improved accuracy of 3x3 invert on poorly-conditioned matrices (bug #2525)

modules/core/src/lapack.cpp

@@ -1101,46 +1101,6 @@ double cv::invert( InputArray _src, OutputArray _dst, int method )
 
                     result = true;
                     d = 1./d;
-                #if CV_SSE2
-                    if(USE_SSE2)
-                    {
-                        __m128 det =_mm_set1_ps((float)d);
-                        __m128 s0 = _mm_loadu_ps((const float*)srcdata);//s0 = Sf(0,0) Sf(0,1) Sf(0,2) ***
-                        __m128 s1 = _mm_loadu_ps((const float*)(srcdata+srcstep));//s1 = Sf(1,0) Sf(1,1) Sf(1,2) ***
-                        __m128 s2 = _mm_set_ps(0.f, Sf(2,2), Sf(2,1), Sf(2,0)); //s2 = Sf(2,0) Sf(2,1) Sf(2,2) ***
-
-                        __m128 r0 =  _mm_shuffle_ps(s1,s1,_MM_SHUFFLE(3,0,2,1)); //r0 = Sf(1,1) Sf(1,2) Sf(1,0) ***
-                        __m128 r1 =  _mm_shuffle_ps(s2,s2,_MM_SHUFFLE(3,1,0,2)); //r1 = Sf(2,2) Sf(2,0) Sf(2,1) ***
-                        __m128 r2 =  _mm_shuffle_ps(s2,s2,_MM_SHUFFLE(3,0,2,1)); //r2 = Sf(2,1) Sf(2,2) Sf(2,0) ***
-
-                        __m128 t0 = _mm_mul_ps(s0, r0);//t0 = Sf(0,0)*Sf(1,1) Sf(0,1)*Sf(1,2) Sf(0,2)*Sf(1,0) ***
-                        __m128 t1 = _mm_mul_ps(s0, r1);//t1 = Sf(0,0)*Sf(2,2) Sf(0,1)*Sf(2,0) Sf(0,2)*Sf(2,1) ***
-                        __m128 t2 = _mm_mul_ps(s1, r2);//t2 = Sf(1,0)*Sf(2,1) Sf(1,1)*Sf(2,2) Sf(1,2)*Sf(2,0) ***
-
-                        __m128 r3 = _mm_shuffle_ps(s0,s0,_MM_SHUFFLE(3,0,2,1));//r3 = Sf(0,1) Sf(0,2) Sf(0,0) ***
-                        __m128 r4 = _mm_shuffle_ps(s0,s0,_MM_SHUFFLE(3,1,0,2));//r4 = Sf(0,2) Sf(0,0) Sf(0,1) ***
-
-                        __m128 t00 = _mm_mul_ps(s1, r3);//t00 = Sf(1,0)*Sf(0,1) Sf(1,1)*Sf(0,2) Sf(1,2)*Sf(0,0) ***
-                        __m128 t11 = _mm_mul_ps(s2, r4);//t11 = Sf(2,0)*Sf(0,2) Sf(2,1)*Sf(0,0) Sf(2,2)*Sf(0,1) ***
-                        __m128 t22 = _mm_mul_ps(s2, r0);//t22 = Sf(2,0)*Sf(1,1) Sf(2,1)*Sf(1,2) Sf(2,2)*Sf(1,0) ***
-
-                        t0 = _mm_mul_ps(_mm_sub_ps(t0,t00), det);//Sf(0,0)*Sf(1,1)   Sf(0,1)*Sf(1,2)   Sf(0,2)*Sf(1,0) ***
-                                                                //-Sf(1,0)*Sf(0,1)  -Sf(1,1)*Sf(0,2)  -Sf(1,2)*Sf(0,0)
-                        t1 = _mm_mul_ps(_mm_sub_ps(t1,t11), det);//Sf(0,0)*Sf(2,2)   Sf(0,1)*Sf(2,0)   Sf(0,2)*Sf(2,1) ***
-                                                                //-Sf(2,0)*Sf(0,2)  -Sf(2,1)*Sf(0,0)  -Sf(2,2)*Sf(0,1)
-                        t2 = _mm_mul_ps(_mm_sub_ps(t2,t22), det);//Sf(1,0)*Sf(2,1)   Sf(1,1)*Sf(2,2)   Sf(1,2)*Sf(2,0) ***
-                                                                //-Sf(2,0)*Sf(1,1)  -Sf(2,1)*Sf(1,2)  -Sf(2,2)*Sf(1,0)
-                        _mm_store_ps(t, t0);
-                        _mm_store_ps(t+4, t1);
-                        _mm_store_ps(t+8, t2);
-
-                        Df(0,0) = t[9]; Df(0,1) = t[6]; Df(0,2) = t[1];
-                        Df(1,0) = t[10]; Df(1,1) = t[4]; Df(1,2) = t[2];
-                        Df(2,0) = t[8]; Df(2,1) = t[5]; Df(2,2) = t[0];
-                    }
-                    else
-                #endif
-                    {
                     t[0] = (float)(((double)Sf(1,1) * Sf(2,2) - (double)Sf(1,2) * Sf(2,1)) * d);
                     t[1] = (float)(((double)Sf(0,2) * Sf(2,1) - (double)Sf(0,1) * Sf(2,2)) * d);
                     t[2] = (float)(((double)Sf(0,1) * Sf(1,2) - (double)Sf(0,2) * Sf(1,1)) * d);
@@ -1158,7 +1118,6 @@ double cv::invert( InputArray _src, OutputArray _dst, int method )
                     Df(2,0) = t[6]; Df(2,1) = t[7]; Df(2,2) = t[8];
                 }
             }
-            }
             else
             {
                 double d = det3(Sd);

modules/core/test/test_math.cpp

@@ -2453,6 +2453,21 @@ REGISTER_TYPED_TEST_CASE_P(Core_CheckRange, Negative, Positive, Bounds, Zero);
 typedef ::testing::Types<signed char,unsigned char, signed short, unsigned short, signed int> mat_data_types;
 INSTANTIATE_TYPED_TEST_CASE_P(Negative_Test, Core_CheckRange, mat_data_types);
 
+TEST(Core_Invert, small)
+{
+    cv::Mat a = (cv::Mat_<float>(3,3) << 2.42104644730331, 1.81444796521479, -3.98072565304758, 0, 7.08389214348967e-3, 5.55326770986007e-3, 0,0, 7.44556154284261e-3);
+    //cv::randu(a, -1, 1);
+    
+    cv::Mat b = a.t()*a;
+    cv::Mat c, i = Mat_<float>::eye(3, 3);
+    cv::invert(b, c, cv::DECOMP_LU); //std::cout << b*c << std::endl;
+    ASSERT_LT( cv::norm(b*c, i, CV_C), 0.1 );
+    cv::invert(b, c, cv::DECOMP_SVD); //std::cout << b*c << std::endl;
+    ASSERT_LT( cv::norm(b*c, i, CV_C), 0.1 );
+    cv::invert(b, c, cv::DECOMP_CHOLESKY); //std::cout << b*c << std::endl;
+    ASSERT_LT( cv::norm(b*c, i, CV_C), 0.1 );
+}
+
 /////////////////////////////////////////////////////////////////////////////////////////////////////
 
 TEST(Core_CovarMatrix, accuracy) { Core_CovarMatrixTest test; test.safe_run(); }