Emily Boudreaux
2bca6e447c
we need an autodiff library at some point (or we need to roll our own but I do not think that makes sense). CppAD is well tested and header only and easy to include. It is also Liscene compatible with GPL v3.0. Here we bring it in as a dependency
133 lines
3.4 KiB
C++
133 lines
3.4 KiB
C++
# ifndef CPPAD_CORE_ABS_HPP
|
|
# define CPPAD_CORE_ABS_HPP
|
|
/* --------------------------------------------------------------------------
|
|
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-20 Bradley M. Bell
|
|
|
|
CppAD is distributed under the terms of the
|
|
Eclipse Public License Version 2.0.
|
|
|
|
This Source Code may also be made available under the following
|
|
Secondary License when the conditions for such availability set forth
|
|
in the Eclipse Public License, Version 2.0 are satisfied:
|
|
GNU General Public License, Version 2.0 or later.
|
|
---------------------------------------------------------------------------- */
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
$begin abs$$
|
|
$spell
|
|
fabs
|
|
Vec
|
|
std
|
|
faq
|
|
Taylor
|
|
Cpp
|
|
namespace
|
|
const
|
|
abs
|
|
$$
|
|
|
|
$section AD Absolute Value Functions: abs, fabs$$
|
|
|
|
$head Syntax$$
|
|
$icode%y% = abs(%x%)
|
|
%$$
|
|
$icode%y% = fabs(%x%)%$$
|
|
|
|
$head x, y$$
|
|
See the $cref/possible types/unary_standard_math/Possible Types/$$
|
|
for a unary standard math function.
|
|
|
|
$head Atomic$$
|
|
In the case where $icode x$$ is an AD type,
|
|
this is an $cref/atomic operation/glossary/Operation/Atomic/$$.
|
|
|
|
$head Complex Types$$
|
|
The functions $code abs$$ and $icode fabs$$
|
|
are not defined for the base types
|
|
$code std::complex<float>$$ or $code std::complex<double>$$
|
|
because the complex $code abs$$ function is not complex differentiable
|
|
(see $cref/complex types faq/Faq/Complex Types/$$).
|
|
|
|
$head Derivative$$
|
|
CppAD defines the derivative of the $code abs$$ function is
|
|
the $cref sign$$ function; i.e.,
|
|
$latex \[
|
|
{\rm abs}^{(1)} ( x ) = {\rm sign} (x ) =
|
|
\left\{ \begin{array}{rl}
|
|
+1 & {\rm if} \; x > 0 \\
|
|
0 & {\rm if} \; x = 0 \\
|
|
-1 & {\rm if} \; x < 0
|
|
\end{array} \right.
|
|
\] $$
|
|
The result for $icode%x% == 0%$$ used to be a directional derivative.
|
|
|
|
$head Example$$
|
|
$children%
|
|
example/general/fabs.cpp
|
|
%$$
|
|
The file
|
|
$cref fabs.cpp$$
|
|
contains an example and test of this function.
|
|
|
|
$end
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
|
|
// BEGIN CppAD namespace
|
|
namespace CppAD {
|
|
|
|
template <class Base>
|
|
AD<Base> AD<Base>::abs_me (void) const
|
|
{
|
|
AD<Base> result;
|
|
result.value_ = abs(value_);
|
|
CPPAD_ASSERT_UNKNOWN( Parameter(result) );
|
|
|
|
// check if there is a recording in progress
|
|
local::ADTape<Base>* tape = AD<Base>::tape_ptr();
|
|
if( tape == nullptr )
|
|
return result;
|
|
|
|
// check if operand is a constant parameter
|
|
if( tape_id_ != tape->id_ )
|
|
return result;
|
|
|
|
if(ad_type_ == dynamic_enum)
|
|
{ // dynamic paramter argument
|
|
result.taddr_ = tape->Rec_.put_dyn_par(
|
|
result.value_, local::abs_dyn, taddr_
|
|
);
|
|
result.tape_id_ = tape_id_;
|
|
result.ad_type_ = dynamic_enum;
|
|
}
|
|
else
|
|
{ // variable argument
|
|
CPPAD_ASSERT_UNKNOWN( local::NumRes(local::AbsOp) == 1 );
|
|
CPPAD_ASSERT_UNKNOWN( local::NumArg(local::AbsOp) == 1 );
|
|
|
|
// corresponding operand address
|
|
tape->Rec_.PutArg(taddr_);
|
|
|
|
// put operator in the tape
|
|
result.taddr_ = tape->Rec_.PutOp(local::AbsOp);
|
|
|
|
// make result a variable
|
|
result.tape_id_ = tape_id_;
|
|
result.ad_type_ = variable_enum;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
template <class Base>
|
|
AD<Base> abs(const AD<Base> &x)
|
|
{ return x.abs_me(); }
|
|
|
|
template <class Base>
|
|
AD<Base> abs(const VecAD_reference<Base> &x)
|
|
{ return x.ADBase().abs_me(); }
|
|
|
|
} // END CppAD namespace
|
|
|
|
# endif
|