poly_roots_unittest.cpp

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/* +------------------------------------------------------------------------+
   |                     Mobile Robot Programming Toolkit (MRPT)            |
   |                          https://www.mrpt.org/                         |
   |                                                                        |
   | Copyright (c) 2005-2020, Individual contributors, see AUTHORS file     |
   | See: https://www.mrpt.org/Authors - All rights reserved.               |
   | Released under BSD License. See: https://www.mrpt.org/License          |
   +------------------------------------------------------------------------+ */

#include <gtest/gtest.h>
#include <mrpt/core/format.h>
#include <mrpt/math/poly_roots.h>
#include <cmath>

using namespace std;

const double eps = 1e-9;

TEST(poly_roots, solve_poly2)
{
    // `a*x^2 + b*x + c = 0`
    // Table:
    //     coefs (a,b,c)    num_real_roots   root1  root2
    double coefs_roots[][6] = {{1, -2, 1, 2, 1.0, 1.0},
                               {1, 0, -1, 2, -1.0, 1.0},
                               {1, -1, -56, 2, -7.0, 8.0},
                               {5.0, 0, 1, 0, 0, 0},
                               {2.0, 0, 0, 2, 0, 0}};

    for (auto& coefs_root : coefs_roots)
    {
        const double a = coefs_root[0], b = coefs_root[1], c = coefs_root[2];
        const int num_roots_good = static_cast<int>(coefs_root[3]);
        const double r1_good = coefs_root[4], r2_good = coefs_root[5];

        double r1, r2;
        int num_roots = mrpt::math::solve_poly2(a, b, c, r1, r2);

        const std::string sTestStr = mrpt::format(
            "\nSolving: %.02f * x^2 + %.02f * x + %.02f = 0\n", a, b, c);

        EXPECT_EQ(num_roots, num_roots_good);
        if (num_roots >= 1)
        {
            EXPECT_NEAR(r1, r1_good, eps) << sTestStr;
        }
        if (num_roots >= 2)
        {
            EXPECT_NEAR(r2, r2_good, eps) << sTestStr;
        }
    }
}

TEST(poly_roots, solve_poly3)
{
    // `x^3+ a*x^2 + b*x + c = 0`
    // Table:
    //     coefs (a,b,c)    num_real_roots   root1  root2
    double coefs_roots[][7] = {{-6, 11, -6, 3, 1.0, 2.0, 3.0},
                               {2, 3, 4, 1, -1.650629191439386, 0, 0},
                               {0, -91, -90, 3, -1.0, -9.0, 10.0}};

    for (auto& coefs_root : coefs_roots)
    {
        const double a = coefs_root[0], b = coefs_root[1], c = coefs_root[2];
        const int num_roots_good = static_cast<int>(coefs_root[3]);
        const double roots_good[3] = {coefs_root[4], coefs_root[5],
                                      coefs_root[6]};

        double roots[3];
        int num_roots = mrpt::math::solve_poly3(roots, a, b, c);

        const std::string sTestStr = mrpt::format(
            "\nSolving: x^3 + %.02f * x^2 + %.02f * x + %.02f = 0\n", a, b, c);

        EXPECT_EQ(num_roots, num_roots_good);
        for (int k = 0; k < num_roots; k++)
        {
            bool match = false;
            for (int j = 0; j < num_roots; j++)
                if (std::abs(roots[k] - roots_good[j]) < eps) match = true;

            EXPECT_TRUE(match) << sTestStr << "k: " << k << std::endl;
        }
    }
}

TEST(poly_roots, solve_poly4)
{
    // `x^4 * a*x^3+ b*x^2 + c*x + d = 0`
    // Table:
    //     coefs (a,b,c)    num_real_roots   roots
    double coefs_roots[][9] = {{-10, 35, -50, 24, 4, 1.0, 2.0, 3.0, 4.0},
                               {-14, 35, 50, 0, 4, -1, 0, 5, 10}};

    for (auto& coefs_root : coefs_roots)
    {
        const double a = coefs_root[0], b = coefs_root[1], c = coefs_root[2],
                     d = coefs_root[3];
        const int num_roots_good = static_cast<int>(coefs_root[4]);
        const double roots_good[4] = {coefs_root[5], coefs_root[6],
                                      coefs_root[7], coefs_root[8]};

        double roots[4];
        int num_roots = mrpt::math::solve_poly4(roots, a, b, c, d);

        const std::string sTestStr = mrpt::format(
            "\nSolving: x^4 + %.02f * x^3 + %.02f * x^2 + %.02f * x + %.02f = "
            "0\n",
            a, b, c, d);

        EXPECT_EQ(num_roots, num_roots_good);
        for (int k = 0; k < num_roots; k++)
        {
            bool match = false;
            for (int j = 0; j < num_roots; j++)
                if (std::abs(roots[k] - roots_good[j]) < eps) match = true;

            EXPECT_TRUE(match) << sTestStr << "k: " << k << std::endl;
        }
    }
}