PointToPointConnection

class PointToPointConnection(*args)

Composition function f \circ g where g acts on points and f produces points.

Available constructors:

PointToPointEvaluation(f_Function, g_Function)

PointToPointEvaluation(f_FieldToPoint, g_PointToField)

Parameters:
f_Function, g_Function : Function

Function that acts on points and produces points

f_FieldToPoint : FieldToPointFunction

Function that acts on fields and produces points

g_PointToField : PointToFieldFunction

Function that acts on points and produces fields

Notes

This class is a particular case of the general class Function. Thus it implements the evaluation operator and the evaluation of the gradient and the hessian.

By default, the gradient and hessian are evaluated using centered finite differences described in CenteredFiniteDifferenceGradient and CenteredFiniteDifferenceHessian.

Methods

draw(*args) Draw the output of function as a Graph.
getCallsNumber() Accessor to the number of times the function has been called.
getClassName() Accessor to the object’s name.
getDescription() Accessor to the description of the inputs and outputs.
getEvaluation() Accessor to the evaluation function.
getEvaluationCallsNumber() Accessor to the number of times the function has been called.
getGradient() Accessor to the gradient function.
getGradientCallsNumber() Accessor to the number of times the gradient of the function has been called.
getHessian() Accessor to the hessian function.
getHessianCallsNumber() Accessor to the number of times the hessian of the function has been called.
getId() Accessor to the object’s id.
getInputDescription() Accessor to the description of the input vector.
getInputDimension() Accessor to the dimension of the input vector.
getMarginal(*args) Accessor to marginal.
getName() Accessor to the object’s name.
getOutputDescription() Accessor to the description of the output vector.
getOutputDimension() Accessor to the number of the outputs.
getParameter() Accessor to the parameter values.
getParameterDescription() Accessor to the parameter description.
getParameterDimension() Accessor to the dimension of the parameter.
getShadowedId() Accessor to the object’s shadowed id.
getVisibility() Accessor to the object’s visibility state.
gradient(inP) Return the Jacobian transposed matrix of the function at a point.
hasName() Test if the object is named.
hasVisibleName() Test if the object has a distinguishable name.
hessian(inP) Return the hessian of the function at a point.
parameterGradient(inP) Accessor to the gradient against the parameter.
setDescription(description) Accessor to the description of the inputs and outputs.
setEvaluation(evaluation) Accessor to the evaluation function.
setGradient(gradient) Accessor to the gradient function.
setHessian(hessian) Accessor to the hessian function.
setInputDescription(inputDescription) Accessor to the description of the input vector.
setName(name) Accessor to the object’s name.
setOutputDescription(outputDescription) Accessor to the description of the output vector.
setParameter(parameter) Accessor to the parameter values.
setParameterDescription(description) Accessor to the parameter description.
setShadowedId(id) Accessor to the object’s shadowed id.
setVisibility(visible) Accessor to the object’s visibility state.
__call__  
__init__(*args)

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

draw(*args)

Draw the output of function as a Graph.

Available usages:

draw(inputMarg, outputMarg, CP, xiMin, xiMax, ptNb)

draw(firstInputMarg, secondInputMarg, outputMarg, CP, xiMin_xjMin, xiMax_xjMax, ptNbs)

draw(xiMin, xiMax, ptNb)

draw(xiMin_xjMin, xiMax_xjMax, ptNbs)

Parameters:
outputMarg, inputMarg : int, outputMarg, inputMarg \geq 0

outputMarg is the index of the marginal to draw as a function of the marginal with index inputMarg.

firstInputMarg, secondInputMarg : int, firstInputMarg, secondInputMarg \geq 0

In the 2D case, the marginal outputMarg is drawn as a function of the two marginals with indexes firstInputMarg and secondInputMarg.

CP : sequence of float

Central point.

xiMin, xiMax : float

Define the interval where the curve is plotted.

xiMin_xjMin, xiMax_xjMax : sequence of float of dimension 2.

In the 2D case, define the intervals where the curves are plotted.

ptNb : int ptNb > 0 or list of ints of dimension 2 ptNb_k > 0, k=1,2

The number of points to draw the curves.

Notes

We note f: \Rset^n \rightarrow \Rset^p where \vect{x} = (x_1, \dots, x_n) and f(\vect{x}) = (f_1(\vect{x}), \dots,f_p(\vect{x})), with n\geq 1 and p\geq 1.

  • In the first usage:

Draws graph of the given 1D outputMarg marginal f_k: \Rset^n \rightarrow \Rset as a function of the given 1D inputMarg marginal with respect to the variation of x_i in the interval [x_i^{min}, x_i^{max}], when all the other components of \vect{x} are fixed to the corresponding ones of the central point CP. Then OpenTURNS draws the graph: t\in [x_i^{min}, x_i^{max}] \mapsto f_k(CP_1, \dots, CP_{i-1}, t,  CP_{i+1} \dots, CP_n).

  • In the second usage:

Draws the iso-curves of the given outputMarg marginal f_k as a function of the given 2D firstInputMarg and secondInputMarg marginals with respect to the variation of (x_i, x_j) in the interval [x_i^{min}, x_i^{max}] \times [x_j^{min}, x_j^{max}], when all the other components of \vect{x} are fixed to the corresponding ones of the central point CP. Then OpenTURNS draws the graph: (t,u) \in [x_i^{min}, x_i^{max}] \times [x_j^{min}, x_j^{max}] \mapsto f_k(CP_1, \dots, CP_{i-1}, t, CP_{i+1}, \dots, CP_{j-1}, u,  CP_{j+1} \dots, CP_n).

  • In the third usage:

The same as the first usage but only for function f: \Rset \rightarrow \Rset.

  • In the fourth usage:

The same as the second usage but only for function f: \Rset^2 \rightarrow \Rset.

Examples

>>> import openturns as ot
>>> from openturns.viewer import View
>>> f = ot.SymbolicFunction('x', 'sin(2*pi_*x)*exp(-x^2/2)')
>>> graph = f.draw(-1.2, 1.2, 100)
>>> View(graph).show()
getCallsNumber()

Accessor to the number of times the function has been called.

Returns:
calls_number : int

Integer that counts the number of times the function has been called since its creation.

getClassName()

Accessor to the object’s name.

Returns:
class_name : str

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

getDescription()

Accessor to the description of the inputs and outputs.

Returns:
description : Description

Description of the inputs and the outputs.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                         ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getDescription())
[x1,x2,y0]
getEvaluation()

Accessor to the evaluation function.

Returns:
function : EvaluationImplementation

The evaluation function.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                         ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getEvaluation())
[x1,x2]->[2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6]
getEvaluationCallsNumber()

Accessor to the number of times the function has been called.

Returns:
evaluation_calls_number : int

Integer that counts the number of times the function has been called since its creation.

getGradient()

Accessor to the gradient function.

Returns:
gradient : GradientImplementation

The gradient function.

getGradientCallsNumber()

Accessor to the number of times the gradient of the function has been called.

Returns:
gradient_calls_number : int

Integer that counts the number of times the gradient of the Function has been called since its creation. Note that if the gradient is implemented by a finite difference method, the gradient calls number is equal to 0 and the different calls are counted in the evaluation calls number.

getHessian()

Accessor to the hessian function.

Returns:
hessian : HessianImplementation

The hessian function.

getHessianCallsNumber()

Accessor to the number of times the hessian of the function has been called.

Returns:
hessian_calls_number : int

Integer that counts the number of times the hessian of the Function has been called since its creation. Note that if the hessian is implemented by a finite difference method, the hessian calls number is equal to 0 and the different calls are counted in the evaluation calls number.

getId()

Accessor to the object’s id.

Returns:
id : int

Internal unique identifier.

getInputDescription()

Accessor to the description of the input vector.

Returns:
description : Description

Description of the input vector.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                          ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getInputDescription())
[x1,x2]
getInputDimension()

Accessor to the dimension of the input vector.

Returns:
inputDim : int

Dimension of the input vector d.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                          ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getInputDimension())
2
getMarginal(*args)

Accessor to marginal.

Parameters:
indices : int or list of ints

Set of indices for which the marginal is extracted.

Returns:
marginal : Function

Function corresponding to either f_i or (f_i)_{i \in indices}, with f:\Rset^n \rightarrow \Rset^p and f=(f_0 , \dots, f_{p-1}).

getName()

Accessor to the object’s name.

Returns:
name : str

The name of the object.

getOutputDescription()

Accessor to the description of the output vector.

Returns:
description : Description

Description of the output vector.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                          ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getOutputDescription())
[y0]
getOutputDimension()

Accessor to the number of the outputs.

Returns:
number_outputs : int

Dimension of the output vector d'.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                          ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getOutputDimension())
1
getParameter()

Accessor to the parameter values.

Returns:
parameter : Point

The parameter values.

getParameterDescription()

Accessor to the parameter description.

Returns:
parameter : Description

The parameter description.

getParameterDimension()

Accessor to the dimension of the parameter.

Returns:
parameterDimension : int

Dimension of the parameter.

getShadowedId()

Accessor to the object’s shadowed id.

Returns:
id : int

Internal unique identifier.

getVisibility()

Accessor to the object’s visibility state.

Returns:
visible : bool

Visibility flag.

gradient(inP)

Return the Jacobian transposed matrix of the function at a point.

Parameters:
point : sequence of float

Point where the Jacobian transposed matrix is calculated.

Returns:
gradient : Matrix

The Jacobian transposed matrix of the function at point.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6','x1 + x2'])
>>> print(f.gradient([3.14, 4]))
[[ 13.5345   1       ]
 [  4.00001  1       ]]
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.

hessian(inP)

Return the hessian of the function at a point.

Parameters:
point : sequence of float

Point where the hessian of the function is calculated.

Returns:
hessian : SymmetricTensor

Hessian of the function at point.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6','x1 + x2'])
>>> print(f.hessian([3.14, 4]))
sheet #0
[[ 20          -0.00637061 ]
 [ -0.00637061  0          ]]
sheet #1
[[  0           0          ]
 [  0           0          ]]
parameterGradient(inP)

Accessor to the gradient against the parameter.

Returns:
gradient : Matrix

The gradient.

setDescription(description)

Accessor to the description of the inputs and outputs.

Parameters:
description : sequence of str

Description of the inputs and the outputs.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                          ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getDescription())
[x1,x2,y0]
>>> f.setDescription(['a','b','y'])
>>> print(f.getDescription())
[a,b,y]
setEvaluation(evaluation)

Accessor to the evaluation function.

Parameters:
function : EvaluationImplementation

The evaluation function.

setGradient(gradient)

Accessor to the gradient function.

Parameters:
gradient_function : GradientImplementation

The gradient function.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                          ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> f.setGradient(ot.CenteredFiniteDifferenceGradient(
...  ot.ResourceMap.GetAsScalar('CenteredFiniteDifferenceGradient-DefaultEpsilon'),
...  f.getEvaluation()))
setHessian(hessian)

Accessor to the hessian function.

Parameters:
hessian_function : HessianImplementation

The hessian function.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                         ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> f.setHessian(ot.CenteredFiniteDifferenceHessian(
...  ot.ResourceMap.GetAsScalar('CenteredFiniteDifferenceHessian-DefaultEpsilon'),
...  f.getEvaluation()))
setInputDescription(inputDescription)

Accessor to the description of the input vector.

Parameters:
description : Description

Description of the input vector.

setName(name)

Accessor to the object’s name.

Parameters:
name : str

The name of the object.

setOutputDescription(outputDescription)

Accessor to the description of the output vector.

Parameters:
description : Description

Description of the output vector.

setParameter(parameter)

Accessor to the parameter values.

Parameters:
parameter : sequence of float

The parameter values.

setParameterDescription(description)

Accessor to the parameter description.

Parameters:
parameter : Description

The parameter description.

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.