hadamard-bound.h File Reference

#include <linbox/field/field-traits.h>
#include <linbox/integer.h>
#include <linbox/matrix/matrix-category.h>
#include <linbox/matrix/matrix-traits.h>
#include <limits>

Data Structures
struct	HadamardLogBoundDetails
struct	RationalSolveHadamardBoundData

Namespaces
namespace	LinBox
	Namespace in which all linbox code resides.

Functions
template<class ConstIterator>
bool	vectorLogNorm (double &logNorm, const ConstIterator &begin, const ConstIterator &end)
template<class IMatrix>
void	HadamardRowLogBound (double &logBound, double &minLogNorm, const IMatrix &A)
	Precise Hadamard bound (bound on determinant) by taking the row-wise euclidean norm.
template<class IMatrix>
void	HadamardRowLogBound (double &logBound, double &minLogNorm, const IMatrix &A, const MatrixCategories::RowColMatrixTag &tag)
template<class IMatrix>
void	HadamardRowLogBound (double &logBound, double &minLogNorm, const IMatrix &A, const MatrixCategories::RowMatrixTag &tag)
template<class IMatrix>
void	HadamardRowLogBound (double &logBound, double &minLogNorm, const IMatrix &A, const MatrixCategories::BlackboxTag &tag)
template<class IMatrix>
void	HadamardColLogBound (double &logBound, double &minLogNorm, const IMatrix &A)
	Precise Hadamard bound (bound on determinant) by taking the column-wise euclidean norm.
template<class IMatrix>
void	HadamardColLogBound (double &logBound, double &minLogNorm, const IMatrix &A, const MatrixCategories::RowColMatrixTag &tag)
template<class IMatrix>
void	HadamardColLogBound (double &logBound, double &minLogNorm, const IMatrix &A, const MatrixCategories::RowMatrixTag &tag)
template<class IMatrix>
void	HadamardColLogBound (double &logBound, double &minLogNorm, const IMatrix &A, const MatrixCategories::BlackboxTag &tag)
template<class IMatrix>
HadamardLogBoundDetails	DetailedHadamardBound (const IMatrix &A)
	Precise Hadamard bound (bound on determinant) by taking the minimum of the column-wise and the row-wise euclidean norm.
template<class IMatrix>
double	HadamardBound (const IMatrix &A)
	Precise Hadamard bound (bound on determinant) by taking the minimum of the column-wise and the row-wise euclidean norm.
template<class IMatrix, class MTag>
Integer &	InfinityNorm (Integer &max, const IMatrix &A, const MTag &tag)
	Returns the maximal absolute value.
template<class IMatrix>
Integer &	InfinityNorm (Integer &max, const IMatrix &A, const MatrixCategories::RowColMatrixTag &tag)
template<class IMatrix>
double	FastHadamardBound (const IMatrix &A, const Integer &infnorm)
	Returns the bit size of the Hadamard bound.
template<class IMatrix>
double	FastHadamardBound (const IMatrix &A, const MatrixCategories::RowColMatrixTag &tag)
template<class IMatrix>
double	FastHadamardBound (const IMatrix &A, const MatrixCategories::BlackboxTag &tag)
template<class IMatrix>
double	FastHadamardBound (const IMatrix &A)
template<class IMatrix>
double	FastCharPolyDumasPernetWanBound (const IMatrix &A, const Integer &infnorm)
	Bound on the coefficients of the characteristic polynomial.
template<class IMatrix>
double	FastCharPolyGoldsteinGrahamBound (const IMatrix &A, const Integer &infnorm)
	A.J.
template<class IMatrix>
double	FastCharPolyHadamardBound (const IMatrix &A)
template<class Matrix, class Vector>
std::enable_if< std::is_same< typenameFieldTraits< typenameMatrix::Field >::categoryTag, RingCategories::IntegerTag >::value, RationalSolveHadamardBoundData >::type	RationalSolveHadamardBound (const Matrix &A, const Vector &b)
	Bound on the rational solution of a linear system Ax = b.
template<class Matrix, class Vector>
std::enable_if< std::is_same< typenameFieldTraits< typenameMatrix::Field >::categoryTag, RingCategories::RationalTag >::value, RationalSolveHadamardBoundData >::type	RationalSolveHadamardBound (const Matrix &A, const Vector &b)
	@fixme Needed to solve-cra.h, but can't be used yet.