/*
 * This file is part of ELKI:
 * Environment for Developing KDD-Applications Supported by Index-Structures
 *
 * Copyright (C) 2022
 * ELKI Development Team
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU Affero General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program 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 Affero General Public License for more details.
 *
 * You should have received a copy of the GNU Affero General Public License
 * along with this program. If not, see <http://www.gnu.org/licenses/>.
 */
package elki.math.statistics.distribution;

import java.util.Random;

import elki.utilities.optionhandling.OptionID;
import elki.utilities.optionhandling.parameterization.Parameterization;
import elki.utilities.optionhandling.parameters.DoubleParameter;

import net.jafama.FastMath;

/**
 * Kappa distribution, by Hosking.
 * <p>
 * TODO: add references.
 * 
 * @author Erich Schubert
 * @since 0.6.0
 */
public class KappaDistribution implements Distribution {
  /**
   * Parameters: location and scale
   */
  double location, scale;

  /**
   * Shape parameters.
   */
  double shape1, shape2;

  /**
   * Constructor.
   * 
   * @param location Location
   * @param scale Scale
   * @param shape1 Shape parameter
   * @param shape2 Shape parameter
   */
  public KappaDistribution(double location, double scale, double shape1, double shape2) {
    this.location = location;
    this.scale = scale;
    this.shape1 = shape1;
    this.shape2 = shape2;
    if(shape2 >= 0.) {
      if(shape1 < -1.) {
        throw new ArithmeticException("Invalid shape1 parameter - must be greater than -1 if shape2 >= 0.!");
      }
    }
    else if(shape1 != 0.) {
      if(shape1 < 1. || shape1 > 1. / shape2) {
        throw new ArithmeticException("Invalid shape1 parameter - must be -1 to +1/shape2 if shape2 < 0.!");
      }
    }
  }

  /**
   * Probability density function.
   * 
   * @param val Value
   * @param loc Location
   * @param scale Scale
   * @param shape1 Shape parameter
   * @param shape2 Shape parameter
   * @return PDF
   */
  public static double pdf(double val, double loc, double scale, double shape1, double shape2) {
    val = (val - loc) / scale;
    final double logc = logcdf(val, shape1, shape2);
    if(shape1 == 1.) {
      // Then val will usually become 0.
      return val >= 1 ? 0 : FastMath.exp(logc * (1. - shape2)) / scale;
    }
    if(shape1 != 0.) {
      val = shape1 * val;
      if(val >= 1) {
        return 0;
      }
      val = (1. - 1. / shape1) * FastMath.log1p(-val);
    }
    if(Double.isInfinite(val)) {
      return 0;
    }
    val = FastMath.exp(-val);
    return Double.isInfinite(val) ? 0. : val / scale * FastMath.exp(logc * (1. - shape2));
  }

  @Override
  public double pdf(double val) {
    return pdf(val, location, scale, shape1, shape2);
  }

  /**
   * Probability density function.
   * 
   * @param val Value
   * @param loc Location
   * @param scale Scale
   * @param shape1 Shape parameter
   * @param shape2 Shape parameter
   * @return PDF
   */
  public static double logpdf(double val, double loc, double scale, double shape1, double shape2) {
    val = (val - loc) / scale;
    final double logc = logcdf(val, shape1, shape2);
    if(shape1 != 0.) {
      val = shape1 * val;
      if(val >= 1) {
        return Double.NEGATIVE_INFINITY;
      }
      val = (1. - 1. / shape1) * FastMath.log1p(-val);
    }
    if(Double.isInfinite(val)) {
      return Double.NEGATIVE_INFINITY;
    }
    return -val - FastMath.log(scale) + logc * (1. - shape2);
  }

  @Override
  public double logpdf(double val) {
    return logpdf(val, location, scale, shape1, shape2);
  }

  /**
   * Cumulative density function.
   * 
   * @param val Value
   * @param loc Location
   * @param scale Scale
   * @param shape1 Shape parameter
   * @param shape2 Shape parameter
   * @return CDF
   */
  public static double cdf(double val, double loc, double scale, double shape1, double shape2) {
    val = (val - loc) / scale;
    if(val == Double.NEGATIVE_INFINITY) {
      return 0.;
    }
    if(val == Double.POSITIVE_INFINITY) {
      return 1.;
    }
    if(val != val) {
      return Double.NaN;
    }
    if(shape1 == 0.) {
      val = FastMath.exp(-val);
    }
    else {
      double tmp = shape1 * val;
      if(tmp == Double.NEGATIVE_INFINITY) {
        return shape2 == 0 ? 1 : 0.;
      }
      if(tmp >= 1.) {
        return shape2 == 0 ? 0 : 1.;
      }
      val = FastMath.exp(FastMath.log1p(-tmp) / shape1);
    }
    if(shape2 == 0.) {
      return FastMath.exp(-val);
    }
    final double tmp = shape2 * val;
    return tmp < 1. ? FastMath.exp(FastMath.log1p(-tmp) / shape2) : 0.;
  }

  /**
   * Cumulative density function.
   * 
   * @param val Value
   * @param loc Location
   * @param scale Scale
   * @param shape1 Shape parameter
   * @param shape2 Shape parameter
   * @return CDF
   */
  public static double logcdf(double val, double loc, double scale, double shape1, double shape2) {
    return logcdf((val - loc) / scale, shape1, shape2);
  }

  /**
   * Cumulative density function, for location = 0, scale = 1
   * 
   * @param val Value
   * @param shape1 Shape parameter
   * @param shape2 Shape parameter
   * @return CDF
   */
  public static double logcdf(double val, double shape1, double shape2) {
    if(val == Double.NEGATIVE_INFINITY) {
      return Double.NEGATIVE_INFINITY;
    }
    if(val == Double.POSITIVE_INFINITY) {
      return 0.;
    }
    if(val != val) {
      return Double.NaN;
    }
    if(shape1 == 0.) {
      val = FastMath.exp(-val);
    }
    else {
      double tmp = shape1 * val;
      if(tmp == Double.NEGATIVE_INFINITY) {
        return shape2 == 0 ? 0. : Double.NEGATIVE_INFINITY;
      }
      if(tmp >= 1.) {
        return shape2 == 0 ? Double.NEGATIVE_INFINITY : 0.;
      }
      val = FastMath.exp(FastMath.log1p(-tmp) / shape1);
    }
    if(shape2 == 0.) {
      return -val;
    }
    final double tmp = shape2 * val;
    return tmp < 1. ? FastMath.log1p(-tmp) / shape2 : Double.NEGATIVE_INFINITY;
  }

  @Override
  public double cdf(double val) {
    return cdf(val, location, scale, shape1, shape2);
  }

  /**
   * Quantile function.
   * 
   * @param val Value
   * @param loc Location
   * @param scale Scale
   * @param shape1 Shape parameter
   * @param shape2 Shape parameter
   * @return Quantile
   */
  public static double quantile(double val, double loc, double scale, double shape1, double shape2) {
    if(!(val >= 0.) || !(val <= 1.)) {
      return Double.NaN;
    }
    if(val == 0.) {
      if(shape2 <= 0.) {
        return shape1 < 0. ? loc + scale / shape1 : Double.NEGATIVE_INFINITY;
      }
      else {
        return loc + (shape1 != 0. //
            ? scale / shape1 * (1. - FastMath.pow(shape2, -shape1)) //
            : scale * FastMath.log(shape2));
      }
    }
    if(val == 1.) {
      return shape1 <= 0. ? Double.NEGATIVE_INFINITY : loc + scale / shape1;
    }
    val = -FastMath.log(val);
    if(shape2 != 0.) {
      val = (1 - FastMath.exp(-shape2 * val)) / shape2;
    }
    val = -FastMath.log(val);
    if(shape1 != 0.) {
      val = (1 - FastMath.exp(-shape1 * val)) / shape1;
    }
    return loc + scale * val;
  }

  @Override
  public double quantile(double val) {
    return quantile(val, location, scale, shape1, shape2);
  }

  @Override
  public double nextRandom(Random random) {
    return quantile(random.nextDouble(), location, scale, shape1, shape2);
  }

  @Override
  public String toString() {
    return "KappaDistribution(location=" + location + ", scale=" + scale + ", shape1=" + shape1 + ", shape2=" + shape2 + ")";
  }

  /**
   * Parameterization class
   * 
   * @author Erich Schubert
   */
  public static class Par implements Distribution.Parameterizer {
    /**
     * First shape parameter.
     */
    public static final OptionID SHAPE1_ID = new OptionID("distribution.kappa.shape1", "First shape parameter of kappa distribution.");

    /**
     * Second shape parameter.
     */
    public static final OptionID SHAPE2_ID = new OptionID("distribution.kappa.shape2", "Second shape parameter of kappa distribution.");

    /** Parameters. */
    double location, scale, shape1, shape2;

    @Override
    public void configure(Parameterization config) {
      new DoubleParameter(LOCATION_ID) //
          .grab(config, x -> location = x);
      new DoubleParameter(SCALE_ID) //
          .grab(config, x -> scale = x);
      new DoubleParameter(SHAPE1_ID) //
          .grab(config, x -> shape1 = x);
      new DoubleParameter(SHAPE2_ID) //
          .grab(config, x -> shape2 = x);
    }

    @Override
    public KappaDistribution make() {
      return new KappaDistribution(location, scale, shape1, shape2);
    }
  }
}
