Enable use of AD<Base> where Base is Adolc's adouble Type

Enable use of AD<Base> where Base is Adolc's adouble Type
Syntax
This file is located in the example directory. It can be copied into the current working directory and included with the command:



     # include "base_adolc.hpp"

Example
The file mul_level_adolc.cpp contains an example use of Adolc's adouble type for a CppAD Base type. It returns true if it succeeds and false otherwise. The file ode_taylor_adolc.cpp contains a more realistic (and complex) example.

Include File
This file base_adolc.hpp requires adouble to be defined. In addition it is included before <cppad/cppad.hpp>, but it is to include parts of CppAD that are used by this file. This is done with the following include command:

 
# include <adolc/adouble.h>
# include <cppad/base_require.hpp>

CondExpOp
The type adouble supports a conditional assignment function with the syntax



     condassign(

a, b, c, d

which evaluates to

a = (b > 0) ? c : d

This enables one to include conditionals in the recording of adouble operations and later evaluation for different values of the independent variables (in the same spirit as the CppAD CondExp function).

 
namespace CppAD {
	inline adouble CondExpOp(
		enum  CppAD::CompareOp     cop ,
		const adouble            &left ,
		const adouble           &right ,
		const adouble        &trueCase ,
		const adouble       &falseCase )
	{	adouble result;
		switch( cop )
		{
			case CompareLt: // left < right
			condassign(result, right - left, trueCase, falseCase);
			break;

			case CompareLe: // left <= right
			condassign(result, left - right, falseCase, trueCase);
			break;

			case CompareEq: // left == right
			condassign(result, left - right, falseCase, trueCase);
			condassign(result, right - left, falseCase, result);
			break;

			case CompareGe: // left >= right
			condassign(result, right - left, falseCase, trueCase);
			break;

			case CompareGt: // left > right
			condassign(result, left - right, trueCase, falseCase);
			break;
			default:
			CppAD::ErrorHandler::Call(
				true     , __LINE__ , __FILE__ ,
				"CppAD::CondExp",
				"Error: for unknown reason."
			);
			result = trueCase;
		}
		return result;
	}
}

EqualOpSeq
The Adolc user interface does not specify a way to determine if two adouble variables correspond to the same operations sequence. Make EqualOpSeq an error if it gets used:

 
namespace CppAD {
	inline bool EqualOpSeq(const adouble &x, const adouble &y)
	{	CppAD::ErrorHandler::Call(
			true     , __LINE__ , __FILE__ ,
			"CppAD::EqualOpSeq(x, y)",
			"Error: adouble does not support EqualOpSeq."
		);
		return false;
	}
}

Identical
The Adolc user interface does not specify a way to determine if an adouble depends on the independent variables. To be safe (but slow) return false in all the cases below.

 
namespace CppAD {
	inline bool IdenticalPar(const adouble &x)
	{	return false; }
	inline bool IdenticalZero(const adouble &x)
	{	return false; }
	inline bool IdenticalOne(const adouble &x)
	{	return false; }
	inline bool IdenticalEqualPar(const adouble &x, const adouble &y)
	{	return false; }
}

Integer

 
	inline int Integer(const adouble &x)
	{    return static_cast<int>( x.getValue() ); }

epsilon

 
namespace CppAD {
	template <>
	inline adouble epsilon<adouble>(void)
	{	double eps = std::numeric_limits<double>::epsilon(); 
		return adouble( eps );
	}
}

Ordered

 
namespace CppAD {
	inline bool GreaterThanZero(const adouble &x)
	{    return (x > 0); }
	inline bool GreaterThanOrZero(const adouble &x)
	{    return (x >= 0); }
	inline bool LessThanZero(const adouble &x)
	{    return (x < 0); }
	inline bool LessThanOrZero(const adouble &x)
	{    return (x <= 0); }
	inline bool abs_geq(const adouble& x, const adouble& y)
	{	return fabs(x) >= fabs(y); }
}

Unary Standard Math
The following required functions are defined by the Adolc package for the adouble base case:

acos, asin, atan, cos, cosh, exp, log, sin, sinh, sqrt, tan.

sign
This required function is defined using the codassign function so that its adouble operation sequence does not depend on the value of x .

 
namespace CppAD {
	inline adouble sign(const adouble& x)
	{	adouble s_plus, s_minus;
		// set s_plus to sign(x)/2,  except for case x == 0, s_plus = -.5
		condassign(s_plus,  +x, -.5, .5);
		// set s_minus to -sign(x)/2, except for case x == 0, s_minus = -.5
		condassign(s_minus, -x, -.5, .5);
		// set s to sign(x)
		return s_plus - s_minus;
	}
}

abs
This required function uses the adolc fabs function:

 
namespace CppAD {
	inline adouble abs(const adouble& x)
	{	return fabs(x); }
}

pow
This required function is defined by the Adolc package for the adouble base case.

Input File: example/base_adolc.hpp