com.barrybecker4.optimization.parameter.redistribution.GaussianRedistribution Maven / Gradle / Ivy

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/** Copyright by Barry G. Becker, 2000-2011. Licensed under MIT License: http://www.opensource.org/licenses/MIT  */
package com.barrybecker4.optimization.parameter.redistribution;

import com.barrybecker4.common.math.MathUtil;
import com.barrybecker4.common.math.Range;
import com.barrybecker4.common.math.function.ArrayFunction;
import com.barrybecker4.common.math.function.ErrorFunction;
import com.barrybecker4.common.math.function.Function;
import com.barrybecker4.common.math.function.FunctionInverter;

/**
 * Convert the uniform distribution to a normal (gaussian) one.
 * @author Barry Becker
 */
public class GaussianRedistribution extends AbstractRedistributionFunction {

    private double mean;
    private double stdDeviation;

    private static final int NUM_MAP_VALUES = 10;
    private static final double SQRT2 = Math.sqrt(2.0);

    private Function errorFunction;


    public GaussianRedistribution(double mean, double standardDeviation) {
        verifyInRange(mean);
        errorFunction = new ErrorFunction();
        this.mean = mean;
        this.stdDeviation = standardDeviation;
        initializeFunction();
    }

    @Override
    protected void initializeFunction() {
        double[]  functionMap;
        double inc = 1.0 / (NUM_MAP_VALUES-1);
        double[] cdfFunction = new double[NUM_MAP_VALUES];
        cdfFunction[0] = 0;

        double x = 0;
        for (int index=1; index < NUM_MAP_VALUES; index++) {
            x += inc;
            double v = cdf(x);
            cdfFunction[index] = v;
        }
        double lowMissing = cdf(0);
        double highMissing = 1.0 - cdfFunction[NUM_MAP_VALUES-1];

        System.out.println("lowMissing=" + lowMissing + " highMissing="+highMissing);

        // reallocate the part that is missing.
        int numMapValsm1 = NUM_MAP_VALUES-1;
        for (int i=1; i 1.0 && i 0.9 && max <1.01);

        cdfFunction[NUM_MAP_VALUES-1] = 1.0;
        Range xRange = new Range(0.0, 1.0);
        FunctionInverter inverter = new FunctionInverter(cdfFunction);
        functionMap = inverter.createInverseFunction(xRange);
        redistributionFunction = new ArrayFunction(functionMap, cdfFunction);
    }

    /**
     * 1/2 (1 + erf((x-mean)/(SQRT2 *stdDeviation))
     * @param x x coordinate position.
     * @return cdf cumulative distribution function value
     */
    private double cdf(double x) {

        double denom = SQRT2 * stdDeviation;
        double xx = (Math.min(1.0, x) - mean) / denom;
        double erf = errorFunction.getValue(xx);
        return 0.5 * (1.0 + erf);
    }

    public static void main( String[] args )
    {
        new GaussianRedistribution(0.5, 10.0);
    }

}