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