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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();
}
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