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`(self, \*args)	Append a component (in-place).
`at`(self, \*args)	Access to an element of the collection.
`clear`(self)	Reset the collection to zero dimension.
`dot`(self, rhs)	Compute the scalar product.
`find`(self, val)	Find the index of a given value.
`getClassName`(self)	Accessor to the object’s name.
`getDimension`(self)	Accessor to the vector’s dimension.
`getId`(self)	Accessor to the object’s id.
`getName`(self)	Accessor to the object’s name.
`getShadowedId`(self)	Accessor to the object’s shadowed id.
`getSize`(self)	Accessor to the vector’s dimension (or size).
`getVisibility`(self)	Accessor to the object’s visibility state.
`hasName`(self)	Test if the object is named.
`hasVisibleName`(self)	Test if the object has a distinguishable name.
`isDecreasing`(self)	Check if the components are in decreasing order.
`isEmpty`(self)	Tell if the collection is empty.
`isIncreasing`(self)	Check if the components are in increasing order.
`isMonotonic`(self)	Check if the components are in nonincreasing or nondecreasing order.
`isNonDecreasing`(self)	Check if the components are in nondecreasing order.
`isNonIncreasing`(self)	Check if the components are in nonincreasing order.
`norm`(self)	Compute the Euclidean ( $L^2$ ) norm.
`norm1`(self)	Compute the $L^1$ norm.
`normInf`(self)	Compute the $L^{\inf}$ norm.
`normSquare`(self)	Compute the squared Euclidean norm.
`normalize`(self)	Compute the normalized vector with respect to its Euclidean norm.
`normalizeSquare`(self)	Compute the normalized vector with respect to its squared Euclidean norm.
`resize`(self, newSize)	Change the size of the collection.
`setName`(self, name)	Accessor to the object’s name.
`setShadowedId`(self, id)	Accessor to the object’s shadowed id.
`setVisibility`(self, visible)	Accessor to the object’s visibility state.

clean

__init__(self, \*args)¶: Initialize self. See help(type(self)) for accurate signature.

add(self, \*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(self, \*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(self)¶

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(self, 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(self, val)¶

Find the index of a given value.

Parameters

valcollection value type: The value to find

Returns

indexint: The index of the first occurence of the value, or the size of the container if not found. When several values match, only the first index is returned.

getClassName(self)¶

Accessor to the object’s name.

Returns

class_namestr: The object class name (object.__class__.__name__).

getDimension(self)¶

Accessor to the vector’s dimension.

Returns

nint: The number of components in the vector.

getId(self)¶

Accessor to the object’s id.

Returns

idint: Internal unique identifier.

getName(self)¶

Accessor to the object’s name.

Returns

namestr: The name of the object.

getShadowedId(self)¶

Accessor to the object’s shadowed id.

Returns

idint: Internal unique identifier.

getSize(self)¶

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

Returns

nint: The number of components in the vector.

getVisibility(self)¶

Accessor to the object’s visibility state.

Returns

visiblebool: Visibility flag.

hasName(self)¶

Test if the object is named.

Returns

hasNamebool: True if the name is not empty.

hasVisibleName(self)¶

Test if the object has a distinguishable name.

Returns

hasVisibleNamebool: True if the name is not empty and not the default one.

isDecreasing(self)¶

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(self)¶

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(self)¶

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(self)¶

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(self)¶

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(self)¶

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(self)¶

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(self)¶

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(self)¶

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(self)¶

Compute the squared Euclidean norm.

Returns

normfloat: The vector’s squared Euclidean norm.

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An Open source initiative for the Treatment of Uncertainties, Risks'N Statistics

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