Models a numeric interval. More...

#include <interval.hpp>

Public Types
using	value_t = ValueType
	The numeric type of the bounds.

Public Member Functions
	Interval ()
	Default constructor.
	Interval (value_t value)
	Construct an interval from a single value.
	Interval (value_t lower, value_t upper)
	Construct an interval from lower and upper bounds.
value_t	lower () const
	Returns the lower bound of the interval.
value_t	upper () const
	Returns the upper bound of the interval.
bool	contains (value_t value) const
	Whether a scalar lies in this interval (endpoints included).
value_t	median () const
	Returns the midpoint of the interval.
value_t	radius () const
	Returns the half-width of the interval.
Interval &	operator+= (const Interval &rhs)
	In-place addition of another interval.
Interval &	operator+= (value_t rhs)
	In-place addition of a scalar.
Interval &	operator-= (const Interval &rhs)
	In-place subtraction of another interval.
Interval &	operator-= (value_t rhs)
	In-place subtraction of a scalar.
Interval &	operator*= (const Interval &rhs)
	In-place multiplication by another interval.
Interval &	operator*= (value_t rhs)
	In-place multiplication by a scalar.
Interval &	operator/= (const Interval &rhs)
	In-place division by another interval.
Interval &	operator/= (value_t rhs)
	In-place division by a scalar.

Related Symbols
(Note that these are not member symbols.)
template<typename ValueType>
std::ostream &	operator<< (std::ostream &os, const Interval< ValueType > &i)
	Overload stream insertion to print an interval.
template<typename T1, typename T2>
bool	operator== (const Interval< T1 > &lhs, const Interval< T2 > &rhs)
	Compare two intervals for equality.
template<typename T1, typename T2>
bool	operator!= (const Interval< T1 > &lhs, const Interval< T2 > &rhs)
	Compare two intervals for inequality.
template<typename T1, typename T2>
bool	operator< (const Interval< T1 > &lhs, const Interval< T2 > &rhs)
	Whether one interval is certainly less than another.
template<typename T1, typename T2>
bool	operator> (const Interval< T1 > &lhs, const Interval< T2 > &rhs)
	Whether one interval is greater than another.
template<typename T1, typename T2>
bool	operator<= (const Interval< T1 > &lhs, const Interval< T2 > &rhs)
	Whether one interval is less than or equal to another.
template<typename T1, typename T2>
bool	operator>= (const Interval< T1 > &lhs, const Interval< T2 > &rhs)
	Whether one interval is greater than or equal to another.
template<typename T>
Interval< T >	operator- (const Interval< T > &a)
	Negation of an interval.
template<typename T>
Interval< T >	operator+ (Interval< T > lhs, const Interval< T > &rhs)
	Addition of two intervals.
template<typename T>
Interval< T >	operator- (Interval< T > lhs, const Interval< T > &rhs)
	Subtraction of two intervals.
template<typename T>
Interval< T >	operator* (Interval< T > lhs, const Interval< T > &rhs)
	Multiplication of two intervals.
template<typename T>
Interval< T >	operator/ (Interval< T > lhs, const Interval< T > &rhs)
	Division of two intervals.

Detailed Description

template<typename ValueType>
class sigma::Interval< ValueType >

Models a numeric interval.

An interval is defined by a lower and upper bound. This class wraps boost::numeric::interval and provides a median (midpoint) and radius (half-width) interface consistent with the rest of the sigma library.

Template Parameters

ValueType The floating-point type of the bounds

Constructor & Destructor Documentation

◆ Interval() [1/3]

template<typename ValueType>

sigma::Interval< ValueType >::Interval ( )

inline

Default constructor.

Constructs an interval with both bounds set to 0.0.

Exceptions

none	No throw guarantee

◆ Interval() [2/3]

template<typename ValueType>

sigma::Interval< ValueType >::Interval ( value_t value )

inline

Construct an interval from a single value.

Constructs an interval with both bounds set to the given value.

Parameters

value The value to set both bounds to

Exceptions

none	No throw guarantee

◆ Interval() [3/3]

template<typename ValueType>

sigma::Interval< ValueType >::Interval	(	value_t	lower,
		value_t	upper )

inline

Construct an interval from lower and upper bounds.

Parameters

lower	The lower bound of the interval
upper	The upper bound of the interval

Exceptions

none	No throw guarantee

Member Function Documentation

◆ contains()

template<typename ValueType>

bool sigma::Interval< ValueType >::contains ( value_t value ) const

inline

Whether a scalar lies in this interval (endpoints included).

Returns true if lower() <= value <= upper(). Boundary values are considered contained.

Parameters

value The scalar to test

Returns: True if value lies in the closed interval from lower() to upper()

Exceptions

none	No throw guarantee

◆ lower()

template<typename ValueType>

value_t sigma::Interval< ValueType >::lower ( ) const

inline

Returns the lower bound of the interval.

Returns: The lower bound value

Exceptions

none	No throw guarantee

◆ median()

template<typename ValueType>

value_t sigma::Interval< ValueType >::median ( ) const

inline

Returns the midpoint of the interval.

Returns: The midpoint value

Exceptions

none	No throw guarantee

◆ operator*=() [1/2]

template<typename ValueType>

Interval & sigma::Interval< ValueType >::operator*= ( const Interval< ValueType > & rhs )

inline

In-place multiplication by another interval.

Parameters

rhs	The interval to multiply by

Returns: Reference to this interval after multiplication

Exceptions

none	No throw guarantee

◆ operator*=() [2/2]

template<typename ValueType>

Interval & sigma::Interval< ValueType >::operator*= ( value_t rhs )

inline

In-place multiplication by a scalar.

Parameters

rhs	The scalar to multiply by

Returns: Reference to this interval after multiplication

Exceptions

none	No throw guarantee

◆ operator+=() [1/2]

template<typename ValueType>

Interval & sigma::Interval< ValueType >::operator+= ( const Interval< ValueType > & rhs )

inline

In-place addition of another interval.

Parameters

rhs	The interval to add

Returns: Reference to this interval after addition

Exceptions

none	No throw guarantee

◆ operator+=() [2/2]

template<typename ValueType>

Interval & sigma::Interval< ValueType >::operator+= ( value_t rhs )

inline

In-place addition of a scalar.

Parameters

rhs	The scalar to add

Returns: Reference to this interval after addition

Exceptions

none	No throw guarantee

◆ operator-=() [1/2]

template<typename ValueType>

Interval & sigma::Interval< ValueType >::operator-= ( const Interval< ValueType > & rhs )

inline

In-place subtraction of another interval.

Parameters

rhs	The interval to subtract

Returns: Reference to this interval after subtraction

Exceptions

none	No throw guarantee

◆ operator-=() [2/2]

template<typename ValueType>

Interval & sigma::Interval< ValueType >::operator-= ( value_t rhs )

inline

In-place subtraction of a scalar.

Parameters

rhs	The scalar to subtract

Returns: Reference to this interval after subtraction

Exceptions

none	No throw guarantee

◆ operator/=() [1/2]

template<typename ValueType>

Interval & sigma::Interval< ValueType >::operator/= ( const Interval< ValueType > & rhs )

inline

In-place division by another interval.

Parameters

rhs	The interval to divide by

Returns: Reference to this interval after division

Exceptions

none	No throw guarantee

◆ operator/=() [2/2]

template<typename ValueType>

Interval & sigma::Interval< ValueType >::operator/= ( value_t rhs )

inline

In-place division by a scalar.

Parameters

rhs	The scalar to divide by

Returns: Reference to this interval after division

Exceptions

none	No throw guarantee

◆ radius()

template<typename ValueType>

value_t sigma::Interval< ValueType >::radius ( ) const

inline

Returns the half-width of the interval.

This is the distance from the median to either endpoint.

Returns: The half-width value

Exceptions

none	No throw guarantee

◆ upper()

template<typename ValueType>

value_t sigma::Interval< ValueType >::upper ( ) const

inline

Returns the upper bound of the interval.

Returns: The upper bound value

Exceptions

none	No throw guarantee

◆ operator!=()

template<typename T1, typename T2>

bool operator!=	(	const Interval< T1 > &	lhs,
		const Interval< T2 > &	rhs )

Compare two intervals for inequality.

Template Parameters

T1	The numerical type of the left-hand interval
T2	The numerical type of the right-hand interval

Parameters

lhs	The first interval
rhs	The second interval

Returns: Whether the instances are not equivalent

◆ operator*()

template<typename T>

Interval< T > operator*	(	Interval< T >	lhs,
		const Interval< T > &	rhs )

Multiplication of two intervals.

Template Parameters

T	The numerical type of the intervals

Parameters

lhs	The left-hand interval
rhs	The right-hand interval

Returns: A new interval that is the product of lhs and rhs

Exceptions

none	No throw guarantee

◆ operator+()

template<typename T>

Interval< T > operator+	(	Interval< T >	lhs,
		const Interval< T > &	rhs )

Addition of two intervals.

Template Parameters

T	The numerical type of the intervals

Parameters

lhs	The left-hand interval
rhs	The right-hand interval

Returns: A new interval that is the sum of lhs and rhs

Exceptions

none	No throw guarantee

◆ operator-() [1/2]

template<typename T>

Interval< T > operator- ( const Interval< T > & a )

Negation of an interval.

Template Parameters

T	The numerical type of the interval

Parameters

a	The interval to negate

Returns: A new interval with negated bounds

Exceptions

none	No throw guarantee

◆ operator-() [2/2]

template<typename T>

Interval< T > operator-	(	Interval< T >	lhs,
		const Interval< T > &	rhs )

Subtraction of two intervals.

Template Parameters

T	The numerical type of the intervals

Parameters

lhs	The left-hand interval
rhs	The right-hand interval

Returns: A new interval that is the difference of lhs and rhs

Exceptions

none	No throw guarantee

◆ operator/()

template<typename T>

Interval< T > operator/	(	Interval< T >	lhs,
		const Interval< T > &	rhs )

Division of two intervals.

If the interval contains zero the resulting interval will loose most of its information.

Template Parameters

T	The numerical type of the intervals

Parameters

lhs	The left-hand interval
rhs	The right-hand interval

Returns: A new interval that is the quotient of lhs and rhs

Exceptions

none	No throw guarantee

◆ operator<()

template<typename T1, typename T2>

bool operator<	(	const Interval< T1 > &	lhs,
		const Interval< T2 > &	rhs )

Whether one interval is certainly less than another.

Returns true only when lhs lies entirely below rhs, i.e. lhs.upper() < rhs.lower().

Template Parameters

T1	The numerical type of the left-hand interval
T2	The numerical type of the right-hand interval

Parameters

lhs	The first interval
rhs	The second interval

Returns: Whether lhs is certainly less than rhs

◆ operator<<()

template<typename ValueType>

std::ostream & operator<<	(	std::ostream &	os,
		const Interval< ValueType > &	i )

Overload stream insertion to print an interval.

Template Parameters

ValueType The numerical type of the bounds

Parameters

os	The ostream to write to
i	The interval to write

Returns: The modified ostream instance

Exceptions

std::ios_base::failure if anything goes wrong while writing. Weak throw guarantee.

◆ operator<=()

template<typename T1, typename T2>

bool operator<=	(	const Interval< T1 > &	lhs,
		const Interval< T2 > &	rhs )

Whether one interval is less than or equal to another.

Template Parameters

T1	The numerical type of the left-hand interval
T2	The numerical type of the right-hand interval

Parameters

lhs	The first interval
rhs	The second interval

Returns: Whether lhs is less than or equal to rhs

◆ operator==()

template<typename T1, typename T2>

bool operator==	(	const Interval< T1 > &	lhs,
		const Interval< T2 > &	rhs )

Compare two intervals for equality.

Template Parameters

T1	The numerical type of the left-hand interval
T2	The numerical type of the right-hand interval

Parameters

lhs	The first interval
rhs	The second interval

Returns: Whether the instances are equivalent

◆ operator>()

template<typename T1, typename T2>

bool operator>	(	const Interval< T1 > &	lhs,
		const Interval< T2 > &	rhs )

Whether one interval is greater than another.

Template Parameters

T1	The numerical type of the left-hand interval
T2	The numerical type of the right-hand interval

Parameters

lhs	The first interval
rhs	The second interval

Returns: Whether lhs is certainly greater than rhs

◆ operator>=()

template<typename T1, typename T2>

bool operator>=	(	const Interval< T1 > &	lhs,
		const Interval< T2 > &	rhs )

Whether one interval is greater than or equal to another.

Template Parameters

T1	The numerical type of the left-hand interval
T2	The numerical type of the right-hand interval

Parameters

lhs	The first interval
rhs	The second interval

Returns: Whether lhs is greater than or equal to rhs

The documentation for this class was generated from the following files:

include/sigma/eigen_compat.hpp
include/sigma/interval.hpp

Public Types

Public Member Functions

Related Symbols

Detailed Description

Constructor & Destructor Documentation

◆ Interval() [1/3]

◆ Interval() [2/3]

◆ Interval() [3/3]

Member Function Documentation

◆ contains()

◆ lower()

◆ median()

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/=() [1/2]

◆ operator/=() [2/2]

◆ radius()

◆ upper()

Friends And Related Symbol Documentation

◆ operator!=()

◆ operator*()

◆ operator+()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator/()

◆ operator<()

◆ operator<<()

◆ operator<=()

◆ operator==()

◆ operator>()

◆ operator>=()