FMUFunction¶

class FMUFunction(*args)

Override NumericalMathFunction from Python.

Parameters: path_fmu : String, path to the FMU file. inputs_fmu : Sequence of strings Names of the variable from the fmu to be used as input variables. outputs_fmu : Sequence of strings, Names of the variable from the fmu to be used as output variables. inputs : Sequence of strings Optional names to use as variables descriptions. outputs : Sequence of strings Optional names to use as variables descriptions. n_cpus : Integer Number of cores to use for multiprocessing. initialization_script : String (optional) Path to the initialization script. kind : String, one of “ME” (model exchange) or “CS” (co-simulation) Select a kind of FMU if both are available. Note: Contrary to pyfmi, the default here is “CS” (co-simulation). The rationale behind this choice is is that co-simulation may be used to impose a solver not available in pyfmi.

Methods

 GetValidConstants() Return the list of valid constants. GetValidFunctions() Return the list of valid functions. GetValidOperators() Return the list of valid operators. __call__(*args) addCacheContent(inSample, outSample) Add input numerical points and associated output to the cache. clearCache() Empty the content of the cache. clearHistory() Empty the content of the history. disableCache() Disable the cache mechanism. disableHistory() Disable the history mechanism. draw(*args) Draw the output of function as a Graph. enableCache() Enable the cache mechanism. enableHistory() Enable the history mechanism. getCacheHits() Accessor to the number of computations saved thanks to the cache mecanism. getCacheInput() Accessor to all the input numerical points stored in the cache mecanism. getCacheOutput() Accessor to all the output numerical points stored in the cache mecanism. 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. getHistoryInput() Accessor to the history of the input values. getHistoryOutput() Accessor to the history of the output values. getId() Accessor to the object’s id. getImplementation(*args) Accessor to the underlying implementation. getInputDescription() Accessor to the description of the inputs. getInputDimension() Accessor to the number of the inputs. getInputParameterHistory() Accessor to the history of the input parameter values. getInputPointHistory() Accessor to the history of the input point values. getMarginal(*args) Accessor to marginal. getName() Accessor to the object’s name. getOutputDescription() Accessor to the description of the outputs. 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(*args) Return the Jacobian transposed matrix of the function at a point. hessian(*args) Return the hessian of the function at a point. isCacheEnabled() Test whether the cache mechanism is enabled or not. isHistoryEnabled() Test whether the history mechanism is enabled or not. parameterGradient(*args) 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. setName(name) Accessor to the object’s name. setParameter(parameter) Accessor to the parameter values. setParameterDescription(description) Accessor to the parameter description.
GetValidConstants()

Return the list of valid constants.

Returns: list_constants : Description List of the constants we can use within OpenTURNS.

Examples

>>> import openturns as ot
>>> print(ot.NumericalMathFunction.GetValidConstants()[0])
_e -> Euler's constant (2.71828...)

GetValidFunctions()

Return the list of valid functions.

Returns: list_functions : Description List of the functions we can use within OpenTURNS.

Examples

>>> import openturns as ot
>>> print(ot.NumericalMathFunction.GetValidFunctions()[0])
sin(arg) -> sine function

GetValidOperators()

Return the list of valid operators.

Returns: list_operators : Description List of the operators we can use within OpenTURNS.

Examples

>>> import openturns as ot
>>> print(ot.NumericalMathFunction.GetValidOperators()[0])
= -> assignement, can only be applied to variable names (priority -1)

addCacheContent(inSample, outSample)

Add input numerical points and associated output to the cache.

Parameters: input_sample : 2-d sequence of float Input numerical points to be added to the cache. output_sample : 2-d sequence of float Output numerical points associated with the input_sample to be added to the cache.
clearCache()

Empty the content of the cache.

clearHistory()

Empty the content of the history.

disableCache()

Disable the cache mechanism.

disableHistory()

Disable the history mechanism.

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.NumericalMathFunction('x', 'sin(2*_pi*x)*exp(-x^2/2)', 'y')
>>> graph = f.draw(-1.2, 1.2, 100)
>>> View(graph).show()

enableCache()

Enable the cache mechanism.

enableHistory()

Enable the history mechanism.

getCacheHits()

Accessor to the number of computations saved thanks to the cache mecanism.

Returns: cacheHits : int Integer that counts the number of computations saved thanks to the cache mecanism.
getCacheInput()

Accessor to all the input numerical points stored in the cache mecanism.

Returns: cacheInput : NumericalSample All the input numerical points stored in the cache mecanism.
getCacheOutput()

Accessor to all the output numerical points stored in the cache mecanism.

Returns: cacheInput : NumericalSample All the output numerical points stored in the cache mecanism.
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.NumericalMathFunction(['x1', 'x2'], ['y'],
...                          ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getDescription())
[x1,x2,y]

getEvaluation()

Accessor to the evaluation function.

Returns: The evaluation function.

Examples

>>> import openturns as ot
>>> f = ot.NumericalMathFunction(['x1', 'x2'], ['y'],
...                          ['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()

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 NumericalMathFunction 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: 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 NumericalMathFunction 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.
getHistoryInput()

Accessor to the history of the input values.

Returns: input_history : NumericalSample All the input numerical points stored in the history mecanism.
getHistoryOutput()

Accessor to the history of the output values.

Returns: output_history : NumericalSample All the output numerical points stored in the history mecanism.
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 inputs.

Returns: description : Description Description of the inputs.

Examples

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

getInputDimension()

Accessor to the number of the inputs.

Returns: number_inputs : int Number of inputs.

Examples

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

getInputParameterHistory()

Accessor to the history of the input parameter values.

Returns: history : NumericalSample All the input parameters stored in the history mecanism.
getInputPointHistory()

Accessor to the history of the input point values.

Returns: history : NumericalSample All the input points stored in the history mecanism.
getMarginal(*args)

Accessor to marginal.

Parameters: indices : int or list of ints Set of indices for which the marginal is extracted. marginal : NumericalMathFunction 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 outputs.

Returns: description : Description Description of the outputs.

Examples

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

getOutputDimension()

Accessor to the number of the outputs.

Returns: number_outputs : int Number of outputs.

Examples

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

getParameter()

Accessor to the parameter values.

Returns: parameter : NumericalPoint 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(*args)

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.NumericalMathFunction(['x1', 'x2'], ['y','z'],
...                ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6','x1 + x2'])
[[ 13.5345   1       ]
[  4.00001  1       ]]

hessian(*args)

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.NumericalMathFunction(['x1', 'x2'], ['y','z'],
...                ['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          ]]

isCacheEnabled()

Test whether the cache mechanism is enabled or not.

Returns: isCacheEnabled : bool Flag telling whether the cache mechanism is enabled. It is disabled by default.
isHistoryEnabled()

Test whether the history mechanism is enabled or not.

Returns: isHistoryEnabled : bool Flag telling whether the history mechanism is enabled. It is disabled by default.
parameterGradient(*args)

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.NumericalMathFunction(['x1', 'x2'], ['y'],
...                          ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getDescription())
[x1,x2,y]
>>> f.setDescription(['a','b','y'])
>>> print(f.getDescription())
[a,b,y]

setEvaluation(evaluation)

Accessor to the evaluation function.

Parameters: The evaluation function.
setGradient(gradient)

Parameters: gradient_function : NumericalMathGradientImplementation The gradient function.

Examples

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

setHessian(hessian)

Accessor to the hessian function.

Parameters: hessian_function : NumericalMathHessianImplementation The hessian function.

Examples

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

setName(name)

Accessor to the object’s name.

Parameters: name : str The name of the object.
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.