KarhunenLoeveP1Algorithm¶
(Source code, png, hires.png, pdf)

-
class
KarhunenLoeveP1Algorithm
(*args)¶ Computation of Karhunen-Loeve decomposition using P1 approximation.
Parameters: - mesh :
Mesh
The mesh
that discretizes the domain
.
- covariance :
CovarianceModel
The covariance function to decompose.
- s : float,
The threshold used to select the most significant eigenmodes, defined in
KarhunenLoeveAlgorithm
.
Notes
The Karhunen-Loeve
algorithm solves the Fredholm problem associated to the covariance function
: see
KarhunenLoeveAlgorithm
to get the notations.The Karhunen-Loeve
approximation uses the
functional basis
where
are the basis functions of the
finite element space associated to
, which vertices are
.
The covariance function
is approximated by its
approximation
on
:
The Galerkin approach and the collocation one are equivalent in the
approach and both lead to the following formulation:
where
with
,
.
Examples
Create a Karhunen-Loeve P1 algorithm:
>>> import openturns as ot >>> mesh = ot.IntervalMesher([10]*2).build(ot.Interval([-1.0]*2, [1.0]*2)) >>> s = 0.01 >>> model = ot.AbsoluteExponential([1.0]*2) >>> algorithm = ot.KarhunenLoeveP1Algorithm(mesh, model, s)
Run it!
>>> algorithm.run() >>> result = algorithm.getResult()
Methods
getClassName
()Accessor to the object’s name. getCovarianceModel
()Accessor to the covariance model. getId
()Accessor to the object’s id. getMesh
()Accessor to the mesh. getName
()Accessor to the object’s name. getResult
()Get the result structure. getShadowedId
()Accessor to the object’s shadowed id. getThreshold
()Accessor to the threshold used to select the most significant eigenmodes. getVisibility
()Accessor to the object’s visibility state. hasName
()Test if the object is named. hasVisibleName
()Test if the object has a distinguishable name. run
()Computation of the eigenvalues and eigenfunctions values at nodes. setCovarianceModel
(covariance)Accessor to the covariance model. setName
(name)Accessor to the object’s name. setShadowedId
(id)Accessor to the object’s shadowed id. setThreshold
(threshold)Accessor to the limit ratio on eigenvalues. setVisibility
(visible)Accessor to the object’s visibility state. -
__init__
(*args)¶ Initialize self. See help(type(self)) for accurate signature.
-
getClassName
()¶ Accessor to the object’s name.
Returns: - class_name : str
The object class name (object.__class__.__name__).
-
getCovarianceModel
()¶ Accessor to the covariance model.
Returns: - covModel :
CovarianceModel
The covariance model.
- covModel :
-
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.
-
getResult
()¶ Get the result structure.
Returns: - resKL :
KarhunenLoeveResult
The structure containing all the results of the Fredholm problem.
Notes
The structure contains all the results of the Fredholm problem.
- resKL :
-
getShadowedId
()¶ Accessor to the object’s shadowed id.
Returns: - id : int
Internal unique identifier.
-
getThreshold
()¶ Accessor to the threshold used to select the most significant eigenmodes.
Returns: - s : float, positive
The threshold
.
Notes
OpenTURNS truncates the sequence
at the index
defined in (3).
-
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.
-
run
()¶ Computation of the eigenvalues and eigenfunctions values at nodes.
Notes
Runs the algorithm and creates the result structure
KarhunenLoeveResult
.
-
setCovarianceModel
(covariance)¶ Accessor to the covariance model.
Parameters: - covModel :
CovarianceModel
The covariance model.
- covModel :
-
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.
-
setThreshold
(threshold)¶ Accessor to the limit ratio on eigenvalues.
Parameters: - s : float,
The threshold
defined in (3).
- s : float,
-
setVisibility
(visible)¶ Accessor to the object’s visibility state.
Parameters: - visible : bool
Visibility flag.
- mesh :