import orbital.math.*;
import java.util.Arrays;
import orbital.math.functional.*;
import orbital.moon.math.functional.CoordinateCompositeFunction;

public class StatisticsDemo {
    private static final java.io.PrintStream log = System.out;
    // get us a value factory for creating arithmetic objects
    private static final Values vf = Values.getDefaultInstance();
    public static void main(String arg[]) throws Exception {
        descriptive();
        linRegCompare();
        regression();
    } 
    private static void descriptive() {
        log.println("DESCRIPTIVE: Descriptive statistics");
        double v[] = {
            2.16, 2.44, 2.90, 2.04, .58, 1.26, 1.52, 4.02, 1.90, 2.22, 5.08, 3.44, 5.24, -.56, 2.7, 3.06, 3.1, 2.9, 4.26, 1.36, 5, 1.74, 2.52, 4.04, 1.14, 0.1, 6.52, 5.16, .46, 7.72, 3.34, .74, 1.04, 3.2, 5.3, 5.08, 5.08, 2.36, 2.2, 5.12, 3.76, 2.14, 3.34, 4.78, 4.8, 5.38, .62, 3.2, 4.14, 3.58
        };
        log.println("arithmeticMean=" + Stat.arithmeticMean(v) + " geometricMean=" + Stat.geometricMean(v) + " harmonicMean=" + Stat.harmonicMean(v));
        log.println("mean=" + Stat.mean(v) + ", var=" + Stat.variance(v) + ", stdDev=" + Stat.standardDeviation(v) + ", covar=" + Stat.coefficientOfVariation(v));
        java.util.Arrays.sort(v);
        log.println("sorted: " + MathUtilities.format(v));
        log.println("median=" + Stat.median(v) + ", quantile(0.25)=" + Stat.quantile(v, .25) + ", quantile(0.75)=" + Stat.quantile(v, .75) + ", trimmed(.2)=" + Stat.trimmedMean(v, .2) + ", meandev=" + Stat.meanDeviation(v) + "\n");
    } 

    private static void linRegCompare() {
        log.println("LINREGCOMPARE: compare two linear regressions");

        // Linear Regression Statistics
        log.println("Linear Regression: in two dee (2D)");
        double vx[] = {
            10, 10, 10, 10, 10, 20, 20, 20, 20, 20, 50, 50, 50, 50, 50, 100, 100, 100, 100, 100
        };
        double vy[] = {
            51.4, 44.2, 56.4, 33.6, 46.6, 51.5, 49.5, 52.6, 43.8, 75.4, 81.9, 100.2, 79.3, 72.9, 84.6, 135.6, 128.4, 112.6, 122.2, 129.2
        };
        log.println("mean=" + Stat.mean(vx) + "|" + Stat.mean(vy) + ", stdDev=" + Stat.standardDeviation(vx) + "|" + Stat.standardDeviation(vy) + ", correlation=" + Stat.coefficientOfCorrelation(vx, vy));
        double _ba = Stat.coefficientOfCorrelation(vx, vy) * Stat.standardDeviation(vy) / Stat.standardDeviation(vx);
        double _aa = Stat.mean(vy) - _ba * Stat.mean(vx);
        log.println("Simplified formula results in... y=" + _aa + "+" + _ba + "*x");

        Matrix A = vf.newInstance(vx.length, 2);
        A.setColumn(0, vf.valueOf(vx));
        A.setColumn(1, vf.valueOf(vy));
        Function           fls[] = {
            Functions.one, Functions.id
        };
        final Function fl[] = {
            new CoordinateCompositeFunction(fls)
        };
        log.println("Exact linear regression results in... " + Stat.regression(fl, A));
        java.util.Arrays.sort(vx);
        java.util.Arrays.sort(vy);
        log.println("median=" + Stat.median(vx) + "|" + Stat.median(vy) + ", quantile(0.25)=" + Stat.quantile(vx, .25) + "|" + Stat.quantile(vy, .25) + ", quantile(0.75)=" + Stat.quantile(vx, .75) + "|" + Stat.quantile(vy, .75) + ", trimmed(.1)=" + Stat.trimmedMean(vx, .1) + "|" + Stat.trimmedMean(vy, .1));
        log.println();
    } 

    private static void regression() {
        log.println("REGRESSION: Example for general linear regression");
        double             data[][] = {
            {1, 0},
            {2, 0},
            {3, 2},
            {4, 6},
            {5, 12}
        };
        Matrix             Ex = vf.valueOf(data);
        Function           fs[] = {
            Functions.one, Functions.id, Functions.square
        };
        final Function func = new CoordinateCompositeFunction(fs);
        log.println("regression: " + Ex + " regression...");
        Function f = Stat.functionalRegression(func, Ex);
        log.println("regression: found: " + f);
        log.println("regression: lets look if it fits and what it interpolates");
        Arithmetic x;
        for (int i = 1; i <= 5; i++) {
            x = vf.valueOf(i);
            log.println(x + "|" + f.apply(x) + "\t");
        } 
        x = vf.valueOf(4.5);
        log.println(x + "|" + f.apply(x) + "\t");
        x = vf.valueOf(5.5);
        log.println(x + "|" + f.apply(x) + "\t");
    } 
}