 |
KerMor
0.9
Model order reduction for nonlinear dynamical systems and nonlinear approximation
|
|
KerMor
0.9
Model order reduction for nonlinear dynamical systems and nonlinear approximation
|
Base class for all KerMor Kernels. More...
Base class for all KerMor Kernels.
All Kernels have to inherit from this class.
Definition at line 18 of file BaseKernel.m.
Public Member Functions | |
| 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 K = | evaluate (matrix< double > x,matrix< double > y) |
| Evaluation method for the current kernel. 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 | |
| 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... | |
Protected Attributes | |
| fG = 1 | |
| fP = "[]" | |
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) |
| kernels.BaseKernel.BaseKernel | ( | ) |
Definition at line 130 of file BaseKernel.m.
References KerMorObject.KerMorObject(), and DPCMObject.registerProps().
|
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 169 of file BaseKernel.m.
References G, IsRBF, IsScProd, and P.
Referenced by kernels.KernelExpansion.clone().
| function bool = kernels.BaseKernel.eq | ( | B | ) |
Checks if a kernel equals another kernel.
Definition at line 155 of file BaseKernel.m.
References KerMorObject.KerMorObject().
Evaluation method for the current kernel.
| 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 to be assumed. |
| K | The evaluation matrix \(\K(x,y) \in \R^{n\times m}\) of the kernel \(\K\), with entries \(\K(x_i,y_j)\) at \(i,j\). |
Implemented in kernels.InvMultiquadrics, kernels.ARBFKernel, and kernels.GaussKernel.
Referenced by kernels.ParamTimeKernelExpansion.getGlobalLipschitz(), kernels.KernelExpansion.getKernelMatrix(), kernels.KernelExpansion.getKernelMatrixColumn(), kernels.ParamTimeKernelExpansion.getKernelVector(), and kernels.KernelExpansion.getKernelVector().
|
pure virtual |
Returns the global lipschitz constant of this kernel.
Exprimental state as not implemented & checked for all kernels.
Implemented in kernels.BellFunction, kernels.InvMultiquadrics, kernels.CombinationKernel, kernels.SigmoidKernel, kernels.NoKernel, kernels.PolyKernel, and kernels.LinearKernel.
Referenced by kernels.ParamTimeKernelExpansion.getGlobalLipschitz(), kernels.KernelExpansion.getGlobalLipschitz(), and getLipschitzFunction().
| function fcn = kernels.BaseKernel.getLipschitzFunction | ( | ) |
Method that allows error estimators to obtain a lipschitz constant estimation function from this kernel.
The default is simply each kernel's global lipschitz constant function. However, subclasses may override this method in order to return a better (maybe local) lipschitz constant estimation function. See the BellFunction implementation, for example.
Definition at line 136 of file BaseKernel.m.
References getGlobalLipschitz().
|
pure virtual |
Computes the partial derivatives with respect to each component of the first argument.
| x | The point where to evaluate the partial derivatives. Must be a single column \(d\times 1\) vector. |
| y | The corresponding center points at which the partial derivatives with respect to the first argument are to be computed. Can be either a column vector \(d\times 1\) or a matrix \(d\times n\) containing \(n\) multiple centers. |
| Nabla | A \(d \times n\) matrix of partial derivatives with respect to the first argument evaluated using all second arguments. |
Referenced by kernels.ParamTimeKernelExpansion.getStateJacobian().
|
protected |
Definition at line 123 of file BaseKernel.m.
Referenced by kernels.LinearKernel.evaluate(), kernels.PolyKernel.evaluate(), and kernels.ARBFKernel.getSqDiffNorm().
|
protected |
Definition at line 125 of file BaseKernel.m.
Referenced by kernels.LinearKernel.evaluate(), kernels.PolyKernel.evaluate(), kernels.GaussKernel.getNabla(), and kernels.ARBFKernel.getSqDiffNorm().
| kernels.BaseKernel.G = 1 |
The matrix \(\vG\) that induces the state space scalar product \(\spG{x}{y}\) and norm \(\noG{x-y}\) to use.
Must be a positive definite, symmetric matrix \(\vG\).
Default: 1
SetObservable set to true. Definition at line 45 of file BaseKernel.m.
Referenced by clone(), kernels.SigmoidKernel.evaluate(), and kernels.NoKernel.NoKernel().
| kernels.BaseKernel.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 \(\phi\).
Set in subclasses according to current kernel.
Default: false
SetAccess = Protected, GetAccess = Public Definition at line 88 of file BaseKernel.m.
Referenced by kernels.ARBFKernel.ARBFKernel(), and clone().
| kernels.BaseKernel.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 \(\phi\).
Set in subclasses according to current kernel.
Default: false
SetAccess = Protected, GetAccess = Public Definition at line 105 of file BaseKernel.m.
Referenced by clone(), kernels.LinearKernel.LinearKernel(), kernels.PolyKernel.PolyKernel(), and kernels.SigmoidKernel.SigmoidKernel().
| kernels.BaseKernel.P = "[]" |
Projection/selection matrix \(\vP\) for argument components.
Set this value to the indices of the components of any argument passed to the kernel that should be effectively used. This property is mainly used with parameter kernels in order to extract relevant entries. Leave to [] if all values should be used.
Subclasses must take care to use this property if set.
Default: []
SetObservable set to true. Definition at line 65 of file BaseKernel.m.
Referenced by clone(), kernels.SigmoidKernel.evaluate(), and kernels.NoKernel.NoKernel().
1.8.6