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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Classes
struct	Eigen::NumTraits< mpfr_complex >
	This templated struct permits us to use the mpfr_complex type in Eigen matrices. 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 T>
bool	bertini::IsLargeChange (T const &numerator, T const &denomenator)
template<typename T>
bool	bertini::IsSmallValue (T const &testme)
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 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 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 Derived>
void	bertini::Precision (Eigen::MatrixBase< Derived > &v, unsigned prec)
	Set the precision of an Eigen object.
template<typename Derived>
unsigned	bertini::Precision (Eigen::MatrixBase< Derived > const &v)
	Get the precision of an Eigen object. If the object is empty, it's the precision of a default-constructed Scalar. If it actually has content, then it's the precision of the first element.
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 NumberType>
Mat< NumberType >	bertini::RandomOfUnits (uint rows, uint cols)
	Make a random matrix of units (numbers with norm 1).
template<typename NumberType>
Vec< NumberType >	bertini::RandomOfUnits (uint size)
	Make a random vector of units (numbers with norm 1).

Detailed Description

Bertini extensions of the Eigen linear algebra library.

Function Documentation

IsEmpty()

template<typename Derived>

bool bertini::IsEmpty ( Eigen::MatrixBase< Derived > const & v )

inline

Checks whether the number of rows and columns are either 0.

IsLargeChange()

template<typename T>

bool bertini::IsLargeChange ( T const & numerator, T const & denomenator )

inline

Test two numbers for having large ratio.

The basis for comparison is Eigen's fuzzy precision, Eigen::NumTraits<T>::dummy_precision();

Note

For doubles, the threshold is 1e-12, for mpfr_real is 1e3*current precision.

Parameters

numerator	The numerator for the ratio.
denomenator	The denomenator for the ratio.

Returns

true, if the ratio is very large, false otherwise

IsSmallValue()

template<typename T>

bool bertini::IsSmallValue ( T const & testme )

inline

Test a numbers being very small.

Compares the number against machine epsilon (or software epsilon if a multiple precision type), times 100.

Note

Machine epsilon for doubles is about 1e-16, for mpfr_real, it's 10^-current precision.

Parameters

testme

The number to test

Returns

true, if the number is very small. False otherwise.

IsSymmRelDiffSmall()

template<typename T>

bool bertini::IsSymmRelDiffSmall ( T const & a, T const & b, typename Eigen::NumTraits< T >::Real const & e )

inline

Check whether two values are very close to each other.

The tolerance for being close See \url http://www.boost.org/doc/libs/1_34_0/libs/test/doc/components/test_tools/floating_point_comparison.html, for example.

KahanMatrix()

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.

LUPartialPivotDecompositionSuccessful()

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.

Returns

Success if things are ok. LargeChange or SmallValue if one is found.

This function requires a square non-empty matrix.

Template Parameters

Derived

Matrix type from Eigen.

Precision() [1/2]

template<typename Derived>

void bertini::Precision	(	Eigen::MatrixBase< Derived > &	v,
		unsigned	prec )

Set the precision of an Eigen object.

Parameters

v	the matrix to change
prec	the new precision

Precision() [2/2]

template<typename Derived>

unsigned bertini::Precision ( Eigen::MatrixBase< Derived > const & v )

inline

Get the precision of an Eigen object. If the object is empty, it's the precision of a default-constructed Scalar. If it actually has content, then it's the precision of the first element.

If you require that the object be of uniform precision when you check, use PrecisionRequireUniform

PrecisionRequireUniform()

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.

Exceptions

runtime_error

if not uniform precision Dies in an Eigen assert if empty (assuming you didn't disable these)

RandomOfUnits() [1/2]

template<typename NumberType>

Mat< NumberType > bertini::RandomOfUnits ( uint rows, uint cols )

inline

Make a random matrix of units (numbers with norm 1).

Returns

The random matrix of units.

Parameters

rows	The number of rows.
cols	The number of columns.

Template Parameters

NumberType

the type of number to fill the matrix with.

RandomOfUnits() [2/2]

template<typename NumberType>

Vec< NumberType > bertini::RandomOfUnits ( uint size )

inline

Make a random vector of units (numbers with norm 1).

Returns

The random vector of units.

Parameters

size	The length of the vector.

Template Parameters

NumberType

the type of number to fill the vector with.