# ExponentialCauchy¶

class ExponentialCauchy(*args)

Absolute exponential covariance model.

Available constructors:

ExponentialCauchy(theta, sigma)
Parameters: theta : sequence of floats Scale coefficients. The spatial dimension is the size of vector. sigma : sequence of floats Amplitude coefficients . Should be of size 1

Notes

The second order model instanciate both a openturns.AbsoluteExponential as covariance function and openturns.CauchyModel as spectral model.

Examples

>>> import openturns as ot
>>> model = ot.ExponentialCauchy([10.0, 10.0], [1.0])
>>> t = [0.1, 0.3]
>>> s = [0.2, 0.4]
>>> print(model.computeCovariance(s, t))
[[ 0.980199 ]]
>>> tau = [0.1, 0.3]
>>> print(model.computeCovariance(tau))
[[ 0.960789 ]]
>>> f = 0.3
>>> print(model.computeSpectralDensity(f))
[[ (0.00315075,0) ]]
>>> f = 10
>>> print(model.computeSpectralDensity(f))
[[ (2.56648e-09,0) ]]


Methods

 computeCovariance(*args) Evaluate the covariance function. computeSpectralDensity(frequency) Evaluate the spectral density function for a specific frequency. discretize(timeGrid) Discretize the second order on a given RegularGrid/Mesh model using its covariance function. getAmplitude() Get the amplitude parameter of the second order model. getClassName() Accessor to the object’s name. getCovarianceModel() Return the covariance model. getDimension() Get the dimension of the SecondOrderModel. getId() Accessor to the object’s id. getName() Accessor to the object’s name. getScale() Get the scale parameter of the second order model. getShadowedId() Accessor to the object’s shadowed id. getSpatialDimension() Get the spatial dimension of the spectral density function. getSpectralModel() Return the spectral model. getVisibility() Accessor to the object’s visibility state. hasName() Test if the object is named. hasVisibleName() Test if the object has a distinguishable name. setModels(covarianceModel, spectralModel) Set both the covariance and spectral models of a second order model. setName(name) Accessor to the object’s name. setShadowedId(id) Accessor to the object’s shadowed id. setVisibility(visible) Accessor to the object’s visibility state.
 getInputDimension getOutputDimension
__init__(*args)

Initialize self. See help(type(self)) for accurate signature.

computeCovariance(*args)

Evaluate the covariance function.

Available usages:

computeCovariance(s, t)

computeCovariance(tau)

Parameters: s, t : floats or sequence of floats. Inputs. tau : float or sequence of floats. Input. covariance : CovarianceMatrix The evaluation of the covariance function.

Notes

computeCovariance evaluates the covariance model at :

We note that the first usage calls the second as model is stationary. Thus,
= with .
computeSpectralDensity(frequency)

Evaluate the spectral density function for a specific frequency.

Parameters: f : float Frequency value. spd : HermitianMatrixs The evaluation of spectral density function at frequency f.

Notes

computeSpectralDensity evaluates the spectral model at :

where is a covariance matrix that explains the covariance structure and

discretize(timeGrid)

Discretize the second order on a given RegularGrid/Mesh model using its covariance function.

Parameters: meshOrGrid : Mesh or time grid of size associated with the process. covarianceMatrix : CovarianceMatrix Covariance matrix (if the process is of dimension ).

Notes

This method makes a discretization of the covariance model on meshOrGrid composed of the vertices and returns the covariance matrix:

getAmplitude()

Get the amplitude parameter of the second order model.

Returns: amplitude : Point The used amplitude parameter.
getClassName()

Accessor to the object’s name.

Returns: class_name : str The object class name (object.__class__.__name__).
getCovarianceModel()

Return the covariance model.

Returns: covarianceModel : CovarianceModel The covariance model of the second order model.
getDimension()

Get the dimension of the SecondOrderModel.

Returns: dimension : int Dimension of the SecondOrderModel.
getId()

Accessor to the object’s id.

Returns: id : int Internal unique identifier.
getName()

Accessor to the object’s name.

Returns: name : str The name of the object.
getScale()

Get the scale parameter of the second order model.

Returns: scale : Point The used scale parameter.
getShadowedId()

Accessor to the object’s shadowed id.

Returns: id : int Internal unique identifier.
getSpatialDimension()

Get the spatial dimension of the spectral density function.

Returns: spatialDimension : int SpatialDimension of the SecondOrderModel.
getSpectralModel()

Return the spectral model.

Returns: spectralModel : SpectralModel The spectral model of the second order model.
getVisibility()

Accessor to the object’s visibility state.

Returns: visible : bool Visibility flag.
hasName()

Test if the object is named.

Returns: hasName : bool True if the name is not empty.
hasVisibleName()

Test if the object has a distinguishable name.

Returns: hasVisibleName : bool True if the name is not empty and not the default one.
setModels(covarianceModel, spectralModel)

Set both the covariance and spectral models of a second order model.

Parameters: covarianceModel : CovarianceModel The covariance model of the second order model. spectralModel : SpectralModel The spectral model of the second order model.
setName(name)

Accessor to the object’s name.

Parameters: name : str The name of the object.
setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters: id : int Internal unique identifier.
setVisibility(visible)

Accessor to the object’s visibility state.

Parameters: visible : bool Visibility flag.