ostk.mathematics.object.RealInterval¶

class RealInterval( self: ostk.mathematics.object.RealInterval, lower_bound: ostk.core.type.Real, upper_bound: ostk.core.type.Real, type: ostk::mathematics::object::IntervalBase::Type, )¶

Bases: pybind11_object

Create an interval with specified bounds and type.

Parameters:

lower_bound (float) -- The lower bound of the interval.
upper_bound (float) -- The upper bound of the interval.
type (RealInterval.Type) -- The type of interval (Closed, Open, HalfOpenLeft, HalfOpenRight).

Example

>>> interval = RealInterval(0.0, 1.0, RealInterval.Type.Closed)  # [0, 1]
>>> interval = RealInterval(0.0, 1.0, RealInterval.Type.Open)    # (0, 1)

Methods

`clip`	Clip a list of intervals with a clipping interval.
`closed`	Create a closed interval [a, b].
`contains`	Overloaded function.
`get_gaps`	Find gaps between intervals in a list.
`get_intersection_with`	Get the intersection of this interval with another interval.
`get_lower_bound`	Get the lower bound of the interval.
`get_union_with`	Get the union of this interval with another interval.
`get_upper_bound`	Get the upper bound of the interval.
`half_open_left`	Create a half-open interval (a, b].
`half_open_right`	Create a half-open interval [a, b).
`intersects`	Check if this interval intersects with another interval.
`is_defined`	Check if the interval is defined.
`is_degenerate`	Check if the interval is degenerate (single point).
`logical_and`	Perform logical AND operation on two lists of intervals.
`logical_or`	Perform logical OR operation on two lists of intervals.
`merge`	Merge overlapping intervals in a list.
`open`	Create an open interval (a, b).
`sort`	Sort a list of intervals.
`to_string`	Convert the interval to a string representation.
`undefined`	Create an undefined interval.

class Type(self: ostk.mathematics.object.RealInterval.Type, value: int)¶

Bases: pybind11_object

Members:

Undefined

Closed

Open

HalfOpenLeft

HalfOpenRight

property name¶

static clip( intervals: list[ostk.mathematics.object.RealInterval], clipping_interval: ostk.mathematics.object.RealInterval, ) → list[ostk.mathematics.object.RealInterval]¶

Clip a list of intervals with a clipping interval.

Parameters:

intervals (list) -- List of intervals to clip.
clipping_interval (RealInterval) -- The interval to clip with.

Returns:

List of clipped intervals.

Return type:

list

Example

>>> intervals = [RealInterval.closed(0.0, 2.0), RealInterval.closed(3.0, 5.0)]
>>> clipping = RealInterval.closed(1.0, 4.0)
>>> clipped = RealInterval.clip(intervals, clipping)

static closed( lower_bound: ostk.core.type.Real, upper_bound: ostk.core.type.Real, ) → ostk.mathematics.object.RealInterval¶

Create a closed interval [a, b].

Parameters:

lower_bound (float) -- The lower bound (inclusive).
upper_bound (float) -- The upper bound (inclusive).

Returns:

A closed interval.

Return type:

RealInterval

Example

>>> interval = RealInterval.closed(0.0, 1.0)  # [0, 1]
>>> interval.contains(0.0)  # True
>>> interval.contains(1.0)  # True

contains(*args, **kwargs)¶

Overloaded function.

contains(self: ostk.mathematics.object.RealInterval, real: ostk.core.type.Real) -> bool
Check if the interval contains a real number.
Args:
real (float): The real number to check.

Returns:
bool: True if the interval contains the number, False otherwise.

Example:
>>> interval = RealInterval.closed(0.0, 1.0) >>> interval.contains(0.5) # True >>> interval.contains(1.5) # False
contains(self: ostk.mathematics.object.RealInterval, interval: ostk.mathematics.object.RealInterval) -> bool
Check if this interval contains another interval.
Args:
interval (RealInterval): The interval to check containment for.

Returns:
bool: True if this interval contains the other interval, False otherwise.

Example:
>>> interval1 = RealInterval.closed(0.0, 2.0) >>> interval2 = RealInterval.closed(0.5, 1.5) >>> interval1.contains(interval2) # True

static get_gaps( intervals: list[ostk.mathematics.object.RealInterval], bound: ostk.mathematics.object.RealInterval = RealInterval.undefined(), ) → list[ostk.mathematics.object.RealInterval]¶

Find gaps between intervals in a list.

Parameters:

intervals (list) -- List of intervals to find gaps between.
bound (RealInterval, optional) -- Bounding interval to consider gaps within. Defaults to undefined.

Returns:

List of intervals representing gaps.

Return type:

list

Example

>>> intervals = [RealInterval.closed(0.0, 1.0), RealInterval.closed(2.0, 3.0)]
>>> gaps = RealInterval.get_gaps(intervals)  # Gap from 1.0 to 2.0

get_intersection_with( self: ostk.mathematics.object.RealInterval, interval: ostk.mathematics.object.RealInterval, ) → ostk.mathematics.object.RealInterval¶

Get the intersection of this interval with another interval.

Parameters:: interval (RealInterval) -- The interval to intersect with.
Returns:: The intersection interval, or undefined if no intersection.
Return type:: RealInterval

Example

>>> interval1 = RealInterval.closed(0.0, 2.0)
>>> interval2 = RealInterval.closed(1.0, 3.0)
>>> intersection = interval1.get_intersection_with(interval2)
>>> # intersection represents [1.0, 2.0]

get_lower_bound( self: ostk.mathematics.object.RealInterval, ) → ostk.core.type.Real¶

Get the lower bound of the interval.

Returns:: The lower bound value.
Return type:: float

Example

>>> interval = RealInterval.closed(0.0, 1.0)
>>> interval.get_lower_bound()  # 0.0

get_union_with( self: ostk.mathematics.object.RealInterval, interval: ostk.mathematics.object.RealInterval, ) → ostk.mathematics.object.RealInterval¶

Get the union of this interval with another interval.

Parameters:: interval (RealInterval) -- The interval to union with.
Returns:: The union interval.
Return type:: RealInterval

Example

>>> interval1 = RealInterval.closed(0.0, 1.0)
>>> interval2 = RealInterval.closed(0.5, 2.0)
>>> union = interval1.get_union_with(interval2)
>>> # union represents [0.0, 2.0]

get_upper_bound( self: ostk.mathematics.object.RealInterval, ) → ostk.core.type.Real¶

Get the upper bound of the interval.

Returns:: The upper bound value.
Return type:: float

Example

>>> interval = RealInterval.closed(0.0, 1.0)
>>> interval.get_upper_bound()  # 1.0

static half_open_left( lower_bound: ostk.core.type.Real, upper_bound: ostk.core.type.Real, ) → ostk.mathematics.object.RealInterval¶

Create a half-open interval (a, b].

Parameters:

lower_bound (float) -- The lower bound (exclusive).
upper_bound (float) -- The upper bound (inclusive).

Returns:

A half-open left interval.

Return type:

RealInterval

Example

>>> interval = RealInterval.half_open_left(0.0, 1.0)  # (0, 1]
>>> interval.contains(0.0)  # False
>>> interval.contains(1.0)  # True

static half_open_right( lower_bound: ostk.core.type.Real, upper_bound: ostk.core.type.Real, ) → ostk.mathematics.object.RealInterval¶

Create a half-open interval [a, b).

Parameters:

lower_bound (float) -- The lower bound (inclusive).
upper_bound (float) -- The upper bound (exclusive).

Returns:

A half-open right interval.

Return type:

RealInterval

Example

>>> interval = RealInterval.half_open_right(0.0, 1.0)  # [0, 1)
>>> interval.contains(0.0)  # True
>>> interval.contains(1.0)  # False

intersects( self: ostk.mathematics.object.RealInterval, interval: ostk.mathematics.object.RealInterval, ) → bool¶

Check if this interval intersects with another interval.

Parameters:: interval (RealInterval) -- The interval to check intersection with.
Returns:: True if intervals intersect, False otherwise.
Return type:: bool

Example

>>> interval1 = RealInterval.closed(0.0, 2.0)
>>> interval2 = RealInterval.closed(1.0, 3.0)
>>> interval1.intersects(interval2)  # True

is_defined(self: ostk.mathematics.object.RealInterval) → bool¶

Check if the interval is defined.

Returns:: True if the interval is defined, False otherwise.
Return type:: bool

Example

>>> interval = RealInterval.closed(0.0, 1.0)
>>> interval.is_defined()  # True

is_degenerate(self: ostk.mathematics.object.RealInterval) → bool¶

Check if the interval is degenerate (single point).

Returns:: True if the interval represents a single point, False otherwise.
Return type:: bool

Example

>>> interval = RealInterval.closed(1.0, 1.0)
>>> interval.is_degenerate()  # True

static logical_and( intervals_1: list[ostk.mathematics.object.RealInterval], intervals_2: list[ostk.mathematics.object.RealInterval], ) → list[ostk.mathematics.object.RealInterval]¶

Perform logical AND operation on two lists of intervals.

Parameters:

intervals_1 (list) -- First list of intervals.
intervals_2 (list) -- Second list of intervals.

Returns:

List of intervals representing the intersection of both lists.

Return type:

list

Example

>>> intervals1 = [RealInterval.closed(0.0, 2.0)]
>>> intervals2 = [RealInterval.closed(1.0, 3.0)]
>>> result = RealInterval.logical_and(intervals1, intervals2)  # [1.0, 2.0]

static logical_or( intervals_1: list[ostk.mathematics.object.RealInterval], intervals_2: list[ostk.mathematics.object.RealInterval], ) → list[ostk.mathematics.object.RealInterval]¶

Perform logical OR operation on two lists of intervals.

Parameters:

intervals_1 (list) -- First list of intervals.
intervals_2 (list) -- Second list of intervals.

Returns:

List of intervals representing the union of both lists.

Return type:

list

Example

>>> intervals1 = [RealInterval.closed(0.0, 1.0)]
>>> intervals2 = [RealInterval.closed(2.0, 3.0)]
>>> result = RealInterval.logical_or(intervals1, intervals2)

static merge( intervals: list[ostk.mathematics.object.RealInterval], ) → list[ostk.mathematics.object.RealInterval]¶

Merge overlapping intervals in a list.

Parameters:: intervals (list) -- List of intervals to merge.
Returns:: List of merged intervals with no overlaps.
Return type:: list

Example

>>> intervals = [RealInterval.closed(0.0, 2.0), RealInterval.closed(1.0, 3.0)]
>>> merged = RealInterval.merge(intervals)  # [RealInterval.closed(0.0, 3.0)]

static open( lower_bound: ostk.core.type.Real, upper_bound: ostk.core.type.Real, ) → ostk.mathematics.object.RealInterval¶

Create an open interval (a, b).

Parameters:

lower_bound (float) -- The lower bound (exclusive).
upper_bound (float) -- The upper bound (exclusive).

Returns:

An open interval.

Return type:

RealInterval

Example

>>> interval = RealInterval.open(0.0, 1.0)  # (0, 1)
>>> interval.contains(0.0)  # False
>>> interval.contains(1.0)  # False
>>> interval.contains(0.5)  # True

static sort( intervals: list[ostk.mathematics.object.RealInterval], by_lower_bound: bool = True, ascending: bool = True, ) → list[ostk.mathematics.object.RealInterval]¶

Sort a list of intervals.

Parameters:

intervals (list) -- List of intervals to sort.
by_lower_bound (bool, optional) -- Sort by lower bound if True, upper bound if False. Defaults to True.
ascending (bool, optional) -- Sort in ascending order if True, descending if False. Defaults to True.

Returns:

Sorted list of intervals.

Return type:

list

Example

>>> intervals = [RealInterval.closed(2.0, 3.0), RealInterval.closed(0.0, 1.0)]
>>> sorted_intervals = RealInterval.sort(intervals)

to_string( self: ostk.mathematics.object.RealInterval, ) → ostk.core.type.String¶

Convert the interval to a string representation.

Returns:: String representation of the interval.
Return type:: str

Example

>>> interval = RealInterval.closed(0.0, 1.0)
>>> interval.to_string()  # "[0, 1]"

static undefined() → ostk.mathematics.object.RealInterval¶

Create an undefined interval.

Returns:: An undefined interval.
Return type:: RealInterval

Example

>>> undefined_interval = RealInterval.undefined()
>>> undefined_interval.is_defined()  # False