1%feature("docstring") OT::ExponentiallyDampedCosineModel
2"Exponentially damped cosine covariance function.
3
4Available constructors:
5    ExponentiallyDampedCosineModel(*spatialDim=1*)
6
7    ExponentiallyDampedCosineModel(*scale, amplitude, f*)
8
9Parameters
10----------
11spatialDim : int
12    Spatial dimension :math:`n`.
13    By default, equal to 1.
14scale : sequence of floats
15    Scale coefficient :math:`\vect{\theta}\in \Rset^n`.
16    The size of :math:`\vect{\theta}` is the input dimension.
17amplitude : sequence of positive floats
18    Amplitude of the process :math:`\vect{\sigma} \in \Rset^d`.
19    Must be of size equal to 1.
20    By default, equal to :math:`[1]`.
21f : positive float
22    Frequency parameter.
23
24Notes
25-----
26The *exponentially damped cosine* function is a stationary covariance function with dimension :math:`d=1`.
27
28We consider the scalar stochastic process :math:`X: \Omega \times\cD \mapsto \Rset`, where :math:`\omega \in \Omega` is an event, :math:`\cD` is a domain of :math:`\Rset^n`.
29
30The  *exponentially damped cosine* covariance function is defined by:
31
32.. math::
33
34    C(\vect{s}, \vect{t}) = \sigma^2 e^{\left(-\left\|\dfrac{\vect{s}-\vect{t}}{\vect{\theta}}\right\|_2\right)} \cos\left(2 \pi f \left\|\dfrac{\vect{s}-\vect{t}}{\vect{\theta}}\right\|_2 \right), \quad \forall (\vect{s}, \vect{t}) \in \cD
35
36The correlation function :math:`\rho` writes:
37
38.. math::
39
40    \rho(\vect{s}, \vect{t}) = e^{\left(-\left\| \vect{s}- \vect{t}\right\|_2\right)} \cos\left(2 \pi f \left\| \vect{s}-\vect{t} \right\|_2 \right), \quad \forall (\vect{s}, \vect{t}) \in \cD
41
42
43
44
45See Also
46--------
47CovarianceModel
48
49Examples
50--------
51Create a standard exponentially damped cosine covariance function:
52
53>>> import openturns as ot
54>>> covModel = ot.ExponentiallyDampedCosineModel(2)
55>>> t = [0.1, 0.3]
56>>> s = [0.5, 0.4]
57>>> print(covModel(s, t))
58[[ -0.564137 ]]
59>>> tau = [0.1, 0.1]
60>>> print(covModel(tau))
61[[ 0.547367 ]]
62
63Create a exponentially damped cosine  covariance function specifying the amplitude and the scale:
64
65>>> covModel2 = ot.ExponentiallyDampedCosineModel([3.3], [1.2], 5.0)
66
67Create a  exponentially damped cosine  covariance function specifying the amplitude and the scale:
68
69>>> covModel3 = ot.ExponentiallyDampedCosineModel([1.5, 2.5], [3.5], 5.0)"
70
71// ---------------------------------------------------------------------
72
73%feature("docstring") OT::ExponentiallyDampedCosineModel::setFrequency
74"Frequency accessor.
75
76Parameters
77----------
78f : positive float
79    Frequency parameter."
80
81// ---------------------------------------------------------------------
82
83%feature("docstring") OT::ExponentiallyDampedCosineModel::getFrequency
84"Frequency accessor.
85
86Returns
87-------
88f : positive float
89    Frequency parameter."
90