hermitian<T,N>
Description
Hermitian<T,N> is a family of Kernels. Specifically, it is a family of Mercer Kernels. The N-th Hermitian kernel is equal to the N-th order derivative of the Gaussian kernel. They are named after Hermite polynomials, which may be used to identify the derivatives of the Gaussian kernels.
If k is an object of class hermite<T,N>, u and v are objects of class T, and N is a integral constant, then k(u,v) returns
where 
is Rodrigues’ formula for Hermite polynomials
Figure 1 shows the Hermitian kernel for N=0 through N=5 for a scalar input type.
Figure 1: Hermitian kernels, parametrised by 
, with N=0 at the top left through N=5 at the bottom right.
Example
vector< double > x(10); vector< double > v(10); hermitian< vector< double >, 2 > kernel(1.0); cout << kernel( x, v ) << endl;
Definition
Defined in the KML header <kml/hermitian.hpp>.
Template Parameters
| Parameter | Description | Default |
| T | The hermitian argument type | |
| N | The order of the hermitian | |
Model of
Type requirements
T must be a vector type or a scalar type.
Members
| Member | Where defined | Description |
| hermitian() | Default Constructible | The default constructor |
| result_type | Input value | The type of the result: input_value<T> |