1%feature("docstring") OT::InverseTrendTransform
2"Inverse Trend transformation.
3
4Parameters
5----------
6myInverseTrendFunc : :class:`~openturns.Function`
7    The  inverse trend function :math:`f_{trend}^{-1}`.
8
9
10Notes
11-----
12A multivariate stochastic  process :math:`X: \Omega \times\cD \rightarrow \Rset^d` of dimension *d* where :math:`\cD \in \Rset^n` may write as the sum of a trend function :math:`f_{trend}: \Rset^n \rightarrow \Rset^d` and a stationary multivariate stochastic process :math:`X_{stat}: \Omega \times\cD \rightarrow \Rset^d` of dimension *d* as follows:
13
14.. math::
15
16    X(\omega,\vect{t}) = X_{stat}(\omega,\vect{t}) + f_{trend}(\vect{t})
17
18
19We note :math:`(\vect{x}_0, \dots, \vect{x}_{N-1})` the values of one field of the process *X*, associated to the mesh :math:`\cM = (\vect{t}_0, \dots, \vect{t}_{N-1})` of :math:`\cD`. We note :math:`(\vect{x}^{stat}_0, \dots, \vect{x}^{stat}_{N-1})` the values of the resulting stationary field. Then we have:
20
21.. math::
22
23    \vect{x}^{stat}_i = \vect{x}_i - f_{trend}(\vect{t}_i)
24
25The inverse trend transformation enables to get the :math:`X_{stat}` process or to get the :math:`(\vect{x}^{stat}_0, \dots, \vect{x}^{stat}_{N-1})` field.
26
27
28Examples
29--------
30Create a trend function: :math:`f_{trend} : \Rset \mapsto \Rset` where :math:`f_{trend}(t,s)=-(1+2t+t^2)`:
31
32>>> import openturns as ot
33>>> h = ot.SymbolicFunction(['t'], ['-(1+2*t+t^2)'])
34>>> mesh = ot.RegularGrid(0.0, 0.1, 11)
35>>> fTrendInv = ot.InverseTrendTransform(h, mesh)
36
37"
38
39// ---------------------------------------------------------------------
40%feature("docstring") OT::InverseTrendTransform::getInverse
41"Accessor to the  trend function.
42
43Returns
44-------
45myTrendTransform : :class:`~openturns.TrendTransform`
46    The :math:`f_{trend}` function.
47
48"
49