JAutoDiff : An Automatic Differentiation Library (Pure Java)

Automatic differentiation is a technique to compute the derivatives of functions algebraically.
There are many implementation in C/C++ (ex. FADBAD++, ADOL-C, etc.), while are few in Java.

JAutoDiff is an automatic differentiation library coded in 100% pure Java.
This library provides a framework to compute derivatives of functions on arbitrary types of field using generics.

This software is released under the MIT License, see LICENSE.txt.

Sample : ADTest.java

package nilgiri.math.autodiff;

import org.junit.Test;


import junit.framework.Assert;
import nilgiri.math.DoubleReal;
import nilgiri.math.DoubleRealFactory;

public class ADTest {
	private final DoubleRealFactory RNFactory = DoubleRealFactory.instance();
	private final DifferentialRealFunctionFactory<DoubleReal> DFFactory = new DifferentialRealFunctionFactory<DoubleReal>(RNFactory);

	private void test(double i_expected, DifferentialFunction<DoubleReal> i_f){
		String func_str = i_f.toString();
		double func_value = i_f.getValue().doubleValue();
		
		System.out.println(func_str +" = "+ func_value +" is expected as "+ i_expected);
		Assert.assertEquals(func_str, i_expected, func_value);
	}

	@Test
	public void testFunc() {
		double vx = 3.0;
		double vy = 5.0;
		double vq = 8.0;

		Variable<DoubleReal> x = DFFactory.var("x", new DoubleReal(vx));
		Variable<DoubleReal> y = DFFactory.var("y", new DoubleReal(vy));
		Constant<DoubleReal> q = DFFactory.val(new DoubleReal(vq));

		//================================================================================
		//Construct functions
		//================================================================================
		//h = q*x*( cos(x*y) + y )
		DifferentialFunction<DoubleReal> h = q.mul(x).mul( DFFactory.cos( x.mul(y) ).plus(y) );
		
		//ph/px = q*( cos(x*y) + y ) + q*x*( -sin(x*y)*y ) 
		DifferentialFunction<DoubleReal> dhpx = h.diff(x);

		//ph/py = q*x*( -sin(x*y)*x + 1.0) 
		DifferentialFunction<DoubleReal> dhpy = h.diff(y);
		
		//p2h/px2 = q*( -sin(x*y)*y + y ) + q*( -sin(x*y)*y ) + q*x*( -cos(x*y)*y*y ) 
		DifferentialFunction<DoubleReal> d2hpxpx = dhpx.diff(x);

		//p2h/pypx = q*( -sin(x*y)*x + 1.0 ) + q*x*( -sin(x*y) - cos(x*y)*y*y ) 
		DifferentialFunction<DoubleReal> d2hpypx = dhpx.diff(y);

		//================================================================================
		//Test functions { h, ph/px, ph/py, p2h/px2, p2h/pypx }.
		//================================================================================
		test(vq*vx*( Math.cos(vx*vy) + vy ), h);
		test(vq*( Math.cos(vx*vy) + vy ) + vq*vx*(-Math.sin(vx*vy)*vy ), dhpx);
		test(vq*vx*( -Math.sin(vx*vy)*vx + 1.0 ), dhpy);
		test(vq*( -Math.sin(vx*vy)*vy ) + vq*( -Math.sin(vx*vy)*vy ) + vq*vx*(-Math.cos(vx*vy)*vy*vy), d2hpxpx);
		test(vq*( -Math.sin(vx*vy)*vx + 1.0 ) + vq*vx*( -Math.sin(vx*vy) - Math.cos(vx*vy)*vx*vy ), d2hpypx);

		//================================================================================
		//Change values of the variables.
		//================================================================================
		vx = 4.0;
		vy = 7.0;
		x.set(new DoubleReal(vx));
		y.set(new DoubleReal(vy));

		//================================================================================
		//Re-Test functions { h, ph/px, ph/py, p2h/px2, p2h/pypx }.
		//================================================================================
		//No reconstruction of the functions is necessary 
		//to get values of the functions for new values of variables.
		test(vq*vx*( Math.cos(vx*vy) + vy ), h);
		test(vq*( Math.cos(vx*vy) + vy ) + vq*vx*(-Math.sin(vx*vy)*vy ), dhpx);
		test(vq*vx*( -Math.sin(vx*vy)*vx + 1.0 ), dhpy);
		test(vq*( -Math.sin(vx*vy)*vy ) + vq*( -Math.sin(vx*vy)*vy ) + vq*vx*(-Math.cos(vx*vy)*vy*vy), d2hpxpx);
		test(vq*( -Math.sin(vx*vy)*vx + 1.0 ) + vq*vx*( -Math.sin(vx*vy) - Math.cos(vx*vy)*vx*vy ), d2hpypx);

	}
}

Result

((8.0*x)*(cos((x*y))+y)) = 101.7674900913883 is expected as 101.7674900913883
((8.0*(cos((x*y))+y))+((8.0*x)*-(sin((x*y))*y))) = -44.112044121724594 is expected as -44.112044121724594
((8.0*x)*(-(sin((x*y))*x)+1.0)) = -22.82072449131241 is expected as -22.82072449131241
((8.0*-(sin((x*y))*y))+((8.0*-(sin((x*y))*y))+((8.0*x)*-((cos((x*y))*y)*y)))) = 403.78972050272347 is expected as 403.78972050272347
((8.0*(-(sin((x*y))*x)+1.0))+((8.0*x)*-(((cos((x*y))*x)*y)+sin((x*y))))) = 250.27383230163406 is expected as 250.27383230163406
((8.0*x)*(cos((x*y))+y)) = 193.19661227796587 is expected as 193.19661227796587
((8.0*(cos((x*y))+y))+((8.0*x)*-(sin((x*y))*y))) = -12.383743511471195 is expected as -12.383743511471195
((8.0*x)*(-(sin((x*y))*x)+1.0)) = -2.6759409034072377 is expected as -2.6759409034072377
((8.0*-(sin((x*y))*y))+((8.0*-(sin((x*y))*y))+((8.0*x)*-((cos((x*y))*y)*y)))) = 1479.024550089191 is expected as 1479.024550089191
((8.0*(-(sin((x*y))*x)+1.0))+((8.0*x)*-(((cos((x*y))*x)*y)+sin((x*y))))) = 853.1568857652521 is expected as 853.1568857652521