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# ifndef CPPAD_SUB_OP_INCLUDED
# define CPPAD_SUB_OP_INCLUDED

/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-07 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 ForSubvvOp$$ $comment CppAD Developer Documentation$$
$spell
        Subpv
        Subvp
        Subvv
        Taylor
        const
        inline
        Op
$$


$index subtract, forward operator$$
$index forward, subtract operator$$
$index operator, subtract forward$$
$index ForSub$$

$section Forward Mode Subtraction Operators$$

$head Syntax$$

$syntax%inline void ForSubvvOp(size_t %d%,
        %Base% *%z%, const %Base% *%x%, const %Base% *%y%)%$$
$pre
$$
$syntax%inline void ForSubpvOp(size_t %d%,
        %Base% *%z%, const %Base% *%p%, const %Base% *%y%)%$$
$pre
$$
$syntax%inline void ForSubvpOp(size_t %d%,
        %Base% *%z%, const %Base% *%x%, const %Base% *%p%)%$$


$head Description$$
Computes the $italic d$$ order Taylor coefficient for $latex Z$$ where
$table
Operation  $cnext Value  $rnext
Subvv       $cnext $latex Z = X - Y$$ $rnext
Subpv       $cnext $latex Z = P - Y$$ $rnext
Subvp       $cnext $latex Z = X - P$$ 
$tend

$head x$$
The vector $italic x$$ has length $latex d+1$$ and contains the
$th d$$ order Taylor coefficient row vector for $italic X$$.

$head y$$
The vector $italic y$$ has length $latex d+1$$ and contains the
$th d$$ order Taylor coefficient row vector for $italic Y$$.

$head p$$
The scalar $syntax%*%p%$$ contains the value of the parameter $italic P$$.

$head z$$
The vector $italic z$$ has length $latex d+1$$.
On input it contains the
$th d-1$$ order Taylor coefficient row vector for $italic Z$$.
On output it contains the
$th d$$ order Taylor coefficient row vector for $italic Z$$; i.e.,
$syntax%%z%[%d%]%$$ is set equal to the $th d$$ Taylor coefficient for
the function $italic Z$$.

$end
------------------------------------------------------------------------------
$begin RevSubvvOp$$ $comment CppAD Developer Documentation$$
$spell
        Subpv
        Subvp
        Subvv
        Taylor
        const
        inline
        Op
        px
        py
        pz
$$

$mindex RevSubvvOp reverse minus subtract$$
$section Reverse Mode Subtraction Operator$$

$head Syntax$$

$syntax%inline void RevSubvvOp(size_t %d%,
        const %Base% *%pz%, %Base% *%px%, %Base% *%py%)%$$

$syntax%inline void RevSubpvOp(size_t %d%,
        const %Base% *%pz%, %Base% *%py%)%$$

$syntax%inline void RevSubvpOp(size_t %d%,
        const %Base% *%pz%, %Base% *%px%)%$$

$head Description$$
We are given the partial derivatives for a function
$latex G(z, x, y)$$ and we wish to compute the partial derivatives for
the function
$latex \[
        H(x, y) = G [ Z(x, y) , x , y ]
\]$$
where $latex Z(x, y)$$ is defined as the 
$th d$$ order Taylor coefficient row vector for $italic Z$$ as
a function of the corresponding vectors for 
$italic X$$ and $italic Y$$ where

$table
Operation  $cnext Value  $rnext
Subvv       $cnext $latex Z = X - Y$$ $rnext
Subpv       $cnext $latex Z = P - Y$$ $rnext
Subvp       $cnext $latex Z = X - P$$ 
$tend

Note that $italic Z$$ has been used both the original subtraction 
function and for the corresponding mapping of Taylor coefficients.

$head pz$$
The vector $italic pz$$ has length $latex d+1$$ and 
$syntax%%pz%[%j%]%$$ contains the partial for $italic G$$
with respect to the $th j$$ order Taylor coefficient for $italic Z$$.

$head On Input$$

$subhead px$$
The vector $italic px$$ has length $latex d+1$$ and 
$syntax%%px%[%j%]%$$ contains the partial for $italic G$$
with respect to the $th j$$ order Taylor coefficient for $italic X$$.

$subhead py$$
The vector $italic py$$ has length $latex d+1$$ and 
$syntax%%py%[%j%]%$$ contains the partial for $italic G$$
with respect to the $th j$$ order Taylor coefficient for $italic Y$$.

$head On Output$$

$subhead px$$
If present,
the vector $italic px$$ has length $latex d+1$$ and 
$syntax%%px%[%j%]%$$ contains the partial for $italic H$$
with respect to the $th j$$ order Taylor coefficient for $italic X$$.

$subhead py$$
If present,
the vector $italic py$$ has length $latex d+1$$ and 
$syntax%%py%[%j%]%$$ contains the partial for $italic H$$
with respect to the $th j$$ order Taylor coefficient for $italic Y$$.


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

// BEGIN CppAD namespace
namespace CppAD {

// --------------------------- Subvv -----------------------------------------

template <class Base>
inline void ForSubvvOp(size_t d, 
        Base *z, const Base *x, const Base *y)
{
        z[d] = x[d] - y[d];
}

template <class Base>
inline void RevSubvvOp(size_t d, 
        const Base *pz, Base *px, Base *py)
{
        // number of indices to access
        size_t i = d + 1;

        while(i)
        {       --i;
                px[i] += pz[i];
                py[i] -= pz[i];
        }
}

// --------------------------- Subpv -----------------------------------------

template <class Base>
inline void ForSubpvOp(size_t d, 
        Base *z, const Base *p, const Base *y)
{
        if( d == 0 )
                z[d] = (*p) - y[d];
        else    z[d] = - y[d];

}

template <class Base>
inline void RevSubpvOp(size_t d, 
        const Base *pz, Base *py)
{
        // number of indices to access
        size_t i = d + 1;

        while(i)
        {       --i;
                py[i] -= pz[i];
        }
}

// --------------------------- Subvp -----------------------------------------

template <class Base>
inline void ForSubvpOp(size_t d, 
        Base *z, const Base *x, const Base *p)
{
        if( d == 0 )
                z[d] = x[d] - (*p);
        else    z[d] = x[d];

}

template <class Base>
inline void RevSubvpOp(size_t d, 
        const Base *pz, Base *px)
{
        // number of indices to access
        size_t i = d + 1;

        while(i)
        {       --i;
                px[i] += pz[i];
        }
}

} // END CppAD namespace

# endif

---