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.

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.