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.kernel;
  
  import smile.math.Math;
  
  /**
   * The Gaussian Mercer Kernel. k(u, v) = e<sup>-||u-v||<sup>2</sup> / (2 * &sigma;<sup>2</sup>)</sup>,
   * where &sigma; &gt; 0 is the scale parameter of the kernel.
   * <p>
   * The Gaussian kernel is a good choice for a great deal of applications,
   * although sometimes it is remarked as being overused.
  
   * @author Haifeng Li
   */
  public class GaussianKernel implements MercerKernel<double[]> {
      private static final long serialVersionUID = 1L;
  
      /**
       * The width of the kernel.
       */
      private double gamma;
      
      /**
       * Constructor.
       * @param sigma the smooth/width parameter of Gaussian kernel.
       */
      public GaussianKernel(double sigma) {
          if (sigma <= 0)
              throw new IllegalArgumentException("sigma is not positive.");
  
          this.gamma = 0.5 / (sigma * sigma);
      }
  
      @Override
      public String toString() {
          return String.format("Gaussian Kernel (\u02E0 = %.4f)", Math.sqrt(0.5/gamma));
      }
  
      @Override
      public double k(double[] x, double[] y) {
          if (x.length != y.length)
              throw new IllegalArgumentException(String.format("Arrays have different length: x[%d], y[%d]", x.length, y.length));
  
          return Math.exp(-gamma * Math.squaredDistance(x, y));
      }
  }
  