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133 lines
3.8 KiB
C++
133 lines
3.8 KiB
C++
/*
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* Copyright Nick Thompson, 2021
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* Use, modification and distribution are subject to the
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* Boost Software License, Version 1.0. (See accompanying file
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* LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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*/
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#include "math_unit_test.hpp"
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#include <random>
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#include <boost/math/tools/cubic_roots.hpp>
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#ifdef BOOST_HAS_FLOAT128
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#include <boost/multiprecision/float128.hpp>
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using boost::multiprecision::float128;
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#endif
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using boost::math::tools::cubic_roots;
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using boost::math::tools::cubic_root_residual;
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using std::cbrt;
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template<class Real>
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void test_zero_coefficients()
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{
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Real a = 0;
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Real b = 0;
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Real c = 0;
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Real d = 0;
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auto roots = cubic_roots(a,b,c,d);
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CHECK_EQUAL(roots[0], Real(0));
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CHECK_EQUAL(roots[1], Real(0));
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CHECK_EQUAL(roots[2], Real(0));
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a = 1;
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roots = cubic_roots(a,b,c,d);
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CHECK_EQUAL(roots[0], Real(0));
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CHECK_EQUAL(roots[1], Real(0));
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CHECK_EQUAL(roots[2], Real(0));
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a = 1;
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d = 1;
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// x^3 + 1 = 0:
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roots = cubic_roots(a,b,c,d);
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CHECK_EQUAL(roots[0], Real(-1));
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CHECK_NAN(roots[1]);
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CHECK_NAN(roots[2]);
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d = -1;
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// x^3 - 1 = 0:
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roots = cubic_roots(a,b,c,d);
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CHECK_EQUAL(roots[0], Real(1));
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CHECK_NAN(roots[1]);
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CHECK_NAN(roots[2]);
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d = -2;
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// x^3 - 2 = 0
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roots = cubic_roots(a,b,c,d);
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// Let's go for equality here!
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CHECK_EQUAL(roots[0], cbrt(Real(2)));
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CHECK_NAN(roots[1]);
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CHECK_NAN(roots[2]);
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d = -8;
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roots = cubic_roots(a,b,c,d);
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CHECK_EQUAL(roots[0], Real(2));
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CHECK_NAN(roots[1]);
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CHECK_NAN(roots[2]);
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// (x-1)(x-2)(x-3) = x^3 - 6x^2 + 11x - 6
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roots = cubic_roots(Real(1), Real(-6), Real(11), Real(-6));
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CHECK_ULP_CLOSE(roots[0], Real(1), 2);
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CHECK_ULP_CLOSE(roots[1], Real(2), 2);
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CHECK_ULP_CLOSE(roots[2], Real(3), 2);
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// Double root:
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// (x+1)^2(x-2) = x^3 - 3x - 2:
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// Note: This test is unstable wrt to perturbations!
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roots = cubic_roots(Real(1), Real(0), Real(-3), Real(-2));
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CHECK_ULP_CLOSE(-1, roots[0], 2);
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CHECK_ULP_CLOSE(-1, roots[1], 2);
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CHECK_ULP_CLOSE(2, roots[2], 2);
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std::uniform_real_distribution<Real> dis(-2,2);
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std::mt19937 gen(12345);
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// Expected roots
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std::array<Real, 3> r;
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int trials = 10;
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for (int i = 0; i < trials; ++i) {
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// Mathematica:
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// Expand[(x - r0)*(x - r1)*(x - r2)]
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// - r0 r1 r2 + (r0 r1 + r0 r2 + r1 r2) x
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// - (r0 + r1 + r2) x^2 + x^3
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for (auto & root : r) {
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root = static_cast<Real>(dis(gen));
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}
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std::sort(r.begin(), r.end());
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Real a = 1;
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Real b = -(r[0] + r[1] + r[2]);
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Real c = r[0]*r[1] + r[0]*r[2] + r[1]*r[2];
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Real d = -r[0]*r[1]*r[2];
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auto roots = cubic_roots(a, b, c, d);
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// I could check the condition number here, but this is fine right?
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if(!CHECK_ULP_CLOSE(r[0], roots[0], 25)) {
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std::cerr << " Polynomial x^3 + " << b << "x^2 + " << c << "x + " << d << " has roots {";
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std::cerr << r[0] << ", " << r[1] << ", " << r[2] << "}, but the computed roots are {";
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std::cerr << roots[0] << ", " << roots[1] << ", " << roots[2] << "}\n";
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}
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CHECK_ULP_CLOSE(r[1], roots[1], 25);
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CHECK_ULP_CLOSE(r[2], roots[2], 25);
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for (auto root : roots) {
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auto res = cubic_root_residual(a, b,c,d, root);
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CHECK_LE(abs(res[0]), 20*res[1]);
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}
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}
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}
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int main()
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{
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test_zero_coefficients<float>();
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test_zero_coefficients<double>();
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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test_zero_coefficients<long double>();
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#endif
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#ifdef BOOST_HAS_FLOAT128
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// For some reason, the quadmath is way less accurate than the float/double/long double:
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//test_zero_coefficients<float128>();
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#endif
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return boost::math::test::report_errors();
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}
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