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diff --git a/src/boost/libs/math/test/norms_test.cpp b/src/boost/libs/math/test/norms_test.cpp
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+/*
+ * (C) Copyright Nick Thompson 2018.
+ * 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 <cmath>
+#include <vector>
+#include <array>
+#include <forward_list>
+#include <algorithm>
+#include <random>
+#include <limits>
+#include <boost/core/lightweight_test.hpp>
+#include <boost/numeric/ublas/vector.hpp>
+#include <boost/math/constants/constants.hpp>
+#include <boost/math/tools/norms.hpp>
+#include <boost/multiprecision/cpp_bin_float.hpp>
+#include <boost/multiprecision/cpp_complex.hpp>
+
+using std::abs;
+using std::pow;
+using std::sqrt;
+using boost::multiprecision::cpp_bin_float_50;
+using boost::multiprecision::cpp_complex_50;
+using boost::math::tools::lp_norm;
+using boost::math::tools::l1_norm;
+using boost::math::tools::l2_norm;
+using boost::math::tools::sup_norm;
+using boost::math::tools::lp_distance;
+using boost::math::tools::l1_distance;
+using boost::math::tools::l2_distance;
+using boost::math::tools::sup_distance;
+using boost::math::tools::total_variation;
+
+/*
+ * Test checklist:
+ * 1) Does it work with multiprecision?
+ * 2) Does it work with .cbegin()/.cend() if the data is not altered?
+ * 3) Does it work with ublas and std::array? (Checking Eigen and Armadillo will make the CI system really unhappy.)
+ * 4) Does it work with std::forward_list if a forward iterator is all that is required?
+ * 5) Does it work with complex data if complex data is sensible?
+ */
+
+// To stress test, set global_seed = 0, global_size = huge.
+static const constexpr size_t global_seed = 834;
+static const constexpr size_t global_size = 64;
+
+template<class T>
+std::vector<T> generate_random_vector(size_t size, size_t seed)
+{
+ if (seed == 0)
+ {
+ std::random_device rd;
+ seed = rd();
+ }
+ std::vector<T> v(size);
+
+ std::mt19937 gen(seed);
+
+ if constexpr (std::is_floating_point<T>::value)
+ {
+ std::normal_distribution<T> dis(0, 1);
+ for (size_t i = 0; i < v.size(); ++i)
+ {
+ v[i] = dis(gen);
+ }
+ return v;
+ }
+ else if constexpr (std::is_integral<T>::value)
+ {
+ // Rescaling by larger than 2 is UB!
+ std::uniform_int_distribution<T> dis(std::numeric_limits<T>::lowest()/2, (std::numeric_limits<T>::max)()/2);
+ for (size_t i = 0; i < v.size(); ++i)
+ {
+ v[i] = dis(gen);
+ }
+ return v;
+ }
+ else if constexpr (boost::is_complex<T>::value)
+ {
+ std::normal_distribution<typename T::value_type> dis(0, 1);
+ for (size_t i = 0; i < v.size(); ++i)
+ {
+ v[i] = {dis(gen), dis(gen)};
+ }
+ return v;
+ }
+ else if constexpr (boost::multiprecision::number_category<T>::value == boost::multiprecision::number_kind_complex)
+ {
+ std::normal_distribution<long double> dis(0, 1);
+ for (size_t i = 0; i < v.size(); ++i)
+ {
+ v[i] = {dis(gen), dis(gen)};
+ }
+ return v;
+ }
+ else if constexpr (boost::multiprecision::number_category<T>::value == boost::multiprecision::number_kind_floating_point)
+ {
+ std::normal_distribution<long double> dis(0, 1);
+ for (size_t i = 0; i < v.size(); ++i)
+ {
+ v[i] = dis(gen);
+ }
+ return v;
+ }
+ else
+ {
+ BOOST_ASSERT_MSG(false, "Could not identify type for random vector generation.");
+ return v;
+ }
+}
+
+
+template<class Real>
+void test_lp()
+{
+ Real tol = 50*std::numeric_limits<Real>::epsilon();
+
+ std::array<Real, 3> u{1,0,0};
+ Real l3 = lp_norm(u.begin(), u.end(), 3);
+ BOOST_TEST(abs(l3 - 1) < tol);
+
+ u[0] = -8;
+ l3 = lp_norm(u.cbegin(), u.cend(), 3);
+ BOOST_TEST(abs(l3 - 8) < tol);
+
+ std::vector<Real> v(500);
+ for (size_t i = 0; i < v.size(); ++i) {
+ v[i] = 7;
+ }
+ Real l8 = lp_norm(v, 8);
+ Real expected = 7*pow(v.size(), static_cast<Real>(1)/static_cast<Real>(8));
+ BOOST_TEST(abs(l8 - expected) < tol*abs(expected));
+
+ // Does it work with ublas vectors?
+ // Does it handle the overflow of intermediates?
+ boost::numeric::ublas::vector<Real> w(4);
+ Real bignum = sqrt((std::numeric_limits<Real>::max)())/256;
+ for (size_t i = 0; i < w.size(); ++i)
+ {
+ w[i] = bignum;
+ }
+ Real l20 = lp_norm(w.cbegin(), w.cend(), 4);
+ expected = bignum*pow(w.size(), static_cast<Real>(1)/static_cast<Real>(4));
+ BOOST_TEST(abs(l20 - expected) < tol*expected);
+
+ v = generate_random_vector<Real>(global_size, global_seed);
+ Real scale = 8;
+ Real l7 = scale*lp_norm(v, 7);
+ for (auto & x : v)
+ {
+ x *= -scale;
+ }
+ Real l7_ = lp_norm(v, 7);
+ BOOST_TEST(abs(l7_ - l7) < tol*l7);
+}
+
+
+template<class Complex>
+void test_complex_lp()
+{
+ typedef typename Complex::value_type Real;
+ Real tol = 50*std::numeric_limits<Real>::epsilon();
+ std::vector<Complex> v{{1,0}, {0,0}, {0,0}};
+ Real l3 = lp_norm(v.cbegin(), v.cend(), 3);
+ BOOST_TEST(abs(l3 - 1) < tol);
+
+ l3 = lp_norm(v, 3);
+ BOOST_TEST(abs(l3 - 1) < tol);
+
+ v = generate_random_vector<Complex>(global_size, global_seed);
+ Real scale = 8;
+ Real l7 = scale*lp_norm(v, 7);
+ for (auto & x : v)
+ {
+ x *= -scale;
+ }
+ Real l7_ = lp_norm(v, 7);
+ BOOST_TEST(abs(l7_ - l7) < tol*l7);
+}
+
+template<class Z>
+void test_integer_lp()
+{
+ double tol = 100*std::numeric_limits<double>::epsilon();
+
+ std::array<Z, 3> u{1,0,0};
+ double l3 = lp_norm(u.begin(), u.end(), 3);
+ BOOST_TEST(abs(l3 - 1) < tol);
+
+ auto v = generate_random_vector<Z>(global_size, global_seed);
+ Z scale = 2;
+ double l7 = scale*lp_norm(v, 7);
+ for (auto & x : v)
+ {
+ x *= scale;
+ }
+ double l7_ = lp_norm(v, 7);
+ BOOST_TEST(abs(l7_ - l7) < tol*l7);
+}
+
+template<class Real>
+void test_lp_distance()
+{
+ Real tol = 100*std::numeric_limits<Real>::epsilon();
+
+ std::vector<Real> u{1,0,0};
+ std::vector<Real> v{0,0,0};
+
+ Real dist = lp_distance(u,u, 3);
+ BOOST_TEST(abs(dist) < tol);
+
+ dist = lp_distance(u,v, 3);
+ BOOST_TEST(abs(dist - 1) < tol);
+
+ v = generate_random_vector<Real>(global_size, global_seed);
+ u = generate_random_vector<Real>(global_size, global_seed+1);
+ Real dist1 = lp_distance(u, v, 7);
+ Real dist2 = lp_distance(v, u, 7);
+
+ BOOST_TEST(abs(dist1 - dist2) < tol*dist1);
+}
+
+template<class Complex>
+void test_complex_lp_distance()
+{
+ using Real = typename Complex::value_type;
+ Real tol = 100*std::numeric_limits<Real>::epsilon();
+
+ std::vector<Complex> u{{1,0},{0,0},{0,0}};
+ std::vector<Complex> v{{0,0},{0,0},{0,0}};
+
+ Real dist = boost::math::tools::lp_distance(u,u, 3);
+ BOOST_TEST(abs(dist) < tol);
+
+ dist = boost::math::tools::lp_distance(u,v, 3);
+ BOOST_TEST(abs(dist - 1) < tol);
+
+ v = generate_random_vector<Complex>(global_size, global_seed);
+ u = generate_random_vector<Complex>(global_size, global_seed + 1);
+ Real dist1 = lp_distance(u, v, 7);
+ Real dist2 = lp_distance(v, u, 7);
+
+ BOOST_TEST(abs(dist1 - dist2) < tol*dist1);
+}
+
+template<class Z>
+void test_integer_lp_distance()
+{
+ double tol = 100*std::numeric_limits<double>::epsilon();
+
+ std::array<Z, 3> u{1,0,0};
+ std::array<Z, 3> w{0,0,0};
+ double l3 = lp_distance(u, w, 3);
+ BOOST_TEST(abs(l3 - 1) < tol);
+
+ auto v = generate_random_vector<Z>(global_size, global_seed);
+ Z scale = 2;
+ for (auto & x : v)
+ {
+ x *= scale;
+ }
+ auto s = generate_random_vector<Z>(global_size, global_seed + 1);
+ double dist1 = lp_distance(v, s, 7);
+ double dist2 = lp_distance(s, v, 7);
+ BOOST_TEST(abs(dist1 - dist2) < tol*dist2);
+}
+
+
+template<class Z>
+void test_integer_total_variation()
+{
+ double eps = std::numeric_limits<double>::epsilon();
+ std::vector<Z> v{1,1};
+ double tv = boost::math::tools::total_variation(v);
+ BOOST_TEST_EQ(tv, 0);
+
+ v[1] = 2;
+ tv = boost::math::tools::total_variation(v.begin(), v.end());
+ BOOST_TEST_EQ(tv, 1);
+
+ v.resize(16);
+ for (size_t i = 0; i < v.size(); ++i) {
+ v[i] = i;
+ }
+
+ tv = boost::math::tools::total_variation(v);
+ BOOST_TEST_EQ(tv, v.size() -1);
+
+ for (size_t i = 0; i < v.size(); ++i)
+ {
+ v[i] = i*i;
+ }
+
+ tv = boost::math::tools::total_variation(v);
+ BOOST_TEST_EQ(tv, (v.size() - 1)*(v.size() - 1));
+
+ // Work with std::array?
+ std::array<Z, 2> w{1,1};
+ tv = boost::math::tools::total_variation(w);
+ BOOST_TEST_EQ(tv,0);
+
+ std::array<Z, 4> u{1, 2, 1, 2};
+ tv = boost::math::tools::total_variation(u);
+ BOOST_TEST_EQ(tv, 3);
+
+ v = generate_random_vector<Z>(global_size, global_seed);
+ double tv1 = 2*total_variation(v);
+ Z scale = 2;
+ for (auto & x : v)
+ {
+ x *= scale;
+ }
+ double tv2 = total_variation(v);
+ BOOST_TEST(abs(tv1 - tv2) < tv1*eps);
+}
+
+template<class Real>
+void test_total_variation()
+{
+ Real tol = std::numeric_limits<Real>::epsilon();
+ std::vector<Real> v{1,1};
+ Real tv = total_variation(v.begin(), v.end());
+ BOOST_TEST(tv >= 0 && abs(tv) < tol);
+
+ tv = total_variation(v);
+ BOOST_TEST(tv >= 0 && abs(tv) < tol);
+
+ v[1] = 2;
+ tv = total_variation(v.begin(), v.end());
+ BOOST_TEST(abs(tv - 1) < tol);
+
+ v.resize(50);
+ for (size_t i = 0; i < v.size(); ++i) {
+ v[i] = i;
+ }
+
+ tv = total_variation(v.begin(), v.end());
+ BOOST_TEST(abs(tv - (v.size() -1)) < tol);
+
+ for (size_t i = 0; i < v.size(); ++i) {
+ v[i] = i*i;
+ }
+
+ tv = total_variation(v.begin(), v.end());
+ BOOST_TEST(abs(tv - (v.size() - 1)*(v.size() - 1)) < tol);
+
+
+ v = generate_random_vector<Real>(global_size, global_seed);
+ Real scale = 8;
+ Real tv1 = scale*total_variation(v);
+ for (auto & x : v)
+ {
+ x *= -scale;
+ }
+ Real tv2 = total_variation(v);
+ BOOST_TEST(abs(tv1 - tv2) < tol*tv1);
+}
+
+template<class Real>
+void test_sup_norm()
+{
+ Real tol = std::numeric_limits<Real>::epsilon();
+ std::vector<Real> v{-2,1,0};
+ Real s = boost::math::tools::sup_norm(v.begin(), v.end());
+ BOOST_TEST(abs(s - 2) < tol);
+
+ s = boost::math::tools::sup_norm(v);
+ BOOST_TEST(abs(s - 2) < tol);
+
+ // Work with std::array?
+ std::array<Real, 3> w{-2,1,0};
+ s = boost::math::tools::sup_norm(w);
+ BOOST_TEST(abs(s - 2) < tol);
+
+ v = generate_random_vector<Real>(global_size, global_seed);
+ Real scale = 8;
+ Real sup1 = scale*sup_norm(v);
+ for (auto & x : v)
+ {
+ x *= -scale;
+ }
+ Real sup2 = sup_norm(v);
+ BOOST_TEST(abs(sup1 - sup2) < tol*sup1);
+}
+
+template<class Z>
+void test_integer_sup_norm()
+{
+ double eps = std::numeric_limits<double>::epsilon();
+ std::vector<Z> v{2,1,0};
+ Z s = sup_norm(v.begin(), v.end());
+ BOOST_TEST_EQ(s, 2);
+
+ s = sup_norm(v);
+ BOOST_TEST_EQ(s,2);
+
+ v = generate_random_vector<Z>(global_size, global_seed);
+ double sup1 = 2*sup_norm(v);
+ Z scale = 2;
+ for (auto & x : v)
+ {
+ x *= scale;
+ }
+ double sup2 = sup_norm(v);
+ BOOST_TEST(abs(sup1 - sup2) < sup1*eps);
+}
+
+template<class Complex>
+void test_complex_sup_norm()
+{
+ typedef typename Complex::value_type Real;
+ Real tol = std::numeric_limits<Real>::epsilon();
+ std::vector<Complex> w{{0,-8}, {1,1}, {3,2}};
+ Real s = sup_norm(w.cbegin(), w.cend());
+ BOOST_TEST(abs(s-8) < tol);
+
+ s = sup_norm(w);
+ BOOST_TEST(abs(s-8) < tol);
+
+ auto v = generate_random_vector<Complex>(global_size, global_seed);
+ Real scale = 8;
+ Real sup1 = scale*sup_norm(v);
+ for (auto & x : v)
+ {
+ x *= -scale;
+ }
+ Real sup2 = sup_norm(v);
+ BOOST_TEST(abs(sup1 - sup2) < tol*sup1);
+}
+
+template<class Real>
+void test_l0_pseudo_norm()
+{
+ std::vector<Real> v{0,0,1};
+ size_t count = boost::math::tools::l0_pseudo_norm(v.begin(), v.end());
+ BOOST_TEST_EQ(count, 1);
+
+ // Compiles with cbegin()/cend()?
+ count = boost::math::tools::l0_pseudo_norm(v.cbegin(), v.cend());
+ BOOST_TEST_EQ(count, 1);
+
+ count = boost::math::tools::l0_pseudo_norm(v);
+ BOOST_TEST_EQ(count, 1);
+
+ std::array<Real, 3> w{0,0,1};
+ count = boost::math::tools::l0_pseudo_norm(w);
+ BOOST_TEST_EQ(count, 1);
+}
+
+template<class Complex>
+void test_complex_l0_pseudo_norm()
+{
+ std::vector<Complex> v{{0,0}, {0,0}, {1,0}};
+ size_t count = boost::math::tools::l0_pseudo_norm(v.begin(), v.end());
+ BOOST_TEST_EQ(count, 1);
+
+ count = boost::math::tools::l0_pseudo_norm(v);
+ BOOST_TEST_EQ(count, 1);
+}
+
+template<class Z>
+void test_hamming_distance()
+{
+ std::vector<Z> v{1,2,3};
+ std::vector<Z> w{1,2,4};
+ size_t count = boost::math::tools::hamming_distance(v, w);
+ BOOST_TEST_EQ(count, 1);
+
+ count = boost::math::tools::hamming_distance(v, v);
+ BOOST_TEST_EQ(count, 0);
+}
+
+template<class Real>
+void test_l1_norm()
+{
+ Real tol = std::numeric_limits<Real>::epsilon();
+ std::vector<Real> v{1,1,1};
+ Real l1 = l1_norm(v.begin(), v.end());
+ BOOST_TEST(abs(l1 - 3) < tol);
+
+ l1 = l1_norm(v);
+ BOOST_TEST(abs(l1 - 3) < tol);
+
+ std::array<Real, 3> w{1,1,1};
+ l1 = l1_norm(w);
+ BOOST_TEST(abs(l1 - 3) < tol);
+
+ v = generate_random_vector<Real>(global_size, global_seed);
+ Real scale = 8;
+ Real l1_1 = scale*l1_norm(v);
+ for (auto & x : v)
+ {
+ x *= -scale;
+ }
+ Real l1_2 = l1_norm(v);
+ BOOST_TEST(abs(l1_1 - l1_2) < tol*l1_1);
+}
+
+template<class Z>
+void test_integer_l1_norm()
+{
+ double eps = std::numeric_limits<double>::epsilon();
+ std::vector<Z> v{1,1,1};
+ Z l1 = boost::math::tools::l1_norm(v.begin(), v.end());
+ BOOST_TEST_EQ(l1, 3);
+
+ v = generate_random_vector<Z>(global_size, global_seed);
+ double l1_1 = 2*l1_norm(v);
+ Z scale = 2;
+ for (auto & x : v)
+ {
+ x *= scale;
+ }
+ double l1_2 = l1_norm(v);
+ BOOST_TEST(l1_1 > 0);
+ BOOST_TEST(l1_2 > 0);
+ if (abs(l1_1 - l1_2) > 2*l1_1*eps)
+ {
+ std::cout << std::setprecision(std::numeric_limits<double>::digits10);
+ std::cout << "L1_1 = " << l1_1 << "\n";
+ std::cout << "L1_2 = " << l1_2 << "\n";
+ BOOST_TEST(abs(l1_1 - l1_2) < 2*l1_1*eps);
+ }
+}
+
+template<class Complex>
+void test_complex_l1_norm()
+{
+ typedef typename Complex::value_type Real;
+ Real tol = std::numeric_limits<Real>::epsilon();
+ std::vector<Complex> v{{1,0}, {0,1},{0,-1}};
+ Real l1 = l1_norm(v.begin(), v.end());
+ BOOST_TEST(abs(l1 - 3) < tol);
+
+ l1 = l1_norm(v);
+ BOOST_TEST(abs(l1 - 3) < tol);
+
+ v = generate_random_vector<Complex>(global_size, global_seed);
+ Real scale = 8;
+ Real l1_1 = scale*l1_norm(v);
+ for (auto & x : v)
+ {
+ x *= -scale;
+ }
+ Real l1_2 = l1_norm(v);
+ BOOST_TEST(abs(l1_1 - l1_2) < tol*l1_1);
+}
+
+template<class Real>
+void test_l1_distance()
+{
+ Real tol = std::numeric_limits<Real>::epsilon();
+ std::vector<Real> v{1,2,3};
+ std::vector<Real> w{1,1,1};
+ Real l1 = boost::math::tools::l1_distance(v, v);
+ BOOST_TEST(abs(l1) < tol);
+
+ l1 = boost::math::tools::l1_distance(w, v);
+ BOOST_TEST(abs(l1 - 3) < tol);
+
+ l1 = boost::math::tools::l1_distance(v, w);
+ BOOST_TEST(abs(l1 - 3) < tol);
+
+ v = generate_random_vector<Real>(global_size, global_seed);
+ w = generate_random_vector<Real>(global_size, global_seed+1);
+ Real dist1 = l1_distance(v, w);
+ Real dist2 = l1_distance(w, v);
+ BOOST_TEST(abs(dist1 - dist2) < tol*dist1);
+}
+
+template<class Z>
+void test_integer_l1_distance()
+{
+ double tol = std::numeric_limits<double>::epsilon();
+ std::vector<Z> v{1,2,3};
+ std::vector<Z> w{1,1,1};
+ double l1 = boost::math::tools::l1_distance(v, v);
+ BOOST_TEST(abs(l1) < tol);
+
+ l1 = boost::math::tools::l1_distance(w, v);
+ BOOST_TEST(abs(l1 - 3) < tol);
+
+ l1 = boost::math::tools::l1_distance(v, w);
+ BOOST_TEST(abs(l1 - 3) < tol);
+
+ v = generate_random_vector<Z>(global_size, global_seed);
+ w = generate_random_vector<Z>(global_size, global_seed + 1);
+ double dist1 = l1_distance(v, w);
+ double dist2 = l1_distance(w, v);
+ BOOST_TEST(abs(dist1 - dist2) < tol*dist1);
+}
+
+template<class Complex>
+void test_complex_l1_distance()
+{
+ typedef typename Complex::value_type Real;
+ Real tol = std::numeric_limits<Real>::epsilon();
+ std::vector<Complex> v{{1,0}, {0,1},{0,-1}};
+ Real l1 = boost::math::tools::l1_distance(v, v);
+ BOOST_TEST(abs(l1) < tol);
+
+ std::vector<Complex> w{{2,0}, {0,1},{0,-1}};
+ l1 = boost::math::tools::l1_distance(v.cbegin(), v.cend(), w.cbegin());
+ BOOST_TEST(abs(l1 - 1) < tol);
+
+ v = generate_random_vector<Complex>(global_size, global_seed);
+ w = generate_random_vector<Complex>(global_size, global_seed + 1);
+ Real dist1 = l1_distance(v, w);
+ Real dist2 = l1_distance(w, v);
+ BOOST_TEST(abs(dist1 - dist2) < tol*dist1);
+}
+
+
+template<class Real>
+void test_l2_norm()
+{
+ using std::sqrt;
+ Real tol = std::numeric_limits<Real>::epsilon();
+ std::vector<Real> v{1,1,1,1};
+ Real l2 = boost::math::tools::l2_norm(v.begin(), v.end());
+ BOOST_TEST(abs(l2 - 2) < tol);
+
+ l2 = boost::math::tools::l2_norm(v);
+ BOOST_TEST(abs(l2 - 2) < tol);
+
+ std::array<Real, 4> w{1,1,1,1};
+ l2 = boost::math::tools::l2_norm(w);
+ BOOST_TEST(abs(l2 - 2) < tol);
+
+ Real bignum = 4*sqrt((std::numeric_limits<Real>::max)());
+ v[0] = bignum;
+ v[1] = 0;
+ v[2] = 0;
+ v[3] = 0;
+ l2 = boost::math::tools::l2_norm(v.begin(), v.end());
+ BOOST_TEST(abs(l2 - bignum) < tol*l2);
+
+ v = generate_random_vector<Real>(global_size, global_seed);
+ Real scale = 8;
+ Real l2_1 = scale*l2_norm(v);
+ for (auto & x : v)
+ {
+ x *= -scale;
+ }
+ Real l2_2 = l2_norm(v);
+ BOOST_TEST(l2_1 > 0);
+ BOOST_TEST(l2_2 > 0);
+ BOOST_TEST(abs(l2_1 - l2_2) < tol*l2_1);
+}
+
+template<class Z>
+void test_integer_l2_norm()
+{
+ double tol = 100*std::numeric_limits<double>::epsilon();
+ std::vector<Z> v{1,1,1,1};
+ double l2 = boost::math::tools::l2_norm(v.begin(), v.end());
+ BOOST_TEST(abs(l2 - 2) < tol);
+
+ v = generate_random_vector<Z>(global_size, global_seed);
+ Z scale = 2;
+ double l2_1 = scale*l2_norm(v);
+ for (auto & x : v)
+ {
+ x *= scale;
+ }
+ double l2_2 = l2_norm(v);
+ BOOST_TEST(l2_1 > 0);
+ BOOST_TEST(l2_2 > 0);
+ BOOST_TEST(abs(l2_1 - l2_2) < tol*l2_1);
+}
+
+template<class Complex>
+void test_complex_l2_norm()
+{
+ typedef typename Complex::value_type Real;
+ Real tol = 100*std::numeric_limits<Real>::epsilon();
+ std::vector<Complex> v{{1,0}, {0,1},{0,-1}, {1,0}};
+ Real l2 = boost::math::tools::l2_norm(v.begin(), v.end());
+ BOOST_TEST(abs(l2 - 2) < tol);
+
+ l2 = boost::math::tools::l2_norm(v);
+ BOOST_TEST(abs(l2 - 2) < tol);
+
+ v = generate_random_vector<Complex>(global_size, global_seed);
+ Real scale = 8;
+ Real l2_1 = scale*l2_norm(v);
+ for (auto & x : v)
+ {
+ x *= -scale;
+ }
+ Real l2_2 = l2_norm(v);
+ BOOST_TEST(abs(l2_1 - l2_2) < tol*l2_1);
+}
+
+template<class Real>
+void test_l2_distance()
+{
+ Real tol = std::numeric_limits<Real>::epsilon();
+ std::vector<Real> v{1,1,1,1};
+ Real l2 = boost::math::tools::l2_distance(v, v);
+ BOOST_TEST(abs(l2) < tol);
+
+ v = generate_random_vector<Real>(global_size, global_seed);
+ auto w = generate_random_vector<Real>(global_size, global_seed + 1);
+ Real dist1 = l2_distance(v, w);
+ Real dist2 = l2_distance(w, v);
+ BOOST_TEST(abs(dist1 - dist2) < tol*dist1);
+}
+
+
+template<class Z>
+void test_integer_l2_distance()
+{
+ double tol = std::numeric_limits<double>::epsilon();
+ std::vector<Z> v{1,1,1,1};
+ double l2 = boost::math::tools::l2_distance(v, v);
+ BOOST_TEST(abs(l2) < tol);
+
+ v = generate_random_vector<Z>(global_size, global_seed);
+ auto w = generate_random_vector<Z>(global_size, global_seed + 1);
+ double dist1 = l2_distance(v, w);
+ double dist2 = l2_distance(w, v);
+ BOOST_TEST(abs(dist1 - dist2) < tol*dist1);
+}
+
+template<class Complex>
+void test_complex_l2_distance()
+{
+ typedef typename Complex::value_type Real;
+ Real tol = 100*std::numeric_limits<Real>::epsilon();
+ std::vector<Complex> v{{1,0}, {0,1},{0,-1}, {1,0}};
+ Real l2 = boost::math::tools::l2_distance(v, v);
+ BOOST_TEST(abs(l2) < tol);
+
+ v = generate_random_vector<Complex>(global_size, global_seed);
+ auto w = generate_random_vector<Complex>(global_size, global_seed + 1);
+ Real dist1 = l2_distance(v, w);
+ Real dist2 = l2_distance(w, v);
+ BOOST_TEST(abs(dist1 - dist2) < tol*dist1);
+}
+
+template<class Real>
+void test_sup_distance()
+{
+ Real tol = std::numeric_limits<Real>::epsilon();
+ std::vector<Real> v{1,1,1,1};
+ std::vector<Real> w{0,0,0,0};
+ Real sup = boost::math::tools::sup_distance(v, v);
+ BOOST_TEST(abs(sup) < tol);
+ sup = boost::math::tools::sup_distance(v, w);
+ BOOST_TEST(abs(sup -1) < tol);
+
+ v = generate_random_vector<Real>(global_size, global_seed);
+ w = generate_random_vector<Real>(global_size, global_seed + 1);
+ Real dist1 = sup_distance(v, w);
+ Real dist2 = sup_distance(w, v);
+ BOOST_TEST(abs(dist1 - dist2) < tol*dist1);
+}
+
+
+template<class Z>
+void test_integer_sup_distance()
+{
+ double tol = std::numeric_limits<double>::epsilon();
+ std::vector<Z> v{1,1,1,1};
+ std::vector<Z> w{0,0,0,0};
+ double sup = boost::math::tools::sup_distance(v, v);
+ BOOST_TEST(abs(sup) < tol);
+
+ sup = boost::math::tools::sup_distance(v, w);
+ BOOST_TEST(abs(sup -1) < tol);
+
+ v = generate_random_vector<Z>(global_size, global_seed);
+ w = generate_random_vector<Z>(global_size, global_seed + 1);
+ double dist1 = sup_distance(v, w);
+ double dist2 = sup_distance(w, v);
+ BOOST_TEST(abs(dist1 - dist2) < tol*dist1);
+}
+
+template<class Complex>
+void test_complex_sup_distance()
+{
+ typedef typename Complex::value_type Real;
+ Real tol = 100*std::numeric_limits<Real>::epsilon();
+ std::vector<Complex> v{{1,0}, {0,1},{0,-1}, {1,0}};
+ Real sup = boost::math::tools::sup_distance(v, v);
+ BOOST_TEST(abs(sup) < tol);
+
+ v = generate_random_vector<Complex>(global_size, global_seed);
+ auto w = generate_random_vector<Complex>(global_size, global_seed + 1);
+ Real dist1 = sup_distance(v, w);
+ Real dist2 = sup_distance(w, v);
+ BOOST_TEST(abs(dist1 - dist2) < tol*dist1);
+}
+
+int main()
+{
+ test_l0_pseudo_norm<unsigned>();
+ test_l0_pseudo_norm<int>();
+ test_l0_pseudo_norm<float>();
+ test_l0_pseudo_norm<double>();
+ test_l0_pseudo_norm<long double>();
+ test_l0_pseudo_norm<cpp_bin_float_50>();
+
+ test_complex_l0_pseudo_norm<std::complex<float>>();
+ test_complex_l0_pseudo_norm<std::complex<double>>();
+ test_complex_l0_pseudo_norm<std::complex<long double>>();
+ test_complex_l0_pseudo_norm<cpp_complex_50>();
+
+ test_hamming_distance<int>();
+ test_hamming_distance<unsigned>();
+
+ test_l1_norm<float>();
+ test_l1_norm<double>();
+ test_l1_norm<long double>();
+ test_l1_norm<cpp_bin_float_50>();
+
+ test_integer_l1_norm<int>();
+ test_integer_l1_norm<unsigned>();
+
+ test_complex_l1_norm<std::complex<float>>();
+ test_complex_l1_norm<std::complex<double>>();
+ test_complex_l1_norm<std::complex<long double>>();
+ test_complex_l1_norm<cpp_complex_50>();
+
+ test_l1_distance<float>();
+ test_l1_distance<cpp_bin_float_50>();
+
+ test_integer_l1_distance<int>();
+ test_integer_l1_distance<unsigned>();
+
+ test_complex_l1_distance<std::complex<float>>();
+ test_complex_l1_distance<cpp_complex_50>();
+
+ test_complex_l2_norm<std::complex<float>>();
+ test_complex_l2_norm<std::complex<double>>();
+ test_complex_l2_norm<std::complex<long double>>();
+ test_complex_l2_norm<cpp_complex_50>();
+
+ test_l2_norm<float>();
+ test_l2_norm<double>();
+ test_l2_norm<long double>();
+ test_l2_norm<cpp_bin_float_50>();
+
+ test_integer_l2_norm<int>();
+ test_integer_l2_norm<unsigned>();
+
+ test_l2_distance<double>();
+ test_l2_distance<cpp_bin_float_50>();
+
+ test_integer_l2_distance<int>();
+ test_integer_l2_distance<unsigned>();
+
+ test_complex_l2_distance<std::complex<double>>();
+ test_complex_l2_distance<cpp_complex_50>();
+
+ test_lp<float>();
+ test_lp<double>();
+ test_lp<long double>();
+ test_lp<cpp_bin_float_50>();
+
+ test_complex_lp<std::complex<float>>();
+ test_complex_lp<std::complex<double>>();
+ test_complex_lp<std::complex<long double>>();
+ test_complex_lp<cpp_complex_50>();
+
+ test_integer_lp<int>();
+ test_integer_lp<unsigned>();
+
+ test_lp_distance<double>();
+ test_lp_distance<cpp_bin_float_50>();
+
+ test_complex_lp_distance<std::complex<double>>();
+ test_complex_lp_distance<cpp_complex_50>();
+
+ test_integer_lp_distance<int>();
+ test_integer_lp_distance<unsigned>();
+
+ test_sup_norm<float>();
+ test_sup_norm<double>();
+ test_sup_norm<long double>();
+ test_sup_norm<cpp_bin_float_50>();
+
+ test_integer_sup_norm<int>();
+ test_integer_sup_norm<unsigned>();
+
+ test_complex_sup_norm<std::complex<float>>();
+ test_complex_sup_norm<std::complex<double>>();
+ test_complex_sup_norm<std::complex<long double>>();
+ test_complex_sup_norm<cpp_complex_50>();
+
+ test_sup_distance<double>();
+ test_sup_distance<cpp_bin_float_50>();
+
+ test_integer_sup_distance<int>();
+ test_integer_sup_distance<unsigned>();
+
+ test_complex_sup_distance<std::complex<double>>();
+ test_complex_sup_distance<cpp_complex_50>();
+
+ test_total_variation<float>();
+ test_total_variation<double>();
+ test_total_variation<long double>();
+ test_total_variation<cpp_bin_float_50>();
+
+ test_integer_total_variation<uint32_t>();
+ test_integer_total_variation<int>();
+
+ return boost::report_errors();
+}
generated by cgit v1.2.3 (git 2.39.1) at 2024-12-21 12:17:32 +0000