Added minor extraction and inverse for 3x3 matrices

minor extraction is called getMinor since minor is a gcc macro ...
should find a better name

src/algebra/TinyMatrix.hpp

@@ -96,7 +96,6 @@ public:
     return std::move(Ax);
   }
 
-
   KOKKOS_INLINE_FUNCTION
   friend std::ostream& operator<<(std::ostream& os, const TinyMatrix& A)
   {
@@ -367,6 +366,34 @@ T det(const TinyMatrix<3,T>& A)
     +A(2,0)*(A(0,1)*A(1,2)-A(1,1)*A(0,2));
 }
 
+template <size_t N, typename T>
+KOKKOS_INLINE_FUNCTION
+TinyMatrix<N-1,T> getMinor(const TinyMatrix<N,T>& A,
+                        const size_t& I,
+                        const size_t& J)
+{
+  static_assert(N>=2, "minor calculation requires at least 2x2 matrices");
+  Assert((I<N) and (J<N));
+  TinyMatrix<N-1, T> M;
+  for (size_t i=0; i<I; ++i) {
+    for (size_t j=0; j<J; ++j) {
+      M(i,j)=A(i,j);
+    }
+    for (size_t j=J+1; j<N; ++j) {
+      M(i,j-1)=A(i,j);
+    }
+  }
+  for (size_t i=I+1; i<N; ++i) {
+    for (size_t j=0; j<J; ++j) {
+      M(i-1,j)=A(i,j);
+    }
+    for (size_t j=J+1; j<N; ++j) {
+      M(i-1,j-1)=A(i,j);
+    }
+  }
+  return std::move(M);
+}
+
 template <size_t N, typename T>
 KOKKOS_INLINE_FUNCTION
 TinyMatrix<N,T> inverse(const TinyMatrix<N,T>& A);
@@ -404,10 +431,14 @@ TinyMatrix<3,T> inverse(const TinyMatrix<3,T>& A)
   static_assert(std::is_arithmetic<T>::value, "inverse is not defined for non arithmetic types");
   static_assert(std::is_floating_point<T>::value, "inverse is defined for floating point types only");
 
-  std::cerr << "inverse not implemented in 3D\n";
-  std::exit(1);
+  const T determinent = det(A);
+  const T inv_determinent = 1./determinent;
 
-  return std::move(TinyMatrix<3,T>(identity));
+  TinyMatrix<3,T> cofactor_T(det(getMinor(A,0,0)), det(getMinor(A,1,0)), det(getMinor(A,2,0)),
+                             det(getMinor(A,0,1)), det(getMinor(A,1,1)), det(getMinor(A,2,1)),
+                             det(getMinor(A,0,2)), det(getMinor(A,1,2)), det(getMinor(A,2,2)));
+
+  return std::move(cofactor_T *= inv_determinent);
 }
 
 #endif // TINYMATRIX_HPP