# PythonFunction¶

class PythonFunction(*args)

Override Function from Python.

Parameters: inputDim : positive int Dimension of the input vector outputDim : positive int Dimension of the output vector func : a callable python object, optional Called when evaluated on a single point. Default is None. func_sample : a callable python object, optional Called when evaluated on multiple points at once. Default is None. gradient : a callable python objects, optional Returns the gradient as a 2-d sequence of float. Default is None (uses finite-difference). hessian : a callable python object, optional Returns the hessian as a 3-d sequence of float. Default is None (uses finite-difference). n_cpus : integer Number of cpus on which func should be distributed using multiprocessing. If -1, it uses all the cpus available. If 1, it does nothing. If n_cpus and func_sample are both given as arguments, n_cpus will be ignored and samples will be handled by func_sample. Default is None. copy : bool, optional If True, input sample is converted into a Python 2-d sequence before calling func_sample. Otherwise, it is passed directy to func_sample. Default is False. You must provide at least func or func_sample arguments. For efficiency reasons, these functions do not receive a :class:~openturns.Point or :class:~openturns.Sample as arguments, but a proxy object which gives access to internal object data. This object supports indexing, but nothing more. It must be wrapped into anoter object, for instance :class:~openturns.Point in func and :class:~openturns.Sample in func_sample, or in a Numpy array, for vectorized operations.

Notes

Notice that if func_sample is provided, n_cpus is ignored. Note also that if PythonFunction is distributed (n_cpus > 1), the traceback of a raised exception by a func call is lost due to the way multiprocessing dispatches and handles func calls. This can be solved by temporarily deactivating n_cpus during the development of the wrapper or by manually handling the distribution of the wrapper with external libraries like joblib that keep track of a raised exception and shows the traceback to the user.

Examples

>>> import openturns as ot
>>> def a_exec(X):
...     Y = [3.0 * X[0] - X[1]]
...     return Y
...     dY = [[3.0], [-1.0]]
...     return dY
>>> X = [100.0, 100.0]
>>> Y = f(X)
>>> print(Y)
[200]
>>> print(dY)
[[  3 ]
[ -1 ]]


Same example, but optimized for best performance with Numpy when function is going to be evaluated on large samples.

>>> import openturns as ot
>>> import numpy as np
>>> def a_exec_sample(X):
...     Xarray = np.array(X, copy=False)
...     Y = 3.0 * Xarray[:,0] - Xarray[:,1]
...     return np.expand_dims(Y, axis=1)
...     dY = [[3.0], [-1.0]]
...     return dY
>>> X = [100.0, 100.0]
>>> Y = f(X)
>>> print(Y)
[200]
>>> print(dY)
[[  3 ]
[ -1 ]]


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. getImplementation(*args) Accessor to the underlying implementation. 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. gradient(inP) Return the Jacobian transposed matrix of the function at a point. 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(inputDescription) Accessor to the description of the output vector. setParameter(parameter) Accessor to the parameter values. setParameterDescription(description) Accessor to the parameter description.
 __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 is the index of the marginal to draw as a function of the marginal with index inputMarg. firstInputMarg, secondInputMarg : int, 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 or list of ints of dimension 2 The number of points to draw the curves.

Notes

We note where and , with and .

• In the first usage:

Draws graph of the given 1D outputMarg marginal as a function of the given 1D inputMarg marginal with respect to the variation of in the interval , when all the other components of are fixed to the corresponding ones of the central point CP. Then OpenTURNS draws the graph: .

• In the second usage:

Draws the iso-curves of the given outputMarg marginal as a function of the given 2D firstInputMarg and secondInputMarg marginals with respect to the variation of in the interval , when all the other components of are fixed to the corresponding ones of the central point CP. Then OpenTURNS draws the graph: .

• In the third usage:

The same as the first usage but only for function .

• In the fourth usage:

The same as the second usage but only for function .

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()

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.
getImplementation(*args)

Accessor to the underlying implementation.

Returns: impl : Implementation The implementation class.
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 .

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. marginal : Function Function corresponding to either or , with and .
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 .

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.
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. 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'])
[[ 13.5345   1       ]
[  4.00001  1       ]]

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. 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)

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.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(inputDescription)

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.