# LevelSet¶

class LevelSet(*args)

Level set.

Available constructors:

LevelSet(dim=1)

LevelSet(function=ot.SymbolicFunction([‘x’], [‘1.0’]), level=0.0)

Parameters: dim : int, Dimension of the LevelSet. function : Function A function such that: defining the LevelSet. level : float Level defining the LevelSet.

Notes

A LevelSet is a Domain defined as follows:

Examples

>>> import openturns as ot
>>> function = ot.SymbolicFunction(['x1', 'x2'], ['x1^4 + x2^4'])
>>> s = 1.0
>>> levelSet = ot.LevelSet(function, s)

Attributes: thisown The membership flag

Methods

 contains(*args) Check if the given point is inside of the domain. getClassName() Accessor to the object’s name. getDimension() Get the dimension of the domain. getFunction() Get the function defining the level set. getId() Accessor to the object’s id. getLevel() Get the level defining the level set. getName() Accessor to the object’s name. getShadowedId() Accessor to the object’s shadowed id. getVisibility() Accessor to the object’s visibility state. hasName() Test if the object is named. hasVisibleName() Test if the object has a distinguishable name. intersect(other) Return the levelSet equals to the intersection between the LevelSet and another one. join(other) Return the levelSet equals to the union between the LevelSet and another one. setFunction(function) Set the function defining the level set. setLevel(level) Set the level defining the level set. setLowerBound(bound) Set the lower bound of the bounding box. setName(name) Accessor to the object’s name. setShadowedId(id) Accessor to the object’s shadowed id. setUpperBound(bound) Set the upper bound of the bounding box. setVisibility(visible) Accessor to the object’s visibility state.
 getLowerBound getUpperBound
__init__(*args)

Initialize self. See help(type(self)) for accurate signature.

contains(*args)

Check if the given point is inside of the domain.

Parameters: point : sequence of float Point with the same dimension as the current domain’s dimension. isInside : bool Flag telling whether the given point is inside of the domain.
getClassName()

Accessor to the object’s name.

Returns: class_name : str The object class name (object.__class__.__name__).
getDimension()

Get the dimension of the domain.

Returns: dim : int Dimension of the domain.
getFunction()

Get the function defining the level set.

Returns: function : Function A function such that: defining the LevelSet.

Examples

>>> import openturns as ot
>>> function = ot.SymbolicFunction(['x'], ['3*x-1'])
>>> levelSet = ot.LevelSet(function, 0.0)
>>> print(levelSet.getFunction().getEvaluation())
[x]->[3*x-1]

getId()

Accessor to the object’s id.

Returns: id : int Internal unique identifier.
getLevel()

Get the level defining the level set.

Returns: level : float Level defining the LevelSet.

Examples

>>> import openturns as ot
>>> function = ot.SymbolicFunction(['x'], ['3*x-1'])
>>> levelSet = ot.LevelSet(function, 0.0)
>>> print(levelSet.getLevel())
0.0

getName()

Accessor to the object’s name.

Returns: name : str The name of the object.
getShadowedId()

Accessor to the object’s shadowed id.

Returns: id : int Internal unique identifier.
getVisibility()

Accessor to the object’s visibility state.

Returns: visible : bool Visibility flag.
hasName()

Test if the object is named.

Returns: hasName : bool True if the name is not empty.
hasVisibleName()

Test if the object has a distinguishable name.

Returns: hasVisibleName : bool True if the name is not empty and not the default one.
intersect(other)

Return the levelSet equals to the intersection between the LevelSet and another one.

Parameters: otherLevelSet : A LevelSet defined by . levelSet : LevelSet levelSet equals to the intersection between the LevelSet and otherLevelSet i.e. levelSet is defined by: .

Examples

>>> import openturns as ot
>>> # First level set
>>> function = ot.SymbolicFunction(['x'], ['3*x-1'])
>>> levelSet1 = ot.LevelSet(function, 0.5)
>>> # Second level set
>>> function = ot.SymbolicFunction(['x'], ['x'])
>>> levelSet2 = ot.LevelSet(function, 0.5)
>>> # Intersection between levelSet1 and levelSet2
>>> intersection = levelSet1.intersect(levelSet2)
>>> # Tests
>>> print(intersection.contains([1.0]))
False
>>> print(intersection.contains([0.25]))
True

join(other)

Return the levelSet equals to the union between the LevelSet and another one.

Parameters: otherLevelSet : A LevelSet defined by . levelSet : LevelSet levelSet equals to the union between the LevelSet and otherLevelSet i.e. levelSet is defined by: .

Examples

>>> import openturns as ot
>>> # First level set
>>> function = ot.SymbolicFunction(['x'], ['3*x-1'])
>>> levelSet1 = ot.LevelSet(function, 0.0)
>>> # Second level set
>>> function = ot.SymbolicFunction(['x'], ['x'])
>>> levelSet2 = ot.LevelSet(function, 0.0)
>>> # Union between levelSet1 and levelSet2
>>> join = levelSet1.join(levelSet2)
>>> # Tests
>>> print(join.contains([0.5]))
False
>>> print(join.contains([0.25]))
True

setFunction(function)

Set the function defining the level set.

Parameters: function : Function A function such that: defining the LevelSet.

Examples

>>> import openturns as ot
>>> levelSet = ot.LevelSet()
>>> function = ot.SymbolicFunction(['x'], ['3*x-1'])
>>> levelSet.setFunction(function)

setLevel(level)

Set the level defining the level set.

Parameters: level : float Level defining the LevelSet.

Examples

>>> import openturns as ot
>>> levelSet = ot.LevelSet()
>>> levelSet.setLevel(3.0)

setLowerBound(bound)

Set the lower bound of the bounding box.

Parameters: bound : sequence of floats Lower bound of the bounding box of the level set. It allows to clip the level set.
setName(name)

Accessor to the object’s name.

Parameters: name : str The name of the object.
setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters: id : int Internal unique identifier.
setUpperBound(bound)

Set the upper bound of the bounding box.

Parameters: bound : sequence of floats Upper bound of the bounding box of the level set. It allows to clip the level set.
setVisibility(visible)

Accessor to the object’s visibility state.

Parameters: visible : bool Visibility flag.
thisown

The membership flag