diff --git a/src/lol/math/polynomial.h b/src/lol/math/polynomial.h index 5efdb87f..19692388 100644 --- a/src/lol/math/polynomial.h +++ b/src/lol/math/polynomial.h @@ -24,7 +24,6 @@ #include #endif - namespace lol { @@ -188,42 +187,50 @@ struct polynomial * u³ = -n/2a + √((n/a)² + 4m³/27)/2 * v³ = -n/2a - √((n/a)² + 4m³/27)/2 */ - T const delta = (m * m) / (a * a) + 4 * m * m * m / 27; + T const delta = (n * n) / (a * a) + 4 * m * m * m / 27; - std::complex u3, v3; + /* Because 3×u×v = -m and m is not complex + * angle(u³) + angle(v³) must equal 0. + * + * This is why we compute u³ and v³ by norm and angle separately instead of + * using a std::complex class + */ + T u3_norm, u3_angle; + T v3_norm, v3_angle; if (delta < 0) { - u3 = std::complex(-n/(2.0f*a), sqrt(abs(delta))); - v3 = std::complex(-n/(2.0f*a), -sqrt(abs(delta))); + v3_norm = u3_norm = sqrt((-n/(2.0f*a)) * (-n/(2.0f*a)) + abs(delta)) / 2.f; + + u3_angle = atan2(sqrt(abs(delta)), (-n/(2.0f*a))); + v3_angle = -u3_angle; } else { - u3 = std::complex(-n/(2.0f*a) + sqrt(delta), 0); - v3 = std::complex(-n/(2.0f*a) - sqrt(delta), 0); - } + u3_norm = -n/(2.0f*a) + sqrt(delta) / 2.f; + v3_norm = -n/(2.0f*a) - sqrt(delta) / 2.f; - std::cout << "delta,u3,v3: " << delta << ", " << u3 << "," << v3 << std::endl; + u3_angle = u3_norm >= 0 ? 0 : M_PI; + v3_angle = v3_norm >= 0 ? 0 : -M_PI; - T const u3_angle = atan2(u3.imag(), u3.real()); - T const v3_angle = atan2(v3.imag(), v3.real()); - - std::cout << "u3_angle,v3_angle: " << u3_angle << "," << v3_angle << std::endl; + u3_norm = abs(u3_norm); + v3_norm = abs(v3_norm); + } std::complex complex_solutions[3]; for (int i = 0 ; i < 3 ; ++i) { - T u_angle = u3_angle / 3 + i * 2 * M_PI / 3; - T v_angle = v3_angle / 3 - i * 2 * M_PI / 3; - - std::cout << i << " => u_angle,v_angle: " << u_angle << "," << v_angle << std::endl; + T u_angle = u3_angle / 3.f + i * 2.f * M_PI / 3.f; + T v_angle = v3_angle / 3.f - i * 2.f * M_PI / 3.f; complex_solutions[i] = - pow(abs(u3), 1.0f/3.0f) * std::complex(cos(u_angle), sin(u_angle)) + - pow(abs(v3), 1.0f/3.0f) * std::complex(cos(v_angle), sin(v_angle)); + pow(u3_norm, 1.f / 3.f) * std::complex(cos(u_angle), sin(u_angle)) + + pow(v3_norm, 1.f / 3.f) * std::complex(cos(v_angle), sin(v_angle)); } + std::cout << "complex_solutions: " << complex_solutions[0] << ", " << complex_solutions[1] << ", " << complex_solutions[2] << std::endl; + return array {complex_solutions[0].real(), complex_solutions[1].real(), complex_solutions[2].real()}; } #endif diff --git a/src/t/math/polynomial.cpp b/src/t/math/polynomial.cpp index 622a55fe..ee9512f0 100644 --- a/src/t/math/polynomial.cpp +++ b/src/t/math/polynomial.cpp @@ -282,6 +282,16 @@ lolunit_declare_fixture(PolynomialTest) std::cout << roots1[0] << ", " << roots1[1] << ", " << roots1[2] << std::endl; } + + lolunit_declare_test(RootsDegree3_2) + { + polynomial p { -1.f, 0.f, 0.f, 1.f }; + auto roots1 = p.roots(); + + lolunit_assert_equal(roots1.count(), 3); + + std::cout << roots1[0] << ", " << roots1[1] << ", " << roots1[2] << std::endl; + } #endif lolunit_declare_test(Chebyshev)