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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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InvMULTIQUADRICS Summary of this class goes here Detailed explanation goes here. More...
InvMULTIQUADRICS Summary of this class goes here Detailed explanation goes here.
Definition at line 18 of file InvMultiquadrics.m.
Public Member Functions | |
| InvMultiquadrics (beta, c) | |
| Constructor offering the possibility to initialize kernel specifics at creation time. More... | |
| function c = | getGlobalLipschitz () |
| function Nabla = | getNabla (colvec< double > x,matrix< double > y) |
| function K = | evaluate (matrix< double > x,matrix< double > y) |
| Evaluates the inverse multiquadrics kernel. More... | |
| function Ks = | evaluateScalar (r) |
| function copy = | clone () |
 Public Member Functions inherited from kernels.ARBFKernel | |
| ARBFKernel () | |
| 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... | |
| 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 | |
| beta = -1 | |
| The negative exponent. More... | |
| c = 1 | |
| The offset value. More... | |
| Public Attributes inherited from kernels.ARBFKernel | |
| 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.InvMultiquadrics.InvMultiquadrics | ( | beta, | |
| c | |||
| ) |
Constructor offering the possibility to initialize kernel specifics at creation time.
Definition at line 63 of file InvMultiquadrics.m.
References beta, c, and DPCMObject.registerProps().
| function copy = kernels.InvMultiquadrics.clone | ( | ) |
Definition at line 132 of file InvMultiquadrics.m.
Evaluates the inverse multiquadrics kernel.
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 | An evaluation matrix \(K \in \R^{n\times m}\) of the evaluated multiquadrics with entries \(K_{i,j} = 1/(c^2+\epsilon^2\norm{x_i-y_j}{G}^2)\). |
Reimplemented from kernels.ARBFKernel.
Definition at line 108 of file InvMultiquadrics.m.
References beta, c, kernels.ARBFKernel.Gamma, and kernels.ARBFKernel.getSqDiffNorm().
| function Ks = kernels.InvMultiquadrics.evaluateScalar | ( | r | ) |
Definition at line 127 of file InvMultiquadrics.m.
References beta, c, and kernels.ARBFKernel.Gamma.
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virtual |
| x | The state variable vector \(\vx(t)\) |
| y | The output variable vector \(\vy(t) = \vC(t,\vmu)\vx(t),~t=0\ldots T\) (general notation) |
Definition at line 95 of file InvMultiquadrics.m.
| kernels.InvMultiquadrics.beta = -1 |
The negative exponent.
SetObservable set to true. Definition at line 32 of file InvMultiquadrics.m.
Referenced by clone(), evaluate(), evaluateScalar(), and InvMultiquadrics().
| kernels.InvMultiquadrics.c = 1 |
The offset value.
SetObservable set to true. Definition at line 46 of file InvMultiquadrics.m.
Referenced by clone(), evaluate(), evaluateScalar(), and InvMultiquadrics().
1.8.6