Point

class Point(*args)

Real vector.

Parameters:
dimensionint, n > 0, 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.

getClassName()

Accessor to the object's name.

getDimension()

Accessor to the vector's dimension.

getId()

Accessor to the object's id.

getName()

Accessor to the object's name.

getShadowedId()

Accessor to the object's shadowed id.

getSize()

Accessor to the vector's dimension (or size).

getVisibility()

Accessor to the object's visibility state.

hasName()

Test if the object is named.

hasVisibleName()

Test if the object has a distinguishable name.

isDecreasing()

Check if the components are in decreasing order.

isEmpty()

Tell if the collection is empty.

isIncreasing()

Check if the components are in increasing order.

isMonotonic()

Check if the components are in nonincreasing or nondecreasing order.

isNonDecreasing()

Check if the components are in nondecreasing order.

isNonIncreasing()

Check if the components are in nonincreasing order.

norm()

Compute the Euclidean (L^2) norm.

norm1()

Compute the L^1 norm.

normInf()

Compute the L^{\inf} norm.

normSquare()

Compute the squared Euclidean norm.

normalize()

Compute the normalized vector with respect to its Euclidean norm.

normalizeSquare()

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 (L^2) norm.

The Euclidean (L^2) norm of a vector is defined as:

\norm{\vect{x}} = \norm{\vect{x}}_2
                = \sqrt{\sum_{i=1}^n x_i^2}

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 L^1 norm.

The L^1 norm of a vector is defined as:

\norm{\vect{x}}_1 = \sum_{i=1}^n |x_i|

Returns:
normfloat

The vector’s L^1 norm.

Examples

>>> import openturns as ot
>>> x = ot.Point([1.0, 2.0, 3.0])
>>> x.norm1()
6.0
normInf()

Compute the L^{\inf} norm.

The L^{\inf} norm of a vector is defined as:

\norm{\vect{x}}_{\inf} = \max_{i=1}^n |x_i|

Returns:
normfloat

The vector’s L^{\inf} 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

norm

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_vectorPoint

The normalized vector with respect to its Euclidean norm.

Raises:
RuntimeErrorIf the Euclidean norm is zero.

See also

norm

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_vectorPoint

The normalized vector with respect to its squared Euclidean norm.

Raises:
RuntimeErrorIf the squared Euclidean norm is zero.

See also

normSquare

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

Randomize the lines of a Sample

Randomize the lines of a Sample
A quick start guide to the `Point` and `Sample` classes

A quick start guide to the Point and Sample classes

A quick start guide to the `Point` and `Sample` classes
Estimate Wilks and empirical quantile

Estimate Wilks and empirical quantile

Estimate Wilks and empirical quantile
Estimate correlation coefficients

Estimate correlation coefficients

Estimate correlation coefficients
Compare unconditional and conditional histograms

Compare unconditional and conditional histograms

Compare unconditional and conditional histograms
Compute SRC indices confidence intervals

Compute SRC indices confidence intervals

Compute SRC indices confidence intervals
Fit a non parametric distribution

Fit a non parametric distribution

Fit a non parametric distribution
Kolmogorov-Smirnov : understand the statistics

Kolmogorov-Smirnov : understand the statistics

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Estimate a scalar ARMA process

Estimate a scalar ARMA process

Estimate a scalar ARMA process
Export a field to VTK

Export a field to VTK

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Create a custom covariance model

Create a custom covariance model

Create a custom covariance model
Draw a field

Draw a field

Draw a field
Trend computation

Trend computation

Trend computation
Over-fitting and model selection

Over-fitting and model selection

Over-fitting and model selection
Create a polynomial chaos metamodel by integration on the cantilever beam

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Advanced polynomial chaos construction

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Advanced polynomial chaos construction
Create a polynomial chaos metamodel

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Create a sparse chaos by integration

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Compute Sobol' indices confidence intervals

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Kriging : propagate uncertainties

Kriging : propagate uncertainties

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Kriging : draw the likelihood

Kriging : draw the likelihood

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Example of multi output Kriging on the fire satellite model

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Kriging: metamodel of the Branin-Hoo function

Kriging: metamodel of the Branin-Hoo function

Kriging: metamodel of the Branin-Hoo function
Sequentially adding new points to a kriging

Sequentially adding new points to a kriging

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Kriging :configure the optimization solver

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Metamodel of a field function

Metamodel of a field function

Metamodel of a field function
Evaluate the mean of a random vector by simulations

Evaluate the mean of a random vector by simulations

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Analyse the central tendency of a cantilever beam

Analyse the central tendency of a cantilever beam

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Use the post-analytical importance sampling algorithm

Use the post-analytical importance sampling algorithm

Use the post-analytical importance sampling algorithm
Estimate a flooding probability

Estimate a flooding probability

Estimate a flooding probability
Use the Importance Sampling algorithm

Use the Importance Sampling algorithm

Use the Importance Sampling algorithm
Exploitation of simulation algorithm results

Exploitation of simulation algorithm results

Exploitation of simulation algorithm results
Use the FORM algorithm in case of several design points

Use the FORM algorithm in case of several design points

Use the FORM algorithm in case of several design points
Non parametric Adaptive Importance Sampling (NAIS)

Non parametric Adaptive Importance Sampling (NAIS)

Non parametric Adaptive Importance Sampling (NAIS)
Subset Sampling

Subset Sampling

Subset Sampling
Test the design point with the Strong Maximum Test

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Time variant system reliability problem

Time variant system reliability problem

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Axial stressed beam : comparing different methods to estimate a probability

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An illustrated example of a FORM probability estimate

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Estimate Sobol indices on a field to point function

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FAST sensitivity indices

FAST sensitivity indices

FAST sensitivity indices
Estimate Sobol' indices for a function with multivariate output

Estimate Sobol’ indices for a function with multivariate output

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Use the ANCOVA indices

Use the ANCOVA indices

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The HSIC sensitivity indices: the Ishigami model

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Example of sensitivity analyses on the wing weight model

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Create mixed deterministic and probabilistic designs of experiments

Create mixed deterministic and probabilistic designs of experiments

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Create a composed function

Create a composed function

Create a composed function
Create an aggregated function

Create an aggregated function

Create an aggregated function
Create a linear combination of functions

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Defining Python and symbolic functions: a quick start introduction to functions

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Function manipulation

Function manipulation

Function manipulation
Calibration without observed inputs

Calibration without observed inputs

Calibration without observed inputs
Calibration of the deflection of a tube

Calibration of the deflection of a tube

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Calibration of the logistic model

Calibration of the logistic model

Calibration of the logistic model
Calibration of the Chaboche mechanical model

Calibration of the Chaboche mechanical model

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Calibration of the flooding model

Calibration of the flooding model

Calibration of the flooding model
Sampling from an unnormalized probability density

Sampling from an unnormalized probability density

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Customize your Metropolis-Hastings algorithm

Customize your Metropolis-Hastings algorithm

Customize your Metropolis-Hastings algorithm
Linear Regression with interval-censored observations

Linear Regression with interval-censored observations

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Estimate an integral

Estimate an integral

Estimate an integral
Mix/max search and sensitivity from design

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Quick start guide to optimization

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Optimization of the Rastrigin test function

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EfficientGlobalOptimization examples

EfficientGlobalOptimization examples

EfficientGlobalOptimization examples
Estimate moments iteratively

Estimate moments iteratively

Estimate moments iteratively
Estimate extrema iteratively

Estimate extrema iteratively

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Estimate threshold exceedance iteratively

Estimate threshold exceedance iteratively

Estimate threshold exceedance iteratively