LevelSet¶

class LevelSet(*args)¶

Level set.

Available constructors:

LevelSet(dim=1)

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

Parameters

dimint, $dim \geq 0$: Dimension of the LevelSet.
functionFunction: A function such that: $f: \Rset^{dim} \mapsto \Rset$ defining the LevelSet.
operatorComparisonOperator: Comparison operator against the level.
levelfloat: Level $s$ defining the LevelSet.

Notes

A LevelSet is a Domain defined as follows:

$\{ \vect{x} \in \Rset^{dim} \, | \, f(\vect{x}) \leq s \}$

Examples

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

Methods

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

__init__(self, \*args)¶: Initialize self. See help(type(self)) for accurate signature.

contains(self, \*args)¶

Check if the given point is inside of the domain.

Parameters

pointsequence of float: Point with the same dimension as the current domain’s dimension.

Returns

isInsidebool: Flag telling whether the given point is inside of the domain.

getClassName(self)¶

Accessor to the object’s name.

Returns

class_namestr: The object class name (object.__class__.__name__).

getDimension(self)¶

Get the dimension of the domain.

Returns

dimint: Dimension of the domain.

getFunction(self)¶

Get the function defining the level set.

Returns

functionFunction: A function such that: $f: \Rset^{dim} \mapsto \Rset$ defining the LevelSet.

Examples

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

getId(self)¶

Accessor to the object’s id.

Returns

idint: Internal unique identifier.

getLevel(self)¶

Get the level defining the level set.

Returns

levelfloat: Level $s$ defining the LevelSet.

Examples

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

getLowerBound(self)¶

Get the lower bound of the bounding box.

Returns

boundPoint: Lower bound of the bounding box of the level set. It allows to clip the level set.

getName(self)¶

Accessor to the object’s name.

Returns

namestr: The name of the object.

getOperator(self)¶

Operator accessor.

Returns

opComparisonOperator: Comparison operator against the level.

getShadowedId(self)¶

Accessor to the object’s shadowed id.

Returns

idint: Internal unique identifier.

getUpperBound(self)¶

Get the upper bound of the bounding box.

Returns

boundPoint: Upper bound of the bounding box of the level set. It allows to clip the level set.

getVisibility(self)¶

Accessor to the object’s visibility state.

Returns

visiblebool: Visibility flag.

hasName(self)¶

Test if the object is named.

Returns

hasNamebool: True if the name is not empty.

hasVisibleName(self)¶

Test if the object has a distinguishable name.

Returns

hasVisibleNamebool: True if the name is not empty and not the default one.

intersect(self, other)¶

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

Parameters

otherLevelSet :: A LevelSet defined by $(f_2, s_2)$ .

Returns

levelSetLevelSet: levelSet equals to the intersection between the LevelSet and otherLevelSet i.e. levelSet is defined by: $\{\vect{x} \in \Rset^{dim} | f(\vect{x}) \leq s \, \mbox{and} \, f_2(\vect{x}) \leq s_2\}$ .

Examples

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

join(self, other)¶

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

Parameters

otherLevelSet :: A LevelSet defined by $(f_2, s_2)$ .

Returns

levelSetLevelSet: levelSet equals to the union between the LevelSet and otherLevelSet i.e. levelSet is defined by: $\{\vect{x} \in \Rset^{dim} | f(\vect{x}) \leq s \, \mbox{or} \, f_2(\vect{x}) \leq s_2\}$ .

Examples

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

setFunction(self, function)¶

Set the function defining the level set.

Parameters

functionFunction: A function such that: $f: \Rset^{dim} \mapsto \Rset$ defining the LevelSet.

Examples

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

setLevel(self, level)¶

Set the level defining the level set.

Parameters

levelfloat: Level $s$ defining the LevelSet.

Examples

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

setLowerBound(self, bound)¶

Set the lower bound of the bounding box.

Parameters

boundsequence of floats: Lower bound of the bounding box of the level set. It allows to clip the level set.

setName(self, name)¶

Accessor to the object’s name.

Parameters

namestr: The name of the object.

setOperator(self, op)¶

Operator accessor.

Parameters

opComparisonOperator: Comparison operator against the level.

setShadowedId(self, id)¶

Accessor to the object’s shadowed id.

Parameters

idint: Internal unique identifier.

setUpperBound(self, bound)¶

Set the upper bound of the bounding box.

Parameters

boundsequence of floats: Upper bound of the bounding box of the level set. It allows to clip the level set.

setVisibility(self, visible)¶

Accessor to the object’s visibility state.

Parameters

visiblebool: Visibility flag.

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