1%feature("docstring") OT::P1LagrangeEvaluation
2"Data based math evaluation implementation.
3
4Available constructors:
5
6    P1LagrangeEvaluation(*field*)
7
8Parameters
9----------
10field : :class:`~openturns.Field`
11    Field :math:`\cF` defining the parameters of a P1 Lagrange interpolation function.
12
13See also
14--------
15Function, AggregatedEvaluation, DualLinearCombinationEvaluation,
16LinearFunction
17
18Notes
19-----
20It returns a :class:`~openturns.Function` that implements the P1 Lagrange interpolation function :math:`f : \cD_N \rightarrow \Rset^p` :
21
22.. math::
23    \forall \vect{x} \in \Rset^n, f(\vect{x}) = \sum_{\vect{\xi}_i\in\cV(\vect{x})}\alpha_i f(\vect{\xi}_i)
24
25where :math:`\cD_N` is a :class:`~openturns.Mesh`, :math:`\cV(\vect{x})` is the simplex in :math:`\cD_N` that contains :math:`\vect{x}`, :math:`\alpha_i` are the barycentric coordinates of :math:`\vect{x}` wrt the vertices :math:`\vect{\xi}_i` of :math:`\cV(\vect{x})`:
26
27.. math::
28    \vect{x}=\sum_{\vect{\xi}_i\in\cV(\vect{x})}\alpha_i\vect{\xi}_i
29
30Examples
31--------
32Create a P1 Lagrange evaluation:
33
34>>> import openturns as ot
35>>> field = ot.Field(ot.RegularGrid(0.0, 1.0, 4), [[0.5], [1.5], [1.0], [-0.5]])
36>>> evaluation = ot.P1LagrangeEvaluation(field)
37>>> print(evaluation([2.3]))
38[0.55]"
39// ---------------------------------------------------------------------
40
41%feature("docstring") OT::P1LagrangeEvaluation::getField
42"Accessor to the field defining the functions.
43
44Returns
45-------
46field : :class:`~openturns.Field`
47    The field defining the function."
48
49// ---------------------------------------------------------------------
50
51%feature("docstring") OT::P1LagrangeEvaluation::setField
52"Accessor to the field defining the functions.
53
54Parameters
55----------
56field : :class:`~openturns.Field`
57    The field defining the function."
58