%feature("docstring") OT::InverseBoxCoxTransform
"BoxCox transformation.

Available constructors:
    InverseBoxCoxTransform(*lambdaVect, shiftVect = 0*)

    InverseBoxCoxTransform(*lambda, shift=0*)

Parameters
----------
lambdaVect : :class:`~openturns.Point`
    The  :math:`(\lambda_1, \dots, \lambda_d)` parameter.
shiftVect : :class:`~openturns.Point`
    The  :math:`(\alpha_1, \dots, \alpha_d)` parameter. 

    Default is :math:`(\alpha_1, \dots, \alpha_d)=(0, \dots, 0)`.
lambda : float
    The  :math:`\lambda` parameter in the univariate case.
shift : float
    The   :math:`\alpha` parameter in the univariate case.

    Default is :math:`\alpha = 0`.


Notes
-----
The 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`:

.. math::

    \begin{array}{lcl}
      h_{\lambda_i, \alpha_i}^{-1}(y) & = &
      \left\{
      \begin{array}{ll}
    \displaystyle (\lambda_i y + 1)^{\frac{1}{\lambda_i}} - \alpha_i & \lambda_i \neq 0 \\
    \displaystyle \exp(y) - \alpha_i                         & \lambda_i = 0
      \end{array}
      \right.
    \end{array}

The  Box Cox transformation writes:

.. math::

    h_{\lambda_i, \alpha_i}^{-1} (x)= 
    \left\{
    \begin{array}{ll}
    \dfrac{(x+\alpha_i)^\lambda_i-1}{\lambda} & \lambda_i \neq 0 \\
    \log(x+\alpha_i)                        & \lambda_i = 0
    \end{array}
    \right.

for all :math:`x+\alpha_i >0`.

Examples
--------

Create an inverse Box Cox tranformation:

>>> import openturns as ot
>>> myLambda = 0.1
>>> myInverseBoxCox = ot.InverseBoxCoxTransform(myLambda)
"

// ---------------------------------------------------------------------
%feature("docstring") OT::InverseBoxCoxTransform::getLambda
"Accessor to the :math:`\vect{\lambda}` parameter.

Returns
-------
myLambda : :class:`~openturns.Point`
    The :math:`\vect{\lambda}` parameter.

"
// ---------------------------------------------------------------------
%feature("docstring") OT::InverseBoxCoxTransform::getShift
"Accessor to the :math:`\vect{\alpha}` parameter.

Returns
-------
myLambda : :class:`~openturns.Point`
    The :math:`\vect{\Lambda}` parameter.

"
// ---------------------------------------------------------------------
%feature("docstring") OT::InverseBoxCoxTransform::getInverse
"Accessor to the  Box Cox transformation.

Returns
-------
myInverseBoxCox : :class:`~openturns.BoxCoxTransform`
    The Box Cox transformation.

"
