element_ptr A, const size_t lda, const size_t *P, const FFLAS::ParSeqHelper::Sequential seq)

template<class Field , class Cut , class Param >
void	applyP (const Field &F, const FFLAS::FFLAS_SIDE Side, const FFLAS::FFLAS_TRANSPOSE Trans, const size_t m, const size_t ibeg, const size_t iend, typename Field::Element_ptr A, const size_t lda, const size_t *P, const FFLAS::ParSeqHelper::Parallel< Cut, Param > par)

template<class Field >
void	MonotonicApplyP (const Field &F, const FFLAS::FFLAS_SIDE Side, const FFLAS::FFLAS_TRANSPOSE Trans, const size_t M, const size_t ibeg, const size_t iend, typename Field::Element_ptr A, const size_t lda, const size_t *P, const size_t R)
	Apply a R-monotonically increasing permutation P, to the matrix A. 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_ptr A, const size_t lda, const size_t P, const size_t Q, typename Field::Element_ptr B, const size_t ldb, int *info)
	Solve the system or . More...

template<class Field >
Field::Element_ptr	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_ptr A, const size_t lda, const size_t P, const size_t Q, typename Field::Element_ptr X, const size_t ldx, typename Field::ConstElement_ptr 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_ptr A, const size_t lda, typename Field::Element_ptr 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_ptr A, const size_t lda, typename Field::Element_ptr X, const size_t ldx, typename Field::ConstElement_ptr B, const size_t ldb, int *info)
	Rectangular system solver. More...

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_ptr A, const size_t lda, const size_t threshold=__FFLASFFPACK_FTRTRI_THRESHOLD)
	Compute the inverse of a triangular matrix. More...

template<class Field >
void	trinv_left (const Field &F, const size_t N, typename Field::ConstElement_ptr L, const size_t ldl, typename Field::Element_ptr X, const size_t ldx)

template<class Field >
void	ftrtrm (const Field &F, const FFLAS::FFLAS_SIDE side, const FFLAS::FFLAS_DIAG diag, const size_t N, typename Field::Element_ptr A, const size_t lda)
	Compute the product of two triangular matrices of opposite shape. More...

template<class Field >
void	ftrstr (const Field &F, const FFLAS::FFLAS_SIDE side, const FFLAS::FFLAS_UPLO Uplo, const FFLAS::FFLAS_DIAG diagA, const FFLAS::FFLAS_DIAG diagB, const size_t N, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr B, const size_t ldb, const size_t threshold=__FFLASFFPACK_FTRSTR_THRESHOLD)
	Solve a triangular system with a triangular right hand side of the same shape. More...

template<class Field >
void	ftrssyr2k (const Field &F, const FFLAS::FFLAS_UPLO Uplo, const FFLAS::FFLAS_DIAG diagA, const size_t N, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr B, const size_t ldb, const size_t threshold=__FFLASFFPACK_FTRSSYR2K_THRESHOLD)
	Solve a triangular system in a symmetric sum: find B upper/lower triangular such that A^T B + B^T A = C where C is symmetric. More...

template<class Field >
bool	fsytrf (const Field &F, const FFLAS::FFLAS_UPLO UpLo, const size_t N, typename Field::Element_ptr A, const size_t lda, const size_t threshold=__FFLASFFPACK_FSYTRF_THRESHOLD)
	Triangular factorization of symmetric matrices. More...

template<class Field >
bool	fsytrf (const Field &F, const FFLAS::FFLAS_UPLO UpLo, const size_t N, typename Field::Element_ptr A, const size_t lda, const FFLAS::ParSeqHelper::Sequential seq, const size_t threshold=__FFLASFFPACK_FSYTRF_THRESHOLD)

template<class Field , class Cut , class Param >
bool	fsytrf (const Field &F, const FFLAS::FFLAS_UPLO UpLo, const size_t N, typename Field::Element_ptr A, const size_t lda, const FFLAS::ParSeqHelper::Parallel< Cut, Param > par, const size_t threshold=__FFLASFFPACK_FSYTRF_THRESHOLD)

template<class Field >
bool	fsytrf_nonunit (const Field &F, const FFLAS::FFLAS_UPLO UpLo, const size_t N, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr D, const size_t incD, const size_t threshold=__FFLASFFPACK_FSYTRF_THRESHOLD)
	Triangular factorization of symmetric matrices. More...

template<class Field >
size_t	PLUQ (const Field &F, const FFLAS::FFLAS_DIAG Diag, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t P, size_t Q)
	Compute a PLUQ factorization of the given matrix. More...

template<class Field >
size_t	pPLUQ (const Field &F, const FFLAS::FFLAS_DIAG Diag, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t P, size_t Q)

template<class Field >
size_t	PLUQ (const Field &F, const FFLAS::FFLAS_DIAG Diag, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t P, size_t Q, const FFLAS::ParSeqHelper::Sequential &PSHelper, size_t BCThreshold=__FFLASFFPACK_PLUQ_THRESHOLD)

template<class Field , class Cut , class Param >
size_t	PLUQ (const Field &F, const FFLAS::FFLAS_DIAG Diag, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t P, size_t Q, const FFLAS::ParSeqHelper::Parallel< Cut, Param > &PSHelper)

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_ptr A, const size_t lda, size_t P, size_t Qt, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive, const size_t cutoff=__FFLASFFPACK_LUDIVINE_THRESHOLD)
	Compute the CUP or PLE factorization of the given matrix. More...

template<class Field >
size_t	LUdivine_construct (const Field &F, const FFLAS::FFLAS_DIAG Diag, const size_t M, const size_t N, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr X, const size_t ldx, typename Field::Element_ptr u, const size_t incu, size_t *P, bool computeX, const FFPACK_MINPOLY_TAG MinTag=FfpackDense, const size_t kg_mc=0, const size_t kg_mb=0, const size_t kg_j=0)

template<class Field >
size_t	ColumnEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t P, size_t Qt, bool transform=false, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
	Compute the Column Echelon form of the input matrix in-place. More...

template<class Field >
size_t	pColumnEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t P, size_t Qt, bool transform=false, size_t numthreads=0, const FFPACK_LU_TAG LuTag=FfpackTileRecursive)

template<class Field , class PSHelper >
size_t	ColumnEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t P, size_t Qt, const bool transform, const FFPACK_LU_TAG LuTag, const PSHelper &psH)

template<class Field >
size_t	RowEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t P, size_t Qt, const bool transform=false, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
	Compute the Row Echelon form of the input matrix in-place. More...

template<class Field >
size_t	pRowEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t P, size_t Qt, const bool transform=false, size_t numthreads=0, const FFPACK_LU_TAG LuTag=FfpackTileRecursive)

template<class Field , class PSHelper >
size_t	RowEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t P, size_t Qt, const bool transform, const FFPACK_LU_TAG LuTag, const PSHelper &psH)

template<class Field >
size_t	ReducedColumnEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t P, size_t Qt, const bool transform=false, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
	Compute the Reduced Column Echelon form of the input matrix in-place. More...

template<class Field >
size_t	pReducedColumnEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t P, size_t Qt, const bool transform=false, size_t numthreads=0, const FFPACK_LU_TAG LuTag=FfpackTileRecursive)

template<class Field , class PSHelper >
size_t	ReducedColumnEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t P, size_t Qt, const bool transform, const FFPACK_LU_TAG LuTag, const PSHelper &psH)

template<class Field >
size_t	ReducedRowEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t P, size_t Qt, const bool transform=false, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
	Compute the Reduced Row Echelon form of the input matrix in-place. More...

template<class Field >
size_t	pReducedRowEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t P, size_t Qt, const bool transform=false, size_t numthreads=0, const FFPACK_LU_TAG LuTag=FfpackTileRecursive)

template<class Field , class PSHelper >
size_t	ReducedRowEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t P, size_t Qt, const bool transform, const FFPACK_LU_TAG LuTag, const PSHelper &psH)

template<class Field >
size_t	GaussJordan (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, const size_t colbeg, const size_t rowbeg, const size_t colsize, size_t P, size_t Q, const FFPACK::FFPACK_LU_TAG LuTag)
	Gauss-Jordan algorithm computing the Reduced Row echelon form and its transform matrix. More...

template<class Field >
Field::Element_ptr	Invert (const Field &F, const size_t M, typename Field::Element_ptr 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_ptr	Invert (const Field &F, const size_t M, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr X, const size_t ldx, int &nullity)
	Invert the given matrix or computes its nullity if it is singular. More...

template<class Field >
Field::Element_ptr	Invert2 (const Field &F, const size_t M, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr X, const size_t ldx, int &nullity)
	Invert the given matrix or computes its nullity if it is singular. More...

template<class PolRing >
std::list< typename PolRing::Element > &	CharPoly (const PolRing &R, std::list< typename PolRing::Element > &charp, const size_t N, typename PolRing::Domain_t::Element_ptr A, const size_t lda, typename PolRing::Domain_t::RandIter &G, const FFPACK_CHARPOLY_TAG CharpTag=FfpackAuto, const size_t degree=__FFLASFFPACK_ARITHPROG_THRESHOLD)
	Compute the characteristic polynomial of the matrix A. More...

template<class PolRing >
PolRing::Element &	CharPoly (const PolRing &R, typename PolRing::Element &charp, const size_t N, typename PolRing::Domain_t::Element_ptr A, const size_t lda, typename PolRing::Domain_t::RandIter &G, const FFPACK_CHARPOLY_TAG CharpTag=FfpackAuto, const size_t degree=__FFLASFFPACK_ARITHPROG_THRESHOLD)
	Compute the characteristic polynomial of the matrix A. More...

template<class PolRing >
PolRing::Element &	CharPoly (const PolRing &R, typename PolRing::Element &charp, const size_t N, typename PolRing::Domain_t::Element_ptr A, const size_t lda, const FFPACK_CHARPOLY_TAG CharpTag=FfpackAuto, const size_t degree=__FFLASFFPACK_ARITHPROG_THRESHOLD)
	Compute the characteristic polynomial of the matrix A. More...

template<class Field , class Polynomial >
std::list< Polynomial > &	KellerGehrig (const Field &F, std::list< Polynomial > &charp, const size_t N, typename Field::ConstElement_ptr A, const size_t lda)

template<class Field , class Polynomial >
int	KGFast (const Field &F, std::list< Polynomial > &charp, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t kg_mc, size_t kg_mb, size_t *kg_j)

template<class Field , class Polynomial >
std::list< Polynomial > &	KGFast_generalized (const Field &F, std::list< Polynomial > &charp, const size_t N, typename Field::Element_ptr A, const size_t lda)

template<class Field >
void	fgemv_kgf (const Field &F, const size_t N, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr X, const size_t incX, typename Field::Element_ptr Y, const size_t incY, const size_t kg_mc, const size_t kg_mb, const size_t kg_j)

template<class Field , class Polynomial , class RandIter >
std::list< Polynomial > &	LUKrylov (const Field &F, std::list< Polynomial > &charp, const size_t N, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr U, const size_t ldu, RandIter &G)

template<class Field , class Polynomial >
std::list< Polynomial > &	Danilevski (const Field &F, std::list< Polynomial > &charp, const size_t N, typename Field::Element_ptr A, const size_t lda)

template<class PolRing >
void	RandomKrylovPrecond (const PolRing &PR, std::list< typename PolRing::Element > &completedFactors, const size_t N, typename PolRing::Domain_t::Element_ptr A, const size_t lda, size_t &Nb, typename PolRing::Domain_t::Element_ptr &B, size_t &ldb, typename PolRing::Domain_t::RandIter &g, const size_t degree=__FFLASFFPACK_ARITHPROG_THRESHOLD)

template<class PolRing >
std::list< typename PolRing::Element > &	ArithProg (const PolRing &PR, std::list< typename PolRing::Element > &frobeniusForm, const size_t N, typename PolRing::Domain_t::Element_ptr A, const size_t lda, const size_t degree)

template<class Field , class Polynomial >
std::list< Polynomial > &	LUKrylov_KGFast (const Field &F, std::list< Polynomial > &charp, const size_t N, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr X, const size_t ldx)

template<class Field , class Polynomial >
Polynomial &	MinPoly (const Field &F, Polynomial &minP, const size_t N, typename Field::ConstElement_ptr A, const size_t lda)
	Compute the minimal polynomial of the matrix A. More...

template<class Field , class Polynomial , class RandIter >
Polynomial &	MinPoly (const Field &F, Polynomial &minP, const size_t N, typename Field::ConstElement_ptr A, const size_t lda, RandIter &G)
	Compute the minimal polynomial of the matrix A. More...

template<class Field , class Polynomial >
Polynomial &	MatVecMinPoly (const Field &F, Polynomial &minP, const size_t N, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr v, const size_t incv)
	Compute the minimal polynomial of the matrix A and a vector v, namely the first linear dependency relation in the Krylov basis . More...

template<class Field , class Polynomial >
Polynomial &	MatVecMinPoly (const Field &F, Polynomial &minP, const size_t N, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr v, const size_t incv, typename Field::Element_ptr K, const size_t ldk, size_t *P)

template<class Field , class Polynomial >
Polynomial &	Hybrid_KGF_LUK_MinPoly (const Field &F, Polynomial &minP, const size_t N, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr X, const size_t ldx, size_t *P, const FFPACK_MINPOLY_TAG MinTag=FFPACK::FfpackDense, const size_t kg_mc=0, const size_t kg_mb=0, const size_t kg_j=0)

template<class Field >
size_t	Rank (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda)
	Computes the rank of the given matrix using a PLUQ factorization. More...

template<class Field >
size_t	pRank (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t numthreads=0)

template<class Field , class PSHelper >
size_t	Rank (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, const PSHelper &psH)

template<class Field >
bool	IsSingular (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda)
	Returns true if the given matrix is singular. More...

template<class Field >
Field::Element &	Det (const Field &F, typename Field::Element &det, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t P=NULL, size_t Q=NULL)
	Returns the determinant of the given square matrix. More...

template<class Field >
Field::Element &	pDet (const Field &F, typename Field::Element &det, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t numthreads=0, size_t P=NULL, size_t Q=NULL)

template<class Field , class PSHelper >
Field::Element &	Det (const Field &F, typename Field::Element &det, const size_t N, typename Field::Element_ptr A, const size_t lda, const PSHelper &psH, size_t P=NULL, size_t Q=NULL)

template<class Field >
Field::Element_ptr	Solve (const Field &F, const size_t M, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr x, const int incx, typename Field::ConstElement_ptr b, const int incb)
	Solves a linear system AX = b using PLUQ factorization. More...

template<class Field , class PSHelper >
Field::Element_ptr	Solve (const Field &F, const size_t M, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr x, const int incx, typename Field::ConstElement_ptr b, const int incb, PSHelper &psH)

template<class Field >
Field::Element_ptr	pSolve (const Field &F, const size_t M, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr x, const int incx, typename Field::ConstElement_ptr b, const int incb, size_t numthreads=0)

template<class Field >
*void	RandomNullSpaceVector (const Field &F, const FFLAS::FFLAS_SIDE Side, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr X, const size_t incX)
	Solve L X = B or X L = B in place. 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_ptr A, const size_t lda, typename Field::Element_ptr &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_ptr A, const size_t lda, size_t *&rkprofile, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
	Computes the row rank profile of A. More...

template<class Field >
size_t	pRowRankProfile (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t *&rkprofile, size_t numthreads=0, const FFPACK_LU_TAG LuTag=FfpackTileRecursive)

template<class Field , class PSHelper >
size_t	RowRankProfile (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t *&rkprofile, const FFPACK_LU_TAG LuTag, PSHelper &psH)

template<class Field >
size_t	ColumnRankProfile (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t *&rkprofile, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
	Computes the column rank profile of A. More...

template<class Field >
size_t	pColumnRankProfile (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t *&rkprofile, size_t numthreads=0, const FFPACK_LU_TAG LuTag=FfpackTileRecursive)

template<class Field , class PSHelper >
size_t	ColumnRankProfile (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t *&rkprofile, const FFPACK_LU_TAG LuTag, PSHelper &psH)

void	RankProfileFromLU (const size_t P, const size_t N, const size_t R, size_t rkprofile, const FFPACK_LU_TAG LuTag)
	Recovers the column/row rank profile from the permutation of an LU decomposition. More...

size_t	LeadingSubmatrixRankProfiles (const size_t M, const size_t N, const size_t R, const size_t LSm, const size_t LSn, const size_t P, const size_t Q, size_t RRP, size_t CRP)
	Recovers the row and column rank profiles of any leading submatrix from the PLUQ decomposition. More...

template<class Field >
size_t	RowRankProfileSubmatrixIndices (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr 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_ptr 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_ptr A, const size_t lda, typename Field::Element_ptr &X, size_t &R)
	Computes 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_ptr A, const size_t lda, typename Field::Element_ptr &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 >
void	getTriangular (const Field &F, const FFLAS::FFLAS_UPLO Uplo, const FFLAS::FFLAS_DIAG diag, const size_t M, const size_t N, const size_t R, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr T, const size_t ldt, const bool OnlyNonZeroVectors=false)
	Extracts a triangular matrix from a compact storage A=L\U of rank R. More...

template<class Field >
void	getTriangular (const Field &F, const FFLAS::FFLAS_UPLO Uplo, const FFLAS::FFLAS_DIAG diag, const size_t M, const size_t N, const size_t R, typename Field::Element_ptr A, const size_t lda)
	Cleans up a compact storage A=L\U to reveal a triangular matrix of rank R. More...

template<class Field >
void	getEchelonForm (const Field &F, const FFLAS::FFLAS_UPLO Uplo, const FFLAS::FFLAS_DIAG diag, const size_t M, const size_t N, const size_t R, const size_t *P, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr T, const size_t ldt, const bool OnlyNonZeroVectors=false, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
	Extracts a matrix in echelon form from a compact storage A=L\U of rank R obtained by RowEchelonForm or ColumnEchelonForm. More...

template<class Field >
void	getEchelonForm (const Field &F, const FFLAS::FFLAS_UPLO Uplo, const FFLAS::FFLAS_DIAG diag, const size_t M, const size_t N, const size_t R, const size_t *P, typename Field::Element_ptr A, const size_t lda, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
	Cleans up a compact storage A=L\U obtained by RowEchelonForm or ColumnEchelonForm to reveal an echelon form of rank R. More...

template<class Field >
void	getEchelonTransform (const Field &F, const FFLAS::FFLAS_UPLO Uplo, const FFLAS::FFLAS_DIAG diag, const size_t M, const size_t N, const size_t R, const size_t P, const size_t Q, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr T, const size_t ldt, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
	Extracts a transformation matrix to echelon form from a compact storage A=L\U of rank R obtained by RowEchelonForm or ColumnEchelonForm. More...

template<class Field >
void	getReducedEchelonForm (const Field &F, const FFLAS::FFLAS_UPLO Uplo, const size_t M, const size_t N, const size_t R, const size_t *P, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr T, const size_t ldt, const bool OnlyNonZeroVectors=false, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
	Extracts a matrix in echelon form from a compact storage A=L\U of rank R obtained by ReducedRowEchelonForm or ReducedColumnEchelonForm with transform = true. More...

template<class Field >
void	getReducedEchelonForm (const Field &F, const FFLAS::FFLAS_UPLO Uplo, const size_t M, const size_t N, const size_t R, const size_t *P, typename Field::Element_ptr A, const size_t lda, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
	Cleans up a compact storage A=L\U of rank R obtained by ReducedRowEchelonForm or ReducedColumnEchelonForm with transform = true. More...

template<class Field >
void	getReducedEchelonTransform (const Field &F, const FFLAS::FFLAS_UPLO Uplo, const size_t M, const size_t N, const size_t R, const size_t P, const size_t Q, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr T, const size_t ldt, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
	Extracts a transformation matrix to echelon form from a compact storage A=L\U of rank R obtained by RowEchelonForm or ColumnEchelonForm. More...

void	PLUQtoEchelonPermutation (const size_t N, const size_t R, const size_t P, size_t outPerm)
	Auxiliary routine: determines the permutation that changes a PLUQ decomposition into a echelon form revealing PLUQ decomposition. More...

template<class Field >
size_t	LTBruhatGen (const Field &Fi, const FFLAS::FFLAS_DIAG diag, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t P, size_t Q)
	LTBruhatGen Suppose A is Left Triangular Matrix This procedure computes the Bruhat Representation of A and return the rank of A. More...

template<class Field >
void	getLTBruhatGen (const Field &Fi, const size_t N, const size_t r, const size_t P, const size_t Q, typename Field::Element_ptr R, const size_t ldr)
	GetLTBruhatGen This procedure Computes the Rank Revealing Matrix based on the Bruhta representation of a Matrix. More...

template<class Field >
void	getLTBruhatGen (const Field &Fi, const FFLAS::FFLAS_UPLO Uplo, const FFLAS::FFLAS_DIAG diag, const size_t N, const size_t r, const size_t P, const size_t Q, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr T, const size_t ldt)
	GetLTBruhatGen This procedure computes the matrix L or U f the Bruhat Representation Suppose that A is the bruhat representation of a matrix. More...

size_t	LTQSorder (const size_t N, const size_t r, const size_t P, const size_t Q)
	LTQSorder This procedure computes the order of quasiseparability of a matrix. More...

template<class Field >
size_t	CompressToBlockBiDiagonal (const Field &Fi, const FFLAS::FFLAS_UPLO Uplo, size_t N, size_t s, size_t r, const size_t P, const size_t Q, typename Field::Element_ptr A, size_t lda, typename Field::Element_ptr X, size_t ldx, size_t K, size_t M, size_t *T)
	CompressToBlockBiDiagonal This procedure compress a compact representation of a row echelon form or column echelon form. More...

template<class Field >
void	ExpandBlockBiDiagonalToBruhat (const Field &Fi, const FFLAS::FFLAS_UPLO Uplo, size_t N, size_t s, size_t r, typename Field::Element_ptr A, size_t lda, typename Field::Element_ptr X, size_t ldx, size_t NbBlocks, size_t K, size_t M, size_t *T)
	ExpandBlockBiDiagonal This procedure expand a compact representation of a row echelon form or column echelon form. More...

void	Bruhat2EchelonPermutation (size_t N, size_t R, const size_t P, const size_t Q, size_t *M)
	Bruhat2EchelonPermutation (N,R,P,Q) Compute M such that LM or MU is in echelon form where L or U are factors of the Bruhat Rpresentation. More...

size_t *	TInverter (size_t *T, size_t r)

template<class Field >
void	ComputeRPermutation (const Field &Fi, size_t N, size_t r, const size_t P, const size_t Q, size_t R, size_t MU, size_t *ML)

template<class Field >
void	productBruhatxTS (const Field &Fi, size_t N, size_t s, size_t r, const size_t P, const size_t Q, const typename Field::Element_ptr Xu, size_t ldu, size_t NbBlocksU, size_t Ku, size_t Tu, size_t MU, const typename Field::Element_ptr Xl, size_t ldl, size_t NbBlocksL, size_t Kl, size_t Tl, size_t ML, typename Field::Element_ptr B, size_t t, size_t ldb, typename Field::Element_ptr C, size_t ldc)
	productBruhatxTS Comput the product between the CRE compact representation of a matrix A and B a tall matrix More...

template<class Field >
Field::Element_ptr	LQUPtoInverseOfFullRankMinor (const Field &F, const size_t rank, typename Field::Element_ptr A_factors, const size_t lda, const size_t *QtPointer, typename Field::Element_ptr X, const size_t ldx)
	LQUPtoInverseOfFullRankMinor. More...