SecondOrderModel¶

class
SecondOrderModel
(*args)¶ Second order model.
Notes
We consider a multivariate stochastic process of dimension , where is an event, is a domain of , is a multivariate index and .
We note the random variable at index defined by and a realization of the process , for a given defined by .
The SecondOrderModel class enable to get both spectral information of such process thanks to the
SpectralModel
class and spatial/temporal information using theCovarianceModel
information.A SecondOrderModel object can be created only through its derived classes:
ExponentialCauchy
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. 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. getImplementation
(*args)Accessor to the underlying implementation. getName
()Accessor to the object’s name. getSpatialDimension
()Get the spatial dimension of the spectral density function. getSpectralModel
()Return the spectral model. setModels
(covarianceModel, spectralModel)Set both the covariance and spectral models of a second order model. setName
(name)Accessor to the object’s name. 
__init__
(*args)¶ x.__init__(…) initializes x; see help(type(x)) for 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.
Returns: 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.
Returns: 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
orRegularGrid
Mesh or time grid of size associated with the process.
Returns: 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:

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.

getImplementation
(*args)¶ Accessor to the underlying implementation.
Returns: impl : Implementation
The implementation class.

getName
()¶ Accessor to the object’s name.
Returns: name : str
The name of the object.

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.

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.
