maths.h File Reference

#include "sopt/config.h"
#include <algorithm>
#include <complex>
#include <type_traits>
#include <Eigen/Core>
#include "sopt/exception.h"
#include "sopt/types.h"

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Classes
class	sopt::details::ProjectPositiveQuadrant< SCALAR >
	Expression to create projection onto positive orthant. More...
class	sopt::details::ProjectPositiveQuadrant< std::complex< SCALAR > >
	Specialization for complex numbers. More...

Namespaces
	sopt
	sopt::details

Typedefs
template<typename SCALAR >
using	sopt::details::SoftThreshhold = decltype(std::bind(soft_threshhold< SCALAR >, std::placeholders::_1, typename real_type< SCALAR >::type(1)))
	Helper template type alias to instantiate soft_threshhold that takes an Eigen object. More...

Functions
template<typename T >
real_type< typename T::Scalar >::type	sopt::standard_deviation (Eigen::ArrayBase< T > const &x)
	Computes the standard deviation of a vector. More...
template<typename T >
real_type< typename T::Scalar >::type	sopt::standard_deviation (Eigen::MatrixBase< T > const &x)
	Computes the standard deviation of a vector. More...
template<typename SCALAR >
std::enable_if< std::is_arithmetic< SCALAR >::value or is_complex< SCALAR >::value, SCALAR >::type	sopt::soft_threshhold (SCALAR const &x, typename real_type< SCALAR >::type const &threshhold)
	abs(x) < threshhold ? 0: x - sgn(x) * threshhold More...
template<typename T >
Eigen::CwiseUnaryOp< const details::ProjectPositiveQuadrant< typename T::Scalar >, const T >	sopt::positive_quadrant (Eigen::DenseBase< T > const &input)
	Expression to create projection onto positive quadrant. More...
template<typename T >
Eigen::CwiseUnaryOp< const details::SoftThreshhold< typename T::Scalar >, const T >	sopt::soft_threshhold (Eigen::DenseBase< T > const &input, typename real_type< typename T::Scalar >::type const &threshhold)
	Expression to create soft-threshhold. More...
template<typename T0 , typename T1 >
std::enable_if< std::is_arithmetic< typename T0::Scalar >::value and std::is_arithmetic< typename T1::Scalar >::value, Eigen::CwiseBinaryOp< typename T0::Scalar(*)(typename T0::Scalar const &, typename T1::Scalar const &), const T0, const T1 > >::type	sopt::soft_threshhold (Eigen::DenseBase< T0 > const &input, Eigen::DenseBase< T1 > const &threshhold)
	Expression to create soft-threshhold with multiple parameters. More...
template<typename T0 , typename T1 >
std::enable_if< is_complex< typename T0::Scalar >::value and std::is_arithmetic< typename T1::Scalar >::value, Eigen::CwiseBinaryOp< typename T0::Scalar(*)(typename T0::Scalar const &, typename T0::Scalar const &), const T0, decltype(std::declval< const T1 >).template cast< typename T0::Scalar >))> >::type	sopt::soft_threshhold (Eigen::DenseBase< T0 > const &input, Eigen::DenseBase< T1 > const &threshhold)
	Expression to create soft-threshhold with multiple parameters. More...
template<typename T0 , typename T1 >
real_type< typename T0::Scalar >::type	sopt::l1_norm (Eigen::ArrayBase< T0 > const &input, Eigen::ArrayBase< T1 > const &weights)
	Computes weighted L1 norm. More...
template<typename T0 , typename T1 >
real_type< typename T0::Scalar >::type	sopt::l1_norm (Eigen::MatrixBase< T0 > const &input, Eigen::MatrixBase< T1 > const &weight)
	Computes weighted L1 norm. More...
template<typename T0 >
real_type< typename T0::Scalar >::type	sopt::l1_norm (Eigen::ArrayBase< T0 > const &input)
	Computes L1 norm. More...
template<typename T0 >
real_type< typename T0::Scalar >::type	sopt::l1_norm (Eigen::MatrixBase< T0 > const &input)
	Computes L1 norm. More...
template<typename T0 , typename T1 >
real_type< typename T0::Scalar >::type	sopt::l2_norm (Eigen::ArrayBase< T0 > const &input, Eigen::ArrayBase< T1 > const &weights)
	Computes weighted L2 norm. More...
template<typename T0 , typename T1 >
real_type< typename T0::Scalar >::type	sopt::l2_norm (Eigen::MatrixBase< T0 > const &input, Eigen::MatrixBase< T1 > const &weights)
	Computes weighted L2 norm. More...
template<typename T0 >
real_type< typename T0::Scalar >::type	sopt::l2_norm (Eigen::ArrayBase< T0 > const &input)
	Computes weighted L2 norm. More...
template<typename T0 >
real_type< typename T0::Scalar >::type	sopt::l2_norm (Eigen::MatrixBase< T0 > const &input)
	Computes weighted L2 norm. More...
template<typename T0 , typename T1 >
real_type< typename T0::Scalar >::type	sopt::tv_norm (Eigen::ArrayBase< T0 > const &input, Eigen::ArrayBase< T1 > const &weights)
	Computes weighted TV norm. More...
template<typename T0 , typename T1 >
real_type< typename T0::Scalar >::type	sopt::tv_norm (Eigen::MatrixBase< T0 > const &input, Eigen::MatrixBase< T1 > const &weights)
	Computes weighted TV norm. More...
template<typename T0 >
real_type< typename T0::Scalar >::type	sopt::tv_norm (Eigen::ArrayBase< T0 > const &input)
	Computes weighted tv norm. More...
template<typename T0 >
real_type< typename T0::Scalar >::type	sopt::tv_norm (Eigen::MatrixBase< T0 > const &input)
	Computes weighted TV norm. More...
t_int	sopt::details::gcd (t_int a, t_int b)
	Greatest common divisor. More...