Interval class

An Interval is defined by its minimum and maximum values, where min <= max.

This implementation offers basic interval arithmetic operations like addition, subtraction, multiplication and division. Operations always return a new interval and will not modify the existing ones. Additionally this class implementions comparison relations for intervals.

This implementation (partly) supports unbounded intervals with borders at +/- infinity and empty sets.

Operator and comparison definitions are based on: Bohlender, Gerd, and Ulrich Kulisch. 2010. "Definition of the Arithmetic Operations and Comparison Relations for an Interval Arithmetic Standard" (https://interval.louisiana.edu/reliable-computing-journal/volume-15/no-1/reliable-computing-15-pp-36-42.pdf). Reliable Computing 15 (1): 36–42.

Note: This implementation does not offer a complete set of operations yet:

  • No handling of unbounded intervals in operators.
  • No proper rounding.
Implemented types

Constructors

Interval(num min, num max)
Creates a new interval with given borders.
Interval.empty()
Returns an immutable empty set.
factory

Properties

hashCode → int
The hash code for this object.
no setteroverride
max ↔ num
Interval bounds.
getter/setter pair
min ↔ num
Interval bounds.
getter/setter pair
runtimeType → Type
A representation of the runtime type of the object.
no setterinherited

Methods

compareTo(Interval other) → int
Compares this object to another object.
override
contains(num element) → bool
Element-of relation. Returns true, if given element is included in this interval. Defined on a real number i and an interval:
containsZero() → bool
Returns true, if this interval contains zero (min <= 0 <= max).
glb(Interval i) → Interval
Returns the greatest lower bound.
includes(Interval i) → bool
Inclusion relation. Returns true, if the given interval is included in this interval.
isBound() → bool
Returns true, if neither min or max values are infinite.
isEmpty() → bool
Returns true, if this is the empty set.
isPositive() → bool
Returns true, if this interval is positive (min >= 0)
length() → num
Returns the length of this interval.
lub(Interval i) → Interval
Returns the least upper bound.
noSuchMethod(Invocation invocation) → dynamic
Invoked when a nonexistent method or property is accessed.
inherited
toString() → String
A string representation of this object.
override

Operators

operator *(Interval i) → Interval
Performs an interval multiplication.
operator +(Interval i) → Interval
Performs an interval addition.
operator -(Interval i) → Interval
Performs an interval subtraction.
operator /(Interval i) → Interval
Performs an interval division.
operator <(Interval i) → bool
Less than operator on intervals.
operator <=(Interval i) → bool
Less or equal than operator on intervals.
operator ==(Object i) → bool
Equals operator on intervals.
override
operator >(Interval i) → bool
Greater than operator on intervals.
operator >=(Interval i) → bool
Greater or equal than operator on intervals.
operator unary-() → Interval
Unary minus on intervals.