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FFPACK Class Reference

#include <ffpack.h>

Inheritance diagram for FFPACK:

List of all members.

Detailed Description

Set of elimination based routines for dense linear algebra with matrices over finite field.

This class only provides a set of static member functions. No instantiation is allowed.

It enlarges the set of BLAS routines of the class FFLAS, with higher level routines based on elimination.

Public Types

enum FFPACK_LUDIVINE_TAG { FfpackLQUP = 1, FfpackSingular = 2, FfpackLSP = 3, FfpackTURBO = 4 }

enum FFPACK_CHARPOLY_TAG {
FfpackLUK = 1, FfpackKG = 2, FfpackHybrid = 3, FfpackKGFast = 4,
FfpackHybrid2 = 5
}

enum FFPACK_MINPOLY_TAG { FfpackDense = 1, FfpackKGF = 2 }

Static Public Methods

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)

template<class Field> bool IsSingular (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda)

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)

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)

template<class Field> Field::Element * Invert (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)

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)

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)

template<class Field> size_t TURBO (const Field &F, const size_t M, const size_t N, typename Field::Element *NW, const size_t ld1, typename Field::Element *NE, const size_t ld2, typename Field::Element *SW, const size_t ld3, typename Field::Element *SE, const size_t ld4)

template<class Field> size_t LUdivine (const Field &F, const enum FFLAS_DIAG Diag, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, const enum FFPACK_LUDIVINE_TAG LuTag=FfpackLQUP, size_t *rowP=NULL)

template<class Field> void applyP (const Field &F, const enum FFLAS_SIDE Side, const enum 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)

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 enum FFPACK_CHARPOLY_TAG CharpTag=FfpackHybrid)

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

template<class Field> void solveLB (const Field &F, const enum 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)

template<class Field> void solveLB2 (const Field &F, const enum 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)

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

Static Protected Methods

template<class Field> void invL (const Field &F, const size_t N, const typename Field::Element *L, const size_t ldl, typename Field::Element *X, const size_t ldx)

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 *X, const size_t *Q, std::vector< std::vector< typename Field::Element > > &minpt)

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> void TriangleCopy (const Field &F, const enum FFLAS_UPLO Side, const enum FFLAS_DIAG Diag, const size_t R, typename Field::Element *T, const size_t ldt, const typename Field::Element *A, const size_t lda)

template<class Field> void RectangleCopy (const Field &F, const size_t M, const size_t N, typename Field::Element *T, const size_t ldt, const typename Field::Element *A, const size_t lda)

template<class Field> void RectangleCopy2 (const Field &F, const size_t M, const size_t N, const long dist2pivot, typename Field::Element *T, const size_t ldt, const typename Field::Element *A, const size_t lda)

template<class Field> void RectangleCopyTURBO (const Field &F, const size_t M, const size_t N, const size_t dist2pivot, const size_t rank, typename Field::Element *T, const size_t ldt, const typename Field::Element *A, const size_t lda)

template<class Field> size_t LUdivine_construct (const Field &F, const enum FFLAS_DIAG Diag, const size_t M, const size_t N, const typename Field::Element *A, const size_t lda, typename Field::Element *X, const size_t ldx, typename Field::Element *u, size_t *P, bool computeX, const enum FFPACK_MINPOLY_TAG MinTag, const size_t kg_mc, const size_t kg_mb, const size_t kg_j)

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

template<class Field> void fgemv_kgf (const Field &F, const size_t N, const typename Field::Element *A, const size_t lda, const typename Field::Element *X, const size_t incX, typename Field::Element *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> std::list< Polynomial > & LUKrylov (const Field &F, std::list< Polynomial > &charp, const size_t N, typename Field::Element *A, const size_t lda, typename Field::Element *U, const size_t ldu, const enum FFPACK_CHARPOLY_TAG CharpTag)

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

Member Enumeration Documentation

enum FFPACK_CHARPOLY_TAG

Enumeration values:

FfpackLUK

FfpackKG

FfpackHybrid

FfpackKGFast

FfpackHybrid2

enum FFPACK_LUDIVINE_TAG

Enumeration values:

FfpackLQUP

FfpackSingular

FfpackLSP

FfpackTURBO

enum FFPACK_MINPOLY_TAG

Enumeration values:

FfpackDense

FfpackKGF

Member Function Documentation

void applyP ( const Field & F,

const enum FFLAS_SIDE Side,

const enum 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

) [inline, static]

std::list< Polynomial > & CharPoly ( const Field & F,

std::list< Polynomial > & charp,

const size_t N,

typename Field::Element * A,

const size_t lda,

const enum FFPACK_CHARPOLY_TAG CharpTag = FfpackHybrid

) [static]

Field::Element Det ( const Field & F,

const size_t M,

const size_t N,

typename Field::Element * A,

const size_t lda

) [inline, static]

void fgemv_kgf ( const Field & F,

const size_t N,

const typename Field::Element * A,

const size_t lda,

const typename Field::Element * X,

const size_t incX,

typename Field::Element * Y,

const size_t incY,

const size_t kg_mc,

const size_t kg_mb,

const size_t kg_j

) [static, protected]

Field::Element* Invert ( 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

) [inline, static]

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

) [inline, static]

void invL ( const Field & F,

const size_t N,

const typename Field::Element * L,

const size_t ldl,

typename Field::Element * X,

const size_t ldx

) [inline, static, protected]

bool IsSingular ( const Field & F,

const size_t M,

const size_t N,

typename Field::Element * A,

const size_t lda

) [inline, static]

std::list< Polynomial > & KellerGehrig ( const Field & F,

std::list< Polynomial > & charp,

const size_t N,

const typename Field::Element * A,

const size_t lda

) [static, protected]

int KGFast ( const Field & F,

std::list< Polynomial > & charp,

const size_t N,

typename Field::Element * A,

const size_t lda,

size_t * kg_mc,

size_t * kg_mc,

size_t * kg_j

) [static, protected]

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

) [inline, static]

LQUPtoInverseOfFullRankMinor Suppose A has been factorized as L.Q.U.P, with rank r. Then Qt.A.Pt has an invertible leading principal r x r submatrix This procedure efficiently computes the inverse of this minor and puts it into X. NOTE: It changes the lower entries of A_factors in the process (NB: unless A was nonsingular and square)
Parameters:

rank: rank of the matrix.

A_factors: matrix containing the L and U entries of the factorization

QtPointer: theLQUP->getQ()->getPointer() (note: getQ returns Qt!)

X: desired location for output

size_t LUdivine ( const Field & F,

const enum FFLAS_DIAG Diag,

const size_t M,

const size_t N,

typename Field::Element * A,

const size_t lda,

size_t * P,

const enum FFPACK_LUDIVINE_TAG LuTag = FfpackLQUP,

size_t * rowP = NULL

) [inline, static]

size_t LUdivine_construct ( const Field & F,

const enum FFLAS_DIAG Diag,

const size_t M,

const size_t N,

const typename Field::Element * A,

const size_t lda,

typename Field::Element * X,

const size_t ldx,

typename Field::Element * u,

size_t * P,

bool computeX,

const enum FFPACK_MINPOLY_TAG MinTag,

const size_t kg_mc,

const size_t kg_mb,

const size_t kg_j

) [static, protected]

std::list< Polynomial > & LUKrylov ( const Field & F,

std::list< Polynomial > & charp,

const size_t N,

typename Field::Element * A,

const size_t lda,

typename Field::Element * U,

const size_t ldu,

const enum FFPACK_CHARPOLY_TAG CharpTag

) [static, protected]

std::list< Polynomial > & LUKrylov_KGFast ( const Field & F,

std::list< Polynomial > & charp,

const size_t N,

typename Field::Element * A,

const size_t lda,

typename Field::Element * X,

const size_t ldx

) [static, protected]

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 enum FFPACK_MINPOLY_TAG MinTag,

const size_t kg_mc,

const size_t kg_mb,

const size_t kg_j

) [static]

size_t newD ( const Field & F,

size_t * d,

bool & KeepOn,

const size_t l,

const size_t N,

typename Field::Element * X,

const size_t * Q,

std::vector< std::vector< typename Field::Element > > & minpt

) [static, protected]

size_t Rank ( const Field & F,

const size_t M,

const size_t N,

typename Field::Element * A,

const size_t lda

) [inline, static]

@doc Computes the rank of the given matrix using a LQUP factorization. The input matrix is modified.
Parameters:

M row dimension of the matrix

N column dimension of the matrix

A input matrix

lda leading dimension of A

void RectangleCopy ( const Field & F,

const size_t M,

const size_t N,

typename Field::Element * T,

const size_t ldt,

const typename Field::Element * A,

const size_t lda

) [inline, static, protected]

void RectangleCopy2 ( const Field & F,

const size_t M,

const size_t N,

const long dist2pivot,

typename Field::Element * T,

const size_t ldt,

const typename Field::Element * A,

const size_t lda

) [inline, static, protected]

void RectangleCopyTURBO ( const Field & F,

const size_t M,

const size_t N,

const size_t dist2pivot,

const size_t rank,

typename Field::Element * T,

const size_t ldt,

const typename Field::Element * A,

const size_t lda

) [inline, static, protected]

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

) [inline, static]

void solveLB ( const Field & F,

const enum 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

) [inline, static]

void solveLB2 ( const Field & F,

const enum 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

) [inline, static]

void TriangleCopy ( const Field & F,

const enum FFLAS_UPLO Side,

const enum FFLAS_DIAG Diag,

const size_t R,

typename Field::Element * T,

const size_t ldt,

const typename Field::Element * A,

const size_t lda

) [inline, static, protected]

void trinv_left ( const Field & F,

const size_t N,

const typename Field::Element * L,

const size_t ldl,

typename Field::Element * X,

const size_t ldx

) [inline, static]

size_t TURBO ( const Field & F,

const size_t M,

const size_t N,

typename Field::Element * NW,

const size_t ld1,

typename Field::Element * NE,

const size_t ld2,

typename Field::Element * SW,

const size_t ld3,

typename Field::Element * SE,

const size_t ld4

) [inline, static]

size_t updateD ( const Field & F,

size_t * d,

size_t k,

std::vector< std::vector< typename Field::Element > > & minpt

) [static, protected]

Generated on Mon Jun 20 09:16:53 2005 for linbox by

1.2.18


Public Types
enum	FFPACK_LUDIVINE_TAG { FfpackLQUP = 1, FfpackSingular = 2, FfpackLSP = 3, FfpackTURBO = 4 }
enum	FFPACK_CHARPOLY_TAG { FfpackLUK = 1, FfpackKG = 2, FfpackHybrid = 3, FfpackKGFast = 4, FfpackHybrid2 = 5 }
enum	FFPACK_MINPOLY_TAG { FfpackDense = 1, FfpackKGF = 2 }
Static Public Methods
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)
template<class Field> bool	IsSingular (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda)
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)
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)
template<class Field> Field::Element *	Invert (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)
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)
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)
template<class Field> size_t	TURBO (const Field &F, const size_t M, const size_t N, typename Field::Element NW, const size_t ld1, typename Field::Element NE, const size_t ld2, typename Field::Element SW, const size_t ld3, typename Field::Element SE, const size_t ld4)
template<class Field> size_t	LUdivine (const Field &F, const enum FFLAS_DIAG Diag, const size_t M, const size_t N, typename Field::Element A, const size_t lda, size_t P, const enum FFPACK_LUDIVINE_TAG LuTag=FfpackLQUP, size_t *rowP=NULL)
template<class Field> void	applyP (const Field &F, const enum FFLAS_SIDE Side, const enum 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)
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 enum FFPACK_CHARPOLY_TAG CharpTag=FfpackHybrid)
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 enum FFPACK_MINPOLY_TAG MinTag, const size_t kg_mc, const size_t kg_mb, const size_t kg_j)
template<class Field> void	solveLB (const Field &F, const enum 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)
template<class Field> void	solveLB2 (const Field &F, const enum 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)
template<class Field> void	trinv_left (const Field &F, const size_t N, const typename Field::Element L, const size_t ldl, typename Field::Element X, const size_t ldx)
Static Protected Methods
template<class Field> void	invL (const Field &F, const size_t N, const typename Field::Element L, const size_t ldl, typename Field::Element X, const size_t ldx)
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 X, const size_t *Q, std::vector< std::vector< typename Field::Element > > &minpt)
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> void	TriangleCopy (const Field &F, const enum FFLAS_UPLO Side, const enum FFLAS_DIAG Diag, const size_t R, typename Field::Element T, const size_t ldt, const typename Field::Element A, const size_t lda)
template<class Field> void	RectangleCopy (const Field &F, const size_t M, const size_t N, typename Field::Element T, const size_t ldt, const typename Field::Element A, const size_t lda)
template<class Field> void	RectangleCopy2 (const Field &F, const size_t M, const size_t N, const long dist2pivot, typename Field::Element T, const size_t ldt, const typename Field::Element A, const size_t lda)
template<class Field> void	RectangleCopyTURBO (const Field &F, const size_t M, const size_t N, const size_t dist2pivot, const size_t rank, typename Field::Element T, const size_t ldt, const typename Field::Element A, const size_t lda)
template<class Field> size_t	LUdivine_construct (const Field &F, const enum FFLAS_DIAG Diag, const size_t M, const size_t N, const typename Field::Element A, const size_t lda, typename Field::Element X, const size_t ldx, typename Field::Element u, size_t P, bool computeX, const enum FFPACK_MINPOLY_TAG MinTag, const size_t kg_mc, const size_t kg_mb, const size_t kg_j)
template<class Field, class Polynomial> std::list< Polynomial > &	KellerGehrig (const Field &F, std::list< Polynomial > &charp, const size_t N, const typename Field::Element *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 A, const size_t lda, size_t kg_mc, size_t kg_mc, size_t kg_j)
template<class Field> void	fgemv_kgf (const Field &F, const size_t N, const typename Field::Element A, const size_t lda, const typename Field::Element X, const size_t incX, typename Field::Element *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> std::list< Polynomial > &	LUKrylov (const Field &F, std::list< Polynomial > &charp, const size_t N, typename Field::Element A, const size_t lda, typename Field::Element U, const size_t ldu, const enum FFPACK_CHARPOLY_TAG CharpTag)
template<class Field, class Polynomial> std::list< Polynomial > &	LUKrylov_KGFast (const Field &F, std::list< Polynomial > &charp, const size_t N, typename Field::Element A, const size_t lda, typename Field::Element X, const size_t ldx)