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# ifndef CPPAD_FOR_ONE_INCLUDED
# define CPPAD_FOR_ONE_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 ForOne$$
$spell
        dy
        typename
        Taylor
        const
$$


$index partial, first order driver$$
$index first, order partial driver$$
$index driver, first order partial$$

$index easy, partial$$
$index driver, easy partial$$
$index partial, easy$$

$section First Order Partial Derivative: Driver Routine$$

$head Syntax$$
$syntax%%dy% = %f%.ForOne(%x%, %j%)%$$


$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 dy$$ to the
partial of $latex F$$ with respect to $latex x_j$$; i.e.,
$latex \[
dy 
= \D{F}{ x_j } (x) 
= \left[ 
        \D{ F_0 }{ x_j } (x) , \cdots , \D{ F_{m-1} }{ x_j } (x) 
\right]
\] $$

$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/ForOne/ForOne Uses Forward/ForOne Uses Forward/$$ below).

$head x$$
The argument $italic x$$ has prototype
$syntax%
        const %Vector% &%x%
%$$
(see $xref/ForOne/Vector/Vector/$$ 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 partial derivative.

$head j$$
The argument $italic j$$ has prototype
$syntax%
        size_t %j%
%$$
an is less than $italic n$$,
$xref/SeqProperty/Domain/domain/$$ space for $italic f$$.
It specifies the component of $italic F$$ 
for which we are computing the partial derivative.

$head dy$$
The result $italic dy$$ has prototype
$syntax%
        %Vector% %dy%
%$$
(see $xref/ForOne/Vector/Vector/$$ below)
and its size is $latex m$$, the dimension of the
$xref/SeqProperty/Range/range/$$ space for $italic f$$.
The value of $italic dy$$ is the partial of $latex F$$ with respect to
$latex x_j$$ evaluated at $italic x$$; i.e.,
for $latex i = 0 , \ldots , m - 1$$
$latex \[.
        dy[i] = \D{ F_i }{ x_j } ( x )
\] $$


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

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

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

//  BEGIN CppAD namespace
namespace CppAD {

template <typename Base>
template <typename Vector>
Vector ADFun<Base>::ForOne(const Vector &x, size_t j)
{       size_t j1;

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

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

        CPPAD_ASSERT_KNOWN(
                x.size() == n,
                "ForOne: Length of x not equal domain dimension for f"
        ); 
        CPPAD_ASSERT_KNOWN(
                j < n,
                "ForOne: the index j is not less than domain dimension for f"
        );

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

        // direction in which are are taking the derivative
        Vector dx(n);
        for(j1 = 0; j1 < n; j1++)
                dx[j1] = Base(0);
        dx[j] = Base(1);

        // dimension the return value
        Vector dy(m);

        // compute the return value
        dy = Forward(1, dx);

        return dy;
}

} // END CppAD namespace

# endif

---