mirror of
https://github.com/firestar5683/StarPilot.git
synced 2026-06-29 02:22:09 +08:00
George Hotz
129 lines
3.2 KiB
C++
129 lines
3.2 KiB
C++
# ifndef CPPAD_SPEED_DET_GRAD_33_HPP
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# define CPPAD_SPEED_DET_GRAD_33_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 det_grad_33$$
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$spell
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cppad
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CppAD
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det
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namespace
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const
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bool
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hpp
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$$
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$section Check Gradient of Determinant of 3 by 3 matrix$$
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$mindex det_grad_33 correct$$
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$head Syntax$$
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$codei%# include <cppad/speed/det_grad_33.hpp>
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%$$
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$icode%ok% = det_grad_33(%x%, %g%)%$$
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$head Purpose$$
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This routine can be used to check a method for computing the
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gradient of the determinant of a matrix.
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$head Inclusion$$
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The template function $code det_grad_33$$ is defined in the $code CppAD$$
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namespace by including
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the file $code cppad/speed/det_grad_33.hpp$$
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(relative to the CppAD distribution directory).
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$head x$$
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The argument $icode x$$ has prototype
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$codei%
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const %Vector% &%x%
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%$$.
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It contains the elements of the matrix $latex X$$ in row major order; i.e.,
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$latex \[
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X_{i,j} = x [ i * 3 + j ]
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\] $$
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$head g$$
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The argument $icode g$$ has prototype
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$codei%
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const %Vector% &%g%
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%$$.
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It contains the elements of the gradient of
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$latex \det ( X )$$ in row major order; i.e.,
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$latex \[
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\D{\det (X)}{X(i,j)} = g [ i * 3 + j ]
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\] $$
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$head Vector$$
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If $icode y$$ is a $icode Vector$$ object,
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it must support the syntax
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$codei%
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%y%[%i%]
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%$$
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where $icode i$$ has type $code size_t$$ with value less than 9.
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This must return a $code double$$ value corresponding to the $th i$$
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element of the vector $icode y$$.
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This is the only requirement of the type $icode Vector$$.
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$head ok$$
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The return value $icode ok$$ has prototype
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$codei%
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bool %ok%
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%$$
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It is true, if the gradient $icode g$$
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passes the test and false otherwise.
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$children%
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omh/det_grad_33_hpp.omh
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%$$
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$head Source Code$$
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The file
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$cref det_grad_33.hpp$$
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contains the source code for this template function.
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$end
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------------------------------------------------------------------------------
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*/
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// BEGIN C++
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# include <limits>
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# include <cppad/utility/near_equal.hpp>
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namespace CppAD {
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template <class Vector>
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bool det_grad_33(const Vector &x, const Vector &g)
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{ bool ok = true;
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typedef typename Vector::value_type Float;
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Float eps = 10. * Float( std::numeric_limits<double>::epsilon() );
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// use expansion by minors to compute the derivative by hand
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double check[9];
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check[0] = + ( x[4] * x[8] - x[5] * x[7] );
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check[1] = - ( x[3] * x[8] - x[5] * x[6] );
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check[2] = + ( x[3] * x[7] - x[4] * x[6] );
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//
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check[3] = - ( x[1] * x[8] - x[2] * x[7] );
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check[4] = + ( x[0] * x[8] - x[2] * x[6] );
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check[5] = - ( x[0] * x[7] - x[1] * x[6] );
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//
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check[6] = + ( x[1] * x[5] - x[2] * x[4] );
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check[7] = - ( x[0] * x[5] - x[2] * x[3] );
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check[8] = + ( x[0] * x[4] - x[1] * x[3] );
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//
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for(size_t i = 0; i < 3 * 3; i++)
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ok &= CppAD::NearEqual(check[i], g[i], eps, eps);
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return ok;
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}
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}
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// END C++
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# endif
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