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/*
 * @(#)ProbabilityDistributions.java        4.4.3    2022-05-28
 *
 * MathParser.org-mXparser DUAL LICENSE AGREEMENT as of date 2022-05-22
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 *
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 * PRODUCT: MathParser.org-mXparser SOFTWARE
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package org.mariuszgromada.math.mxparser.mathcollection;

import java.util.Random;

import org.mariuszgromada.math.mxparser.mXparser;

/**
 * ProbabilityDistributions - random number generators, PDF - Probability Distribution Functions,
 * CDF - Cumulative Distribution Functions, QNT - Quantile Functions (Inverse Cumulative Distribution
 * Functions).
 *
 * @author         Mariusz Gromada

 *                 [email protected]

 *                 MathSpace.pl

 *                 MathParser.org - mXparser project page

 *                 mXparser on GitHub

 *                 mXparser on SourceForge

 *                 mXparser on Bitbucket

 *                 mXparser on CodePlex

 *                 Janet Sudoku - project web page

 *                 Janet Sudoku on GitHub

 *                 Janet Sudoku on CodePlex

 *                 Janet Sudoku on SourceForge

 *                 Janet Sudoku on BitBucket

 *                 Scalar Free

 *                 Scalar Pro

 *                 ScalarMath.org

 *
 * @version        4.3.0
 */
public final class ProbabilityDistributions {
	/**
	 * Random number generator
	 */
	public static Random randomGenerator = new Random();
	/**
	 * Random number from Uniform Continuous distribution over interval [a, b).
	 *
	 * @param a       Interval limit - left / lower.
	 * @param b       Interval limit - right / upper.
	 * @param rnd     Random number generator.
	 * @return        Double.NaN if a or b is null, or b is lower than a -
	 *                otherwise returns random number.
	 */
	public static final double rndUniformContinuous(double a, double b, Random rnd) {
		if (Double.isNaN(a)) return Double.NaN;
		if (Double.isNaN(b)) return Double.NaN;
		if (b < a) return Double.NaN;
		if (a == b) return a;
		double r = a + rnd.nextDouble() * (b - a);
		return r;
	}
	/**
	 * Random number from dUniform Continuous distribution over interval [a, b).
	 * @param a       Interval limit - left / lower.
	 * @param b       Interval limit - right / upper.
	 * @return        Double.NaN if a or b is null, or b is lower than a -
	 *                otherwise returns random number.
	 */
	public static final double rndUniformContinuous(double a, double b) {
		return rndUniformContinuous(a, b, randomGenerator);
	}
	/**
	 * Random number from Uniform Continuous distribution over interval [0, 1).
	 *
	 * @param rnd     Random number generator.
	 * @return        Random number.
	 */
	public static final double rndUniformContinuous(Random rnd) {
		return rnd.nextDouble();
	}
	/**
	 * Random number from Uniform Continuous distribution over interval [0, 1).
	 *
	 * @return        Random number.
	 */
	public static final double randomUniformContinuous() {
		return rndUniformContinuous(randomGenerator);
	}
	/**
	 * PDF - Probability Distribution Function - Uniform Continuous distribution
	 * over interval [a, b).
	 *
	 * @param x       Point to evaluate pdf function.
	 * @param a       Interval limit - left / lower.
	 * @param b       Interval limit - right / upper.
	 * @return        Double.NaN if a or b is null, or b is lower than a -
	 *                otherwise function value.
	 */
	public static final double pdfUniformContinuous(double x, double a, double b) {
		if (Double.isNaN(x)) return Double.NaN;
		if (Double.isNaN(a)) return Double.NaN;
		if (Double.isNaN(b)) return Double.NaN;
		if (b < a) return Double.NaN;
		if (a == b) {
			if (x == a) return 1;
			else return 0;
		}
		if ( (x < a) || (x > b) ) return 0;
		if (x == Double.NEGATIVE_INFINITY) return 0.0;
		if (x == Double.POSITIVE_INFINITY) return 0.0;
		return 1.0 / (b - a);
	}
	/**
	 * CDF - Cumulative Distribution Function - Uniform Continuous distribution
	 * over interval [a, b).
	 *
	 * @param x       Point to evaluate cdf function.
	 * @param a       Interval limit - left / lower.
	 * @param b       Interval limit - right / upper.
	 * @return        Double.NaN if a or b is null, or b is lower than a -
	 *                otherwise function value.
	 */
	public static final double cdfUniformContinuous(double x, double a, double b) {
		if (Double.isNaN(x)) return Double.NaN;
		if (Double.isNaN(a)) return Double.NaN;
		if (Double.isNaN(b)) return Double.NaN;
		if (b < a) return Double.NaN;
		if (a == b) {
			if (x < a) return 0.0;
			else return 1.0;
		}
		if (x < a) return 0.0;
		if (x >= b) return 1.0;
		if (x == Double.NEGATIVE_INFINITY) return 0.0;
		if (x == Double.POSITIVE_INFINITY) return 1.0;
		return (x - a) / (b - a);
	}
	/**
	 * QNT - Quantile Function - Uniform Continuous distribution over interval [a, b).
	 * (Inverse of Cumulative Distribution Function).
	 *
	 * @param q       Quantile.
	 * @param a       Interval limit - left / lower.
	 * @param b       Interval limit - right / upper.
	 * @return        Double.NaN if a or b is null, or b is lower than a
	 *                or q is lower than 0 or q is greater than 1 -
	 *                otherwise function value.
	 */
	public static final double qntUniformContinuous(double q, double a, double b) {
		if (Double.isNaN(q)) return Double.NaN;
		if (Double.isNaN(a)) return Double.NaN;
		if (Double.isNaN(b)) return Double.NaN;
		if ( (q < 0.0) || (q > 1.0) ) return Double.NaN;
		if (b < a) return Double.NaN;
		if (a == b) {
			if (q == 1.0) return b;
			else return Double.NaN;
		}
		if (q == 0.0) return a;
		if (q == 1.0) return b;
		return a + q*(b-a);
	}
	/**
	 * Random number from Uniform Discrete distribution.
	 * over set interval (a, a+1, ..., b-1, b).
	 *
	 * @param a       Interval limit - left / lower.
	 * @param b       Interval limit - right / upper.
	 * @param rnd     Random number generator.
	 * @return        Double.NaN if a or b is null, or b is lower than a -
	 *                otherwise returns random number.
	 */
	public static final double rndInteger(int a, int b, Random rnd) {
		if (Double.isNaN(a)) return Double.NaN;
		if (Double.isNaN(b)) return Double.NaN;
		if (b < a) return Double.NaN;
		if (a == b) return a;
		int n = (b - a) + 1;
		int r = a + rnd.nextInt(n);
		return r;
	}
	/**
	 * Random number from Uniform Discrete distribution.
	 * over set interval (a, a+1, ..., b-1, b).
	 *
	 * @param a       Interval limit - left / lower.
	 * @param b       Interval limit - right / upper.
	 * @return        Double.NaN if a or b is null, or b is lower than a -
	 *                otherwise returns random number.
	 */
	public static final double rndInteger(int a, int b) {
		return rndInteger(a, b, randomGenerator);
	}
	/**
	 * Random integer.
	 *
	 * @param rnd     Random number generator.
	 * @return        Returns random number.
	 */
	public static final int rndInteger(Random rnd) {
		return rnd.nextInt();
	}
	/**
	 * Random index from 0 to n-1,
	 *
	 * @param n          Bound.
	 * @param rnd        Random number generator.
	 * @return           if n < 0 returns -1, otherwise random index.
	 */
	public static final int rndIndex(int n, Random rnd) {
		if (n < 0) return -1;
		return rnd.nextInt(n);
	}
	/**
	 * Random index from 0 to n-1,
	 *
	 * @param n          Bound.
	 * @return           if n < 0 returns -1, otherwise random index.
	 */
	public static final int rndIndex(int n) {
		if (n < 0) return -1;
		return randomGenerator.nextInt(n);
	}
	/**
	 * Random integer.
	 *
	 * @return        Double.NaN if a or b is null, or b is lower than a -
	 *                otherwise returns random number.
	 */
	public static final int rndInteger() {
		return rndInteger(randomGenerator);
	}
	/**
	 * Random number from normal distribution N(mean, stddev).
	 *
	 * @param mean              Mean value.
	 * @param stddev            Standard deviation.
	 * @param rnd               Random number generator.
	 * @return                  Double.NaN if mean or stddev or rnd is null or stddev is lower than 0 -
	 *                          otherwise random number.
	 */
	public static final double rndNormal(double mean, double stddev, Random rnd) {
		if (Double.isNaN(mean)) return Double.NaN;
		if (Double.isNaN(stddev)) return Double.NaN;
		if (rnd == null) return Double.NaN;
		if (stddev < 0) return Double.NaN;
		if (stddev == 0) return mean;
		double x, a, v1;
		double b, v2;
		double r, fac;
		boolean polarTransform;
		do {
			if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
			a = rnd.nextDouble();
			b = rnd.nextDouble();
			v1 = 2.0*a - 1.0;
			v2 = 2.0*b - 1.0;
			r = (v1*v1) + (v2*v2);
			if (r >= 1.0 || r == 0.0) {
				x = 0.0;
				polarTransform = false;
			} else {
				fac = MathFunctions.sqrt( -2.0 * MathFunctions.ln(r) / r);
				x = v1*fac;
				polarTransform = true;
			}
		} while (!polarTransform);
		return mean + (stddev*x);
	}
	/**
	 * Random number from normal distribution N(mean, stddev).
	 *
	 * @param mean              Mean value.
	 * @param stddev            Standard deviation.
	 * @return                  Double.NaN if mean or stddev is null or stddev is lower than 0 -
	 *                          otherwise random number.
	 */
	public static final double rndNormal(double mean, double stddev) {
		return rndNormal(mean, stddev, randomGenerator);
	}
	/**
	 * PDF - Probability Distribution Function - Normal distribution N(mean, stddev).
	 *
	 * @param x                 Point to evaluate pdf function.
	 * @param mean              Mean value.
	 * @param stddev            Standard deviation.
	 * @return                  Double.NaN if mean or stddev is null or stddev is lower than 0 -
	 *                          otherwise function value.
	 */
	public static final double pdfNormal(double x, double mean, double stddev) {
		if (Double.isNaN(x)) return Double.NaN;
		if (Double.isNaN(mean)) return Double.NaN;
		if (Double.isNaN(stddev)) return Double.NaN;
		if (stddev < 0) return Double.NaN;
		if (stddev == 0) {
			if (x == mean) return 1.0;
			else return 0;
		}
		if (x == Double.NEGATIVE_INFINITY) return 0.0;
		if (x == Double.POSITIVE_INFINITY) return 0.0;
		double d = (x - mean) / stddev;
		return MathFunctions.exp( -0.5*d*d ) / ( MathConstants.SQRT2Pi*stddev );
	}
	/**
	 * CDF - Cumulative Distribution Function - Normal distribution N(mean, stddev).
	 *
	 * @param x                 Point to evaluate pdf function.
	 * @param mean              Mean value.
	 * @param stddev            Standard deviation.
	 * @return                  Double.NaN if mean or stddev is null or stddev is lower than 0 -
	 *                          otherwise function value.
	 */
	public static final double cdfNormal(double x, double mean, double stddev) {
		if (Double.isNaN(x)) return Double.NaN;
		if (Double.isNaN(mean)) return Double.NaN;
		if (Double.isNaN(stddev)) return Double.NaN;
		if (stddev < 0) return Double.NaN;
		if (stddev == 0) {
			if (x < mean) return 0.0;
			else return 1.0;
		}
		if (x == Double.NEGATIVE_INFINITY) return 0.0;
		if (x == Double.POSITIVE_INFINITY) return 1.0;
		return 0.5 * SpecialFunctions.erfc( (mean - x) / (stddev * MathConstants.SQRT2));
	}
	/**
	 * QNT - Quantile Function - Normal distribution N(mean, stddev).
	 * (Inverse of Cumulative Distribution Function).
	 *
	 * @param q                 Quantile.
	 * @param mean              Mean value.
	 * @param stddev            Standard deviation.
	 * @return                  Double.NaN if mean or stddev is null or stddev is lower than 0
	 *                          or q is lower than 0 or q is greater than 1 -
	 *                          otherwise function value.
	 */
	public static final double qntNormal(double q, double mean, double stddev) {
		if (Double.isNaN(q)) return Double.NaN;
		if (Double.isNaN(mean)) return Double.NaN;
		if (Double.isNaN(stddev)) return Double.NaN;
		if ( (q < 0.0) || (q > 1.0) ) return Double.NaN;
		if (stddev < 0) return Double.NaN;
		if (stddev == 0) {
			if (q == 1.0) return mean;
			else return Double.NaN;
		}
		if (q == 0.0) return Double.NEGATIVE_INFINITY;
		if (q == 1.0) return Double.POSITIVE_INFINITY;
		return mean - ( stddev * MathConstants.SQRT2 * SpecialFunctions.erfcInv( 2.0*q ) );
	}
}