Analytic inverse implementation (#122)

* Add analytic 2x2 matrix inverse

* Add analytical 3x3 matrix inverse

matrix/SquareMatrix.hpp

@@ -435,6 +435,47 @@ bool inv(const SquareMatrix<Type, M> & A, SquareMatrix<Type, M> & inv)
     return true;
 }
 
+template<typename Type>
+bool inv(const SquareMatrix<Type, 2> & A, SquareMatrix<Type, 2> & inv)
+{
+    Type det = A(0, 0) * A(1, 1) - A(1, 0) * A(0, 1);
+
+    if(fabs(static_cast<float>(det)) < FLT_EPSILON || !is_finite(det)) {
+        return false;
+    }
+
+    inv(0, 0) = A(1, 1);
+    inv(1, 0) = -A(1, 0);
+    inv(0, 1) = -A(0, 1);
+    inv(1, 1) = A(0, 0);
+    inv /= det;
+    return true;
+}
+
+template<typename Type>
+bool inv(const SquareMatrix<Type, 3> & A, SquareMatrix<Type, 3> & inv)
+{
+    Type det = A(0, 0) * (A(1, 1) * A(2, 2) - A(2, 1) * A(1, 2)) -
+               A(0, 1) * (A(1, 0) * A(2, 2) - A(1, 2) * A(2, 0)) +
+               A(0, 2) * (A(1, 0) * A(2, 1) - A(1, 1) * A(2, 0));
+
+    if(fabs(static_cast<float>(det)) < FLT_EPSILON || !is_finite(det)) {
+        return false;
+    }
+
+    inv(0, 0) = A(1, 1) * A(2, 2) - A(2, 1) * A(1, 2);
+    inv(0, 1) = A(0, 2) * A(2, 1) - A(0, 1) * A(2, 2);
+    inv(0, 2) = A(0, 1) * A(1, 2) - A(0, 2) * A(1, 1);
+    inv(1, 0) = A(1, 2) * A(2, 0) - A(1, 0) * A(2, 2);
+    inv(1, 1) = A(0, 0) * A(2, 2) - A(0, 2) * A(2, 0);
+    inv(1, 2) = A(1, 0) * A(0, 2) - A(0, 0) * A(1, 2);
+    inv(2, 0) = A(1, 0) * A(2, 1) - A(2, 0) * A(1, 1);
+    inv(2, 1) = A(2, 0) * A(0, 1) - A(0, 0) * A(2, 1);
+    inv(2, 2) = A(0, 0) * A(1, 1) - A(1, 0) * A(0, 1);
+    inv /= det;
+    return true;
+}
+
 /**
  * inverse based on LU factorization with partial pivotting
  */

test/inverse.cpp

@@ -22,6 +22,27 @@ int main()
     SquareMatrix<float, 3> A_I_check(data_check);
     TEST((A_I - A_I_check).abs().max() < 1e-6f);
 
+    float data_2x2[4] = {12, 2,
+                         -7, 5
+                        };
+    float data_2x2_check[4] = {
+        0.0675675675f, -0.02702702f,
+        0.0945945945f, 0.162162162f
+    };
+
+    SquareMatrix<float, 2> A2x2(data_2x2);
+    SquareMatrix<float, 2> A2x2_I = inv(A2x2);
+    SquareMatrix<float, 2> A2x2_I_check(data_2x2_check);
+    TEST(isEqual(A2x2_I, A2x2_I_check));
+
+    SquareMatrix<float, 2> A2x2_sing = ones<float, 2, 2>();
+    SquareMatrix<float, 2> A2x2_sing_I;
+    TEST(inv(A2x2_sing, A2x2_sing_I) == false);
+
+    SquareMatrix<float, 3> A3x3_sing = ones<float, 3, 3>();
+    SquareMatrix<float, 3> A3x3_sing_I;
+    TEST(inv(A3x3_sing, A3x3_sing_I) == false)
+
     // stess test
     SquareMatrix<float, n_large> A_large;
     A_large.setIdentity();
@@ -34,7 +55,7 @@ int main()
     }
 
     SquareMatrix<float, 3> zero_test = zeros<float, 3, 3>();
-    inv(zero_test);
+    TEST(isEqual(inv(zero_test), zeros<float, 3, 3>()));
 
     // test pivotting
     float data2[81] = {
@@ -64,6 +85,7 @@ int main()
     SquareMatrix<float, 9> A2_I = inv(A2);
     SquareMatrix<float, 9> A2_I_check(data2_check);
     TEST((A2_I - A2_I_check).abs().max() < 1e-3f);
+
     float data3[9] = {
         0, 1, 2,
         3, 4, 5,
@@ -93,6 +115,16 @@ int main()
     TEST(isEqual(A3_I, Z3));
     TEST(isEqual(A3.I(), Z3));
 
+    for(size_t i = 0; i < 9; i++) {
+        A2(0, i) = 0;
+    }
+    A2_I = inv(A2);
+    SquareMatrix<float, 9> Z9 = zeros<float, 9, 9>();
+    TEST(!A2.I(A2_I));
+    TEST(!Z9.I(A2_I));
+    TEST(isEqual(A2_I, Z9));
+    TEST(isEqual(A2.I(), Z9));
+
     // cover NaN
     A3(0, 0) = NAN;
     A3(0, 1) = 0;
@@ -101,6 +133,11 @@ int main()
     TEST(isEqual(A3_I, Z3));
     TEST(isEqual(A3.I(), Z3));
 
+    A2(0, 0) = NAN;
+    A2_I = inv(A2);
+    TEST(isEqual(A2_I, Z9));
+    TEST(isEqual(A2.I(), Z9));
+
     float data4[9] = {
         1.33471626f,  0.74946721f, -0.0531679f,
         0.74946721f,  1.07519593f,  0.08036323f,