build(CppAD): brought in CppAD for autodiff
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
This commit is contained in:
165
build-config/cppad/include/cppad/speed/det_by_minor.hpp
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165
build-config/cppad/include/cppad/speed/det_by_minor.hpp
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# ifndef CPPAD_SPEED_DET_BY_MINOR_HPP
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# define CPPAD_SPEED_DET_BY_MINOR_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 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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$begin det_by_minor$$
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$spell
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CppAD
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cppad
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typedef
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const
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hpp
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Det
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namespace
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$$
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$section Determinant Using Expansion by Minors$$
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$head Syntax$$
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$codei%# include <cppad/speed/det_by_minor.hpp>
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%$$
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$codei%det_by_minor<%Scalar%> %det%(%n%)
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%$$
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$icode%d% = %det%(%a%)
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%$$
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$head Inclusion$$
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The template class $code det_by_minor$$ is defined in the $code CppAD$$
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namespace by including
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the file $code cppad/speed/det_by_minor.hpp$$
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(relative to the CppAD distribution directory).
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$head Constructor$$
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The syntax
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$codei%
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det_by_minor<%Scalar%> %det%(%n%)
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%$$
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constructs the object $icode det$$ which can be used for
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evaluating the determinant of $icode n$$ by $icode n$$ matrices
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using expansion by minors.
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$head Scalar$$
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The type $icode Scalar$$ must satisfy the same conditions
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as in the function $cref/det_of_minor/det_of_minor/Scalar/$$.
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$head n$$
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The argument $icode n$$ has prototype
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$codei%
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size_t %n%
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%$$
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$head det$$
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The syntax
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$codei%
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%d% = %det%(%a%)
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%$$
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returns the determinant of the matrix $icode A$$ using expansion by minors.
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$subhead a$$
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The argument $icode a$$ has prototype
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$codei%
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const %Vector% &%a%
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%$$
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It must be a $icode Vector$$ with length $latex n * n$$ and with
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elements of type $icode Scalar$$.
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The elements of the $latex n \times n$$ matrix $latex A$$ are defined,
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for $latex i = 0 , \ldots , n-1$$ and $latex j = 0 , \ldots , n-1$$, by
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$latex \[
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A_{i,j} = a[ i * m + j]
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\] $$
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$subhead d$$
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The return value $icode d$$ has prototype
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$codei%
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%Scalar% %d%
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%$$
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It is equal to the determinant of $latex A$$.
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$head Vector$$
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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$$ with value less than $latex n * n$$.
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This must return a $icode Scalar$$ value corresponding to the $th i$$
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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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$children%
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speed/example/det_by_minor.cpp%
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omh/det_by_minor_hpp.omh
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%$$
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$head Example$$
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The file
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$cref det_by_minor.cpp$$
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contains an example and test of $code det_by_minor.hpp$$.
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$head Source Code$$
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The file
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$cref det_by_minor.hpp$$
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contains the source 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 <cppad/speed/det_of_minor.hpp>
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# include <vector>
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// BEGIN CppAD namespace
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namespace CppAD {
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template <class Scalar>
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class det_by_minor {
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private:
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size_t m_;
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// made mutable because modified and then restored
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mutable std::vector<size_t> r_;
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mutable std::vector<size_t> c_;
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// make mutable because its value does not matter
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mutable std::vector<Scalar> a_;
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public:
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det_by_minor(size_t m) : m_(m) , r_(m + 1) , c_(m + 1), a_(m * m)
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{
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size_t i;
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// values for r and c that correspond to entire matrix
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for(i = 0; i < m; i++)
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{ r_[i] = i+1;
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c_[i] = i+1;
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}
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r_[m] = 0;
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c_[m] = 0;
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}
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template <class Vector>
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Scalar operator()(const Vector &x) const
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{ size_t i = m_ * m_;
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while(i--)
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a_[i] = x[i];
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return det_of_minor(a_, m_, m_, r_, c_);
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}
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};
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} // END CppAD namespace
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// END C++
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# endif
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