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Tensorics is a java framework which uses a tensor as a central object. A tensor represents a set of values placed in an N-dimensional space. Wherever you are tempted to use maps of maps, a tensor might be a good choice ;-) Tensorics provides methods to create, transform and performing calculations with those tensors.

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/**
 * Copyright (c) 2016 European Organisation for Nuclear Research (CERN), All Rights Reserved.
 */

package org.tensorics.core.fields.doubles;

/**
 * This class provides some utility methods to evaluate the normal distribution cumulative distribution function (CDF)
 * and its inverse.
 * 
 * @author mihostet
 */
public class DoubleStatistics {

    private DoubleStatistics() {
        /* static methods only */
    }

    /**
     * Calculate the standard Gaussian CDF (mu=0, sigma=1). Taken from: G. Marsaglia, Evaluating the Normal
     * Distribution, JStatSoft 11 (4), 2004
     * 
     * @param value The x value
     * @return The standard Gaussian CDF
     */
    public static double standardGaussianCumulativeDistributionFunction(double value) {
        if (value < -8.0) {
            return 0.0;
        }
        if (value > 8.0) {
            return 1.0;
        }
        double s = value, t = 0, b = value, q = value * value, i = 1;
        while (s != t) {
            s = (t = s) + (b *= q / (i += 2));
        }
        return 0.5 + s * Math.exp(-0.5 * q - 0.91893853320467274178);
    }

    /**
     * Calculate the inverse standard Gaussian CDF by performing a recursive binary search on the CDF
     * 
     * @param value The position to calculate the inverse CDF for
     * @param low The lower bound
     * @param high The upper bound
     * @return
     */
    private static double searchInverseGaussianCumulativeDistributionFunction(double value, double low, double high) {
        final double INVERSE_GAUSSIAN_ACCURACY = 0.00000001;
        double mid = low + (high - low) / 2.0;
        if (high - low < INVERSE_GAUSSIAN_ACCURACY) {
            return mid;
        }
        if (standardGaussianCumulativeDistributionFunction(mid) > value) {
            return searchInverseGaussianCumulativeDistributionFunction(value, low, mid);
        } else {
            return searchInverseGaussianCumulativeDistributionFunction(value, mid, high);
        }
    }

    /**
     * Calculate the inverse Gaussian CDF (mu=0, sigma=1)
     * 
     * @param value The position to calculate the inverse CDF for
     * @return The inverse Gaussian CDF for y
     */
    public static double inverseGaussianCumulativeDistributionFunction(double value) {
        if (value < 0.0 || value > 1.0) {
            throw new IllegalArgumentException("y must be in the range [0,1]");
        }
        return searchInverseGaussianCumulativeDistributionFunction(value, -8.0, 8.0);
    }

}