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/*
 * Copyright (c) 2010-2021 Haifeng Li. All rights reserved.
 *
 * Smile is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * Smile is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with Smile.  If not, see .
 */

package smile.interpolation.variogram;

/**
 * Exponential variogram.
 * 
 *     v(r) = c + b * (1 - e^-3r/a)
 * 

 * where a is the range parameter and b is sill paramter. The distance of two
 * pairs increase, the variogram of those two pairs also increase. Eventually,
 * the increase of the distance can not cause the variogram increase. The
 * distance which cause the variogram reach plateau is called range. The sill
 * parameter b is the maximum variogram value (by default, we set c = 0).
 * 
 * The parameter c is the so-called nugget effect. Though the value of the
 * variogram for h = 0 is strictly 0, several factors, such as sampling error
 * and short scale variability, may cause sample values separated by extremely
 * small distances to be quite dissimilar. This causes a discontinuity at the
 * origin of the variogram. The vertical jump from the value of 0 at the origin
 * to the value of the variogram at extremely small separation distances is
 * called the nugget effect.
 * 
 * @author Haifeng Li
 */
public class ExponentialVariogram implements Variogram {
    /** The range parameter. */
    private final double a;
    /** The sill parameter. */
    private final double b;
    /** The nugget effect parameter. */
    private final double c;

    /**
     * Constructor. No nugget effect.
     * @param a the range parameter.
     * @param b the sill parameter.
     */
    public ExponentialVariogram(double a, double b) {
        this(a, b, 0.0);
    }

    /**
     * Constructor.
     * @param a the range parameter.
     * @param b the sill parameter.
     * @param c the nugget effect parameter.
     */
    public ExponentialVariogram(double a, double b, double c) {
        if (a <= 0)
            throw new IllegalArgumentException("Invalid parameter a = " + a);

        if (b <= 0)
            throw new IllegalArgumentException("Invalid parameter b = " + b);

        if (c < 0)
            throw new IllegalArgumentException("Invalid parameter c = " + c);

        this.a = a;
        this.b = b;
        this.c = c;
    }

    @Override
    public double f(double r) {
        return c + b * (1 - Math.exp(-3.0*r/a));
    }

    @Override
    public String toString() {
        return String.format("Exponential Variogram(range = %.4f, sill = %.4f, nugget effect = %.4f)", a, b, c);
    }
}