1%feature("docstring") OT::CauchyModel
2"Cauchy spectral model.
3
4Refer to :ref:`parametric_spectral_model`.
5
6Available constructors:
7    CauchyModel(*theta, sigma*)
8
9Parameters
10----------
11theta : sequence of float
12    Scale coefficients :math:`\theta` of the spectral density function.
13    Vector of size n
14sigma : sequence of float
15    Amplitude coefficients :math:`\sigma` of the spectral density function.
16    Vector of size p
17
18Notes
19-----
20The spectral density function of input dimension **n** and output dimension **p** writes:
21
22.. math::
23
24   \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}
25
26
27Examples
28--------
29>>> import openturns as ot
30>>> spectralModel = ot.CauchyModel([3.0, 2.0], [2.0])
31>>> f = 0.3
32>>> print(spectralModel(f))
33[[ (0.191364,0) ]]
34>>> f = 10
35>>> print(spectralModel(f))
36[[ (1.71084e-07,0) ]]"
37
38// ---------------------------------------------------------------------
39
40%define OT_CauchyModel_computeStandardRepresentative_doc
41"Compute the standard representant of the spectral density function.
42
43Parameters
44----------
45tau : float
46    Frequency value.
47
48Returns
49-------
50rho : Complex
51     Standard representant factor of the spectral density function.
52
53Notes
54-----
55Using definitions in :class:`~openturns.SpectralModel`: the standard representative function writes:
56
57.. math::
58
59  \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}
60
61where :math:`(\vect{f} \odot \vect{\theta})_k = \vect{f}_k \vect{\theta}_k`"
62%enddef
63%feature("docstring") OT::CauchyModel::computeStandardRepresentative
64OT_CauchyModel_computeStandardRepresentative_doc
65
66// ---------------------------------------------------------------------
67