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

`computeDistance`(*args)	Compute the Euclidean distance of a given point to the domain.
`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.
`getLowerBound`()	Get the lower bound of the bounding box.
`getName`()	Accessor to the object's name.
`getOperator`()	Operator accessor.
`getShadowedId`()	Accessor to the object's shadowed id.
`getUpperBound`()	Get the upper bound of the bounding box.
`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.
`setOperator`(op)	Operator accessor.
`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.

__init__(*args)¶

computeDistance(*args)¶

Compute the Euclidean distance of a given point to the domain.

Parameters:

point or samplesequence of float or 2-d sequence of float: Point or Sample with the same dimension as the current domain’s dimension.

Returns:

distancefloat or Sample: Euclidean distance of the point to the domain.

contains(*args)¶

Check if the given point is inside of the domain.

Parameters:

point or samplesequence of float or 2-d sequence of float: Point or Sample with the same dimension as the current domain’s dimension.

Returns:

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

getClassName()¶

Accessor to the object’s name.

Returns:

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

getDimension()¶

Get the dimension of the domain.

Returns:

dimint: Dimension of the domain.

getFunction()¶

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()¶

Accessor to the object’s id.

Returns:

idint: Internal unique identifier.

getLevel()¶

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()¶

Get the lower bound of the bounding box.

Returns:

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

getName()¶

Accessor to the object’s name.

Returns:

namestr: The name of the object.

getOperator()¶

Operator accessor.

Returns:

opComparisonOperator: Comparison operator against the level.

getShadowedId()¶

Accessor to the object’s shadowed id.

Returns:

idint: Internal unique identifier.

getUpperBound()¶

Get the upper bound of the bounding box.

Returns:

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

getVisibility()¶

Accessor to the object’s visibility state.

Returns:

visiblebool: Visibility flag.

hasName()¶

Test if the object is named.

Returns:

hasNamebool: True if the name is not empty.

hasVisibleName()¶

Test if the object has a distinguishable name.

Returns:

hasVisibleNamebool: 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 $(f_2, s_2)$ .

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(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(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(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(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 one to clip the level set.

setName(name)¶

Accessor to the object’s name.

Parameters:

namestr: The name of the object.

setOperator(op)¶

Operator accessor.

Parameters:

opComparisonOperator: Comparison operator against the level.

setShadowedId(id)¶

Accessor to the object’s shadowed id.

Parameters:

idint: Internal unique identifier.

setUpperBound(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 one to clip the level set.

setVisibility(visible)¶

Accessor to the object’s visibility state.

Parameters:

visiblebool: Visibility flag.

Examples using the class¶

Draw minimum volume level sets

OpenTURNS

An Open source initiative for the Treatment of Uncertainties, Risks'N Statistics

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LevelSet¶

Examples using the class¶