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103 lines
2.5 KiB
103 lines
2.5 KiB
# ifndef CPPAD_CORE_SIGN_HPP
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# define CPPAD_CORE_SIGN_HPP
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/* --------------------------------------------------------------------------
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CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell
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CppAD is distributed under multiple licenses. This distribution is under
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the terms of the
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Eclipse Public License Version 1.0.
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A copy of this license is included in the COPYING file of this distribution.
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Please visit http://www.coin-or.org/CppAD/ for information on other licenses.
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-------------------------------------------------------------------------- */
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/*
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$begin sign$$
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$spell
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CppAD
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Dirac
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$$
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$section The Sign: sign$$
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$head Syntax$$
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$icode%y% = sign(%x%)%$$
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$head Description$$
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Evaluates the $code sign$$ function which is defined by
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$latex \[
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{\rm sign} (x) =
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\left\{ \begin{array}{rl}
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+1 & {\rm if} \; x > 0 \\
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0 & {\rm if} \; x = 0 \\
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-1 & {\rm if} \; x < 0
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\end{array} \right.
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\] $$
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$head x, y$$
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See the $cref/possible types/unary_standard_math/Possible Types/$$
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for a unary standard math function.
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$head Atomic$$
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This is an $cref/atomic operation/glossary/Operation/Atomic/$$.
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$head Derivative$$
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CppAD computes the derivative of the $code sign$$ function as zero for all
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argument values $icode x$$.
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The correct mathematical derivative is different and
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is given by
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$latex \[
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{\rm sign}^{(1)} (x) = 2 \delta (x)
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\] $$
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where $latex \delta (x)$$ is the Dirac Delta function.
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$head Example$$
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$children%
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example/general/sign.cpp
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%$$
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The file
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$cref sign.cpp$$
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contains an example and test of this function.
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It returns true if it succeeds and false otherwise.
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$end
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-------------------------------------------------------------------------------
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*/
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// BEGIN CppAD namespace
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namespace CppAD {
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template <class Base>
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AD<Base> AD<Base>::sign_me (void) const
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{
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AD<Base> result;
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result.value_ = sign(value_);
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CPPAD_ASSERT_UNKNOWN( Parameter(result) );
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if( Variable(*this) )
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{ // add this operation to the tape
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CPPAD_ASSERT_UNKNOWN( local::NumRes(local::SignOp) == 1 );
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CPPAD_ASSERT_UNKNOWN( local::NumArg(local::SignOp) == 1 );
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local::ADTape<Base> *tape = tape_this();
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// corresponding operand address
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tape->Rec_.PutArg(taddr_);
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// put operator in the tape
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result.taddr_ = tape->Rec_.PutOp(local::SignOp);
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// make result a variable
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result.tape_id_ = tape->id_;
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}
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return result;
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}
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template <class Base>
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inline AD<Base> sign(const AD<Base> &x)
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{ return x.sign_me(); }
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template <class Base>
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inline AD<Base> sign(const VecAD_reference<Base> &x)
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{ return x.ADBase().sign_me(); }
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} // END CppAD namespace
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# endif
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