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.

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
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 occurence 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_vector

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]
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.