LevelSet¶
- class LevelSet(*args)¶
Level set.
- Parameters:
- function
Function
A function such that: defining the LevelSet.
- operator
ComparisonOperator
, optional Comparison operator against the level. The default value is
LessOrEqual
.- levelfloat, optional
Level defining the LevelSet. The default value is 0.0.
- function
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 >>> 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.
Accessor to the object's name.
Get the dimension of the domain.
Get the function defining the level set.
getLevel
()Get the level defining the level set.
Get the lower bound of the bounding box.
getName
()Accessor to the object's name.
Operator accessor.
Get the upper bound of the bounding box.
hasName
()Test if the object is named.
intersect
(other)Return the intersection with another LevelSet.
join
(other)Return the union with another LevelSet.
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.
setUpperBound
(bound)Set the upper bound of the bounding box.
- __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:
- function
Function
A function such that: defining the LevelSet.
- function
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]
- getLevel()¶
Get the level defining the level set.
- Returns:
- levelfloat
Level 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:
- bound
Point
Lower bound of the bounding box of the level set. It allows one to clip the level set.
- bound
- getName()¶
Accessor to the object’s name.
- Returns:
- namestr
The name of the object.
- getOperator()¶
Operator accessor.
- Returns:
- op
ComparisonOperator
Comparison operator against the level.
- op
- getUpperBound()¶
Get the upper bound of the bounding box.
- Returns:
- bound
Point
Upper bound of the bounding box of the level set. It allows one to clip the level set.
- bound
- hasName()¶
Test if the object is named.
- Returns:
- hasNamebool
True if the name is not empty.
- intersect(other)¶
Return the intersection with another LevelSet.
- Parameters:
- other
LevelSet
A LevelSet defined by .
- other
- Returns:
- levelSet
LevelSet
The intersection between this LevelSet and the LevelSet other, i.e. the LevelSet defined as: .
- levelSet
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 union with another LevelSet.
- Parameters:
- other
LevelSet
A LevelSet defined by .
- other
- Returns:
- levelSet
LevelSet
The union between this LevelSet and the LevelSet other, i.e. the LevelSet defined as: .
- levelSet
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 >>> union = levelSet1.join(levelSet2) >>> # Tests >>> print([0.5] in union) False >>> print([0.25] in union) True
- setFunction(function)¶
Set the function defining the level set.
- Parameters:
- function
Function
A function such that: defining the LevelSet.
- function
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 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:
- op
ComparisonOperator
Comparison operator against the level.
- op
- 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.
Examples using the class¶
Draw minimum volume level sets