Functions
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	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 , 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 &	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	updateD (const Field &F, size_t *d, size_t k, std::vector< std::vector< typename Field::Element > > &minpt)

template<class Field >
size_t	newD (const Field &F, size_t d, bool &KeepOn, const size_t l, const size_t N, typename Field::Element_ptr X, const size_t Q, std::vector< std::vector< typename Field::Element > > &minpt)

template<class Field >
void	CompressRows (Field &F, const size_t M, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr tmp, const size_t ldtmp, const size_t *d, const size_t nb_blocs)

template<class Field >
void	CompressRowsQK (Field &F, const size_t M, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr tmp, const size_t ldtmp, const size_t *d, const size_t deg, const size_t nb_blocs)

template<class Field >
void	DeCompressRows (Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr tmp, const size_t ldtmp, const size_t *d, const size_t nb_blocs)

template<class Field >
void	DeCompressRowsQK (Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr tmp, const size_t ldtmp, const size_t *d, const size_t deg, const size_t nb_blocs)

template<class Field >
void	CompressRowsQA (Field &F, const size_t M, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr tmp, const size_t ldtmp, const size_t *d, const size_t nb_blocs)

template<class Field >
void	DeCompressRowsQA (Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr tmp, const size_t ldtmp, const size_t *d, const size_t nb_blocs)

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::FFPACK_MINPOLY_TAG MinTag, const size_t kg_mc, const size_t kg_mb, const size_t kg_j)

Function Documentation

◆ LUdivine_construct() [1/2]

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`
	)

◆ GaussJordan()

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
	)

inline

Gauss-Jordan algorithm computing the Reduced Row echelon form and its transform matrix.

Bibliography:

Algorithm 2.8 of A. Storjohann Thesis 2000,
Algorithm 11 of Jeannerod C-P., Pernet, C. and Storjohann, A. Rank-profile revealing Gaussian elimination and the CUP matrix decomposition , J. of Symbolic Comp., 2013

Parameters

	M	row dimension of A
	N	column dimension of A
[in,out]	A	an m x n matrix
	lda	leading dimension of A
	P	row permutation
	Q	column permutation
	LuTag	set the base case to a Tile (FfpackGaussJordanTile) or Slab (FfpackGaussJordanSlab) recursive RedEchelon

| I | A11 | A12 | | |-—|--—|--—|-—| | |I | *| A22 | | | |0 | 0| A22 | | |-—|--—|--—|-—| | | 0 | A32 | | |-—|--—|--—|-—|

where the transformation matrix is stored at the pivot column position

◆ KellerGehrig()

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

◆ KGFast()

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
	)

◆ KGFast_generalized()

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
	)

◆ fgemv_kgf()

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
	)

◆ LUKrylov()

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
	)

◆ Danilevski()

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

◆ RandomKrylovPrecond()

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`
	)

inline

Todo:: swap to save space ??

Todo:

Todo:: don't assing K2 c*noc x N but only mas (c,noc) x N and store each one after the other

Todo:: swap to save space ??

Todo:

Todo:: don't assing K2 c*noc x N but only mas (c,noc) x N and store each one after the other

◆ ArithProg()

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
	)

inline

◆ LUKrylov_KGFast()

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
	)

◆ MatVecMinPoly()

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
	)

inline

◆ Hybrid_KGF_LUK_MinPoly()

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`
	)

◆ updateD()

size_t updateD	(	const Field &	F,
		size_t *	d,
		size_t	k,
		std::vector< std::vector< typename Field::Element > > &	minpt
	)

◆ newD()

size_t newD	(	const Field &	F,
		size_t *	d,
		bool &	KeepOn,
		const size_t	l,
		const size_t	N,
		typename Field::Element_ptr	X,
		const size_t *	Q,
		std::vector< std::vector< typename Field::Element > > &	minpt
	)

◆ CompressRows()

void CompressRows	(	Field &	F,
		const size_t	M,
		typename Field::Element_ptr	A,
		const size_t	lda,
		typename Field::Element_ptr	tmp,
		const size_t	ldtmp,
		const size_t *	d,
		const size_t	nb_blocs
	)

inline

◆ CompressRowsQK()

void CompressRowsQK	(	Field &	F,
		const size_t	M,
		typename Field::Element_ptr	A,
		const size_t	lda,
		typename Field::Element_ptr	tmp,
		const size_t	ldtmp,
		const size_t *	d,
		const size_t	deg,
		const size_t	nb_blocs
	)

inline

◆ DeCompressRows()

void DeCompressRows	(	Field &	F,
		const size_t	M,
		const size_t	N,
		typename Field::Element_ptr	A,
		const size_t	lda,
		typename Field::Element_ptr	tmp,
		const size_t	ldtmp,
		const size_t *	d,
		const size_t	nb_blocs
	)

inline

◆ DeCompressRowsQK()

void DeCompressRowsQK	(	Field &	F,
		const size_t	M,
		const size_t	N,
		typename Field::Element_ptr	A,
		const size_t	lda,
		typename Field::Element_ptr	tmp,
		const size_t	ldtmp,
		const size_t *	d,
		const size_t	deg,
		const size_t	nb_blocs
	)

inline

◆ CompressRowsQA()

void CompressRowsQA	(	Field &	F,
		const size_t	M,
		typename Field::Element_ptr	A,
		const size_t	lda,
		typename Field::Element_ptr	tmp,
		const size_t	ldtmp,
		const size_t *	d,
		const size_t	nb_blocs
	)

inline

◆ DeCompressRowsQA()

void DeCompressRowsQA	(	Field &	F,
		const size_t	M,
		const size_t	N,
		typename Field::Element_ptr	A,
		const size_t	lda,
		typename Field::Element_ptr	tmp,
		const size_t	ldtmp,
		const size_t *	d,
		const size_t	nb_blocs
	)

inline

◆ LUdivine_construct() [2/2]

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::FFPACK_MINPOLY_TAG	MinTag,
		const size_t	kg_mc,
		const size_t	kg_mb,
		const size_t	kg_j
	)

Functions

Function Documentation

◆ LUdivine_construct() [1/2]

◆ GaussJordan()

◆ KellerGehrig()

◆ KGFast()

◆ KGFast_generalized()

◆ fgemv_kgf()

◆ LUKrylov()

◆ Danilevski()

◆ RandomKrylovPrecond()

◆ ArithProg()

◆ LUKrylov_KGFast()

◆ MatVecMinPoly()

◆ Hybrid_KGF_LUK_MinPoly()

◆ updateD()

◆ newD()

◆ CompressRows()

◆ CompressRowsQK()

◆ DeCompressRows()

◆ DeCompressRowsQK()

◆ CompressRowsQA()

◆ DeCompressRowsQA()

◆ LUdivine_construct() [2/2]