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Stanford CoreNLP provides a set of natural language analysis tools which can take raw English language text input and give the base forms of words, their parts of speech, whether they are names of companies, people, etc., normalize dates, times, and numeric quantities, mark up the structure of sentences in terms of phrases and word dependencies, and indicate which noun phrases refer to the same entities. It provides the foundational building blocks for higher level text understanding applications.

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package edu.stanford.nlp.math;

/**
 * The class {@code ADMath} was created to extend the
 * current calculations of gradient to automatically include a calculation of the
 * hessian vector product with another vector {@code v}.  It contains all the functions
 * for the DoubleAlgorithmicDifferentiation class. This is used with
 * Stochastic Meta Descent Optimization, but could be extended for use in any application
 * that requires an additional order of differentiation without explicitly creating the code.
 *
 * @author Alex Kleeman
 * @version 2006/12/06
 */

public class ADMath {

  private ADMath() {} // static methods

  public static DoubleAD mult(DoubleAD a,DoubleAD b){
    DoubleAD c = new DoubleAD();
    c.setval( a.getval() * b.getval() );
    c.setdot(a.getdot()*b.getval() + b.getdot()*a.getval());
    return c;
  }

  public static DoubleAD multConst(DoubleAD a,double b){
    DoubleAD c = new DoubleAD();
    c.setval( a.getval() * b );
    c.setdot(a.getdot()*b);
    return c;
  }


  public static DoubleAD divide(DoubleAD a, DoubleAD b){
    DoubleAD c = new DoubleAD();
    c.setval(a.getval()/b.getval());
    c.setdot( (a.getdot()/b.getval()) - a.getval()*b.getdot() / (b.getval()*b.getval()) );
    return c;
  }

  public static DoubleAD divideConst(DoubleAD a, double b){
    DoubleAD c = new DoubleAD();
    c.setval(a.getval()/b);
    c.setdot( a.getdot()/b  );
    return c;
  }


  public static  DoubleAD exp(DoubleAD a){
    DoubleAD c = new DoubleAD();
    c.setval( Math.exp(a.getval()));
    c.setdot(a.getdot() * Math.exp(a.getval()));
    return c;
  }

  public static  DoubleAD log(DoubleAD a){
    DoubleAD c = new DoubleAD();
    c.setval( Math.log(a.getval()));
    c.setdot( a.getdot()/a.getval());
    return c;
  }

  public static  DoubleAD plus(DoubleAD a, DoubleAD b){
    DoubleAD c = new DoubleAD();
    c.setval( a.getval() + b.getval() );
    c.setdot( a.getdot() + b.getdot());
    return c;
  }

  public static  DoubleAD plusConst( DoubleAD a,double b){
    DoubleAD c = new DoubleAD();
    c.setval(  a.getval() + b );
    c.setdot( a.getdot());
    return c;
  }


  public static  DoubleAD minus(DoubleAD a, DoubleAD b){
    DoubleAD c = new DoubleAD();
    c.setval( a.getval() - b.getval() );
    c.setdot( a.getdot() - b.getdot());
    return c;
  }

  public static  DoubleAD minusConst( DoubleAD a,double b){
    DoubleAD c = new DoubleAD();
    c.setval(  a.getval() - b );
    c.setdot( a.getdot());
    return c;
  }


  public static DoubleAD logSum(DoubleAD[] logInputs) {
    return logSum(logInputs,0,logInputs.length);
  }

  // Some of this might need to change for optimal AD


  public static DoubleAD logSum(DoubleAD[] logInputs, int fromIndex, int toIndex) {
    if (logInputs.length == 0)
      throw new IllegalArgumentException();
    if(fromIndex >= 0 && toIndex < logInputs.length && fromIndex >= toIndex)
      return new DoubleAD(Double.NEGATIVE_INFINITY,Double.NEGATIVE_INFINITY);
    int maxIdx = fromIndex;
    double max = logInputs[fromIndex].getval();
    double maxdot = logInputs[fromIndex].getdot();

    for (int i = fromIndex+1; i < toIndex; i++) {
      if (logInputs[i].getval() > max) {
        maxIdx = i;
        maxdot = logInputs[i].getdot();
        max = logInputs[i].getval();
      }
    }

    DoubleAD ret = new DoubleAD();
    boolean haveTerms = false;
    double intermediate = 0.0;
    double intermediateDot = 0.0;
    double cutoff = max - SloppyMath.LOGTOLERANCE;
    // we avoid rearranging the array and so test indices each time!
    for (int i = fromIndex; i < toIndex; i++) {
      if (i != maxIdx && logInputs[i].getval() > cutoff) {
        haveTerms = true;
        double curEXP = Math.exp(logInputs[i].getval() - max);
        intermediate += curEXP;
        intermediateDot += curEXP*logInputs[i].getdot();
      }
    }
    if (haveTerms) {
      ret.setval(max + Math.log(1.0 + intermediate));
      ret.setdot((maxdot + intermediateDot)/(1.0 + intermediate));
    } else {
      ret.setval(max);
      ret.setdot(maxdot);
    }
    return ret;
  }

}