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, bool left_open=false, bool right_open=false)
	Construct an interval from two bounds.
value_t	width () const
	Returns the distance between the interval's bounds.
value_t	median () const
	Returns the midpoint of the interval.
value_t	radius () const
	Returns the half-width of the interval.
bool	empty () const
	Is *this the empty interval?
bool	left_open () const
	Is lower() NOT contained in the interval?
bool	left_closed () const
	Is lower() contained in the interval?
bool	right_open () const
	Is upper() NOT contained in the interval?
bool	right_closed () const
	Is upeer contained in the interval?
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.
bool	contains (const Interval &other) const
	Is `other` fully contained in this interval?
Interval	set_union (const Interval &other) const
	Returns the union of this interval and another interval.
Interval	set_intersection (const Interval &other) const
	Returns the intersection of this interval and another interval.
Interval	operator- () const
	Negation of an 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.
std::string	print_interval_form () const
	Print the interval in interval form.

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 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 empty interval (contains no values).

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,
		bool	left_open = false,
		bool	right_open = false )

Construct an interval from two bounds.

For convenience, the bounds are sorted so that lower() <= upper().

Parameters

lower	The lower bound of the interval
upper	The upper bound of the interval
left_open	Is `lower` just outside the interval?
right_open	Is `upper` just outside the interval?

Exceptions

none	No throw guarantee

Member Function Documentation

◆ contains()

template<typename ValueType>

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

Whether a scalar lies in this interval.

Returns true if lower() <= value <= upper(). Equality to lower()/ upper() is only allowed if lower_closed()/upper_closed() is true, respectively.

Parameters

value The scalar to test

Returns: True if value lies in the interval represented by *this and false otherwise.

Exceptions

none	No throw guarantee

◆ empty()

template<typename ValueType>

bool sigma::Interval< ValueType >::empty ( ) const

inline

Is *this the empty interval?

The empty interval contains no values.

Returns: True if *this is the empty interval, false otherwise.

Exceptions

none	No throw guarantee

◆ left_closed()

template<typename ValueType>

bool sigma::Interval< ValueType >::left_closed ( ) const

inline

Is lower() contained in the interval?

Returns: True if lower() is contained in the interval.

Exceptions

none	No throw guarantee.

◆ left_open()

template<typename ValueType>

bool sigma::Interval< ValueType >::left_open ( ) const

inline

Is lower() NOT contained in the interval?

Returns: True if lower() is NOT contained in the interval

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

std::domain_error if the interval is empty

◆ median()

template<typename ValueType>

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

inline

Returns the midpoint of the interval.

Returns: The midpoint value

Exceptions

std::domain_error if the interval is empty

◆ operator*=() [1/2]

template<typename ValueType>

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

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

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-()

template<typename ValueType>

Interval sigma::Interval< ValueType >::operator- ( ) const

inline

Negation of an interval.

Given the interval [a, b], the negation is [-b, -a]. The openness of the bounds is reversed, e.g., [a, b) becomes (-b, -a].

Returns: A new interval with negated bounds

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

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

◆ print_interval_form()

template<typename ValueType>

std::string sigma::Interval< ValueType >::print_interval_form ( ) const

Print the interval in interval form.

The interval is printed in the form where closed bounds are represented by square brackets and open bounds are represented by parentheses.

Returns: A string representation of the interval.

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. This is a convenience method for width() / value_t{2}

Returns: The half-width value

Exceptions

std::domain_error if the interval is empty

◆ right_closed()

template<typename ValueType>

bool sigma::Interval< ValueType >::right_closed ( ) const

inline

Is upeer contained in the interval?

Returns: True if upper() is contained in the interval.

Exceptions

none	No throw guarantee

◆ right_open()

template<typename ValueType>

bool sigma::Interval< ValueType >::right_open ( ) const

inline

Is upper() NOT contained in the interval?

Returns: True if upper() is NOT contained in the interval

Exceptions

none	No throw guarantee

◆ set_intersection()

template<typename ValueType>

Interval< ValueType > sigma::Interval< ValueType >::set_intersection ( const Interval< ValueType > & other ) const

Returns the intersection of this interval and another interval.

The intersection of two intervals is the largest interval that is contained in both intervals.

Parameters

other The interval to intersect with

Returns: The intersection of this interval and other

Exceptions

None	No throw guarantee.

◆ set_union()

template<typename ValueType>

Interval< ValueType > sigma::Interval< ValueType >::set_union ( const Interval< ValueType > & other ) const

Returns the union of this interval and another interval.

The union of two intervals is the smallest interval that contains both intervals. Because the result must be an interval, union is only defined when then the intervals overlap at least at one point.

Parameters

other The interval to union with

Returns: The union of this interval and other

Exceptions

std::domain_error if the intervals do not overlap. Strong 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

std::domain_error if the interval is empty

◆ width()

template<typename ValueType>

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

inline

Returns the distance between the interval's bounds.

The width of an interval is defined by |upper() - lower()|. The width does NOT depend on the openness of the interval. The width of an empty interval is undefined (and calling this member on an empty interval will cause a domain_error to be thrown)

Returns: The width of the interval

Exceptions

std::domain_error if the interval is empty

◆ 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-()

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 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 )

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

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

include/sigma/interval/eigen_compat.hpp
include/sigma/interval/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()

◆ empty()

◆ left_closed()

◆ left_open()

◆ lower()

◆ median()

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-()

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/=() [1/2]

◆ operator/=() [2/2]

◆ print_interval_form()

◆ radius()

◆ right_closed()

◆ right_open()

◆ set_intersection()

◆ set_union()

◆ upper()

◆ width()

Friends And Related Symbol Documentation

◆ operator!=()

◆ operator*()

◆ operator+()

◆ operator-()

◆ operator/()

◆ operator<<()

◆ operator==()