Merge pull request #27331 from MaximSmolskiy:add-test-for-solveCubic

Add tests for solveCubic #27331

### Pull Request Readiness Checklist

Related to #27323 

I found only randomized tests with number of roots always equal to `1` or `3`, `x^3 = 0` and some simple test for Java and Swift.
Obviously, they don't cover all cases (implementation has strong branching and number of roots can be equal to `-1`, `0` and `2` additionally).
So, I think it will be useful to try explicitly cover more cases (and implementation branches correspondingly)

See details at https://github.com/opencv/opencv/wiki/How_to_contribute#making-a-good-pull-request

- [x] I agree to contribute to the project under Apache 2 License.
- [x] To the best of my knowledge, the proposed patch is not based on a code under GPL or another license that is incompatible with OpenCV
- [x] The PR is proposed to the proper branch
- [x] There is a reference to the original bug report and related work
- [x] There is accuracy test, performance test and test data in opencv_extra repository, if applicable
      Patch to opencv_extra has the same branch name.
- [x] The feature is well documented and sample code can be built with the project CMake

modules/core/include/opencv2/core.hpp

@@ -2004,8 +2004,8 @@ The function solveCubic finds the real roots of a cubic equation:
 
 The roots are stored in the roots array.
 @param coeffs equation coefficients, an array of 3 or 4 elements.
-@param roots output array of real roots that has 1 or 3 elements.
-@return number of real roots. It can be 0, 1 or 2.
+@param roots output array of real roots that has 0, 1, 2 or 3 elements.
+@return number of real roots. It can be -1 (all real numbers), 0, 1, 2 or 3.
 */
 CV_EXPORTS_W int solveCubic(InputArray coeffs, OutputArray roots);
 

modules/core/src/mathfuncs.cpp

@@ -1590,7 +1590,7 @@ int cv::solveCubic( InputArray _coeffs, OutputArray _roots )
     {
         if( a1 == 0 )
         {
-            if( a2 == 0 )
+            if( a2 == 0 ) // constant
                 n = a3 == 0 ? -1 : 0;
             else
             {
@@ -1624,6 +1624,7 @@ int cv::solveCubic( InputArray _coeffs, OutputArray _roots )
     }
     else
     {
+        // cubic equation
         a0 = 1./a0;
         a1 *= a0;
         a2 *= a0;

modules/core/test/test_math.cpp

@@ -2445,6 +2445,158 @@ static void checkRoot(Mat& r, T re, T im)
     }
     GTEST_NONFATAL_FAILURE_("Can't find root") << "(" << re << ", " << im << ")";
 }
+
+TEST(Core_SolveCubicConstant, accuracy)
+{
+    {
+        const std::vector<double> coeffs{0., 0., 0., 1.};
+        std::vector<double> roots;
+        const auto num_roots = solveCubic(coeffs, roots);
+
+        EXPECT_EQ(num_roots, 0);
+    }
+
+    {
+        const std::vector<double> coeffs{0., 0., 0., 0.};
+        std::vector<double> roots;
+        const auto num_roots = solveCubic(coeffs, roots);
+
+        EXPECT_EQ(num_roots, -1);
+    }
+}
+
+TEST(Core_SolveCubicLinear, accuracy)
+{
+    const std::vector<double> coeffs{0., 0., 2., -2.};
+    std::vector<double> roots;
+    const auto num_roots = solveCubic(coeffs, roots);
+
+    EXPECT_EQ(num_roots, 1);
+    EXPECT_EQ(roots[0], 1.);
+}
+
+TEST(Core_SolveCubicQuadratic, accuracy)
+{
+    {
+        const std::vector<double> coeffs{0., 2., -4., 4.};
+        std::vector<double> roots;
+        const auto num_roots = solveCubic(coeffs, roots);
+
+        EXPECT_EQ(num_roots, 0);
+    }
+
+    {
+        const std::vector<double> coeffs{0., 2., -4., 2.};
+        std::vector<double> roots;
+        const auto num_roots = solveCubic(coeffs, roots);
+
+        EXPECT_EQ(num_roots, 1);
+        EXPECT_EQ(roots[0], 1.);
+    }
+
+    {
+        const std::vector<double> coeffs{0., 2., -6., 4.};
+        std::vector<double> roots;
+        const auto num_roots = solveCubic(coeffs, roots);
+
+        EXPECT_EQ(num_roots, 2);
+        EXPECT_EQ(roots[0], 2.);
+        EXPECT_EQ(roots[1], 1.);
+    }
+}
+
+TEST(Core_SolveCubicCubic, accuracy)
+{
+    {
+        const std::vector<double> coeffs{2., -6., 6., -2.};
+        std::vector<double> roots;
+        const auto num_roots = solveCubic(coeffs, roots);
+
+        EXPECT_EQ(num_roots, 1);
+        EXPECT_EQ(roots[0], 1.);
+    }
+
+    {
+        const std::vector<double> coeffs{2., -10., 24., -16.};
+        std::vector<double> roots;
+        const auto num_roots = solveCubic(coeffs, roots);
+
+        EXPECT_EQ(num_roots, 1);
+        EXPECT_EQ(roots[0], 1.);
+    }
+
+    {
+        const std::vector<double> coeffs{2., -10., 16., -8.};
+        std::vector<double> roots;
+        const auto num_roots = solveCubic(coeffs, roots);
+
+        EXPECT_TRUE(num_roots == 2 || num_roots == 3);
+        EXPECT_NEAR(roots[0], 1., 1e-8);
+        EXPECT_NEAR(roots[1], 2., 1e-8);
+        if (num_roots == 3)
+        {
+            EXPECT_NEAR(roots[2], 2., 1e-8);
+        }
+    }
+
+    {
+        const std::vector<double> coeffs{2., -12., 22., -12.};
+        std::vector<double> roots;
+        const auto num_roots = solveCubic(coeffs, roots);
+
+        EXPECT_EQ(num_roots, 3);
+        EXPECT_NEAR(roots[0], 1., 1e-8);
+        EXPECT_NEAR(roots[1], 3., 1e-8);
+        EXPECT_NEAR(roots[2], 2., 1e-8);
+    }
+}
+
+TEST(Core_SolveCubicNormalizedCubic, accuracy)
+{
+    {
+        const std::vector<double> coeffs{-3., 3., -1.};
+        std::vector<double> roots;
+        const auto num_roots = solveCubic(coeffs, roots);
+
+        EXPECT_EQ(num_roots, 1);
+        EXPECT_EQ(roots[0], 1.);
+    }
+
+    {
+        const std::vector<double> coeffs{-5., 12., -8.};
+        std::vector<double> roots;
+        const auto num_roots = solveCubic(coeffs, roots);
+
+        EXPECT_EQ(num_roots, 1);
+        EXPECT_EQ(roots[0], 1.);
+    }
+
+    {
+        const std::vector<double> coeffs{-5., 8., -4.};
+        std::vector<double> roots;
+        const auto num_roots = solveCubic(coeffs, roots);
+
+        EXPECT_TRUE(num_roots == 2 || num_roots == 3);
+        EXPECT_NEAR(roots[0], 1., 1e-8);
+        EXPECT_NEAR(roots[1], 2., 1e-8);
+        if (num_roots == 3)
+        {
+            EXPECT_NEAR(roots[2], 2., 1e-8);
+        }
+    }
+
+    {
+        const std::vector<double> coeffs{-6., 11., -6.};
+        std::vector<double> roots;
+        const auto num_roots = solveCubic(coeffs, roots);
+
+        EXPECT_EQ(num_roots, 3);
+        EXPECT_NEAR(roots[0], 1., 1e-8);
+        EXPECT_NEAR(roots[1], 3., 1e-8);
+        EXPECT_NEAR(roots[2], 2., 1e-8);
+    }
+}
+
 TEST(Core_SolvePoly, regression_5599)
 {
     // x^4 - x^2 = 0, roots: 1, -1, 0, 0