Interval¶
- class Interval(*args)¶
Numerical interval.
- Available constructors:
Interval(dim=0)
Interval(lowerBound, upperBound, finiteLowerBound=[True]*dim, finiteUpperBound=[True]*dim)
- Parameters:
- dimint,
Dimension of the interval. If only dim is mentioned, it leads to create the finite interval . By default, an empty interval is created.
- lowerBound, upperBoundfloat or sequence of float of dimension dim
Define an interval . It is allowed to have for some : it simply defines an empty interval. The lowerBound and the upperBound must be of the same type. If finiteLowerBound and finiteUpperBound are mentioned, they must be sequences.
- finiteLowerBoundsequence of bool of dimension dim
Flags telling for each component of the lower bound whether it is finite or not.
- finiteUpperBoundsequence of bool of dimension dim
Flags telling for each component of the upper bound whether it is finite or not.
Notes
The meaning of a flag is: if flag is True, the corresponding component of the given bound is finite and its value is given by bound . If not, the corresponding component is infinite and its value is either if bound or if bound .
It is possible to add or subtract two intervals and multiply an interval by a scalar.
Examples
>>> import openturns as ot >>> # A finite interval >>> print(ot.Interval([2.0, 3.0], [4.0, 5.0])) [2, 4] [3, 5] >>> # Not finite intervals >>> a = 2.0 >>> print(ot.Interval([a], [1], [True], [False])) [2, (1) +inf[ >>> print(ot.Interval([1], [a], [False], [True])) ]-inf (1), 2] >>> # Operations with intervals: >>> interval1 = ot.Interval([2.0, 3.0], [5.0, 8.0]) >>> interval2 = ot.Interval([1.0, 4.0], [6.0, 13.0]) >>> # Addition >>> print(interval1 + interval2) [3, 11] [7, 21] >>> # Subtraction >>> print(interval1 - interval2) [-4, 4] [-10, 4] >>> # Multiplication >>> print(interval1 * 3) [6, 15] [9, 24]
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.
Tell for each component of the lower bound whether it is finite or not.
Tell for each component of the upper bound whether it is finite or not.
getId
()Accessor to the object's id.
Get the lower bound.
getMarginal
(*args)Marginal accessor.
getName
()Accessor to the object's name.
Accessor to the object's shadowed id.
Get the upper bound.
Accessor to the object's visibility state.
Get the volume of the interval.
hasName
()Test if the object is named.
Test if the object has a distinguishable name.
intersect
(other)Get the intersection with another interval.
isEmpty
()Check if the interval is empty.
Check if the interval is numerically empty.
join
(other)Get the smallest interval containing both the current interval and another one.
numericallyContains
(point)Check if the given point is inside of the discretization of the interval.
setFiniteLowerBound
(finiteLowerBound)Tell for each component of the lower bound whether it is finite or not.
setFiniteUpperBound
(finiteUpperBound)Tell for each component of the upper bound whether it is finite or not.
setLowerBound
(lowerBound)Set the lower bound.
setName
(name)Accessor to the object's name.
setShadowedId
(id)Accessor to the object's shadowed id.
setUpperBound
(upperBound)Set the upper bound.
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.
- getFiniteLowerBound()¶
Tell for each component of the lower bound whether it is finite or not.
- Returns:
- flags
BoolCollection
If the element is False, the corresponding component of the lower bound is infinite. Otherwise, it is finite.
- flags
Examples
>>> import openturns as ot >>> interval = ot.Interval([2.0, 3.0], [4.0, 5.0], [True, False], [True, True]) >>> print(interval.getFiniteLowerBound()) [1,0]
- getFiniteUpperBound()¶
Tell for each component of the upper bound whether it is finite or not.
- Returns:
- flags
BoolCollection
If the element is False, the corresponding component of the upper bound is infinite. Otherwise, it is finite.
- flags
Examples
>>> import openturns as ot >>> interval = ot.Interval([2.0, 3.0], [4.0, 5.0], [True, False], [True, True]) >>> print(interval.getFiniteUpperBound()) [1,1]
- getId()¶
Accessor to the object’s id.
- Returns:
- idint
Internal unique identifier.
- getLowerBound()¶
Get the lower bound.
- Returns:
- lowerBound
Point
Value of the lower bound.
- lowerBound
Examples
>>> import openturns as ot >>> interval = ot.Interval([2.0, 3.0], [4.0, 5.0], [True, False], [True, True]) >>> print(interval.getLowerBound()) [2,3]
- getMarginal(*args)¶
Marginal accessor.
- Parameters:
- indexint or sequence of int
Index or indices of the selected components.
- Returns:
- interval
Interval
The marginal interval.
- interval
- getName()¶
Accessor to the object’s name.
- Returns:
- namestr
The name of the object.
- getShadowedId()¶
Accessor to the object’s shadowed id.
- Returns:
- idint
Internal unique identifier.
- getUpperBound()¶
Get the upper bound.
- Returns:
- upperBound
Point
Value of the upper bound.
- upperBound
Examples
>>> import openturns as ot >>> interval = ot.Interval([2.0, 3.0], [4.0, 5.0], [True, False], [True, True]) >>> print(interval.getUpperBound()) [4,5]
- getVisibility()¶
Accessor to the object’s visibility state.
- Returns:
- visiblebool
Visibility flag.
- getVolume()¶
Get the volume of the interval.
- Returns:
- volumefloat
Volume contained within interval bounds.
Examples
>>> import openturns as ot >>> interval = ot.Interval([2.0, 3.0], [4.0, 5.0], [True, False], [True, True]) >>> print(interval.getVolume()) 4.0
- 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)¶
Get the intersection with another interval.
- Parameters:
- otherInterval
Interval
Interval of the same dimension.
- otherInterval
- Returns:
- interval
Interval
An interval corresponding to the intersection of the current interval with otherInterval.
- interval
Examples
>>> import openturns as ot >>> interval1 = ot.Interval([2.0, 3.0], [5.0, 8.0]) >>> interval2 = ot.Interval([1.0, 4.0], [6.0, 13.0]) >>> print(interval1.intersect(interval2)) [2, 5] [4, 8]
- isEmpty()¶
Check if the interval is empty.
- Returns:
- isEmptybool
True if the interior of the interval is empty.
Examples
>>> import openturns as ot >>> interval = ot.Interval([1.0, 2.0], [1.0, 2.0]) >>> interval.setFiniteLowerBound([True, False]) >>> print(interval.isEmpty()) False
- isNumericallyEmpty()¶
Check if the interval is numerically empty.
- Returns:
- isEmptybool
Flag telling whether the interval is numerically empty, i.e. if its numerical volume is inferior or equal to (defined in the
ResourceMap
: = Domain-SmallVolume).
Examples
>>> import openturns as ot >>> interval = ot.Interval([1.0, 2.0], [1.0, 2.0]) >>> print(interval.isNumericallyEmpty()) True
- join(other)¶
Get the smallest interval containing both the current interval and another one.
- Parameters:
- otherInterval
Interval
Interval of the same dimension.
- otherInterval
- Returns:
- interval
Interval
Smallest interval containing both the current interval and otherInterval.
- interval
Examples
>>> import openturns as ot >>> interval1 = ot.Interval([2.0, 3.0], [5.0, 8.0]) >>> interval2 = ot.Interval([1.0, 4.0], [6.0, 13.0]) >>> print(interval1.join(interval2)) [1, 6] [3, 13]
- numericallyContains(point)¶
Check if the given point is inside of the discretization of the interval.
- Parameters:
- pointsequence of float
Point with the same dimension as the current domain’s dimension.
- Returns:
- isInsidebool
Flag telling whether the point is inside the interval bounds, not taking into account whether bounds are finite or not.
- setFiniteLowerBound(finiteLowerBound)¶
Tell for each component of the lower bound whether it is finite or not.
- Parameters:
- flagssequence of bool
If the element is False, the corresponding component of the lower bound is infinite. Otherwise, it is finite.
Examples
>>> import openturns as ot >>> interval = ot.Interval(2) >>> interval.setFiniteLowerBound([True, False]) >>> print(interval) [0, 1] ]-inf (0), 1]
- setFiniteUpperBound(finiteUpperBound)¶
Tell for each component of the upper bound whether it is finite or not.
- Parameters:
- flagssequence of bool
If the element is False, the corresponding component of the upper bound is infinite. Otherwise, it is finite.
Examples
>>> import openturns as ot >>> interval = ot.Interval(2) >>> interval.setFiniteUpperBound([True, False]) >>> print(interval) [0, 1] [0, (1) +inf[
- setLowerBound(lowerBound)¶
Set the lower bound.
- Parameters:
- lowerBoundsequence of float
Value of the lower bound.
Examples
>>> import openturns as ot >>> interval = ot.Interval(2) >>> interval.setLowerBound([-4, -5]) >>> print(interval) [-4, 1] [-5, 1]
- setName(name)¶
Accessor to the object’s name.
- Parameters:
- namestr
The name of the object.
- setShadowedId(id)¶
Accessor to the object’s shadowed id.
- Parameters:
- idint
Internal unique identifier.
- setUpperBound(upperBound)¶
Set the upper bound.
- Parameters:
- upperBoundsequence of float
Value of the upper bound.
Examples
>>> import openturns as ot >>> interval = ot.Interval(2) >>> interval.setUpperBound([4, 5]) >>> print(interval) [0, 4] [0, 5]
- setVisibility(visible)¶
Accessor to the object’s visibility state.
- Parameters:
- visiblebool
Visibility flag.
Examples using the class¶
Compute squared SRC indices confidence intervals
Fit a distribution by maximum likelihood
Model a singular multivariate distribution
Estimate a GEV on the Venice sea-levels data
Bandwidth sensitivity in kernel smoothing
Fitting a distribution with customized maximum likelihood
Estimate a GEV on the Port Pirie sea-levels data
Estimate a GEV on the Fremantle sea-levels data
Estimate a GEV on race times data
Overview of univariate distribution management
Create a customized distribution or copula
Draw minimum volume level sets
Create a custom covariance model
Use the Box-Cox transformation
Create a process from random vectors and processes
Compute Sobol’ indices confidence intervals
Kriging : cantilever beam model
Kriging the cantilever beam model using HMAT
Example of multi output Kriging on the fire satellite model
Kriging: choose a polynomial trend on the beam model
Kriging with an isotropic covariance function
Kriging :configure the optimization solver
Kriging: metamodel with continuous and categorical variables
Validation of a Karhunen-Loeve decomposition
Viscous free fall: metamodel of a field function
Use the FORM algorithm in case of several design points
An illustrated example of a FORM probability estimate
Cross Entropy Importance Sampling
Create an event based on a process
Estimate a process-based event probability
The HSIC sensitivity indices: the Ishigami model
Various design of experiments in OpenTURNS
Define a function with a field output: the viscous free fall example
Define a connection function with a field output
Calibration of the Chaboche mechanical model
Sampling from an unnormalized probability density
Posterior sampling using a PythonDistribution
Customize your Metropolis-Hastings algorithm
Linear Regression with interval-censored observations
Mix/max search using optimization
Multi-objective optimization using Pagmo
Quick start guide to optimization
Optimization of the Rastrigin test function
EfficientGlobalOptimization examples