kopia lustrzana https://github.com/vsamy/DiFipp
313 wiersze
17 KiB
C++
313 wiersze
17 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 "DigitalFilter.h"
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#include "math_utils.h"
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#include <array>
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// Read this if you are an adulator of the math god: https://arxiv.org/pdf/1709.08321.pdf
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namespace difi {
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namespace details {
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// T: type
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// N: Number of points
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// Central differentiators: http://www.holoborodko.com/pavel/numerical-methods/numerical-derivative/central-differences/
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template <typename T, size_t N> struct GetCDCoeffs { vectN_t<T, N> operator()() const; };
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template <typename T> struct GetCDCoeffs<T, 3> { vectN_t<T, 3> operator()() const { return vectN_t<T, 3>{ T(1), T(0), T(-1) } / T(2); } };
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template <typename T> struct GetCDCoeffs<T, 5> { vectN_t<T, 5> operator()() const { return vectN_t<T, 5>{ T(-1), T(8), T(0), T(8), T(1) } / T(12); } };
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template <typename T> struct GetCDCoeffs<T, 7> { vectN_t<T, 7> operator()() const { return vectN_t<T, 7>{ T(1), T(-9), T(45), T(0), T(-45), T(9), T(-1) } / T(60); } };
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template <typename T> struct GetCDCoeffs<T, 9> { vectN_t<T, 9> operator()() const { return vectN_t<T, 9>{ T(-3), T(32), T(-168), T(672), T(0), T(-672), T(168), T(-32), T(3) } / T(840); } };
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// Low-noise Lanczos differentiators: http://www.holoborodko.com/pavel/numerical-methods/numerical-derivative/lanczos-low-noise-differentiators/
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template <typename T, size_t N>
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struct GetLNLCoeffs {
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vectN_t<T, N> operator()() const
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{
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static_assert(N % 2 == 1. "'N' must be odd.");
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constexpr T GetCoeff = [](size_t n, size_t k) {
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const T m = (n - 1) / 2;
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return T(3) * k / (m * (m + 1) * (2 * m + 1));
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};
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vectN_t<T, N> v{};
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for (Eigen::Index k = 0; k < N; ++k)
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v(k) = GetCoeff(N, k);
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return v;
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}
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};
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template <typename T> struct GetLNLCoeffs<T, 5> { vectN_t<T, 5> operator()() const { return vectN_t<T, 5>{ T(2), T(1), T(0), T(-1), T(-2) } / T(10); } };
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template <typename T> struct GetLNLCoeffs<T, 7> { vectN_t<T, 7> operator()() const { return vectN_t<T, 7>{ T(3), T(2), T(1), T(0), T(-1), T(-2), T(-3) } / T(28); } };
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template <typename T> struct GetLNLCoeffs<T, 9> { vectN_t<T, 9> operator()() const { return vectN_t<T, 9>{ T(4), T(3), T(2), T(1), T(0), T(-1), T(-2), T(-3), T(-4) } / T(60); } };
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template <typename T> struct GetLNLCoeffs<T, 11> { vectN_t<T, 11> operator()() const { return vectN_t<T, 11>{ T(5), T(4), T(3), T(2), T(1), T(0), T(-1), T(-2), T(-3), T(-4), T(-5) } / T(110); } };
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// Super Low-noise Lanczos differentiators: http://www.holoborodko.com/pavel/numerical-methods/numerical-derivative/lanczos-low-noise-differentiators/
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template <typename T, size_t N> struct GetSLNLCoeffs { vectN_t<T, N> operator()() const; };
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template <typename T> struct GetSLNLCoeffs<T, 7> { vectN_t<T, 7> operator()() const { return vectN_t<T, 7>{ T(-22), T(67), T(58), T(0), T(-58), T(-67), T(22) } / T(252); } };
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template <typename T> struct GetSLNLCoeffs<T, 9> { vectN_t<T, 9> operator()() const { return vectN_t<T, 9>{ T(-86), T(142), T(193), T(126), T(0), T(-126), T(-193), T(-142), T(86) } / T(1188); } };
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template <typename T> struct GetSLNLCoeffs<T, 11> { vectN_t<T, 11> operator()() const { return vectN_t<T, 11>{ T(-300), T(294), T(532), T(503), T(296), T(0), T(-296), T(-503), T(-532), T(-294), T(300) } / T(5148); } };
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// Backward Noise-Robust differentiators; http://www.holoborodko.com/pavel/wp-content/uploads/OneSidedNoiseRobustDifferentiators.pdf
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template <typename T, size_t N>
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struct GetFNRCoeffs {
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vectN_t<T, N> operator()() const {
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constexpr const int BinCoeff = N - 2;
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vectN_t<T, N> v{};
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v(0) = T(1);
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v(N - 1) = T(-1);
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for (int i = 1; i < N - 1; ++i)
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v(i) = (Binomial<T>(N, i) - Binomial<T>(N, i - 1)) / std::pow(T(2), T(BinCoeff));
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return v;
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}
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};
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template <typename T> struct GetFNRCoeffs<T, 3> { vectN_t<T, 3> operator()() const { return vectN_t<T, 3>{ T(1), T(0), T(-1) } / T(2); } };
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template <typename T> struct GetFNRCoeffs<T, 4> { vectN_t<T, 4> operator()() const { return vectN_t<T, 4>{ T(1), T(1), T(-1), T(-1) } / T(4); } };
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template <typename T> struct GetFNRCoeffs<T, 5> { vectN_t<T, 5> operator()() const { return vectN_t<T, 5>{ T(1), T(2), T(0), T(-2), T(-1) } / T(8); } };
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template <typename T> struct GetFNRCoeffs<T, 6> { vectN_t<T, 6> operator()() const { return vectN_t<T, 6>{ T(1), T(3), T(2), T(-2), T(-3), T(-1) } / T(16); } };
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template <typename T> struct GetFNRCoeffs<T, 7> { vectN_t<T, 7> operator()() const { return vectN_t<T, 7>{ T(1), T(4), T(5), T(0), T(-5), T(-4), T(-1) } / T(32); } };
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template <typename T> struct GetFNRCoeffs<T, 8> { vectN_t<T, 8> operator()() const { return vectN_t<T, 8>{ T(1), T(5), T(9), T(5), T(-5), T(-9), T(-5), T(-1) } / T(64); } };
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template <typename T> struct GetFNRCoeffs<T, 9> { vectN_t<T, 9> operator()() const { return vectN_t<T, 9>{ T(1), T(6), T(14), T(14), T(0), T(-14), T(-14), T(-6), T(-1) } / T(128); } };
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template <typename T> struct GetFNRCoeffs<T, 10> { vectN_t<T, 10> operator()() const { return vectN_t<T, 10>{ T(1), T(7), T(20), T(28), T(14), T(-14), T(-28), T(-20), T(-7), T(-1) } / T(256); } };
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template <typename T> struct GetFNRCoeffs<T, 11> { vectN_t<T, 11> operator()() const { return vectN_t<T, 11>{ T(1), T(8), T(27), T(48), T(42), T(0), T(-42), T(-48), T(-27), T(-8), T(-1) } / T(512); } };
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// Backward Hybrid Noise-Robust differentiators; http://www.holoborodko.com/pavel/wp-content/uploads/OneSidedNoiseRobustDifferentiators.pdf
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template <typename T, size_t N> struct GetFHNRCoeffs { vectN_t<T, N> operator()() const; };
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template <typename T> struct GetFHNRCoeffs<T, 4> { vectN_t<T, 4> operator()() const { return vectN_t<T, 4>{ T(2), T(-1), T(-2), T(1) } / T(2); } };
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template <typename T> struct GetFHNRCoeffs<T, 5> { vectN_t<T, 5> operator()() const { return vectN_t<T, 5>{ T(7), T(1), T(-10), T(-1), T(3) } / T(10); } };
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template <typename T> struct GetFHNRCoeffs<T, 6> { vectN_t<T, 6> operator()() const { return vectN_t<T, 6>{ T(16), T(1), T(-10), T(-10), T(-6), T(9) } / T(28); } };
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template <typename T> struct GetFHNRCoeffs<T, 7> { vectN_t<T, 7> operator()() const { return vectN_t<T, 7>{ T(12), T(5), T(-8), T(-6), T(-10), T(1), T(6) } / T(28); } };
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template <typename T> struct GetFHNRCoeffs<T, 8> { vectN_t<T, 8> operator()() const { return vectN_t<T, 8>{ T(22), T(7), T(-6), T(-11), T(-14), T(-9), T(-2), T(13) } / T(60); } };
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template <typename T> struct GetFHNRCoeffs<T, 9> { vectN_t<T, 9> operator()() const { return vectN_t<T, 9>{ T(52), T(29), T(-14), T(-17), T(-40), T(-23), T(-26), T(11), T(28) } / T(180); } };
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template <typename T> struct GetFHNRCoeffs<T, 10> { vectN_t<T, 10> operator()() const { return vectN_t<T, 10>{ T(56), T(26), T(-2), T(-17), T(-30), T(-30), T(-28), T(-13), T(4), T(34) } / T(220); } };
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template <typename T> struct GetFHNRCoeffs<T, 11> { vectN_t<T, 11> operator()() const { return vectN_t<T, 11>{ T(320), T(206), T(-8), T(-47), T(-186), T(-150), T(-214), T(-103), T(-92), T(94), T(180) } / T(1540); } };
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template <typename T, size_t N, typename ForwardCoeffs> vectN_t<T, N> GetForwardISDCoeffs()
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{
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vectN_t<T, N> v{};
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const vectN_t<T, N> v0 = ForwardCoeffs{}();
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for (Eigen::Index k = 0; k < N; ++k)
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v(k) = k * v0(k);
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return v(k);
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}
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// Backward Noise-Robust differentiators for irregular space data
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template <typename T, size_t N> struct GetFNRISDCoeffs { vectN_t<T, N> operator()() const { return GetForwardISDCoeffs<T, N, GetFNRCoeffs<T, N>>(); } };
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// Backward Hybrid Noise-Robust differentiators for irregular space data
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template <typename T, size_t N> struct GetFHNRISDCoeffs { vectN_t<T, N> operator()() const { return GetForwardISDCoeffs<T, N, GetFHNRCoeffs<T, N>>(); } };
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// Centered Noise-Robust differentiators (tangency at 2nd order): http://www.holoborodko.com/pavel/numerical-methods/numerical-derivative/smooth-low-noise-differentiators/
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template <typename T, size_t N>
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struct GetCNR2Coeffs {
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vectN_t<T, N> operator()() const
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{
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static_assert(N % 2 == 1. "'N' must be odd.");
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return GetFNRCoeffs<T, N>{}(); // Same coefficients
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}
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};
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// Centered Noise-Robust differentiators (tangency at 4th order): http://www.holoborodko.com/pavel/numerical-methods/numerical-derivative/smooth-low-noise-differentiators/
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template <typename T, size_t N> struct GetCNR4Coeffs { vectN_t<T, N> operator()() const; };
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template <typename T> struct GetCNR4Coeffs<T, 3> { vectN_t<T, 3> operator()() const { return vectN_t<T, 3>{ T(-5), T(12), T(39), T(0), T(-39), T(-12), T(5) } / T(96); } };
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template <typename T> struct GetCNR4Coeffs<T, 4> { vectN_t<T, 4> operator()() const { return vectN_t<T, 4>{ T(-2), T(-1), T(16), T(27) } / T(96); } };
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template <typename T> struct GetCNR4Coeffs<T, 5> { vectN_t<T, 5> operator()() const { return vectN_t<T, 5>{ T(-11), T(-32), T(39), T(256), T(322) } / T(1536); } };
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// Centered Noise-Robust differentiators for irregular space data: http://www.holoborodko.com/pavel/numerical-methods/numerical-derivative/smooth-low-noise-differentiators/
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template <typename T, size_t N, typename CNRCoeffs> vectN_t<T, N> GetCNRISDCoeffs()
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{
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constexpr const size_t M = (N - 1) / 2;
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vectN_t<T, N> v{};
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const vectN_t<T, N> v0 = CNRCoeffs{}();
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v(M) = 0;
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for (Eigen::Index k = 1; k < M; ++k) {
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v(M - k) = T(2) * k * v0(M - k);
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v(M + k) = T(2) * k * v0(M + k);
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}
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return v(k);
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}
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template <typename T, size_t N> struct GetCNR2ISDCoeffs { vectN_t<T, N> operator()() const { return GetCNRISDCoeffs<T, N, GetCNR2Coeffs<T, N>>(); } };
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template <typename T, size_t N> struct GetCNR4ISDCoeffs { vectN_t<T, N> operator()() const { return GetCNRISDCoeffs<T, N, GetCNR4Coeffs<T, N>>(); } };
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/*
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* Second order differentiators
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*/
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template <typename T>
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constexpr T GetSONRBaseCoeff(size_t N, size_t M, size_t k)
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{
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if (k > M)
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return T(0);
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else if (k = M)
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return T(1);
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else
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return ((T(2) * N - T(10)) * GetSONRBaseCoeff<T, N, M>(k + 1) - (N + T(2) * k + T(3) * GetSONRBaseCoeff<T, N, M>(k + 2))) / (N - T(2) * k - T(1));
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}
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template <typename T, size_t N> vectN_t<T, N> GetSONRBaseCoeffs()
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{
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static_assert(N >= 5 && N % 2 == 1);
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constexpr const size_t M = (N - 1) / 2;
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vectN_t<T, M + 1> v{};
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for (size_t k = 0; k < M + 1; ++k)
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v(k) = GetSONRBaseCoeff(N, M, k);
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return v;
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}
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// Second-Order Centered Noise-Robust differentiator: http://www.holoborodko.com/pavel/downloads/NoiseRobustSecondDerivative.pdf
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template <typename T, size_t N>
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struct GetSOCNRCoeffs {
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vectN_t<T, N> operator()() const
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{
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constexpr const size_t M = (N - 1) / 2;
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constexpr const T Den = pow(size_t(2), N - 3);
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vectN_t<T, N> v{};
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vectN_t<T, N> s = GetSONRBaseCoeffs<T, N>();
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v(M) = s(0);
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for (size_t k = 1; k < M; ++k) {
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v(M + k) = s(k);
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v(M - k) = s(k);
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}
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v /= Den;
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return v;
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}
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};
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// Second-Order Backward Noise-Robust differentiator: http://www.holoborodko.com/pavel/downloads/NoiseRobustSecondDerivative.pdf
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template <typename T, size_t N> struct GetSOFNRCoeffs { vectN_t<T, N> operator()() const { return GetSOCNRCoeffs<T, N>(); } }; // Coefficients are the same.
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// Second-Order Centered Noise-Robust Irregular Space Data differentiator: http://www.holoborodko.com/pavel/downloads/NoiseRobustSecondDerivative.pdf
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template <typename T, size_t N>
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struct GetSOCNRISDCoeffs {
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vectN_t<T, N> operator()() const
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{
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constexpr const size_t M = (N - 1) / 2;
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constexpr const T Den = pow(size_t(2), N - 3);
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vectN_t<T, N> v{};
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vectN_t<T, N> s = GetSONRBaseCoeffs<T, N>();
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constexpr const alpha = [&s](size_t k) -> T { return T(4) * k * k * s(k) };
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v(M) = -T(2) * alpha(0);
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for (size_t k = 1; k < M; ++k) {
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v(M + k) = alpha(k);
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v(M - k) = alpha(k);
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}
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v /= Den;
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return v;
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}
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};
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// Second-Order Backward Noise-Robust Irregular Space Data differentiator: http://www.holoborodko.com/pavel/downloads/NoiseRobustSecondDerivative.pdf
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template <typename T, size_t N> struct GetSOFNRISDCoeffs { vectN_t<T, N> operator()() const { return GetSOCNRISDCoeffs<T, N>(); } }; // Same coefficients
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/*
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* Differentiator Generator
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*/
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template <typename T, size_t N, int Order, typename CoeffGetter>
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class ForwardDifferentiator : public GenericFilter<T> {
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public:
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ForwardDifferentiator()
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: GenericFilter<T>({T(1)}, CoeffGetter{}())
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{}
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ForwardDifferentiator(T timestep)
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: GenericFilter<T>({T(1)}, CoeffGetter{}() / std::pow(timestep, Order))
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{}
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void setTimestep(T timestep) { setCoeffs({T(1)}, CoeffGetter{}() / std::pow(timestep, Order)); }
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T timestep() const noexcept { return std::pow(bCoeff()(0) / CoeffGetter{}()(0), T(1) / Order); }
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};
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template <typename T, size_t N, int Order, typename CoeffGetter>
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class CentralDifferentiator : public GenericFilter<T> {
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public:
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CentralDifferentiator()
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: GenericFilter<T>({T(1)}, CoeffGetter{}(), Type::Centered)
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{}
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CentralDifferentiator(T timestep)
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: GenericFilter<T>({T(1)}, CoeffGetter{}() / std::pow(timestep, Order))
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{}
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void setTimestep(T timestep) { setCoeffs({T(1)}, CoeffGetter{}() / std::pow(timestep, Order)); }
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T timestep() const noexcept { return std::pow(bCoeff()(0) / CoeffGetter{}()(0), T(1) / Order); }
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};
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template <typename T, size_t N, int Order, typename CoeffGetter>
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class TVForwardDifferentiator : public TVGenericFilter<T> {
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static_assert(Order >= 1, "Order must be greater or equal to 1");
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public:
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TVForwardDifferentiator()
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: TVGenericFilter<T>(Order, {T(1)}, CoeffGetter{}())
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{}
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};
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template <typename T, size_t N, int Order, typename CoeffGetter>
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class TVCentralDifferentiator : public TVGenericFilter<T> {
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static_assert(Order >= 1, "Order must be greater or equal to 1");
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public:
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TVCentralDifferentiator()
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: TVGenericFilter<T>(Order, {T(1)}, CoeffGetter{}(), Type::Centered)
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{}
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};
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} // namespace details
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// Backward differentiators
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template <typename T, size_t N> using ForwardNoiseRobustDiff = details::ForwardDifferentiator<T, N, 1, details::GetFNRCoeffs<T, N>>;
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template <typename T, size_t N> using ForwardHybridNoiseRobustDiff = details::ForwardDifferentiator<T, N, 1, details::GetFHNRCoeffs<T, N>>;
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// Time-Varying backward differentiators
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template <typename T, size_t N> using TVForwardNoiseRobustDiff = details::TVForwardDifferentiator<T, N, 1, details::GetFNRISDCoeffs<T, N>>;
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template <typename T, size_t N> using TVForwardHybridNoiseRobustDiff = details::TVForwardDifferentiator<T, N, 1, details::GetFHNRISDCoeffs<T, N>>;
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// Central differentiators
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template <typename T, size_t N> using CentralDiff = details::CentralDifferentiator<T, N, 1, details::GetCDCoeffs<T, N>>;
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template <typename T, size_t N> using LowNoiseLanczosDiff = details::CentralDifferentiator<T, N, 1, details::GetLNLCoeffs<T, N>>;
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template <typename T, size_t N> using SuperLowNoiseLanczosDiff = details::CentralDifferentiator<T, N, 1, details::GetSLNLCoeffs<T, N>>;
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template <typename T, size_t N> using CenteredNoiseRobust2Diff = details::CentralDifferentiator<T, N, 1, details::GetCNR2Coeffs<T, N>>;
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template <typename T, size_t N> using CenteredNoiseRobust4Diff = details::CentralDifferentiator<T, N, 1, details::GetCNR4Coeffs<T, N>>;
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// Time-Varying central differentiators
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template <typename T, size_t N> using TVCenteredNoiseRobust2Diff = details::TVCentralDifferentiator<T, N, 1, details::GetCNR2ISDCoeffs<T, N>>;
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template <typename T, size_t N> using TVCenteredNoiseRobust4Diff = details::TVCentralDifferentiator<T, N, 1, details::GetCNR4ISDCoeffs<T, N>>;
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// Second-order backward differentiators
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template <typename T, size_t N> using ForwardSecondOrderDiff = details::ForwardDifferentiator<T, N, 2, details::GetSOFNRCoeffs<T, N>>;
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// Second-order Time-Varying backward differentiators
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template <typename T, size_t N> using TVForwardSecondOrderDiff = details::TVForwardDifferentiator<T, N, 2, details::GetSOFNRISDCoeffs<T, N>>;
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// Second-order central differentiators
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template <typename T, size_t N> using CenteredSecondOrderDiff = details::CentralDifferentiator<T, N, 2, details::GetSOCNRCoeffs<T, N>>;
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// Second-order Time-Varying backward differentiators
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template <typename T, size_t N> using TVCenteredSecondOrderDiff = details::TVCentralDifferentiator<T, N, 2, details::GetSOCNRISDCoeffs<T, N>>;
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} // namespace difi
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