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.
vector< double > x(10); vector< double > v(10); hermitian< vector< double >, 2 > kernel(1.0); cout << kernel( x, v ) << endl;
Defined in the KML header <kml/hermitian.hpp>.
Parameter | Description | Default |
T | The hermitian argument type | |
N | The order of the hermitian | |
T must be a vector type or a scalar type.
Member | Where defined | Description |
hermitian() | Default Constructible | The default constructor |
result_type | Input value | The type of the result: input_value<T> |