package edu.neu.ccs.evergreen.util;

/**
 * Class used to determine the appMean for a set of relation weights.
 */
public class AppMean {
	/**
	 * Determine the appMean given the percentage weights of each relation
	 * present in the formula.
	 * 
	 * @param weights
	 *            Percentage weight of each relation
	 * @return appMean
	 */
	public static double appMean(double weights[]) {
		Polynomial polynomial = null;
		for (int m = 0; m < weights.length; m++) {
			if (weights[m] > 0.0) {
				Polynomial temp = AppSAT.appSAT(m);
				temp = temp.multiply(weights[m]);
				if (polynomial == null) {
					polynomial = temp;
				} else {
					polynomial = polynomial.add(temp);
				}
			}
		}
		if (polynomial == null) {
			return Double.MIN_VALUE;
		}
		return polynomial.eval(maxX0To1(polynomial));
	}

	/**
	 * Find the value of x which maximizes the value of the polynomial given by
	 * the coefficients over the domain 0 to 1 inclusive.
	 * 
	 * @param polynomial
	 *            Polynomial to maximize
	 * @return best value of x
	 */
	public static double maxX0To1(Polynomial polynomial) {
		// find best between maximum and minimum of domain
		double result = 0.0;
		double best = polynomial.eval(0.0);
		double test = polynomial.eval(1.0);
		if (test > best) {
			result = 1.0;
			best = test;
		}
		// if it is more than just a line we need to check
		// for interesting points between 0 and 1
		if (polynomial.degree() > 1) {
			// when the derivative is 0 we have a stationary point
			// which could be a local maximum, minimum, or inflection
			// for each such value check to see if it gives a higher
			// value for y
			double results[] = polynomial.differentiate().solve0();
			if (results.length > 0) {
				for (int i = 0; i < results.length; i++) {
					if ((results[i] > 0.0) && (results[i] < 1.0)) {
						test = polynomial.eval(results[i]);
						if (test > best) {
							result = results[i];
							best = test;
						}
					}
				}
			}
		}
		return result;
	}
}