GaussianProcess¶
(Source code
, png
)
- class GaussianProcess(*args)¶
Gaussian processes.
- Available constructor:
GaussianProcess(trend, covarianceModel, mesh)
GaussianProcess(covarianceModel, mesh)
- Parameters:
- trend
TrendTransform
Trend function of the process. By default the trend is null.
- covarianceModel
CovarianceModel
Temporal covariance model .
- mesh
Mesh
Mesh over which the domain is discretized.
- trend
Notes
GaussianProcess creates the processes, where , from their temporal covariance function , which writes, in the stationary case: . A process is normal, if all its finite dimensional joint distributions are normal (See the method
isNormal()
for a detailed definition).The gaussian processes may have a trend: in that case, the Gaussian process is the sum of the trend function and a zero-mean Gaussian process.
Examples
>>> import openturns as ot >>> ot.RandomGenerator.SetSeed(0) >>> # Amplitude values >>> amplitude = [1.0] >>> # Scale values >>> scale = [1.0] >>> # Second order model with parameters >>> covarianceModel = ot.AbsoluteExponential(scale, amplitude) >>> # Time grid >>> tmin = 0.0 >>> step = 0.1 >>> n = 11 >>> meshGrid = ot.RegularGrid(tmin, step, n) >>> size = 100 >>> myProcess = ot.GaussianProcess(covarianceModel, meshGrid) >>> myProcess.setSamplingMethod(myProcess.CHOLESKY)
Methods
Accessor to the object's name.
Get a continuous realization.
Get the covariance model.
Get the description of the process.
getFuture
(*args)Prediction of the future iterations of the process.
getId
()Accessor to the object's id.
Get the dimension of the domain .
getMarginal
(indices)Get the marginal of the random process.
getMesh
()Get the mesh.
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.
Get the used method for getRealization.
Accessor to the object's shadowed id.
Get the time grid of observation of the process.
getTrend
()Get the trend function.
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.
Tell if the process is trend stationary or not.
setDescription
(description)Set the description of the process.
setMesh
(mesh)Set the mesh.
setName
(name)Accessor to the object's name.
setSamplingMethod
(samplingMethod)Set the used method for getRealization.
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.
- __init__(*args)¶
- 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()¶
Get the covariance model.
- Returns:
- covarianceModel
CovarianceModel
Temporal covariance model .
- covarianceModel
- getDescription()¶
Get the description of the process.
- Returns:
- description
Description
Description of the process.
- description
- 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(indices)¶
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
- 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
- getSamplingMethod()¶
Get the used method for getRealization.
- Returns:
- samplingMethodint
Used method for sampling.
Notes
Available parameters are :
0 (GaussianProcess.CHOLESKY) : Cholesky factor sampling (default method)
1 (GaussianProcess.HMAT) : H-Matrix method (if H-Mat available)
2 (GaussianProcess.GALLIGAOGIBBS) : Gibbs method (in dimension 1 only)
- getShadowedId()¶
Accessor to the object’s shadowed id.
- Returns:
- idint
Internal unique identifier.
- 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()¶
Get the trend function.
- Returns:
- trend
TrendTransform
Trend function.
- 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:
- isTrendStationary()¶
Tell if the process is trend stationary or not.
- Returns:
- isTrendStationarybool
True if the process is trend stationary.
- setDescription(description)¶
Set the description of the process.
- Parameters:
- descriptionsequence of str
Description of the process.
- setName(name)¶
Accessor to the object’s name.
- Parameters:
- namestr
The name of the object.
- setSamplingMethod(samplingMethod)¶
Set the used method for getRealization.
Available parameters are :
0 (GaussianProcess.CHOLESKY) : Cholesky factor sampling (default method)
1 (GaussianProcess.HMAT) : H-Matrix method (if H-Mat available)
2 (GaussianProcess.GALLIGAOGIBBS) : Gibbs method (in dimension 1 only)
- Parameters:
- samplingMethodint
Fix a method for sampling.
- 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.
Examples using the class¶
Estimate a non stationary covariance function
Estimate a stationary covariance function
Create a gaussian process from a cov. model using HMatrix
Use the Box-Cox transformation
Create a process from random vectors and processes
Sample trajectories from a Gaussian Process with correlated outputs
Kriging : generate trajectories from a metamodel
Kriging : draw covariance models
Validation of a Karhunen-Loeve decomposition
Create an event based on a process
Estimate a process-based event probability
Estimate Sobol indices on a field to point function