--- /dev/null
+/*
+ * Copyright Nick Thompson, John Maddock 2020
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#define BOOST_MATH_GENERATE_DAUBECHIES_GRID
+
+#include <iostream>
+#include <vector>
+#include <numeric>
+#include <list>
+#include <cmath>
+#include <cassert>
+#include <fstream>
+#include <Eigen/Eigenvalues>
+#include <boost/hana/for_each.hpp>
+#include <boost/hana/ext/std/integer_sequence.hpp>
+#include <boost/core/demangle.hpp>
+#ifdef BOOST_HAS_FLOAT128
+#include <boost/multiprecision/float128.hpp>
+#endif
+#include <boost/math/constants/constants.hpp>
+#include <boost/math/filters/daubechies.hpp>
+#include <boost/math/special_functions/factorials.hpp>
+#include <boost/multiprecision/cpp_bin_float.hpp>
+
+typedef boost::multiprecision::number<boost::multiprecision::cpp_bin_float<237, boost::multiprecision::backends::digit_base_2, std::allocator<char>, boost::int32_t, -262142, 262143>, boost::multiprecision::et_off> octuple_type;
+
+#ifdef BOOST_HAS_FLOAT128
+typedef boost::multiprecision::float128 float128_t;
+#else
+typedef boost::multiprecision::cpp_bin_float_quad float128_t;
+#endif
+
+template<class Real, int p>
+std::list<std::vector<Real>> integer_grid()
+{
+ std::cout << std::setprecision(std::numeric_limits<Real>::digits10 + 3);
+ using std::abs;
+ using std::sqrt;
+ using std::pow;
+ std::list<std::vector<Real>> grids;
+
+ auto c = boost::math::filters::daubechies_scaling_filter<Real, p>();
+ for (auto & x : c)
+ {
+ x *= boost::math::constants::root_two<Real>();
+ }
+ std::cout << "\n\nTaps in filter = " << c.size() << "\n";
+
+
+ Eigen::Matrix<Real, 2*p - 2, 2*p-2> A;
+ for (int j = 0; j < 2*p-2; ++j) {
+ for (int k = 0; k < 2*p-2; ++k) {
+ if ( (2*j-k + 1) < 0 || (2*j - k + 1) >= 2*p)
+ {
+ A(j,k) = 0;
+ }
+ else {
+ A(j,k) = c[2*j - k + 1];
+ }
+ }
+ }
+
+ Eigen::EigenSolver<decltype(A)> es(A);
+
+ auto complex_eigs = es.eigenvalues();
+
+ std::vector<Real> eigs(complex_eigs.size(), std::numeric_limits<Real>::quiet_NaN());
+
+ std::cout << "Eigenvalues = {";
+ for (long i = 0; i < complex_eigs.size(); ++i) {
+ assert(abs(complex_eigs[i].imag()) < std::numeric_limits<Real>::epsilon());
+ eigs[i] = complex_eigs[i].real();
+ std::cout << eigs[i] << ", ";
+ }
+ std::cout << "}\n";
+
+ // Eigen does not sort the eigenpairs by any criteria on the eigenvalues.
+ // In any case, even if it did, some of the eigenpairs do not correspond to derivatives anyway.
+ for (size_t j = 0; j < eigs.size(); ++j) {
+ auto f = [&](Real x) {
+ return abs(x - Real(1)/Real(1 << j) ) < sqrt(std::numeric_limits<Real>::epsilon());
+ };
+ auto it = std::find_if(eigs.begin(), eigs.end(), f);
+ if (it == eigs.end()) {
+ std::cout << "couldn't find eigenvalue " << Real(1)/Real(1 << j) << "\n";
+ continue;
+ }
+ size_t idx = std::distance(eigs.begin(), it);
+ std::cout << "Eigenvector for derivative " << j << " is at index " << idx << "\n";
+ auto eigenvector_matrix = es.eigenvectors();
+ auto complex_eigenvec = eigenvector_matrix.col(idx);
+
+ std::vector<Real> eigenvec(complex_eigenvec.size() + 2, std::numeric_limits<Real>::quiet_NaN());
+ eigenvec[0] = 0;
+ eigenvec[eigenvec.size()-1] = 0;
+ for (size_t i = 0; i < eigenvec.size() - 2; ++i) {
+ assert(abs(complex_eigenvec[i].imag()) < std::numeric_limits<Real>::epsilon());
+ eigenvec[i+1] = complex_eigenvec[i].real();
+ }
+
+ Real sum = 0;
+ for(size_t k = 1; k < eigenvec.size(); ++k) {
+ sum += pow(k, j)*eigenvec[k];
+ }
+
+ Real alpha = pow(-1, j)*boost::math::factorial<Real>(j)/sum;
+
+ for (size_t i = 1; i < eigenvec.size(); ++i) {
+ eigenvec[i] *= alpha;
+ }
+
+
+ std::cout << "Eigenvector = {";
+ for (size_t i = 0; i < eigenvec.size() -1; ++i) {
+ std::cout << eigenvec[i] << ", ";
+ }
+ std::cout << eigenvec[eigenvec.size()-1] << "}\n";
+
+ sum = 0;
+ for(size_t k = 1; k < eigenvec.size(); ++k) {
+ sum += pow(k, j)*eigenvec[k];
+ }
+
+ std::cout << "Moment sum = " << sum << ", expected = " << pow(-1, j)*boost::math::factorial<Real>(j) << "\n";
+
+ assert(abs(sum - pow(-1, j)*boost::math::factorial<Real>(j))/abs(pow(-1, j)*boost::math::factorial<Real>(j)) < sqrt(std::numeric_limits<Real>::epsilon()));
+
+ grids.push_back(eigenvec);
+ }
+
+
+ return grids;
+}
+
+template<class Real, int p>
+void write_grid(std::ofstream & fs)
+{
+ auto grids = integer_grid<Real, p>();
+ size_t j = 0;
+ fs << std::setprecision(std::numeric_limits< boost::multiprecision::cpp_bin_float_quad>::max_digits10);
+ for (auto it = grids.begin(); it != grids.end(); ++it)
+ {
+ auto const& grid = *it;
+ fs << "template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, " << p << ", ";
+ fs << j << "> { static inline constexpr std::array<Real, " << grid.size() << "> value = { ";
+ for (size_t i = 0; i < grid.size() -1; ++i){
+ fs << "C_(" << static_cast<float128_t>(grid[i]) << "), ";
+ }
+ fs << "C_(" << static_cast<float128_t>(grid[grid.size()-1]) << ") }; };\n";
+ ++j;
+ }
+}
+
+int main()
+{
+ constexpr const size_t p_max = 18;
+ std::ofstream fs{"daubechies_scaling_integer_grid.hpp"};
+ fs << "/*\n"
+ << " * Copyright Nick Thompson, John Maddock 2020\n"
+ << " * Use, modification and distribution are subject to the\n"
+ << " * Boost Software License, Version 1.0. (See accompanying file\n"
+ << " * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)\n"
+ << " */\n"
+ << "// THIS FILE GENERATED BY EXAMPLE/DAUBECHIES_SCALING_INTEGER_GRID.CPP, DO NOT EDIT.\n"
+ << "#ifndef BOOST_MATH_DAUBECHIES_SCALING_INTEGER_GRID_HPP\n"
+ << "#define BOOST_MATH_DAUBECHIES_SCALING_INTEGER_GRID_HPP\n"
+ << "#include <array>\n"
+ << "#include <float.h>\n"
+ << "#include <boost/config.hpp>\n"
+ << "/*\n"
+ << "In order to keep the character count as small as possible and speed up\n"
+ << "compiler parsing times, we define a macro C_ which appends an appropriate\n"
+ << "suffix to each literal, and then casts it to type Real.\n"
+ << "The suffix is as follows:\n\n"
+ << "* Q, when we have __float128 support.\n"
+ << "* L, when we have either 80 or 128 bit long doubles.\n"
+ << "* Nothing otherwise.\n"
+ << "*/\n\n"
+ << "#ifdef BOOST_HAS_FLOAT128\n"
+ << "# define C_(x) static_cast<Real>(x##Q)\n"
+ << "#elif (LDBL_MANT_DIG > DBL_MANT_DIG)\n"
+ << "# define C_(x) static_cast<Real>(x##L)\n"
+ << "#else\n"
+ << "# define C_(x) static_cast<Real>(x)\n"
+ << "#endif\n\n"
+ << "namespace boost::math::detail {\n\n"
+ << "template <typename Real, int p, int order> struct daubechies_scaling_integer_grid_imp;\n\n";
+
+ fs << std::hexfloat << std::setprecision(std::numeric_limits<boost::multiprecision::cpp_bin_float_quad>::max_digits10);
+
+ boost::hana::for_each(std::make_index_sequence<p_max>(), [&](auto idx){
+ write_grid<octuple_type, idx+2>(fs);
+ });
+
+ fs << "\n\ntemplate <typename Real, unsigned p, unsigned order>\n"
+ << "constexpr inline std::array<Real, 2*p> daubechies_scaling_integer_grid()\n"
+ << "{\n"
+ << " static_assert(sizeof(Real) <= 16, \"Integer grids only computed up to 128 bits of precision.\");\n"
+ << " static_assert(p <= " << p_max + 1 << ", \"Integer grids only implemented up to " << p_max + 1 << ".\");\n"
+ << " static_assert(p > 1, \"Integer grids only implemented for p >= 2.\");\n"
+ << " return daubechies_scaling_integer_grid_imp<Real, p, order>::value;\n"
+ << "}\n\n";
+
+ fs << "} // namespaces\n";
+ fs << "#endif\n";
+ fs.close();
+
+ return 0;
+}
projects / ceph.git / blobdiff