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/*
 * @(#)Statistics.java        6.0.0    2024-05-19
 *
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package org.mariuszgromada.math.mxparser.mathcollection;

import org.mariuszgromada.math.mxparser.Argument;
import org.mariuszgromada.math.mxparser.Expression;
import org.mariuszgromada.math.mxparser.mXparser;

/**
 * Statistics - i.e.: mean, variance, standard deviation, etc.
 *
 * @author         Mariusz Gromada

 *                 MathParser.org - mXparser project page

 *                 mXparser on GitHub

 *                 INFIMA place to purchase a commercial MathParser.org-mXparser software license

 *                 [email protected]

 *                 ScalarMath.org - a powerful math engine and math scripting language

 *                 Scalar Lite

 *                 Scalar Pro

 *                 MathSpace.pl

 *
 * @version        5.2.0
 */
public final class Statistics {
	/**
	 * Average from sample function values - iterative operator.
	 *
	 * @param      f                   the expression
	 * @param      index               the name of index argument
	 * @param      from                FROM index = form
	 * @param      to                  TO index = to
	 * @param      delta               BY delta
	 *
	 * @return     product operation (for empty product operations returns 1).
	 *
	 * @see        Expression
	 * @see        Argument
	 */
	public static double avg(Expression f, Argument index, double from, double to, double delta) {
		if ( (Double.isNaN(delta) ) || (Double.isNaN(from) ) || (Double.isNaN(to) ) || (delta == 0) )
			return Double.NaN;
		double sum = 0;
		int n = 0;
		if ( (to >= from) && (delta > 0) ) {
			double i;
			for (i = from; i < to; i+=delta) {
				if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
				sum += MathFunctions.getFunctionValue(f, index, i);
				n++;
			}
			if ( delta - (i - to) > 0.5 * delta) {
				if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
				sum += MathFunctions.getFunctionValue(f, index, to);
				n++;
			}
		} else if ( (to <= from) && (delta < 0) ) {
			double i;
			for (i = from; i > to; i+=delta) {
				if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
				sum += MathFunctions.getFunctionValue(f, index, i);
				n++;
			}
			if ( -delta - (to - i) > -0.5 * delta) {
				if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
				sum += MathFunctions.getFunctionValue(f, index, to);
				n++;
			}
		} else if (from == to)
			return MathFunctions.getFunctionValue(f, index, from);
		return sum / n;
	}
	/**
	 * Bias-corrected variance from sample function values - iterative operator.
	 *
	 * @param      f                   the expression
	 * @param      index               the name of index argument
	 * @param      from                FROM index = form
	 * @param      to                  TO index = to
	 * @param      delta               BY delta
	 *
	 * @return     product operation (for empty product operations returns 1).
	 *
	 * @see        Expression
	 * @see        Argument
	 */
	public static double var(Expression f, Argument index, double from, double to, double delta) {
		if ( (Double.isNaN(delta) ) || (Double.isNaN(from) ) || (Double.isNaN(to) ) || (delta == 0) )
			return Double.NaN;
		return var( MathFunctions.getFunctionValues(f, index, from, to, delta) );
	}
	/**
	 * Bias-corrected standard deviation from sample function values - iterative operator.
	 *
	 * @param      f                   the expression
	 * @param      index               the name of index argument
	 * @param      from                FROM index = form
	 * @param      to                  TO index = to
	 * @param      delta               BY delta
	 *
	 * @return     product operation (for empty product operations returns 1).
	 *
	 * @see        Expression
	 * @see        Argument
	 */
	public static double std(Expression f, Argument index, double from, double to, double delta) {
		if ( (Double.isNaN(delta) ) || (Double.isNaN(from) ) || (Double.isNaN(to) ) || (delta == 0) )
			return Double.NaN;
		return std( MathFunctions.getFunctionValues(f, index, from, to, delta) );
	}
	/**
	 * Sample average.
	 *
	 * @param      numbers             the numbers
	 *
	 * @return     if each number from numbers <> Double.NaN returns
	 *             avg(a_1,...,a_n) a_1,...,a_n in numbers,
	 *             otherwise returns Double.NaN.
	 */
	public static double avg(double... numbers) {
		if (numbers == null) return Double.NaN;
		if (numbers.length == 0) return Double.NaN;
		if (numbers.length == 1) return numbers[0];
		double sum = 0;
		for (double xi : numbers) {
			if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
			if ( Double.isNaN(xi) )
				return Double.NaN;
			sum+=xi;
		}
		return sum / numbers.length;
	}
	/**
	 * Sample variance (biased-corrected).
	 *
	 * @param      numbers             the numbers
	 *
	 * @return     if each number from numbers <> Double.NaN returns
	 *             Var(a_1,...,a_n) a_1,...,a_n in numbers,
	 *             otherwise returns Double.NaN.
	 */
	public static double var(double... numbers) {
		if (numbers == null) return Double.NaN;
		if (numbers.length == 0) return Double.NaN;
		if (numbers.length == 1) {
			if (Double.isNaN(numbers[0])) return Double.NaN;
			return 0;
		}
		double m = avg(numbers);
		double sum = 0;
		for (double xi : numbers) {
			if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
			if ( Double.isNaN(xi) )
				return Double.NaN;
			sum+=(xi-m)*(xi-m);
		}
		return sum / (numbers.length - 1);
	}
	/**
	 * Sample standard deviation (biased-corrected).
	 *
	 * @param      numbers             the numbers
	 *
	 * @return     if each number from numbers <> Double.NaN returns
	 *             Std(a_1,...,a_n) a_1,...,a_n in numbers,
	 *             otherwise returns Double.NaN.
	 */
	public static double std(double... numbers) {
		if (numbers == null) return Double.NaN;
		if (numbers.length == 0) return Double.NaN;
		if (numbers.length == 1) {
			if (Double.isNaN(numbers[0])) return Double.NaN;
			return 0;
		}
		return MathFunctions.sqrt( var(numbers) );
	}
	/**
	 * Sample median
	 * @param numbers   List of number
	 * @return          Sample median, if table was empty or null then Double.NaN is returned.
	 */
	public static double median(double... numbers) {
		if (numbers == null) return Double.NaN;
		if (numbers.length == 0) return Double.NaN;
		if (numbers.length == 1) return numbers[0];
		if (numbers.length == 2) return (numbers[0] + numbers[1]) / 2.0;
		for (double v : numbers) {
			if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
			if (Double.isNaN(v)) return Double.NaN;
		}
		NumberTheory.sortAsc(numbers);
		if ((numbers.length % 2) == 1) {
			int i = (numbers.length-1) / 2;
			return numbers[i];
		} else {
			int i = ( numbers.length / 2 ) - 1;
			return (numbers[i] + numbers[i+1]) / 2.0;
		}
	}
	/**
	 * Sample mode
	 * @param numbers   List of number
	 * @return          Sample median, if table was empty or null then Double.NaN is returned.
	 */
	public static double mode(double... numbers) {
		if (numbers == null) return Double.NaN;
		if (numbers.length == 0) return Double.NaN;
		if (numbers.length == 1) return numbers[0];
		for (double v : numbers) {
			if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
			if (Double.isNaN(v)) return Double.NaN;
		}
		double[][] dist = NumberTheory.getDistValues(numbers, true);
		return dist[0][0];
	}
}