eigen_extensions.hpp File Reference

Bertini extensions of the Eigen linear algebra library. More...

#include "bertini2/num_traits.hpp"
#include <boost/serialization/complex.hpp>
#include <boost/serialization/array.hpp>
#include <boost/serialization/split_member.hpp>
#include <Eigen/Core>
#include <Eigen/Geometry>
#include <Eigen/Eigenvalues>
#include <Eigen/SVD>
#include <Eigen/Dense>

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Namespaces
namespace	Eigen
namespace	bertini

Macros
#define	EIGEN_DENSEBASE_PLUGIN   "bertini2/eigen_serialization_addon.hpp"
	Tell Eigen to mix a Boost.serialization addon into every dense matrix/array.

Typedefs
template<typename NumT>
using	bertini::Vec = Eigen::Matrix<NumT, Eigen::Dynamic, 1>
	A dynamically-sized column vector of NumT.
template<typename NumT>
using	bertini::Mat = Eigen::Matrix<NumT, Eigen::Dynamic, Eigen::Dynamic>
	A dynamically-sized matrix of NumT.

Enumerations
enum class	bertini::MatrixSuccessCode { bertini::Success , bertini::LargeChange , bertini::SmallValue }
	Outcome of a matrix-decomposition sanity check (e.g. LU pivot magnitude). More...

Functions
template<typename Derived>
bool	bertini::IsEmpty (Eigen::MatrixBase< Derived > const &v)
	Checks whether the number of rows and columns are either 0.
template<typename Derived>
bool	bertini::ContainsNaN (Eigen::MatrixBase< Derived > const &v)
	True when any entry of a complex-valued Eigen object has a NaN real or imaginary part.
template<typename Derived>
unsigned	bertini::Precision (Eigen::MatrixBase< Derived > const &v)
	Get the precision of an Eigen object.
template<typename Derived>
unsigned	bertini::PrecisionRequireUniform (Eigen::MatrixBase< Derived > const &v)
	Query the precision of an Eigen object, requiring it to be non-empty, and of uniform precision.
template<typename Derived>
void	bertini::Precision (Eigen::MatrixBase< Derived > &v, unsigned prec)
	Set the precision of an Eigen object.
template<typename T>
bool	bertini::IsSmallValue (T const &testme)
	Test a numbers being very small.
template<typename T>
bool	bertini::IsSymmRelDiffSmall (T const &a, T const &b, typename Eigen::NumTraits< T >::Real const &e)
	Check whether two values are very close to each other.
template<typename T>
bool	bertini::IsLargeChange (T const &numerator, T const &denomenator)
	Test two numbers for having large ratio.
template<typename Derived>
MatrixSuccessCode	bertini::LUPartialPivotDecompositionSuccessful (Eigen::MatrixBase< Derived > const &LU)
	Check the diagonal elements of an LU decomposition for small values and large ratios.
template<typename NumberType>
Eigen::Matrix< NumberType, Eigen::Dynamic, Eigen::Dynamic >	bertini::KahanMatrix (unsigned int mat_size, NumberType c)
	Make a Kahan matrix with a given number type.
template<typename NumberType>
Mat< NumberType >	bertini::RandomOfUnits (unsigned int rows, unsigned int cols)
	Make a random matrix of units (numbers with norm 1).
template<typename NumberType>
Mat< NumberType >	bertini::RandomConjugateOrthonormalMatrix (unsigned int rows, unsigned int cols)
	Make a random conjugate-orthonormal matrix (orthonormal rows when rows<=cols, orthonormal columns when rows>=cols), to the current default precision.
template<typename NumberType>
Vec< NumberType >	bertini::RandomOfUnits (unsigned int size)
	Make a random vector of units (numbers with norm 1).
template<typename DerivedA, typename DerivedB>
bool	bertini::IsSamePoint (Eigen::MatrixBase< DerivedA > const &a, Eigen::MatrixBase< DerivedB > const &b, NumErrorT tol)
	True if two points are the same to within tol in the infinity norm.
template<typename DerivedA, typename DerivedB>
bool	bertini::IsDistinct (Eigen::MatrixBase< DerivedA > const &a, Eigen::MatrixBase< DerivedB > const &b, NumErrorT tol)
	True if two points differ by more than tol in the infinity norm (the negation of :func:IsSamePoint).

Detailed Description

Bertini extensions of the Eigen linear algebra library.

Macro Definition Documentation

EIGEN_DENSEBASE_PLUGIN

#define EIGEN_DENSEBASE_PLUGIN   "bertini2/eigen_serialization_addon.hpp"

Tell Eigen to mix a Boost.serialization addon into every dense matrix/array.