/* $Id: mul_level_adolc.cpp 3738 2015-10-05 13:16:50Z bradbell $ */
/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell

CppAD is distributed under multiple licenses. This distribution is under
the terms of the
                    GNU General Public License Version 3.

A copy of this license is included in the COPYING file of this distribution.
Please visit http://www.coin-or.org/CppAD/ for information on other licenses.
-------------------------------------------------------------------------- */
/*
$begin mul_level_adolc.cpp$$
$spell
	CppAD
	AdolcDir
	adouble
	Vec
$$

$section Using Adolc with Multiple Levels of Taping: Example and Test$$

$head Purpose$$
In this example, we use $code AD< adouble> >$$ (level two taping),
the compute values of the function $latex f : \B{R}^n \rightarrow \B{R}$$ where
$latex \[
	f(x) = \frac{1}{2} \left( x_0^2 + \cdots + x_{n-1}^2 \right)
\] $$
We then use Adolc's $code adouble$$ (level one taping) to compute
the directional derivative
$latex \[
f^{(1)} (x) * v  = x_0 v_0 + \cdots + x_{n-1} v_{n-1}
\] $$.
where $latex v \in \B{R}^n$$.
We then use $code double$$ (no taping) to compute
$latex \[
\frac{d}{dx} \left[ f^{(1)} (x) * v \right] = v
\] $$
This is only meant as an example of multiple levels of taping.
The example $cref hes_times_dir.cpp$$ computes the same value more
efficiently by using the identity:
$latex \[
	\frac{d}{dx} \left[ f^{(1)} (x) * v \right] = f^{(2)} (x) * v
\] $$
The example $cref mul_level.cpp$$ computes the same values using
$code AD< AD<double> >$$ and $code AD<double>$$.

$head Memory Management$$
Adolc uses raw memory arrays that depend on the number of
dependent and independent variables.
The memory management utility $cref thread_alloc$$
is used to manage this memory allocation.

$head Configuration Requirement$$
This example will be compiled and tested provided that
the value $cref adolc_prefix$$ is specified on the
$cref cmake$$ command line.

$head Source$$
$code
$verbatim%example/mul_level_adolc.cpp%0%// BEGIN C++%// END C++%1%$$
$$

$end
*/
// BEGIN C++
# include <adolc/adouble.h>
# include <adolc/taping.h>
# include <adolc/interfaces.h>

// adouble definitions not in Adolc distribution and
// required in order to use CppAD::AD<adouble>
# include <cppad/example/base_adolc.hpp>

# include <cppad/cppad.hpp>

namespace {
	// f(x) = |x|^2 / 2 = .5 * ( x[0]^2 + ... + x[n-1]^2 )
	template <class Type>
	Type f(const CPPAD_TESTVECTOR(Type)& x)
	{	Type sum;

		sum  = 0.;
		size_t i = size_t(x.size());
		for(i = 0; i < size_t(x.size()); i++)
			sum += x[i] * x[i];

		return .5 * sum;
	}
}

bool mul_level_adolc(void)
{	bool ok = true;                // initialize test result
	using CppAD::thread_alloc;        // The CppAD memory allocator

	typedef adouble           a1type;  // for first level of taping
	typedef CppAD::AD<a1type> a2type; // for second level of taping
	size_t n = 5;                          // number independent variables
	size_t j;

	// 10 times machine epsilon
	double eps = 10. * std::numeric_limits<double>::epsilon();

	CPPAD_TESTVECTOR(double) x(n);
	CPPAD_TESTVECTOR(a1type) a1x(n);
	CPPAD_TESTVECTOR(a2type) a2x(n);

	// Values for the independent variables while taping the function f(x)
	for(j = 0; j < n; j++)
		a2x[j] = double(j);
	// Declare the independent variable for taping f(x)
	CppAD::Independent(a2x);

	// Use AD<adouble> to tape the evaluation of f(x)
	CPPAD_TESTVECTOR(a2type) a2y(1);
	a2y[0] = f(a2x);

	// Declare a1f as the corresponding ADFun<adouble> function f(x)
	// (make sure we do not run zero order forward during constructor)
	CppAD::ADFun<a1type> a1f;
	a1f.Dependent(a2x, a2y);

	// Value of the independent variables whitle taping f'(x) * v
	int tag = 0;
	int keep = 1;
	trace_on(tag, keep);
	for(j = 0; j < n; j++)
		a1x[j] <<= double(j);

	// set the argument value x for computing f'(x) * v
	a1f.Forward(0, a1x);

	// compute f'(x) * v
	CPPAD_TESTVECTOR(a1type) a1v(n);
	CPPAD_TESTVECTOR(a1type) a1df(1);
	for(j = 0; j < n; j++)
		a1v[j] = double(n - j);
	a1df = a1f.Forward(1, a1v);

	// declare Adolc function corresponding to f'(x) * v
	double df;
	a1df[0] >>= df;
	trace_off();

	// compute the d/dx of f'(x) * v = f''(x) * v
	size_t m      = 1;                     // # dependent in f'(x) * v

	// w = new double[capacity] where capacity >= m
	size_t capacity;
	double* w  = thread_alloc::create_array<double>(m, capacity);

	// dw = new double[capacity] where capacity >= n
	double* dw = thread_alloc::create_array<double>(n, capacity);

	w[0]  = 1.;
	fos_reverse(tag, int(m), int(n), w, dw);

	for(j = 0; j < n; j++)
	{	double vj = a1v[j].value();
		ok &= CppAD::NearEqual(dw[j], vj, eps, eps);
	}

	// make memory avaialble for other use by this thread
	thread_alloc::delete_array(w);
	thread_alloc::delete_array(dw);
	return ok;
}
// END C++
