Add test file [CI SKIP]

2026-01-19 04:22:09 +00:00 · 2020-03-10 08:17:53 -04:00
parent 8c621d8be4
commit 59fe4d690c
1 changed files with 117 additions and 0 deletions
--- a/test/daubechies_wavelet_test.cpp
+++ b/test/daubechies_wavelet_test.cpp
@@ -0,0 +1,117 @@
+/*
+ * Copyright Nick Thompson, 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)
+ */
+
+#include "math_unit_test.hpp"
+#include <numeric>
+#include <utility>
+#include <iomanip>
+#include <iostream>
+#include <random>
+#include <boost/core/demangle.hpp>
+#include <boost/hana/for_each.hpp>
+#include <boost/hana/ext/std/integer_sequence.hpp>
+#include <boost/math/tools/condition_numbers.hpp>
+#include <boost/math/special_functions/daubechies_wavelet.hpp>
+#include <boost/math/quadrature/trapezoidal.hpp>
+
+#ifdef BOOST_HAS_FLOAT128
+#include <boost/multiprecision/float128.hpp>
+using boost::multiprecision::float128;
+#endif
+
+
+using boost::math::constants::pi;
+using boost::math::constants::root_two;
+
+
+template<class Real>
+void test_wavelet_dyadic_grid()
+{
+    std::cout << "Testing wavelet dyadic grid on type " << boost::core::demangle(typeid(Real).name()) << "\n";
+    auto f = [&](auto i)
+    {
+        auto phijk = boost::math::dyadic_grid<Real, i+2, 0>(0);
+        auto phik = boost::math::detail::daubechies_scaling_integer_grid<Real, i+2, 0>();
+        assert(phik.size() == phijk.size());
+
+        for (size_t k = 0; k < phik.size(); ++k)
+        {
+            CHECK_ULP_CLOSE(phik[k], phijk[k], 0);
+        }
+
+        for (int64_t j = 1; j < 10; ++j)
+        {
+            phijk = boost::math::dyadic_grid<Real, i+2, 0>(j);
+            phik = boost::math::detail::daubechies_scaling_integer_grid<Real, i+2, 0>();
+            for (int64_t l = 0; l < static_cast<int64_t>(phik.size()); ++l)
+            {
+                CHECK_ULP_CLOSE(phik[l], phijk[l*(int64_t(1)<<j)], 0);
+            }
+
+            // This test is from Daubechies, Ten Lectures on Wavelets, Ch 7 "More About Compactly Supported Wavelets",
+            // page 245: \forall y \in \mathbb{R}, \sum_{n \in \mathbb{Z}} \phi(y+n) = 1
+            for (size_t k = 1; k < j; ++k)
+            {
+                auto cond = boost::math::tools::summation_condition_number<Real>(0);
+                for (int64_t l = 0; l < static_cast<int64_t>(phik.size()); ++l)
+                {
+                    int64_t idx = l*(int64_t(1)<<j) + k;
+                    if (idx < phijk.size())
+                    {
+                        cond += phijk[idx];
+                    }
+                }
+                CHECK_MOLLIFIED_CLOSE(Real(1), cond.sum(), 10*cond()*std::numeric_limits<Real>::epsilon());
+            }
+        }
+    };
+
+    boost::hana::for_each(std::make_index_sequence<18>(), f);
+}
+
+
+template<typename Real, int p>
+void test_quadratures()
+{
+    using boost::math::quadrature::trapezoidal;
+    auto psi = boost::math::daubechies_wavelet<Real, p>();
+        
+    Real tol = std::numeric_limits<Real>::epsilon();
+    Real error_estimate = std::numeric_limits<Real>::quiet_NaN();
+    Real L1 = std::numeric_limits<Real>::quiet_NaN();
+    auto [a, b] = psi.support();
+    CHECK_ULP_CLOSE(Real(-p+1), a, 0);
+    CHECK_ULP_CLOSE(Real(p), b, 0);
+    // A wavelet is a function of zero average; ensure the quadrature over its support is zero.
+    /*Real Q = trapezoidal(psi, a, b, tol, 15, &error_estimate, &L1);
+    if (!CHECK_MOLLIFIED_CLOSE(Real(0), Q, Real(0.0001)))
+    {
+        std::cerr << "  Quadrature of " << p << " vanishing moment wavelet does not vanish.\n";
+    }*/
+    // psi is orthogonal to its integer translates: \int \psi(x-k) \psi(x) \, \mathrm{d}x = 0
+    // psi has L2 norm 1:
+
+    // g_n = 1/sqrt(2) <psi(t/2), phi(t-n)> (Mallat, 7.55)
+}
+
+int main()
+{
+    boost::hana::for_each(std::make_index_sequence<18>(), [&](auto i){
+      test_quadratures<float, i+2>();
+      test_quadratures<double, i+2>();
+    });
+
+
+    test_wavelet_dyadic_grid<float>();
+    test_wavelet_dyadic_grid<double>();
+    test_wavelet_dyadic_grid<long double>();
+    #ifdef BOOST_HAS_FLOAT128
+    test_wavelet_dyadic_grid<float128>();
+    #endif
+
+    return boost::math::test::report_errors();
+}