SpectralGaussianProcess¶
(Source code, png, hires.png, pdf)

class
SpectralGaussianProcess
(*args)¶ Spectral Gaussian process.
 Available constructors:
SpectralGaussianProcess(spectralModel, timeGrid)
SpectralGaussianProcess(spectralModel, maxFreq, N)
 Parameters
 timeGrid
RegularGrid
The time grid associated to the process. The algorithm is only implemented when the mesh is a regular grid.
 spectralModel
SpectralModel
 maxFreqfloat
Equal to the maximal frequency minus .
 Nfloat
The number of points in the frequency grid, which is equal to the number of time stamps of the time grid.
 timeGrid
Notes
In the first usage, we fix the time grid and the second order model (spectral density model) which implements the process. The frequency discretization is deduced from the time discretization by the formulas
In the second usage, the process is fixed in the frequency domain. fmax value and N induce the time grid. Care: the maximal frequency used in the computation is not fmax but .
In the third usage, the spectral model is given and the other arguments are the same as the first usage.
In the fourth usage, the spectral model is given and the other arguments are the same as the second usage.
The first call of
getRealization()
might be time consuming because it computes hermitian matrices of size , where is the dimension of the spectral model. These matrices are factorized and stored in order to be used for each call of the getRealization method.Examples
Create a SpectralGaussianProcess from a spectral model and a time grid:
>>> import openturns as ot >>> amplitude = [1.0, 2.0] >>> scale = [4.0, 5.0] >>> spatialCorrelation = ot.CorrelationMatrix(2) >>> spatialCorrelation[0,1] = 0.8 >>> myTimeGrid = ot.RegularGrid(0.0, 0.1, 20) >>> mySpectralModel = ot.CauchyModel(scale, amplitude, spatialCorrelation) >>> mySpectNormProc1 = ot.SpectralGaussianProcess(mySpectralModel, myTimeGrid)
 Attributes
thisown
The membership flag
Methods
Accessor to the object’s name.
Get a continuous realization.
Accessor to the covariance model.
Get the description of the process.
Get the FFT algorithm used to generate realizations of the spectral Gaussian process.
Get the frequency grid used to discretize the spectral model.
Get the frequency step used to discretize the spectral model.
getFuture
(*args)Prediction of the future iterations of the process.
getId
()Accessor to the object’s id.
Get the dimension of the domain .
getMarginal
(*args)Get the marginal of the random process.
Get the maximal frequency used in the computation.
getMesh
()Get the mesh.
Get the number of points in the frequency grid.
getName
()Accessor to the object’s name.
Get the dimension of the domain .
Get a realization of the process.
getSample
(size)Get realizations of the process.
Accessor to the object’s shadowed id.
Get the spectral model.
Get the time grid of observation of the process.
getTrend
()Accessor to the trend.
Accessor to the object’s visibility state.
hasName
()Test if the object is named.
Test if the object has a distinguishable name.
Test whether the process is composite or not.
isNormal
()Test whether the process is normal or not.
Test whether the process is stationary or not.
setDescription
(description)Set the description of the process.
setFFTAlgorithm
(fft)Set the FFT algorithm used to generate realizations of the spectral Gaussian process.
setMesh
(mesh)Set the mesh.
setName
(name)Accessor to the object’s name.
setShadowedId
(id)Accessor to the object’s shadowed id.
setTimeGrid
(timeGrid)Set the time grid of observation of the process.
setVisibility
(visible)Accessor to the object’s visibility state.
AdaptGrid

__init__
(*args)¶ Initialize self. See help(type(self)) for accurate signature.

getClassName
()¶ Accessor to the object’s name.
 Returns
 class_namestr
The object class name (object.__class__.__name__).

getContinuousRealization
()¶ Get a continuous realization.
 Returns
 realization
Function
According to the process, the continuous realizations are built:
either using a dedicated functional model if it exists: e.g. a functional basis process.
or using an interpolation from a discrete realization of the process on : in dimension , a linear interpolation and in dimension , a piecewise constant function (the value at a given position is equal to the value at the nearest vertex of the mesh of the process).
 realization

getCovarianceModel
()¶ Accessor to the covariance model.
 Returns
 cov_model
CovarianceModel
Covariance model, if any.
 cov_model

getDescription
()¶ Get the description of the process.
 Returns
 description
Description
Description of the process.
 description

getFFTAlgorithm
()¶ Get the FFT algorithm used to generate realizations of the spectral Gaussian process.

getFrequencyGrid
()¶ Get the frequency grid used to discretize the spectral model.
 Returns
 freqGrid
RegularGrid
The frequency grid used to discretize the spectral model.
 freqGrid

getFrequencyStep
()¶ Get the frequency step used to discretize the spectral model.
 Returns
 freqStepfloat
The frequency step used to discretize the spectral model.

getFuture
(*args)¶ Prediction of the future iterations of the process.
 Parameters
 stepNumberint,
Number of future steps.
 sizeint, , optional
Number of futures needed. Default is 1.
 Returns
 prediction
ProcessSample
orTimeSeries
future iterations of the process. If , prediction is a
TimeSeries
. Otherwise, it is aProcessSample
.
 prediction

getId
()¶ Accessor to the object’s id.
 Returns
 idint
Internal unique identifier.

getInputDimension
()¶ Get the dimension of the domain .
 Returns
 nint
Dimension of the domain : .

getMarginal
(*args)¶ Get the marginal of the random process.
 Parameters
 kint or list of ints
Index of the marginal(s) needed.
 Returns
 marginals
Process
Process defined with marginal(s) of the random process.
 marginals

getMaximalFrequency
()¶ Get the maximal frequency used in the computation.
 Returns
 freqMaxfloat
The maximal frequency used in the computation: .

getNFrequency
()¶ Get the number of points in the frequency grid.
 Returns
 freqGrid
RegularGrid
The number of points in the frequency grid, which is equal to the number of time stamps of the time grid.
 freqGrid

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

getOutputDimension
()¶ Get the dimension of the domain .
 Returns
 dint
Dimension of the domain .

getRealization
()¶ Get a realization of the process.
 Returns
 realization
Field
Contains a mesh over which the process is discretized and the values of the process at the vertices of the mesh.
 realization

getSample
(size)¶ Get realizations of the process.
 Parameters
 nint,
Number of realizations of the process needed.
 Returns
 processSample
ProcessSample
realizations of the random process. A process sample is a collection of fields which share the same mesh .
 processSample

getShadowedId
()¶ Accessor to the object’s shadowed id.
 Returns
 idint
Internal unique identifier.

getSpectralModel
()¶ Get the spectral model.
 Returns
 specMod
SpectralModel
The spectral model defining the process.
 specMod

getTimeGrid
()¶ Get the time grid of observation of the process.
 Returns
 timeGrid
RegularGrid
Time grid of a process when the mesh associated to the process can be interpreted as a
RegularGrid
. We check if the vertices of the mesh are scalar and are regularly spaced in but we don’t check if the connectivity of the mesh is conform to the one of a regular grid (without any hole and composed of ordered instants).
 timeGrid

getTrend
()¶ Accessor to the trend.
 Returns
 trend
TrendTransform
Trend, if any.
 trend

getVisibility
()¶ Accessor to the object’s visibility state.
 Returns
 visiblebool
Visibility flag.

hasName
()¶ Test if the object is named.
 Returns
 hasNamebool
True if the name is not empty.

hasVisibleName
()¶ Test if the object has a distinguishable name.
 Returns
 hasVisibleNamebool
True if the name is not empty and not the default one.

isComposite
()¶ Test whether the process is composite or not.
 Returns
 isCompositebool
True if the process is composite (built upon a function and a process).

isNormal
()¶ Test whether the process is normal or not.
 Returns
 isNormalbool
True if the process is normal.
Notes
A stochastic process is normal if all its finite dimensional joint distributions are normal, which means that for all and , with , there is and such that:
where , and and is the symmetric matrix:
A Gaussian process is entirely defined by its mean function and its covariance function (or correlation function ).

isStationary
()¶ Test whether the process is stationary or not.
 Returns
 isStationarybool
True if the process is stationary.
Notes
A process is stationary if its distribution is invariant by translation: , , , we have:

setDescription
(description)¶ Set the description of the process.
 Parameters
 descriptionsequence of str
Description of the process.

setFFTAlgorithm
(fft)¶ Set the FFT algorithm used to generate realizations of the spectral Gaussian process.

setName
(name)¶ Accessor to the object’s name.
 Parameters
 namestr
The name of the object.

setShadowedId
(id)¶ Accessor to the object’s shadowed id.
 Parameters
 idint
Internal unique identifier.

setTimeGrid
(timeGrid)¶ Set the time grid of observation of the process.
 Returns
 timeGrid
RegularGrid
Time grid of observation of the process when the mesh associated to the process can be interpreted as a
RegularGrid
. We check if the vertices of the mesh are scalar and are regularly spaced in but we don’t check if the connectivity of the mesh is conform to the one of a regular grid (without any hole and composed of ordered instants).
 timeGrid

setVisibility
(visible)¶ Accessor to the object’s visibility state.
 Parameters
 visiblebool
Visibility flag.

thisown
¶ The membership flag