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/*******************************************************************************
 * 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 Thin Plate Spline Kernel. k(u, v) = (||u-v|| / σ)² log (||u-v|| / σ),
 * where σ > 0 is the scale parameter of the kernel.
 * 
 * @author Haifeng Li
 */
public class ThinPlateSplineKernel implements MercerKernel {

    /**
     * The width of the kernel.
     */
    private double sigma;

    /**
     * Constructor.
     * @param sigma the smooth/width parameter of Thin Plate Spline kernel.
     */
    public ThinPlateSplineKernel(double sigma) {
        if (sigma <= 0)
            throw new IllegalArgumentException("sigma is not positive.");

        this.sigma = sigma;
    }

    @Override
    public String toString() {
        return String.format("Thin Plate Spline Kernel (\u02E0 = %.4f)", sigma);
    }

    @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));
        
        double d = 0.0;

        for (int i = 0; i < x.length; i++) {
            double dxy = x[i] - y[i];
            d += dxy * dxy;
        }
            
        return d/(sigma*sigma) * Math.log(Math.sqrt(d)/sigma);
    }
}