1%feature("docstring") OT::InverseBoxCoxTransform
2"BoxCox transformation.
3
4Available constructors:
5    InverseBoxCoxTransform(*lambdaVect, shiftVect = 0*)
6
7    InverseBoxCoxTransform(*lambda, shift=0*)
8
9Parameters
10----------
11lambdaVect : :class:`~openturns.Point`
12    The  :math:`(\lambda_1, \dots, \lambda_d)` parameter.
13shiftVect : :class:`~openturns.Point`
14    The  :math:`(\alpha_1, \dots, \alpha_d)` parameter.
15
16    Default is :math:`(\alpha_1, \dots, \alpha_d)=(0, \dots, 0)`.
17lambda : float
18    The  :math:`\lambda` parameter in the univariate case.
19shift : float
20    The   :math:`\alpha` parameter in the univariate case.
21
22    Default is :math:`\alpha = 0`.
23
24
25Notes
26-----
27The inverse Box Cox transformation :math:`h_{\vect{\lambda}, \vect{\alpha}}^{-1}: \Rset^d \rightarrow \Rset^d` writes for each component :math:`h_{\lambda_i, \alpha_i}^{-1}: \Rset \rightarrow \Rset`:
28
29.. math::
30
31    \begin{array}{lcl}
32      h_{\lambda_i, \alpha_i}^{-1}(y) & = &
33      \left\{
34      \begin{array}{ll}
35    \displaystyle (\lambda_i y + 1)^{\frac{1}{\lambda_i}} - \alpha_i & \lambda_i \neq 0 \\
36    \displaystyle \exp(y) - \alpha_i                         & \lambda_i = 0
37      \end{array}
38      \right.
39    \end{array}
40
41The  Box Cox transformation writes:
42
43.. math::
44
45    h_{\lambda_i, \alpha_i}^{-1} (x)=
46    \left\{
47    \begin{array}{ll}
48    \dfrac{(x+\alpha_i)^\lambda_i-1}{\lambda} & \lambda_i \neq 0 \\
49    \log(x+\alpha_i)                        & \lambda_i = 0
50    \end{array}
51    \right.
52
53for all :math:`x+\alpha_i >0`.
54
55Examples
56--------
57
58Create an inverse Box Cox tranformation:
59
60>>> import openturns as ot
61>>> myLambda = 0.1
62>>> myInverseBoxCox = ot.InverseBoxCoxTransform(myLambda)
63"
64
65// ---------------------------------------------------------------------
66%feature("docstring") OT::InverseBoxCoxTransform::getLambda
67"Accessor to the :math:`\vect{\lambda}` parameter.
68
69Returns
70-------
71myLambda : :class:`~openturns.Point`
72    The :math:`\vect{\lambda}` parameter.
73
74"
75// ---------------------------------------------------------------------
76%feature("docstring") OT::InverseBoxCoxTransform::getShift
77"Accessor to the :math:`\vect{\alpha}` parameter.
78
79Returns
80-------
81myLambda : :class:`~openturns.Point`
82    The :math:`\vect{\Lambda}` parameter.
83
84"
85// ---------------------------------------------------------------------
86%feature("docstring") OT::InverseBoxCoxTransform::getInverse
87"Accessor to the  Box Cox transformation.
88
89Returns
90-------
91myInverseBoxCox : :class:`~openturns.BoxCoxTransform`
92    The Box Cox transformation.
93
94"
95