content: /*******************************************************************************
   * Copyright (c) 2010 Haifeng Li
   *   
   * Licensed under the Apache License, Version 2.0 (the "License");
   * you may not use this file except in compliance with the License.
   * You may obtain a copy of the License at
   *  
   *     http://www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
   * limitations under the License.
   *******************************************************************************/
  
  package smile.math.rbf;
  
  import smile.math.Function;
  
  /**
   * A radial basis function (RBF) is a real-valued function whose value depends
   * only on the distance from the origin, so that &phi;(x)=&phi;(||x||); or
   * alternatively on the distance from some other point c, called a center, so
   * that &phi;(x,c)=&phi;(||x-c||). Any function &phi; that satisfies the
   * property  is a radial function. The norm is usually Euclidean distance,
   * although other distance functions are also possible. For example by
   * using probability metric it is for some radial functions possible
   * to avoid problems with ill conditioning of the matrix solved to
   * determine coefficients w<sub>i</sub> (see below), since the ||x|| is always
   * greater than zero.
   * <p>
   * Sums of radial basis functions are typically used to approximate given
   * functions:
   * <p>
   * y(x) = &Sigma; w<sub>i</sub> &phi;(||x-c<sub>i</sub>||)
   * <p>
   * where the approximating function y(x) is represented as a sum of N radial
   * basis functions, each associated with a different center c<sub>i</sub>, and weighted
   * by an appropriate coefficient w<sub>i</sub>. The weights w<sub>i</sub> can
   * be estimated using the matrix methods of linear least squares, because
   * the approximating function is linear in the weights.
   * <p>
   * This approximation process can also be interpreted as a simple kind of neural
   * network and has been particularly used in time series prediction and control
   * of nonlinear systems exhibiting sufficiently simple chaotic behavior,
   * 3D reconstruction in computer graphics (for example, hierarchical RBF).
   *
   * @author Haifeng Li
   */
  public interface RadialBasisFunction extends Function {
  
  }
  