%feature("docstring") OT::CauchyModel
"Cauchy spectral model.

Available constructors:
    CauchyModel(*theta, sigma*)

Parameters
----------
theta : sequence of float
    Scale coefficients :math:`\theta` of the spectral density function.
    Vector of size n
sigma : sequence of float
    Amplitude coefficients :math:`\sigma` of the spectral density function.
    Vector of size p

Notes
-----
The spectral density function of input dimension **n** and output dimension **p** writes:

.. math::

   \forall (i,j) \in [0,p-1]^2, S(f)_{i,j} =  \Sigma_{i,j} \prod_{k=1}^{n} \frac{\theta_k}{1 + (2\pi \theta_k f)^2}


Examples
--------
>>> import openturns as ot
>>> spectralModel = ot.CauchyModel([3.0, 2.0], [2.0])
>>> f = 0.3
>>> print(spectralModel(f))
[[ (0.191364,0) ]]
>>> f = 10
>>> print(spectralModel(f))
[[ (1.71084e-07,0) ]]"

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%define OT_CauchyModel_computeStandardRepresentative_doc
"Compute the standard representant of the spectral density function.

Parameters
----------
tau : float
    Frequency value.

Returns
-------
rho : Complex
     Standard representant factor of the spectral density function.

Notes
-----
Using definitions in :class:`~openturns.SpectralModel`: the standard representative function writes:

.. math::

  \forall \vect{f} \in \Rset^n, \rho(\vect{f} \odot \vect{\theta}) =  \prod_{k=1}^{n} \frac{1}{1 + (2\pi \theta_k f)^2}

where :math:`(\vect{f} \odot \vect{\theta})_k = \vect{f}_k \vect{\theta}_k`"
%enddef
%feature("docstring") OT::CauchyModel::computeStandardRepresentative
OT_CauchyModel_computeStandardRepresentative_doc

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