# ifndef CPPAD_JACOBIAN_INCLUDED
# define CPPAD_JACOBIAN_INCLUDED

/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-06 Bradley M. Bell

CppAD is distributed under multiple licenses. This distribution is under
the terms of the 
                    Common Public License Version 1.0.

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 Jacobian$$
$spell
	jac
	typename
	Taylor
	Jacobian
	DetLu
	const
$$

$index Jacobian, driver$$
$index first, derivative$$
$index driver, Jacobian$$

$section Jacobian: Driver Routine$$

$head Syntax$$
$syntax%%jac% = %f%.Jacobian(%x%)%$$


$head Purpose$$
We use $latex F : B^n \rightarrow B^m$$ to denote the
$xref/glossary/AD Function/AD function/$$ corresponding to $italic f$$.
The syntax above sets $italic jac$$ to the
Jacobian of $italic F$$ evaluated at $italic x$$; i.e.,
$latex \[
	jac = F^{(1)} (x)
\] $$

$head f$$
The object $italic f$$ has prototype
$syntax%
	ADFun<%Base%> %f%
%$$
Note that the $xref/ADFun/$$ object $italic f$$ is not $code const$$
(see $xref/Jacobian/Jacobian Uses Forward/Jacobian uses Forward/$$ below).

$head x$$
The argument $italic x$$ has prototype
$syntax%
	const %Vector% &%x%
%$$
(see $xref/Jacobian/Vector/Vector/$$ below)
and its size 
must be equal to $italic n$$, the dimension of the
$xref/SeqProperty/Domain/domain/$$ space for $italic f$$.
It specifies
that point at which to evaluate the Jacobian.

$head jac$$
The result $italic jac$$ has prototype
$syntax%
	%Vector% %jac%
%$$
(see $xref/Jacobian/Vector/Vector/$$ below)
and its size is $latex m * n$$; i.e., the product of the
$xref/SeqProperty/Domain/domain/$$
and
$xref/SeqProperty/Range/range/$$
dimensions for $italic f$$.
For $latex i = 0 , \ldots , m - 1 $$ 
and $latex j = 0 , \ldots , n - 1$$
$latex \[.
	jac[ i * n + j ] = \D{ F_i }{ x_j } ( x )
\] $$


$head Vector$$
The type $italic Vector$$ must be a $xref/SimpleVector/$$ class with
$xref/SimpleVector/Elements of Specified Type/elements of type/$$
$italic Base$$.
The routine $xref/CheckSimpleVector/$$ will generate an error message
if this is not the case.

$head Jacobian Uses Forward$$
After each call to $xref/Forward/$$,
the object $italic f$$ contains the corresponding 
$xref/glossary/Taylor Coefficient/Taylor coefficients/$$.
After $code Jacobian$$,
the previous calls to $xref/Forward/$$ are undefined.

$head Example$$
$children%
	example/jacobian.cpp
%$$
The routine 
$xref/Jacobian.cpp//Jacobian/$$ is both an example and test.
It returns $code true$$, if it succeeds and $code false$$ otherwise.

$end
-----------------------------------------------------------------------------
*/

//  BEGIN CppAD namespace
namespace CppAD {

template <typename Base, typename Vector>
void JacobianFor(ADFun<Base> &f, const Vector &x, Vector &jac)
{	size_t i;
	size_t j;

	size_t m = f.Domain();
	size_t n = f.Range();

	// check Vector is Simple Vector class with Base type elements
	CheckSimpleVector<Base, Vector>();

	CPPAD_ASSERT_UNKNOWN( x.size()   == f.Domain() );
	CPPAD_ASSERT_UNKNOWN( jac.size() == f.Range() * f.Domain() );

	// argument and result for forward mode calculations
	Vector u(m);
	Vector v(n);

	// initialize all the components
	for(j = 0; j < m; j++)
		u[j] = Base(0);
	
	// loop through the different coordinate directions
	for(j = 0; j < m; j++)
	{	// set u to the j-th coordinate direction
		u[j] = Base(1);

		// compute the partial of f w.r.t. this coordinate direction
		v = f.Forward(1, u);

		// reset u to vector of all zeros
		u[j] = Base(0);

		// return the result
		for(i = 0; i < n; i++)
			jac[ i * m + j ] = v[i];
	}
}
template <typename Base, typename Vector>
void JacobianRev(ADFun<Base> &f, const Vector &x, Vector &jac)
{	size_t i;
	size_t j;

	size_t m = f.Domain();
	size_t n = f.Range();

	CPPAD_ASSERT_UNKNOWN( x.size()   == f.Domain() );
	CPPAD_ASSERT_UNKNOWN( jac.size() == f.Range() * f.Domain() );

	// argument and result for reverse mode calculations
	Vector u(m);
	Vector v(n);

	// initialize all the components
	for(i = 0; i < n; i++)
		v[i] = Base(0);
	
	// loop through the different coordinate directions
	for(i = 0; i < n; i++)
	{	if( f.Parameter(i) )
		{	// return zero for this component of f
			for(j = 0; j < m; j++)
				jac[ i * m + j ] = Base(0);
		}
		else
		{ 
			// set v to the i-th coordinate direction
			v[i] = Base(1);

			// compute the derivative of this component of f
			u = f.Reverse(1, v);

			// reset v to vector of all zeros
			v[i] = Base(0);

			// return the result
			for(j = 0; j < m; j++)
				jac[ i * m + j ] = u[j];
		}
	}
}

template <typename Base>
template <typename Vector>
Vector ADFun<Base>::Jacobian(const Vector &x)
{	size_t i;
	size_t m = Domain();
	size_t n = Range();

	CPPAD_ASSERT_KNOWN(
		x.size() == m,
		"Jacobian: length of x not equal domain dimension for F"
	); 

	// point at which we are evaluating the Jacobian
	Forward(0, x);

	// work factor for forward mode
	size_t workForward = m; 

	// work factor for reverse mode
	size_t workReverse = 0;
	for(i = 0; i < n; i++)
	{	if( ! Parameter(i) )
			++workReverse;
	}

	// choose the method with the least work
	Vector jac( n * m );
	if( workForward <= workReverse )
		JacobianFor(*this, x, jac);
	else	JacobianRev(*this, x, jac);

	return jac;
}

} // END CppAD namespace

# endif