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- // (C) Copyright John Maddock 2006.
- // 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 <pch.hpp>
- #define BOOST_TEST_MAIN
- #include <boost/test/unit_test.hpp>
- #include <boost/test/tools/floating_point_comparison.hpp>
- #include <boost/test/results_collector.hpp>
- #include <boost/math/special_functions/beta.hpp>
- #include <boost/math/distributions/skew_normal.hpp>
- #include <boost/math/tools/polynomial.hpp>
- #include <boost/math/tools/roots.hpp>
- #include <boost/math/constants/constants.hpp>
- #include <boost/test/results_collector.hpp>
- #include <boost/test/unit_test.hpp>
- #include <boost/array.hpp>
- #include <boost/type_index.hpp>
- #include "table_type.hpp"
- #include <iostream>
- #include <iomanip>
- #include <boost/multiprecision/cpp_bin_float.hpp>
- #include <boost/multiprecision/cpp_complex.hpp>
- #define BOOST_CHECK_CLOSE_EX(a, b, prec, i) \
- {\
- unsigned int failures = boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed;\
- BOOST_CHECK_CLOSE(a, b, prec); \
- if(failures != boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed)\
- {\
- std::cerr << "Failure was at row " << i << std::endl;\
- std::cerr << std::setprecision(35); \
- std::cerr << "{ " << data[i][0] << " , " << data[i][1] << " , " << data[i][2];\
- std::cerr << " , " << data[i][3] << " , " << data[i][4] << " , " << data[i][5] << " } " << std::endl;\
- }\
- }
- //
- // Implement various versions of inverse of the incomplete beta
- // using different root finding algorithms, and deliberately "bad"
- // starting conditions: that way we get all the pathological cases
- // we could ever wish for!!!
- //
- template <class T, class Policy>
- struct ibeta_roots_1 // for first order algorithms
- {
- ibeta_roots_1(T _a, T _b, T t, bool inv = false, bool neg = false)
- : a(_a), b(_b), target(t), invert(inv), neg(neg) {}
- T operator()(const T& x)
- {
- return boost::math::detail::ibeta_imp(a, b, (neg ? -x : x), Policy(), invert, true) - target;
- }
- private:
- T a, b, target;
- bool invert, neg;
- };
- template <class T, class Policy>
- struct ibeta_roots_2 // for second order algorithms
- {
- ibeta_roots_2(T _a, T _b, T t, bool inv = false, bool neg = false)
- : a(_a), b(_b), target(t), invert(inv), neg(neg) {}
- boost::math::tuple<T, T> operator()(const T& xx)
- {
- typedef typename boost::math::lanczos::lanczos<T, Policy>::type L;
- T x = neg ? -xx : xx;
- T f = boost::math::detail::ibeta_imp(a, b, x, Policy(), invert, true) - target;
- T f1 = invert ?
- -boost::math::detail::ibeta_power_terms(b, a, 1 - x, x, L(), true, Policy())
- : boost::math::detail::ibeta_power_terms(a, b, x, 1 - x, L(), true, Policy());
- T y = 1 - x;
- if(y == 0)
- y = boost::math::tools::min_value<T>() * 8;
- f1 /= y * x;
- // make sure we don't have a zero derivative:
- if(f1 == 0)
- f1 = (invert ? -1 : 1) * boost::math::tools::min_value<T>() * 64;
- return boost::math::make_tuple(f, neg ? -f1 : f1);
- }
- private:
- T a, b, target;
- bool invert, neg;
- };
- template <class T, class Policy>
- struct ibeta_roots_3 // for third order algorithms
- {
- ibeta_roots_3(T _a, T _b, T t, bool inv = false, bool neg = false)
- : a(_a), b(_b), target(t), invert(inv), neg(neg) {}
- boost::math::tuple<T, T, T> operator()(const T& xx)
- {
- typedef typename boost::math::lanczos::lanczos<T, Policy>::type L;
- T x = neg ? -xx : xx;
- T f = boost::math::detail::ibeta_imp(a, b, x, Policy(), invert, true) - target;
- T f1 = invert ?
- -boost::math::detail::ibeta_power_terms(b, a, 1 - x, x, L(), true, Policy())
- : boost::math::detail::ibeta_power_terms(a, b, x, 1 - x, L(), true, Policy());
- T y = 1 - x;
- if(y == 0)
- y = boost::math::tools::min_value<T>() * 8;
- f1 /= y * x;
- T f2 = f1 * (-y * a + (b - 2) * x + 1) / (y * x);
- if(invert)
- f2 = -f2;
- // make sure we don't have a zero derivative:
- if(f1 == 0)
- f1 = (invert ? -1 : 1) * boost::math::tools::min_value<T>() * 64;
- if (neg)
- {
- f1 = -f1;
- }
- return boost::math::make_tuple(f, f1, f2);
- }
- private:
- T a, b, target;
- bool invert, neg;
- };
- double inverse_ibeta_bisect(double a, double b, double z)
- {
- typedef boost::math::policies::policy<> pol;
- bool invert = false;
- int bits = std::numeric_limits<double>::digits;
- //
- // special cases, we need to have these because there may be other
- // possible answers:
- //
- if(z == 1) return 1;
- if(z == 0) return 0;
- //
- // We need a good estimate of the error in the incomplete beta function
- // so that we don't set the desired precision too high. Assume that 3-bits
- // are lost each time the arguments increase by a factor of 10:
- //
- using namespace std;
- int bits_lost = static_cast<int>(ceil(log10((std::max)(a, b)) * 3));
- if(bits_lost < 0)
- bits_lost = 3;
- else
- bits_lost += 3;
- int precision = bits - bits_lost;
- double min = 0;
- double max = 1;
- boost::math::tools::eps_tolerance<double> tol(precision);
- return boost::math::tools::bisect(ibeta_roots_1<double, pol>(a, b, z, invert), min, max, tol).first;
- }
- double inverse_ibeta_bisect_neg(double a, double b, double z)
- {
- typedef boost::math::policies::policy<> pol;
- bool invert = false;
- int bits = std::numeric_limits<double>::digits;
- //
- // special cases, we need to have these because there may be other
- // possible answers:
- //
- if(z == 1) return 1;
- if(z == 0) return 0;
- //
- // We need a good estimate of the error in the incomplete beta function
- // so that we don't set the desired precision too high. Assume that 3-bits
- // are lost each time the arguments increase by a factor of 10:
- //
- using namespace std;
- int bits_lost = static_cast<int>(ceil(log10((std::max)(a, b)) * 3));
- if(bits_lost < 0)
- bits_lost = 3;
- else
- bits_lost += 3;
- int precision = bits - bits_lost;
- double min = -1;
- double max = 0;
- boost::math::tools::eps_tolerance<double> tol(precision);
- return -boost::math::tools::bisect(ibeta_roots_1<double, pol>(a, b, z, invert, true), min, max, tol).first;
- }
- double inverse_ibeta_newton(double a, double b, double z)
- {
- double guess = 0.5;
- bool invert = false;
- int bits = std::numeric_limits<double>::digits;
- //
- // special cases, we need to have these because there may be other
- // possible answers:
- //
- if(z == 1) return 1;
- if(z == 0) return 0;
- //
- // We need a good estimate of the error in the incomplete beta function
- // so that we don't set the desired precision too high. Assume that 3-bits
- // are lost each time the arguments increase by a factor of 10:
- //
- using namespace std;
- int bits_lost = static_cast<int>(ceil(log10((std::max)(a, b)) * 3));
- if(bits_lost < 0)
- bits_lost = 3;
- else
- bits_lost += 3;
- int precision = bits - bits_lost;
- double min = 0;
- double max = 1;
- return boost::math::tools::newton_raphson_iterate(ibeta_roots_2<double, boost::math::policies::policy<> >(a, b, z, invert), guess, min, max, precision);
- }
- double inverse_ibeta_newton_neg(double a, double b, double z)
- {
- double guess = 0.5;
- bool invert = false;
- int bits = std::numeric_limits<double>::digits;
- //
- // special cases, we need to have these because there may be other
- // possible answers:
- //
- if(z == 1) return 1;
- if(z == 0) return 0;
- //
- // We need a good estimate of the error in the incomplete beta function
- // so that we don't set the desired precision too high. Assume that 3-bits
- // are lost each time the arguments increase by a factor of 10:
- //
- using namespace std;
- int bits_lost = static_cast<int>(ceil(log10((std::max)(a, b)) * 3));
- if(bits_lost < 0)
- bits_lost = 3;
- else
- bits_lost += 3;
- int precision = bits - bits_lost;
- double min = -1;
- double max = 0;
- return -boost::math::tools::newton_raphson_iterate(ibeta_roots_2<double, boost::math::policies::policy<> >(a, b, z, invert, true), -guess, min, max, precision);
- }
- double inverse_ibeta_halley(double a, double b, double z)
- {
- double guess = 0.5;
- bool invert = false;
- int bits = std::numeric_limits<double>::digits;
- //
- // special cases, we need to have these because there may be other
- // possible answers:
- //
- if(z == 1) return 1;
- if(z == 0) return 0;
- //
- // We need a good estimate of the error in the incomplete beta function
- // so that we don't set the desired precision too high. Assume that 3-bits
- // are lost each time the arguments increase by a factor of 10:
- //
- using namespace std;
- int bits_lost = static_cast<int>(ceil(log10((std::max)(a, b)) * 3));
- if(bits_lost < 0)
- bits_lost = 3;
- else
- bits_lost += 3;
- int precision = bits - bits_lost;
- double min = 0;
- double max = 1;
- return boost::math::tools::halley_iterate(ibeta_roots_3<double, boost::math::policies::policy<> >(a, b, z, invert), guess, min, max, precision);
- }
- double inverse_ibeta_halley_neg(double a, double b, double z)
- {
- double guess = -0.5;
- bool invert = false;
- int bits = std::numeric_limits<double>::digits;
- //
- // special cases, we need to have these because there may be other
- // possible answers:
- //
- if(z == 1) return 1;
- if(z == 0) return 0;
- //
- // We need a good estimate of the error in the incomplete beta function
- // so that we don't set the desired precision too high. Assume that 3-bits
- // are lost each time the arguments increase by a factor of 10:
- //
- using namespace std;
- int bits_lost = static_cast<int>(ceil(log10((std::max)(a, b)) * 3));
- if(bits_lost < 0)
- bits_lost = 3;
- else
- bits_lost += 3;
- int precision = bits - bits_lost;
- double min = -1;
- double max = 0;
- return -boost::math::tools::halley_iterate(ibeta_roots_3<double, boost::math::policies::policy<> >(a, b, z, invert, true), guess, min, max, precision);
- }
- double inverse_ibeta_schroder(double a, double b, double z)
- {
- double guess = 0.5;
- bool invert = false;
- int bits = std::numeric_limits<double>::digits;
- //
- // special cases, we need to have these because there may be other
- // possible answers:
- //
- if(z == 1) return 1;
- if(z == 0) return 0;
- //
- // We need a good estimate of the error in the incomplete beta function
- // so that we don't set the desired precision too high. Assume that 3-bits
- // are lost each time the arguments increase by a factor of 10:
- //
- using namespace std;
- int bits_lost = static_cast<int>(ceil(log10((std::max)(a, b)) * 3));
- if(bits_lost < 0)
- bits_lost = 3;
- else
- bits_lost += 3;
- int precision = bits - bits_lost;
- double min = 0;
- double max = 1;
- return boost::math::tools::schroder_iterate(ibeta_roots_3<double, boost::math::policies::policy<> >(a, b, z, invert), guess, min, max, precision);
- }
- template <class Real, class T>
- void test_inverses(const T& data)
- {
- using namespace std;
- typedef Real value_type;
- value_type precision = static_cast<value_type>(ldexp(1.0, 1-boost::math::policies::digits<value_type, boost::math::policies::policy<> >()/2)) * 150;
- if(boost::math::policies::digits<value_type, boost::math::policies::policy<> >() < 50)
- precision = 1; // 1% or two decimal digits, all we can hope for when the input is truncated
- for(unsigned i = 0; i < data.size(); ++i)
- {
- //
- // These inverse tests are thrown off if the output of the
- // incomplete beta is too close to 1: basically there is insuffient
- // information left in the value we're using as input to the inverse
- // to be able to get back to the original value.
- //
- if(data[i][5] == 0)
- {
- BOOST_CHECK_EQUAL(inverse_ibeta_halley(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(0));
- BOOST_CHECK_EQUAL(inverse_ibeta_halley_neg(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(0));
- BOOST_CHECK_EQUAL(inverse_ibeta_schroder(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(0));
- BOOST_CHECK_EQUAL(inverse_ibeta_newton(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(0));
- BOOST_CHECK_EQUAL(inverse_ibeta_newton_neg(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(0));
- BOOST_CHECK_EQUAL(inverse_ibeta_bisect(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(0));
- BOOST_CHECK_EQUAL(inverse_ibeta_bisect_neg(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(0));
- }
- else if((1 - data[i][5] > 0.001)
- && (fabs(data[i][5]) > 2 * boost::math::tools::min_value<value_type>())
- && (fabs(data[i][5]) > 2 * boost::math::tools::min_value<double>()))
- {
- value_type inv = inverse_ibeta_halley(Real(data[i][0]), Real(data[i][1]), Real(data[i][5]));
- BOOST_CHECK_CLOSE_EX(Real(data[i][2]), inv, precision, i);
- inv = inverse_ibeta_halley_neg(Real(data[i][0]), Real(data[i][1]), Real(data[i][5]));
- BOOST_ASSERT(boost::math::isfinite(inv));
- BOOST_CHECK_CLOSE_EX(Real(data[i][2]), inv, precision, i);
- inv = inverse_ibeta_schroder(Real(data[i][0]), Real(data[i][1]), Real(data[i][5]));
- BOOST_CHECK_CLOSE_EX(Real(data[i][2]), inv, precision, i);
- inv = inverse_ibeta_newton(Real(data[i][0]), Real(data[i][1]), Real(data[i][5]));
- BOOST_CHECK_CLOSE_EX(Real(data[i][2]), inv, precision, i);
- inv = inverse_ibeta_newton_neg(Real(data[i][0]), Real(data[i][1]), Real(data[i][5]));
- BOOST_CHECK_CLOSE_EX(Real(data[i][2]), inv, precision, i);
- inv = inverse_ibeta_bisect(Real(data[i][0]), Real(data[i][1]), Real(data[i][5]));
- BOOST_CHECK_CLOSE_EX(Real(data[i][2]), inv, precision, i);
- inv = inverse_ibeta_bisect_neg(Real(data[i][0]), Real(data[i][1]), Real(data[i][5]));
- BOOST_CHECK_CLOSE_EX(Real(data[i][2]), inv, precision, i);
- }
- else if(1 == data[i][5])
- {
- BOOST_CHECK_EQUAL(inverse_ibeta_halley(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(1));
- BOOST_CHECK_EQUAL(inverse_ibeta_halley_neg(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(1));
- BOOST_CHECK_EQUAL(inverse_ibeta_schroder(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(1));
- BOOST_CHECK_EQUAL(inverse_ibeta_newton(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(1));
- BOOST_CHECK_EQUAL(inverse_ibeta_newton_neg(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(1));
- BOOST_CHECK_EQUAL(inverse_ibeta_bisect(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(1));
- BOOST_CHECK_EQUAL(inverse_ibeta_bisect_neg(Real(data[i][0]), Real(data[i][1]), Real(data[i][5])), value_type(1));
- }
- }
- }
- #ifndef SC_
- #define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
- #endif
- template <class T>
- void test_beta(T, const char* /* name */)
- {
- //
- // The actual test data is rather verbose, so it's in a separate file
- //
- // The contents are as follows, each row of data contains
- // five items, input value a, input value b, integration limits x, beta(a, b, x) and ibeta(a, b, x):
- //
- # include "ibeta_small_data.ipp"
- test_inverses<T>(ibeta_small_data);
- # include "ibeta_data.ipp"
- test_inverses<T>(ibeta_data);
- # include "ibeta_large_data.ipp"
- test_inverses<T>(ibeta_large_data);
- }
- #if !defined(BOOST_NO_CXX11_AUTO_DECLARATIONS) && !defined(BOOST_NO_CXX11_UNIFIED_INITIALIZATION_SYNTAX) && !defined(BOOST_NO_CXX11_LAMBDAS)
- template <class Complex>
- void test_complex_newton()
- {
- typedef typename Complex::value_type Real;
- std::cout << "Testing complex Newton's Method on type " << boost::typeindex::type_id<Real>().pretty_name() << "\n";
- using std::abs;
- using std::sqrt;
- using boost::math::tools::complex_newton;
- using boost::math::tools::polynomial;
- using boost::math::constants::half;
- Real tol = std::numeric_limits<Real>::epsilon();
- // p(z) = z^2 + 1, roots: \pm i.
- polynomial<Complex> p{{1,0}, {0, 0}, {1,0}};
- Complex guess{1,1};
- polynomial<Complex> p_prime = p.prime();
- auto f = [&](Complex z) { return std::make_pair<Complex, Complex>(p(z), p_prime(z)); };
- Complex root = complex_newton(f, guess);
- BOOST_CHECK(abs(root.real()) <= tol);
- BOOST_CHECK_CLOSE(root.imag(), (Real)1, tol);
- guess = -guess;
- root = complex_newton(f, guess);
- BOOST_CHECK(abs(root.real()) <= tol);
- BOOST_CHECK_CLOSE(root.imag(), (Real)-1, tol);
- // Test that double roots are handled correctly-as correctly as possible.
- // Convergence at a double root is not quadratic.
- // This sets p = (z-i)^2:
- p = polynomial<Complex>({{-1,0}, {0,-2}, {1,0}});
- p_prime = p.prime();
- guess = -guess;
- auto g = [&](Complex z) { return std::make_pair<Complex, Complex>(p(z), p_prime(z)); };
- root = complex_newton(g, guess);
- BOOST_CHECK(abs(root.real()) < 10*sqrt(tol));
- BOOST_CHECK_CLOSE(root.imag(), (Real)1, tol);
- // Test that zero derivatives are handled.
- // p(z) = z^2 + iz + 1
- p = polynomial<Complex>({{1,0}, {0,1}, {1,0}});
- // p'(z) = 2z + i
- p_prime = p.prime();
- guess = Complex(0,-boost::math::constants::half<Real>());
- auto g2 = [&](Complex z) { return std::make_pair<Complex, Complex>(p(z), p_prime(z)); };
- root = complex_newton(g2, guess);
- // Here's the other root, in case code changes cause it to be found:
- //Complex expected_root1{0, half<Real>()*(sqrt(static_cast<Real>(5)) - static_cast<Real>(1))};
- Complex expected_root2{0, -half<Real>()*(sqrt(static_cast<Real>(5)) + static_cast<Real>(1))};
- BOOST_CHECK_CLOSE(expected_root2.imag(),root.imag(), tol);
- BOOST_CHECK(abs(root.real()) < tol);
- // Does a zero root pass the termination criteria?
- p = polynomial<Complex>({{0,0}, {0,0}, {1,0}});
- p_prime = p.prime();
- guess = Complex(0, -boost::math::constants::half<Real>());
- auto g3 = [&](Complex z) { return std::make_pair<Complex, Complex>(p(z), p_prime(z)); };
- root = complex_newton(g3, guess);
- BOOST_CHECK(abs(root.real()) < tol);
- // Does a monstrous root pass?
- Real x = -pow(static_cast<Real>(10), 20);
- p = polynomial<Complex>({{x, x}, {1,0}});
- p_prime = p.prime();
- guess = Complex(0, -boost::math::constants::half<Real>());
- auto g4 = [&](Complex z) { return std::make_pair<Complex, Complex>(p(z), p_prime(z)); };
- root = complex_newton(g4, guess);
- BOOST_CHECK(abs(root.real() + x) < tol);
- BOOST_CHECK(abs(root.imag() + x) < tol);
- }
- // Polynomials which didn't factorize using Newton's method at first:
- void test_daubechies_fails()
- {
- std::cout << "Testing failures from Daubechies filter computation.\n";
- using std::abs;
- using std::sqrt;
- using boost::math::tools::complex_newton;
- using boost::math::tools::polynomial;
- using boost::math::constants::half;
- double tol = 500*std::numeric_limits<double>::epsilon();
- polynomial<std::complex<double>> p{{-185961388.136908293,141732493.98435241}, {601080390,0}};
- std::complex<double> guess{1,1};
- polynomial<std::complex<double>> p_prime = p.prime();
- auto f = [&](std::complex<double> z) { return std::make_pair<std::complex<double>, std::complex<double>>(p(z), p_prime(z)); };
- std::complex<double> root = complex_newton(f, guess);
- std::complex<double> expected_root = -p.data()[0]/p.data()[1];
- BOOST_CHECK_CLOSE(expected_root.imag(), root.imag(), tol);
- BOOST_CHECK_CLOSE(expected_root.real(), root.real(), tol);
- }
- #endif
- #if !defined(BOOST_NO_CXX17_IF_CONSTEXPR)
- template<class Real>
- void test_solve_real_quadratic()
- {
- Real tol = std::numeric_limits<Real>::epsilon();
- using boost::math::tools::quadratic_roots;
- auto [x0, x1] = quadratic_roots<Real>(1, 0, -1);
- BOOST_CHECK_CLOSE(x0, Real(-1), tol);
- BOOST_CHECK_CLOSE(x1, Real(1), tol);
- auto p = quadratic_roots((Real)7, (Real)0, (Real)0);
- BOOST_CHECK_SMALL(p.first, tol);
- BOOST_CHECK_SMALL(p.second, tol);
- // (x-7)^2 = x^2 - 14*x + 49:
- p = quadratic_roots((Real)1, (Real)-14, (Real)49);
- BOOST_CHECK_CLOSE(p.first, Real(7), tol);
- BOOST_CHECK_CLOSE(p.second, Real(7), tol);
- // This test does not pass in multiprecision,
- // due to the fact it does not have an fma:
- if (std::is_floating_point<Real>::value)
- {
- // (x-1)(x-1-eps) = x^2 + (-eps - 2)x + (1)(1+eps)
- Real eps = 2*std::numeric_limits<Real>::epsilon();
- Real b = 256 * (-2 - eps);
- Real c = 256 * (1 + eps);
- p = quadratic_roots((Real)256, b, c);
- BOOST_CHECK_CLOSE(p.first, Real(1), tol);
- BOOST_CHECK_CLOSE(p.second, Real(1) + eps, tol);
- }
- if (std::is_same<Real, double>::value)
- {
- // Kahan's example: This is the test that demonstrates the necessity of the fma instruction.
- // https://en.wikipedia.org/wiki/Loss_of_significance#Instability_of_the_quadratic_equation
- p = quadratic_roots<Real>((Real)94906265.625, (Real )-189812534, (Real)94906268.375);
- BOOST_CHECK_CLOSE_FRACTION(p.first, Real(1), tol);
- BOOST_CHECK_CLOSE_FRACTION(p.second, 1.000000028975958, 4*tol);
- }
- }
- template<class Z>
- void test_solve_int_quadratic()
- {
- double tol = std::numeric_limits<double>::epsilon();
- using boost::math::tools::quadratic_roots;
- auto [x0, x1] = quadratic_roots(1, 0, -1);
- BOOST_CHECK_CLOSE(x0, double(-1), tol);
- BOOST_CHECK_CLOSE(x1, double(1), tol);
- auto p = quadratic_roots(7, 0, 0);
- BOOST_CHECK_SMALL(p.first, tol);
- BOOST_CHECK_SMALL(p.second, tol);
- // (x-7)^2 = x^2 - 14*x + 49:
- p = quadratic_roots(1, -14, 49);
- BOOST_CHECK_CLOSE(p.first, double(7), tol);
- BOOST_CHECK_CLOSE(p.second, double(7), tol);
- }
- template<class Complex>
- void test_solve_complex_quadratic()
- {
- using Real = typename Complex::value_type;
- Real tol = std::numeric_limits<Real>::epsilon();
- using boost::math::tools::quadratic_roots;
- auto [x0, x1] = quadratic_roots<Complex>({1,0}, {0,0}, {-1,0});
- BOOST_CHECK_CLOSE(x0.real(), Real(-1), tol);
- BOOST_CHECK_CLOSE(x1.real(), Real(1), tol);
- BOOST_CHECK_SMALL(x0.imag(), tol);
- BOOST_CHECK_SMALL(x1.imag(), tol);
- auto p = quadratic_roots<Complex>({7,0}, {0,0}, {0,0});
- BOOST_CHECK_SMALL(p.first.real(), tol);
- BOOST_CHECK_SMALL(p.second.real(), tol);
- // (x-7)^2 = x^2 - 14*x + 49:
- p = quadratic_roots<Complex>({1,0}, {-14,0}, {49,0});
- BOOST_CHECK_CLOSE(p.first.real(), Real(7), tol);
- BOOST_CHECK_CLOSE(p.second.real(), Real(7), tol);
- }
- #endif
- void test_failures()
- {
- #if !defined(BOOST_NO_CXX11_LAMBDAS)
- // There is no root:
- BOOST_CHECK_THROW(boost::math::tools::newton_raphson_iterate([](double x) { return std::make_pair(x * x + 1, 2 * x); }, 10.0, -12.0, 12.0, 52), boost::math::evaluation_error);
- BOOST_CHECK_THROW(boost::math::tools::newton_raphson_iterate([](double x) { return std::make_pair(x * x + 1, 2 * x); }, -10.0, -12.0, 12.0, 52), boost::math::evaluation_error);
- // There is a root, but a bad guess takes us into a local minima:
- BOOST_CHECK_THROW(boost::math::tools::newton_raphson_iterate([](double x) { return std::make_pair(boost::math::pow<6>(x) - 2 * boost::math::pow<4>(x) + x + 0.5, 6 * boost::math::pow<5>(x) - 8 * boost::math::pow<3>(x) + 1); }, 0.75, -20., 20., 52), boost::math::evaluation_error);
- // There is no root:
- BOOST_CHECK_THROW(boost::math::tools::halley_iterate([](double x) { return std::make_tuple(x * x + 1, 2 * x, 2); }, 10.0, -12.0, 12.0, 52), boost::math::evaluation_error);
- BOOST_CHECK_THROW(boost::math::tools::halley_iterate([](double x) { return std::make_tuple(x * x + 1, 2 * x, 2); }, -10.0, -12.0, 12.0, 52), boost::math::evaluation_error);
- // There is a root, but a bad guess takes us into a local minima:
- BOOST_CHECK_THROW(boost::math::tools::halley_iterate([](double x) { return std::make_tuple(boost::math::pow<6>(x) - 2 * boost::math::pow<4>(x) + x + 0.5, 6 * boost::math::pow<5>(x) - 8 * boost::math::pow<3>(x) + 1, 30 * boost::math::pow<4>(x) - 24 * boost::math::pow<2>(x)); }, 0.75, -20., 20., 52), boost::math::evaluation_error);
- #endif
- }
- BOOST_AUTO_TEST_CASE( test_main )
- {
- test_beta(0.1, "double");
- #if !defined(BOOST_NO_CXX11_AUTO_DECLARATIONS) && !defined(BOOST_NO_CXX11_UNIFIED_INITIALIZATION_SYNTAX) && !defined(BOOST_NO_CXX11_LAMBDAS)
- test_complex_newton<std::complex<float>>();
- test_complex_newton<std::complex<double>>();
- test_complex_newton<boost::multiprecision::cpp_complex_100>();
- test_daubechies_fails();
- #endif
- #if !defined(BOOST_NO_CXX17_IF_CONSTEXPR)
- test_solve_real_quadratic<float>();
- test_solve_real_quadratic<double>();
- test_solve_real_quadratic<long double>();
- test_solve_real_quadratic<boost::multiprecision::cpp_bin_float_50>();
- test_solve_int_quadratic<int>();
- test_solve_complex_quadratic<std::complex<double>>();
- #endif
- test_failures();
- }
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