# Point¶

class Point(*args)

Real vector.

Parameters: dimension : int, , optional The number of components. value : float, 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)


>>> 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. getClassName() Accessor to the object’s name. getDescription() Accessor to the componentwise description. 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 () norm. norm1() Compute the norm. normInf() Compute the 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. setDescription(description) Accessor to the componentwise description. 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)

Initialize self. See help(type(self)) for accurate signature.

add(*args)

Append a component (in-place).

Parameters: value : type depends on the type of the collection. The component to append.

Examples

>>> import openturns as ot
>>> x = ot.Point(2)
>>> print(x)
[0,0,1]

at(*args)

Parameters: index : positive int Position of the element to access. element : type 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=[]

getClassName()

Accessor to the object’s name.

Returns: class_name : str The object class name (object.__class__.__name__).
getDescription()

Accessor to the componentwise description.

Returns: description : Description Description of the components.
getDimension()

Accessor to the vector’s dimension.

Returns: n : int The number of components in the vector.
getId()

Accessor to the object’s id.

Returns: id : int Internal unique identifier.
getName()

Accessor to the object’s name.

Returns: name : str The name of the object.
getShadowedId()

Accessor to the object’s shadowed id.

Returns: id : int Internal unique identifier.
getSize()

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

Returns: n : int The number of components in the vector.
getVisibility()

Accessor to the object’s visibility state.

Returns: visible : bool Visibility flag.
hasName()

Test if the object is named.

Returns: hasName : bool True if the name is not empty.
hasVisibleName()

Test if the object has a distinguishable name.

Returns: hasVisibleName : bool 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: isEmpty : bool 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: norm : float 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: norm : float 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: norm : float 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: norm : float The vector’s squared Euclidean 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_vector : Point The normalized vector with respect to its Euclidean norm. RuntimeError : If the Euclidean norm is zero.

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_vector : normalized_vector The normalized vector with respect to its squared Euclidean norm. RuntimeError : If the squared Euclidean norm is zero.

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: newSize : positive 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]

setDescription(description)

Accessor to the componentwise description.

Parameters: description : sequence of str Description of the components.
setName(name)

Accessor to the object’s name.

Parameters: name : str The name of the object.
setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters: id : int Internal unique identifier.
setVisibility(visible)

Accessor to the object’s visibility state.

Parameters: visible : bool Visibility flag.