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
153 lines
3.9 KiB
C++
153 lines
3.9 KiB
C++
# ifndef CPPAD_CORE_ATAN2_HPP
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# define CPPAD_CORE_ATAN2_HPP
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/* --------------------------------------------------------------------------
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CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-21 Bradley M. Bell
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CppAD is distributed under the terms of the
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Eclipse Public License Version 2.0.
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This Source Code may also be made available under the following
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Secondary License when the conditions for such availability set forth
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in the Eclipse Public License, Version 2.0 are satisfied:
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GNU General Public License, Version 2.0 or later.
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---------------------------------------------------------------------------- */
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/*
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-------------------------------------------------------------------------------
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$begin atan2$$
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$spell
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Vec
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CppAD
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namespace
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std
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atan
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const
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$$
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$section AD Two Argument Inverse Tangent Function$$
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$head Syntax$$
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$icode%theta% = atan2(%y%, %x%)%$$
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$head Purpose$$
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Determines an angle $latex \theta \in [ - \pi , + \pi ]$$
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such that
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$latex \[
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\begin{array}{rcl}
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\sin ( \theta ) & = & y / \sqrt{ x^2 + y^2 } \\
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\cos ( \theta ) & = & x / \sqrt{ x^2 + y^2 }
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\end{array}
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\] $$
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$head y$$
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The argument $icode y$$ has one of the following prototypes
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$codei%
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const AD<%Base%> &%y%
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const VecAD<%Base%>::reference &%y%
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%$$
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$head x$$
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The argument $icode x$$ has one of the following prototypes
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$codei%
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const AD<%Base%> &%x%
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const VecAD<%Base%>::reference &%x%
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%$$
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$head theta$$
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The result $icode theta$$ has prototype
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$codei%
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AD<%Base%> %theta%
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%$$
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$head Operation Sequence$$
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The AD of $icode Base$$
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operation sequence used to calculate $icode theta$$ is
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$cref/independent/glossary/Operation/Independent/$$
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of $icode x$$ and $icode y$$.
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$head Example$$
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$children%
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example/general/atan2.cpp
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%$$
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The file
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$cref atan2.cpp$$
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contains an example and test of this function.
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$end
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-------------------------------------------------------------------------------
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*/
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namespace CppAD { // BEGIN CppAD namespace
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inline float atan2(float x, float y)
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{ return std::atan2(x, y); }
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inline double atan2(double x, double y)
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{ return std::atan2(x, y); }
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// The code below is used as an example by the CondExp documentation.
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// BEGIN CondExp
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template <class Base>
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AD<Base> atan2 (const AD<Base> &y, const AD<Base> &x)
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{ //
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// zero, pi2, pi
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AD<Base> zero(0.);
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AD<Base> pi2(2. * atan(1.));
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AD<Base> pi(2. * pi2);
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//
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// abs_x, abs_y
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// Not using fabs because its derivative is zero at zero
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AD<Base> abs_x = CondExpGe(x, zero, x, -x);
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AD<Base> abs_y = CondExpGe(y, zero, y, -y);
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//
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// first
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// This is the result for first quadrant: x >= 0 , y >= 0
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AD<Base> alpha = atan(abs_y / abs_x);
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AD<Base> beta = pi2 - atan(abs_x / abs_y);
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AD<Base> first = CondExpGt(abs_x, abs_y, alpha, beta);
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//
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// second
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// This is the result for second quadrant: x <= 0 , y >= 0
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AD<Base> second = pi - first;
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//
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// third
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// This is the result for third quadrant: x <= 0 , y <= 0
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AD<Base> third = - pi + first;
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//
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// fourth
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// This is the result for fourth quadrant: x >= 0 , y <= 0
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AD<Base> fourth = - first;
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//
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// alpha
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// This is the result for x >= 0
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alpha = CondExpGe(y, zero, first, fourth);
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//
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// beta
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// This is the result for x <= 0
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beta = CondExpGe(y, zero, second, third);
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//
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//
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AD<Base> result = CondExpGe(x, zero, alpha, beta);
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return result;
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}
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// END CondExp
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template <class Base>
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AD<Base> atan2 (const VecAD_reference<Base> &y, const AD<Base> &x)
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{ return atan2( y.ADBase() , x ); }
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template <class Base>
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AD<Base> atan2 (const AD<Base> &y, const VecAD_reference<Base> &x)
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{ return atan2( y , x.ADBase() ); }
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template <class Base>
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AD<Base> atan2
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(const VecAD_reference<Base> &y, const VecAD_reference<Base> &x)
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{ return atan2( y.ADBase() , x.ADBase() ); }
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} // END CppAD namespace
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# endif
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