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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.glm.model;

import smile.math.MathEx;

import java.util.stream.IntStream;

/**
 * The response variable is of Binomial distribution.
 *
 * @author Haifeng Li
 */
public interface Binomial {
    /**
     * logit link function. Suppose n * y has a bin(n, p) distribution.
     * That is, y is the sample proportion (rather than number) of successes.
     * So E(y) is independent of n.
     *
     * @param n each sample y[i] is of bin(n[i], p_i) distribution.
     * @return logit link function.
     */
    static Model logit(int[] n) {
        return new Model() {
            @Override
            public String toString() {
                return "Binomial(logit)";
            }

            @Override
            public double link(double mu) {
                return Math.log(mu / (1.0 - mu));
            }

            @Override
            public double invlink(double eta) {
                return 1.0 / (1.0 + Math.exp(-eta));
            }

            @Override
            public double dlink(double mu) {
                return 1.0 / (mu * (1.0 - mu));
            }

            @Override
            public double variance(double mu) {
                return mu * (1.0 - mu);
            }

            @Override
            public double mustart(double y) {
                if (y < 0.0 || y > 1.0) {
                    throw new IllegalArgumentException("Invalid argument (expected 0 <= y <= 1): " + y);
                }

                if (y == 0) return 0.1;
                if (y == 1.0) return 0.9;
                else return y;
            }

            @Override
            public double deviance(double[] y, double[] mu, double[] residuals) {
                return IntStream.range(0, y.length).mapToDouble(i -> {
                    double d = 2.0 * n[i] * (y[i] * Math.log(y[i] / mu[i]) + (1.0 - y[i]) * Math.log((1.0 - y[i]) / (1.0 - mu[i])));
                    residuals[i] = Math.sqrt(d) * Math.signum(y[i] - mu[i]);
                    return d;
                }).sum();
            }

            @Override
            public double nullDeviance(double[] y, double mu) {
                double logmu = -Math.log(mu);
                double logmu1 = -Math.log(1.0 - mu);
                return 2.0 * IntStream.range(0, y.length).mapToDouble(i -> n[i] * (y[i] == 0.0 ? logmu1 : logmu)).sum();
            }

            @Override
            public double logLikelihood(double[] y, double[] mu) {
                return IntStream.range(0, y.length).mapToDouble(i ->
                        (y[i] * mu[i] - Math.log(1 + Math.exp(mu[i]))) / n[i] + MathEx.lchoose(n[i], (int) (n[i] * y[i]))
                ).sum();
            }
        };
    }
}