Point¶
- class Point(*args)¶
Real vector.
- Parameters:
- dimensionint, , optional
The number of components.
- valuefloat, optional
The components value. Default creates a null vector.
Examples
Create a Point
>>> import openturns as ot >>> x = ot.Point(3, 1.0) >>> x class=Point name=Unnamed dimension=3 values=[1,1,1]
Get or set terms
>>> print(x[0]) 1.0 >>> x[0] = 0.0 >>> print(x[0]) 0.0 >>> print(x[:2]) [0,1]
Create a Point from a flat (1d) array, list or tuple
>>> import numpy as np >>> y = ot.Point((0.0, 1.0, 2.0)) >>> y = ot.Point(range(3)) >>> y = ot.Point(np.arange(3))
and back
>>> z = np.array(y)
Addition, subtraction (with compatible dimensions)
>>> print(x + y) [0,2,3] >>> print(x - y) [0,0,-1]
Multiplication, division with a scalar
>>> print(x * 3.0) [0,3,3] >>> print(x / 3.0) [0,0.333333,0.333333]
Methods
add
(*args)Append a component (in-place).
at
(*args)Access to an element of the collection.
clear
()Reset the collection to zero dimension.
dot
(rhs)Compute the scalar product.
find
(val)Find the index of a given value.
Accessor to the object's name.
Accessor to the vector's dimension.
getId
()Accessor to the object's id.
getName
()Accessor to the object's name.
Accessor to the object's shadowed id.
getSize
()Accessor to the vector's dimension (or size).
Accessor to the object's visibility state.
hasName
()Test if the object is named.
Test if the object has a distinguishable name.
Check if the components are in decreasing order.
isEmpty
()Tell if the collection is empty.
Check if the components are in increasing order.
Check if the components are in nonincreasing or nondecreasing order.
Check if the components are in nondecreasing order.
Check if the components are in nonincreasing order.
norm
()Compute the Euclidean () norm.
norm1
()Compute the norm.
normInf
()Compute the norm.
Compute the squared Euclidean norm.
Compute the normalized vector with respect to its Euclidean norm.
Compute the normalized vector with respect to its squared Euclidean norm.
resize
(newSize)Change the size of the collection.
select
(marginalIndices)Selection from indices.
setName
(name)Accessor to the object's name.
setShadowedId
(id)Accessor to the object's shadowed id.
setVisibility
(visible)Accessor to the object's visibility state.
clean
- __init__(*args)¶
- add(*args)¶
Append a component (in-place).
- Parameters:
- valuetype depends on the type of the collection.
The component to append.
Examples
>>> import openturns as ot >>> x = ot.Point(2) >>> x.add(1.) >>> print(x) [0,0,1]
- at(*args)¶
Access to an element of the collection.
- Parameters:
- indexpositive int
Position of the element to access.
- Returns:
- elementtype depends on the type of the collection
Element of the collection at the position index.
- clear()¶
Reset the collection to zero dimension.
Examples
>>> import openturns as ot >>> x = ot.Point(2) >>> x.clear() >>> x class=Point name=Unnamed dimension=0 values=[]
- dot(rhs)¶
Compute the scalar product.
- Parameters:
- pointsequence of float
Scalar product second argument
- Returns:
- dotfloat
Scalar product
Examples
>>> import openturns as ot >>> x = ot.Point([1.0, 2.0, 3.0]) >>> prod = x.dot([4, 5, 6])
- find(val)¶
Find the index of a given value.
- Parameters:
- valcollection value type
The value to find
- Returns:
- indexint
The index of the first occurrence of the value, or the size of the container if not found. When several values match, only the first index is returned.
- getClassName()¶
Accessor to the object’s name.
- Returns:
- class_namestr
The object class name (object.__class__.__name__).
- getDimension()¶
Accessor to the vector’s dimension.
- Returns:
- nint
The number of components in the vector.
- getId()¶
Accessor to the object’s id.
- Returns:
- idint
Internal unique identifier.
- 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.
- getSize()¶
Accessor to the vector’s dimension (or size).
- Returns:
- nint
The number of components in the vector.
- 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.
- isDecreasing()¶
Check if the components are in decreasing order.
Examples
>>> import openturns as ot >>> x = ot.Point([3.0, 2.0, 1.0]) >>> x.isDecreasing() True >>> x = ot.Point([3.0, 3.0, 1.0]) >>> x.isDecreasing() False >>> x = ot.Point([1.0, 3.0, 2.0]) >>> x.isIncreasing() False
- isEmpty()¶
Tell if the collection is empty.
- Returns:
- isEmptybool
True if there is no element in the collection.
Examples
>>> import openturns as ot >>> x = ot.Point(2) >>> x.isEmpty() False >>> x.clear() >>> x.isEmpty() True
- isIncreasing()¶
Check if the components are in increasing order.
Examples
>>> import openturns as ot >>> x = ot.Point([1.0, 2.0, 3.0]) >>> x.isIncreasing() True >>> x = ot.Point([1.0, 1.0, 3.0]) >>> x.isIncreasing() False >>> x = ot.Point([1.0, 3.0, 2.0]) >>> x.isIncreasing() False
- isMonotonic()¶
Check if the components are in nonincreasing or nondecreasing order.
Examples
>>> import openturns as ot >>> x = ot.Point([1.0, 2.0, 3.0]) >>> x.isMonotonic() True >>> x = ot.Point([2.0, 2.0, 1.0]) >>> x.isMonotonic() True >>> x = ot.Point([1.0, 3.0, 2.0]) >>> x.isMonotonic() False
- isNonDecreasing()¶
Check if the components are in nondecreasing order.
Examples
>>> import openturns as ot >>> x = ot.Point([1.0, 2.0, 3.0]) >>> x.isNonDecreasing() True >>> x = ot.Point([1.0, 1.0, 3.0]) >>> x.isNonDecreasing() True >>> x = ot.Point([1.0, 3.0, 2.0]) >>> x.isNonDecreasing() False
- isNonIncreasing()¶
Check if the components are in nonincreasing order.
Examples
>>> import openturns as ot >>> x = ot.Point([3.0, 2.0, 1.0]) >>> x.isNonIncreasing() True >>> x = ot.Point([3.0, 3.0, 1.0]) >>> x.isNonIncreasing() True >>> x = ot.Point([1.0, 3.0, 2.0]) >>> x.isNonIncreasing() False
- norm()¶
Compute the Euclidean () norm.
The Euclidean () norm of a vector is defined as:
- Returns:
- normfloat
The vector’s Euclidean norm.
Examples
>>> import openturns as ot >>> x = ot.Point([1.0, 2.0, 3.0]) >>> x.norm() 3.741657...
- norm1()¶
Compute the norm.
The norm of a vector is defined as:
- Returns:
- normfloat
The vector’s norm.
Examples
>>> import openturns as ot >>> x = ot.Point([1.0, 2.0, 3.0]) >>> x.norm1() 6.0
- normInf()¶
Compute the norm.
The norm of a vector is defined as:
- Returns:
- normfloat
The vector’s norm.
Examples
>>> import openturns as ot >>> x = ot.Point([1.0, 2.0, 3.0]) >>> x.normInf() 3.0
- normSquare()¶
Compute the squared Euclidean norm.
- Returns:
- normfloat
The vector’s squared Euclidean norm.
See also
Examples
>>> import openturns as ot >>> x = ot.Point([1.0, 2.0, 3.0]) >>> x.normSquare() 14.0
- normalize()¶
Compute the normalized vector with respect to its Euclidean norm.
- Returns:
- normalized_vector
Point
The normalized vector with respect to its Euclidean norm.
- normalized_vector
- Raises:
- RuntimeErrorIf the Euclidean norm is zero.
See also
Examples
>>> import openturns as ot >>> x = ot.Point([1.0, 2.0, 3.0]) >>> print(x.normalize()) [0.267261,0.534522,0.801784]
- normalizeSquare()¶
Compute the normalized vector with respect to its squared Euclidean norm.
- Returns:
- normalized_vectornormalized_vector
Point
The normalized vector with respect to its squared Euclidean norm.
- normalized_vectornormalized_vector
- Raises:
- RuntimeErrorIf the squared Euclidean norm is zero.
See also
Examples
>>> import openturns as ot >>> x = ot.Point([1.0, 2.0, 3.0]) >>> print(x.normalizeSquare()) [0.0714286,0.285714,0.642857]
- resize(newSize)¶
Change the size of the collection.
- Parameters:
- newSizepositive int
New size of the collection.
Notes
If the new size is smaller than the older one, the last elements are thrown away, else the new elements are set to the default value of the element type.
Examples
>>> import openturns as ot >>> x = ot.Point(2, 4) >>> print(x) [4,4] >>> x.resize(1) >>> print(x) [4] >>> x.resize(4) >>> print(x) [4,0,0,0]
- select(marginalIndices)¶
Selection from indices.
- Parameters:
- indicessequence of int
Indices to select
- Returns:
- collsequence
Sub-collection of values at the selection indices.
- 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.
- setVisibility(visible)¶
Accessor to the object’s visibility state.
- Parameters:
- visiblebool
Visibility flag.
Examples using the class¶
Randomize the lines of a Sample
A quick start guide to the Point and Sample classes
Estimate Wilks and empirical quantile
Estimate correlation coefficients
Compare unconditional and conditional histograms
Compute squared SRC indices confidence intervals
Estimate a GEV on the Venice sea-levels data
Bandwidth sensitivity in kernel smoothing
Fit a non parametric distribution
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
Kolmogorov-Smirnov : understand the statistics
Estimate a scalar ARMA process
Create a custom covariance model
Over-fitting and model selection
Create a polynomial chaos metamodel by integration on the cantilever beam
Advanced polynomial chaos construction
Create a polynomial chaos metamodel
Create a polynomial chaos for the Ishigami function: a quick start guide to polynomial chaos
Create a sparse chaos by integration
Kriging: propagate uncertainties
Example of multi output Kriging on the fire satellite model
Kriging: metamodel of the Branin-Hoo function
Sequentially adding new points to a kriging
Kriging :configure the optimization solver
Kriging: choose a polynomial trend
Kriging: metamodel with continuous and categorical variables
Evaluate the mean of a random vector by simulations
Analyse the central tendency of a cantilever beam
Use the post-analytical importance sampling algorithm
Estimate a flooding probability
Use the Importance Sampling algorithm
Exploitation of simulation algorithm results
Use the FORM algorithm in case of several design points
Test the design point with the Strong Maximum Test
Time variant system reliability problem
Axial stressed beam : comparing different methods to estimate a probability
An illustrated example of a FORM probability estimate
Cross Entropy Importance Sampling
Using the FORM - SORM algorithms on a nonlinear function
Estimate Sobol indices on a field to point function
Estimate Sobol’ indices for a function with multivariate output
The HSIC sensitivity indices: the Ishigami model
Example of sensitivity analyses on the wing weight model
Create mixed deterministic and probabilistic designs of experiments
Create a linear combination of functions
Defining Python and symbolic functions: a quick start introduction to functions
Calibrate a parametric model: a quick-start guide to calibration
Calibration without observed inputs
Calibration of the logistic model
Calibration of the deflection of a tube
Calibration of the flooding model
Calibration of the Chaboche mechanical model
Sampling from an unnormalized probability density
Customize your Metropolis-Hastings algorithm
Linear Regression with interval-censored observations
Compute leave-one-out error of a polynomial chaos expansion
Compute confidence intervals of a regression model from data
Compute confidence intervals of a univariate noisy function
Mix/max search and sensitivity from design
Quick start guide to optimization
Optimization of the Rastrigin test function
EfficientGlobalOptimization examples
Estimate threshold exceedance iteratively