kopia lustrzana https://github.com/vsamy/DiFipp
68 wiersze
2.7 KiB
C++
68 wiersze
2.7 KiB
C++
// Copyright (c) 2019, Vincent SAMY
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// All rights reserved.
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are met:
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// 1. Redistributions of source code must retain the above copyright notice,
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// this list of conditions and the following disclaimer.
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// 2. Redistributions in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
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// ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
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// WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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// DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
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// ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
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// (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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// LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
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// ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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// The views and conclusions contained in the software and documentation are those
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// of the authors and should not be interpreted as representing official policies,
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// either expressed or implied, of the FreeBSD Project.
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#pragma once
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#include "type_checks.h"
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#include "typedefs.h"
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#include <complex>
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namespace difi {
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/*! \brief Compute polynome coefficients from roots.
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*
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* This is done through Vieta's algorithm: \see https://en.wikipedia.org/wiki/Vieta%27s_formulas
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* \tparam T Floating type.
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*/
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template <typename T>
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struct VietaAlgo {
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static_assert(std::is_arithmetic<internal::complex_sub_type_t<T>>::value, "This struct can only accept arithmetic types or complex.");
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/*! \brief Vieta's algorithm.
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* \note The function return the coefficients in the decreasing order: \f$a_n X^n + a_{n-1}X^{n-1} + ... + a1X + a0\f$.
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* \param roots Set of all roots of the polynome.
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* \return Coefficients of the polynome.
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*/
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static vectX_t<T> polyCoeffFromRoot(const vectX_t<T>& roots);
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};
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template <typename T>
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vectX_t<T> VietaAlgo<T>::polyCoeffFromRoot(const vectX_t<T>& roots)
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{
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vectX_t<T> coeffs = vectX_t<T>::Zero(roots.size() + 1);
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coeffs(0) = T(1);
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for (Eigen::Index i = 0; i < roots.size(); ++i) {
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for (Eigen::Index k = i + 1; k > 0; --k) {
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coeffs(k) -= roots(i) * coeffs(k - 1);
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}
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}
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return coeffs;
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}
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} // namespace difi
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