P1LagrangeEvaluation¶

class P1LagrangeEvaluation(*args)¶

Data based math evaluation implementation.

Available constructors:

P1LagrangeEvaluation(field)

Parameters:

fieldField: Field $\cF$ defining the parameters of a P1 Lagrange interpolation function.

See also

Function, AggregatedEvaluation, DualLinearCombinationEvaluation
LinearFunction

Notes

It returns a Function that implements the P1 Lagrange interpolation function $f : \cD_N \rightarrow \Rset^p$ :

$\forall \vect{x} \in \Rset^n, f(\vect{x}) = \sum_{\vect{\xi}_i\in\cV(\vect{x})}\alpha_i f(\vect{\xi}_i)$

where $\cD_N$ is a Mesh, $\cV(\vect{x})$ is the simplex in $\cD_N$ that contains $\vect{x}$ , $\alpha_i$ are the barycentric coordinates of $\vect{x}$ wrt the vertices $\vect{\xi}_i$ of $\cV(\vect{x})$ :

$\vect{x}=\sum_{\vect{\xi}_i\in\cV(\vect{x})}\alpha_i\vect{\xi}_i$

Examples

Create a P1 Lagrange evaluation:

>>> import openturns as ot
>>> field = ot.Field(ot.RegularGrid(0.0, 1.0, 4), [[0.5], [1.5], [1.0], [-0.5]])
>>> evaluation = ot.P1LagrangeEvaluation(field)
>>> print(evaluation([2.3]))
[0.55]

Methods

`draw`(*args)	Draw the output of function as a `Graph`.
`getCallsNumber`()	Accessor to the number of times the function has been called.
`getCheckOutput`()	Accessor to the output verification flag.
`getClassName`()	Accessor to the object's name.
`getDescription`()	Accessor to the description of the inputs and outputs.
`getEnclosingSimplexAlgorithm`()	Accessor to the algorithm used to find the simplex containing a given point.
`getField`()	Accessor to the field defining the functions.
`getInputDescription`()	Accessor to the description of the inputs.
`getInputDimension`()	Accessor to the number of the inputs.
`getMarginal`(*args)	Accessor to marginal.
`getMesh`()	Accessor to the mesh over which the interpolation is defined.
`getName`()	Accessor to the object's name.
`getNearestNeighbourAlgorithm`()	Accessor to the algorithm used to find the vertex nearest to a given point.
`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.
`getValues`()	Accessor to the values in which the interpolation is done.
`hasName`()	Test if the object is named.
`isActualImplementation`()	Accessor to the validity flag.
`isLinear`()	Accessor to the linearity of the evaluation.
`isLinearlyDependent`(index)	Accessor to the linearity of the evaluation with regard to a specific variable.
`parameterGradient`(inP)	Gradient against the parameters.
`setCheckOutput`(checkOutput)	Accessor to the output verification flag.
`setDescription`(description)	Accessor to the description of the inputs and outputs.
`setEnclosingSimplexAlgorithm`(enclosingSimplex)	Accessor to the algorithm used to find the simplex containing a given point.
`setField`(field)	Accessor to the field defining the functions.
`setInputDescription`(inputDescription)	Accessor to the description of the inputs.
`setMesh`(mesh)	Accessor to the mesh over which the interpolation is defined.
`setName`(name)	Accessor to the object's name.
`setNearestNeighbourAlgorithm`(nearestNeighbour)	Accessor to the algorithm used to find the vertex nearest to a given point.
`setOutputDescription`(outputDescription)	Accessor to the description of the outputs.
`setParameter`(parameters)	Accessor to the parameter values.
`setParameterDescription`(description)	Accessor to the parameter description.
`setStopCallback`(callBack[, state])	Set up a stop callback.
`setValues`(values)	Accessor to the values in which the interpolation is done.

__init__(*args)¶

draw(*args)¶

Draw the output of function as a Graph.

Available usages:

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

draw(firstInputMarg, secondInputMarg, outputMarg, CP, 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.

CPsequence of float

Central point.

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 ones of the central point CP. Then it 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 it 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_numberint: Integer that counts the number of times the function has been called since its creation.

getCheckOutput()¶

Accessor to the output verification flag.

Returns:

check_outputbool: Whether to check return values for nan or inf.

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]

getEnclosingSimplexAlgorithm()¶

Accessor to the algorithm used to find the simplex containing a given point.

Returns:

algoEnclosingSimplexAlgorithm: The algorithm used to find the simplex containing a given point.

getField()¶

Accessor to the field defining the functions.

Returns:

fieldField: The field defining the function.

getInputDescription()¶

Accessor to the description of the inputs.

Returns:

descriptionDescription: Description of the inputs.

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 number of the inputs.

Returns:

number_inputsint: Number of inputs.

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 $f=(f_0 , \dots, f_{p-1})$ .

getMesh()¶

Accessor to the mesh over which the interpolation is defined.

Returns:

meshMesh: The mesh over which the interpolation is defined.

getName()¶

Accessor to the object’s name.

Returns:

namestr: The name of the object.

getNearestNeighbourAlgorithm()¶

Accessor to the algorithm used to find the vertex nearest to a given point.

Returns:

algoNearestNeighbourAlgorithm: The algorithm used to find the vertex nearest to a given point.

getOutputDescription()¶

Accessor to the description of the outputs.

Returns:

descriptionDescription: Description of 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.getOutputDescription())
[y0]

getOutputDimension()¶

Accessor to the number of the outputs.

Returns:

number_outputsint: Number of outputs.

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:

parameter_dimensionint: Dimension of the parameter.

getValues()¶

Accessor to the values in which the interpolation is done.

Returns:

valuesSample: The values in which the interpolation is done.

hasName()¶

Test if the object is named.

Returns:

hasNamebool: True if the name is not empty.

isActualImplementation()¶

Accessor to the validity flag.

Returns:

is_implbool: Whether the implementation is valid.

isLinear()¶

Accessor to the linearity of the evaluation.

Returns:

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

isLinearlyDependent(index)¶

Accessor to the linearity of the evaluation 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 evaluation is linearly dependent on the specified variable, False otherwise.

parameterGradient(inP)¶

Gradient against the parameters.

Parameters:

xsequence of float: Input point

Returns:

parameter_gradientMatrix: The parameters gradient computed at x.

setCheckOutput(checkOutput)¶

Accessor to the output verification flag.

Parameters:

check_outputbool: Whether to check return values for nan or inf.

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]

setEnclosingSimplexAlgorithm(enclosingSimplex)¶

Accessor to the algorithm used to find the simplex containing a given point.

Parameters:

algoEnclosingSimplexAlgorithm: The algorithm used to find the simplex containing a given point.

setField(field)¶

Accessor to the field defining the functions.

Parameters:

fieldField: The field defining the function.

setInputDescription(inputDescription)¶

Accessor to the description of the inputs.

Returns:

descriptionDescription: Description of the inputs.

setMesh(mesh)¶

Accessor to the mesh over which the interpolation is defined.

Parameters:

meshMesh: The mesh over which the interpolation is defined.

setName(name)¶

Accessor to the object’s name.

Parameters:

namestr: The name of the object.

setNearestNeighbourAlgorithm(nearestNeighbour)¶

Accessor to the algorithm used to find the vertex nearest to a given point.

Parameters:

algoNearestNeighbourAlgorithm: The algorithm used to find the vertex nearest to a given point.

setOutputDescription(outputDescription)¶

Accessor to the description of the outputs.

Returns:

descriptionDescription: Description of the outputs.

setParameter(parameters)¶

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.

setValues(values)¶

Accessor to the values in which the interpolation is done.

Parameters:

mesh2-d sequence of floats: The values in which the interpolation is done.

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