FMUFunction

class FMUFunction(*args)

Define a Function from a FMU file.

Parameters

path_fmustr, path to the FMU file.
inputs_fmuSequence of str, default=None: Names of the variable from the fmu to be used as input variables. By default assigns variables with FMI causality INPUT.
outputs_fmuSequence of str, default=None: Names of the variable from the fmu to be used as output variables. By default assigns variables with FMI causality OUTPUT.
inputsSequence of str: Optional names to use as variables descriptions.
outputsSequence of str: Optional names to use as variables descriptions.
n_cpusint: Number of cores to use for multiprocessing.
initialization_scriptstr (optional): Path to the initialization script.
final_timefloat: The output variables value is collected at t=final_time and returned by FMUFunction.
kindstr, 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 that co-simulation may be used to impose a solver not available in pyfmi.

Attributes

thisown: The membership flag

Methods

`__call__`(*args)	Call self as a function.
`draw`(*args)	Draw the output of function as a `Graph`.
`getCallsNumber`()	Accessor to the number of direct calls to the function.
`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 evaluation of 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`()	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.
`isLinear`()	Accessor to the linearity of the function.
`isLinearlyDependent`(index)	Accessor to the linearity of the function with regard to a specific variable.
`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.
`setStopCallback`(callBack[, state])	Set up a stop callback.

draw(*args)

Draw the output of function as a Graph.

Available usages:

draw(inputMarg, outputMarg, centralPoint, xiMin, xiMax, ptNb, scale)

draw(firstInputMarg, secondInputMarg, outputMarg, centralPoint, xiMin_xjMin, xiMax_xjMax, ptNbs, scale, isFilled)

draw(xiMin, xiMax, ptNb, scale)

draw(xiMin_xjMin, xiMax_xjMax, ptNbs, scale)

Parameters

outputMarg, inputMargint, $outputMarg, inputMarg \geq 0$

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

firstInputMarg, secondInputMargint, $firstInputMarg, secondInputMarg \geq 0$

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

centralPointsequence of float

Central point with dimension equal to the input dimension of the function.

xiMin, xiMaxfloat

Define the interval where the curve is plotted.

xiMin_xjMin, xiMax_xjMaxsequence of float of dimension 2.

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

ptNbint $ptNb > 0$

The number of points to draw the curves.

ptNbslist of int of dimension 2 $ptNbs_k > 0, k=1,2$

The number of points to draw the contour in the 2D case.

scalebool

scale indicates whether the logarithmic scale is used either for one or both axes:

ot.GraphImplementation.NONE or 0: no log scale is used,
ot.GraphImplementation.LOGX or 1: log scale is used only for horizontal data,
ot.GraphImplementation.LOGY or 2: log scale is used only for vertical data,
ot.GraphImplementation.LOGXY or 3: log scale is used for both data.

isFilledbool

isFilled indicates whether the contour graph is filled or not

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 components of the centralPoint $\vect{c}$ . Then OpenTURNS draws the graph:

$y = f_k^{(i)}(s)$

for any $s \in [x_i^{min}, x_i^{max}]$ where $f_k^{(i)}(s)$ is defined by the equation:

$f_k^{(i)}(s) = f_k(c_1, \dots, c_{i-1}, s, c_{i+1} \dots, c_n).$

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 components of the centralPoint $\vect{c}$ . Then OpenTURNS draws the graph:

$y = f_k^{(i,j)}(s, t)$

for any $(s, t) \in [x_i^{min}, x_i^{max}] \times [x_j^{min}, x_j^{max}]$ where $f_k^{(i,j)}$ is defined by the equation:

$f_k^{(i,j)}(s,t) = f_k(c_1, \dots, c_{i-1}, s, c_{i+1}, \dots, c_{j-1}, t, c_{j+1} \dots, c_n).$

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 direct calls to the function.

Returns

calls_numberint: Integer that counts the number of times the function has been called directly through the () operator.

getClassName()

Accessor to the object’s name.

Returns

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

getDescription()

Accessor to the description of the inputs and outputs.

Returns

descriptionDescription: 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

functionEvaluationImplementation: 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 evaluation of the function has been called.

Returns

evaluation_calls_numberint: Integer that counts the number of times the evaluation of the function has been called since its creation. This may include indirect calls via finite-difference gradient or Hessian.

getGradient()

Accessor to the gradient function.

Returns

gradientGradientImplementation: The gradient function.

getGradientCallsNumber()

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

Returns

gradient_calls_numberint: 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

hessianHessianImplementation: The hessian function.

getHessianCallsNumber()

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

Returns

hessian_calls_numberint: 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

idint: Internal unique identifier.

getImplementation()

Accessor to the underlying implementation.

Returns

implImplementation: A copy of the underlying implementation object.

getInputDescription()

Accessor to the description of the input vector.

Returns

descriptionDescription: 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

inputDimint: 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

indicesint or list of ints: Set of indices for which the marginal is extracted.

Returns

marginalFunction: 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

namestr: The name of the object.

getOutputDescription()

Accessor to the description of the output vector.

Returns

descriptionDescription: 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_outputsint: 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

parameterPoint: The parameter values.

getParameterDescription()

Accessor to the parameter description.

Returns

parameterDescription: The parameter description.

getParameterDimension()

Accessor to the dimension of the parameter.

Returns

parameterDimensionint: Dimension of the parameter.

gradient(inP)

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

Parameters

pointsequence of float: Point where the Jacobian transposed matrix is calculated.

Returns

gradientMatrix: 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       ]]

hessian(inP)

Return the hessian of the function at a point.

Parameters

pointsequence of float: Point where the hessian of the function is calculated.

Returns

hessianSymmetricTensor: 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          ]]

isLinear()

Accessor to the linearity of the function.

Returns

linearbool: True if the function is linear, False otherwise.

isLinearlyDependent(index)

Accessor to the linearity of the function with regard to a specific variable.

Parameters

indexint: The index of the variable with regard to which linearity is evaluated.

Returns

linearbool: True if the function is linearly dependent on the specified variable, False otherwise.

parameterGradient(inP)

Accessor to the gradient against the parameter.

Returns

gradientMatrix: The gradient.

setDescription(description)

Accessor to the description of the inputs and outputs.

Parameters

descriptionsequence 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

functionEvaluationImplementation: The evaluation function.

setGradient(gradient)

Accessor to the gradient function.

Parameters

gradient_functionGradientImplementation: 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_functionHessianImplementation: 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

descriptionDescription: Description of the input vector.

setName(name)

Accessor to the object’s name.

Parameters

namestr: The name of the object.

setOutputDescription(inputDescription)

Accessor to the description of the output vector.

Parameters

descriptionDescription: Description of the output vector.

setParameter(parameter)

Accessor to the parameter values.

Parameters

parametersequence of float: The parameter values.

setParameterDescription(description)

Accessor to the parameter description.

Parameters

parameterDescription: The parameter description.

setStopCallback(callBack, state=None)

Set up a stop callback.

Can be used to programmatically stop an evaluation.

Parameters

callbackcallable: Returns a bool deciding whether to stop or continue.

property thisown: The membership flag