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KerMor
0.9
Model order reduction for nonlinear dynamical systems and nonlinear approximation
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KerMor
0.9
Model order reduction for nonlinear dynamical systems and nonlinear approximation
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Abstract class for radial basis function / rotation- and translation invariant kernels. More...
Abstract class for radial basis function / rotation- and translation invariant kernels.
All rbf kernels have the form \(\K(x,y) := \phi(\noG{x-y}), \vx\in\R^d\) for some real-valued scalar function \(\phi: [0, \infty] \longrightarrow \R\) and a given norm-inducing matrix \(\vG\).
When combinations of Kernels are used, this interface will have to be changed to a property. Up to now, the class CombinationKernel cannot dynamically adopt to the interface for the case that all contained kernels implement this interface.
This class is part of the framework
Homepage http://www.morepas.org/software/index.htmlDocumentation http://www.morepas.org/software/kermor/index.htmlLicense KerMor license conditionsDefinition at line 18 of file ARBFKernel.m.
Public Member Functions | |
| ARBFKernel () | |
| function K = | evaluate (matrix< double > x,matrix< double > y) |
| Evaluates the rotation and translation invariant kernel. More... | |
| function bool = | eq (B) |
| function copy = | clone (copy) |
| The interface method with returns a copy of the current class instance. More... | |
| function r = | getSqDiffNorm (matrix< double > x,matrix< double > y) |
| Returns the weighted squared norm \(r\) of the difference \(\noG{x-y}^2/\gamma^2\). More... | |
| virtual function phir = | evaluateScalar (matrix< double > r) |
| Allows the evaluation of the function \(\phi(r)\) for scalar \(r\) directly. More... | |
 Public Member Functions inherited from kernels.BaseKernel | |
| BaseKernel () | |
| function fcn = | getLipschitzFunction () |
| Method that allows error estimators to obtain a lipschitz constant estimation function from this kernel. More... | |
| function bool = | eq (B) |
| Checks if a kernel equals another kernel. More... | |
| function copy = | clone (copy) |
| The interface method with returns a copy of the current class instance. More... | |
| virtual function Nabla = | getNabla (x, y) |
| Computes the partial derivatives with respect to each component of the first argument. More... | |
| virtual function c = | getGlobalLipschitz () |
| Returns the global lipschitz constant of this kernel. More... | |
| Public Member Functions inherited from KerMorObject | |
| KerMorObject () | |
| Constructs a new KerMor object. More... | |
| function | display () |
| disp(object2str(this)); More... | |
| function bool = | eq (B) |
| Checks equality of two KerMor objects. More... | |
| function bool = | ne (B) |
| Checks if two KerMorObjects are different. More... | |
| function cn = | getClassName () |
| Returns the simple class name of this object without packages. More... | |
| Public Member Functions inherited from DPCMObject | |
| DPCMObject () | |
| Creates a new DPCM object. More... | |
| DPCMObject () | |
Public Attributes | |
| double | Gamma = 1 |
| Univariate scaling. More... | |
| Public Attributes inherited from kernels.BaseKernel | |
| matrix< double > | G = 1 |
| The matrix \(\vG\) that induces the state space scalar product \(\spG{x}{y}\) and norm \(\noG{x-y}\) to use. More... | |
| matrix< double > | P = "[]" |
| Projection/selection matrix \(\vP\) for argument components. More... | |
| logical | IsRBF = false |
| Flag that determines if the current kernel is a radial basis function, i.e. its evaluation is of the form \(\K(x,y) = \phi(\noG{x-y})\) for some scalar function \(\phi\). More... | |
| logical | IsScProd = false |
| Flag that determines if the current kernel bases on scalar product evaluations, i.e. are of the form \(\K(x,y) = \phi(\spG{x}{y})\) for some scalar function \(\phi\). More... | |
| Public Attributes inherited from DPCMObject | |
| WorkspaceVariableName = "" | |
| The workspace variable name of this class. Optional. More... | |
| ID = "[]" | |
| An ID that allows to uniquely identify this DPCMObject (at least within the current MatLab session/context). More... | |
| PropertiesChanged = "[]" | |
| The Dictionary containing all the property settings as key/value pairs. More... | |
| Public Attributes inherited from handle | |
| addlistener | |
| Creates a listener for the specified event and assigns a callback function to execute when the event occurs. More... | |
| notify | |
| Broadcast a notice that a specific event is occurring on a specified handle object or array of handle objects. More... | |
| delete | |
| Handle object destructor method that is called when the object's lifecycle ends. More... | |
| disp | |
| Handle object disp method which is called by the display method. See the MATLAB disp function. More... | |
| display | |
| Handle object display method called when MATLAB software interprets an expression returning a handle object that is not terminated by a semicolon. See the MATLAB display function. More... | |
| findobj | |
| Finds objects matching the specified conditions from the input array of handle objects. More... | |
| findprop | |
| Returns a meta.property objects associated with the specified property name. More... | |
| fields | |
| Returns a cell array of string containing the names of public properties. More... | |
| fieldnames | |
| Returns a cell array of string containing the names of public properties. See the MATLAB fieldnames function. More... | |
| isvalid | |
| Returns a logical array in which elements are true if the corresponding elements in the input array are valid handles. This method is Sealed so you cannot override it in a handle subclass. More... | |
| eq | |
| Relational functions example. See details for more information. More... | |
| transpose | |
| Transposes the elements of the handle object array. More... | |
| permute | |
| Rearranges the dimensions of the handle object array. See the MATLAB permute function. More... | |
| reshape | |
| hanges the dimensions of the handle object array to the specified dimensions. See the MATLAB reshape function. More... | |
| sort | |
| ort the handle objects in any array in ascending or descending order. More... | |
Additional Inherited Members | |
| Protected Member Functions inherited from KerMorObject | |
| function | checkType (obj, type) |
| Object typechecker. More... | |
| Protected Member Functions inherited from DPCMObject | |
| function | registerProps (varargin) |
| Call this method at any class that defines DPCM observed properties. More... | |
| function | registerProps (varargin) |
| Static Protected Member Functions inherited from DPCMObject | |
| static function obj = | loadobj (obj, from) |
| Re-register any registered change listeners! More... | |
| static function obj = | loadobj (obj, from) |
| Protected Attributes inherited from kernels.BaseKernel | |
| fG = 1 | |
| fP = "[]" | |
| kernels.ARBFKernel.ARBFKernel | ( | ) |
Definition at line 72 of file ARBFKernel.m.
References kernels.BaseKernel.IsRBF.
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virtual |
The interface method with returns a copy of the current class instance.
| target | If clone was called for a subclass of this class, target must contain the new instance of the subclass that is to be the cloned result. |
Implements ICloneable.
Reimplemented in kernels.BellFunction.
Definition at line 108 of file ARBFKernel.m.
References Gamma.
| function bool = kernels.ARBFKernel.eq | ( | B | ) |
Definition at line 103 of file ARBFKernel.m.
Evaluates the rotation and translation invariant kernel.
Default implementation, computes the squared difference norm, takes the square root and calls evaluateScalar with it.
If \(y_j\) is set, the dimensions of \(x_i\) and \(y_j\) must be equal for all \(i,j\).
| x | First set \(x_i \in \R^d\) of \(n\) vectors |
| y | Second set \(y_j \in \R^d\) of \(m\) vectors. If y is empty \(y_i = x_i\) and \(n=m\) is assumed. |
| K | The evaluation matrix \(\K(x, y) \in \R^{n\times m}\) of the radial basis function, with entries \(\K(x_i,y_j)\) at \(i,j\). |
Implements kernels.BaseKernel.
Reimplemented in kernels.InvMultiquadrics.
Definition at line 78 of file ARBFKernel.m.
References evaluateScalar(), and getSqDiffNorm().
Allows the evaluation of the function \(\phi(r)\) for scalar \(r\) directly.
Implementations must accept matrix valued \(r\) and evaluate by component-based means.
| r | The radius matrix \(\vR\in\R^{n\times m}\) |
| phir | The evaluation matrix \(\phi(R)\in\R^{n\times m}\) with entries \(\phi(R)_{ij} = \phi(r_{ij})\). |
Referenced by evaluate(), kernels.BellFunction.ModifiedNewton(), kernels.BellFunction.optFun(), and demos.BellFunctions.SecantGradientPlots().
Returns the weighted squared norm \(r\) of the difference \(\noG{x-y}^2/\gamma^2\).
The evaluation respects and projection matrix \(\vP\) that might be set at kernels.BaseKernel. In this case the matrix \(\vG\) must match the projected sizes of the argument vectors.
If \(y_j\) is set, the dimensions of \(x_i\) and \(y_j\) must be equal for all \(i,j\).
| x | First set \(x_i \in \R^d\) of \(n\) vectors |
| y | Second set \(y_j \in \R^d\) of \(m\) vectors. If y is empty \(y_i = x_i\) and \(n=m\) is assumed. |
| r | The matrix \(\vR \in \R^{n\times m}\) with entries \(R_{ij} = \norm{x_i-y_j}{G}^2/\gamma^2\) |
Sealed set to true. It cannot be overwritten. Definition at line 116 of file ARBFKernel.m.
References kernels.BaseKernel.fG, and kernels.BaseKernel.fP.
Referenced by kernels.GaussKernel.evaluate(), evaluate(), and kernels.InvMultiquadrics.evaluate().
| kernels.ARBFKernel.Gamma = 1 |
Univariate scaling.
Default: 1
SetObservable set to true. Definition at line 55 of file ARBFKernel.m.
Referenced by clone(), kernels.GaussKernel.clone(), kernels.GaussKernel.evaluate(), kernels.InvMultiquadrics.evaluate(), kernels.GaussKernel.evaluateD1(), kernels.GaussKernel.evaluateD2(), kernels.InvMultiquadrics.evaluateScalar(), kernels.GaussKernel.GaussKernel(), kernels.GaussKernel.getNabla(), and kernels.GaussKernel.setGammaForDistance().
1.8.6