Add more matrix operations, with an eye on adouble types

This patch adds several more implementations of operator+ etc for FieldMatrices.
In particular, you can now combine matrices of adoubles (the 'active' type from
the ADOL-C automatic differentiation library) with regular double types.

These new operators are needed for the NonplanarCosseratShellEnergy class,
which is coming in the next patch.

dune/gfe/linearalgebra.hh

@@ -3,17 +3,17 @@
 
 #include <dune/common/fmatrix.hh>
 
-//! calculates ret = A * B
-template< class K, int m, int n, int p >
-Dune::FieldMatrix< K, m, p > operator* ( const Dune::FieldMatrix< K, m, n > &A, const Dune::FieldMatrix< K, n, p > &B)
+template< int m, int n, int p >
+auto operator* ( const Dune::FieldMatrix< adouble, m, n > &A, const Dune::FieldMatrix< adouble, n, p > &B)
+  -> Dune::FieldMatrix<adouble, m, p>
 {
-    typedef typename Dune::FieldMatrix< K, m, p > :: size_type size_type;
-    Dune::FieldMatrix< K, m, p > ret;
+    typedef typename Dune::FieldMatrix< adouble, m, p > :: size_type size_type;
+    Dune::FieldMatrix< adouble, m, p > ret;
 
     for( size_type i = 0; i < m; ++i ) {
 
         for( size_type j = 0; j < p; ++j ) {
-            ret[ i ][ j ] = K( 0 );
+            ret[ i ][ j ] = 0.0;
             for( size_type k = 0; k < n; ++k )
                 ret[ i ][ j ] += A[ i ][ k ] * B[ k ][ j ];
         }
@@ -21,20 +21,115 @@ Dune::FieldMatrix< K, m, p > operator* ( const Dune::FieldMatrix< K, m, n > &A,
     return ret;
 }
 
-//! calculates ret = A - B
+template< int m, int n, int p >
+auto operator* ( const Dune::FieldMatrix< adouble, m, n > &A, const Dune::FieldMatrix< double, n, p > &B)
+  -> Dune::FieldMatrix<adouble, m, p>
+{
+    typedef typename Dune::FieldMatrix< adouble, m, p > :: size_type size_type;
+    Dune::FieldMatrix< adouble, m, p > ret;
+
+    for( size_type i = 0; i < m; ++i ) {
+
+        for( size_type j = 0; j < p; ++j ) {
+            ret[ i ][ j ] = 0.0;
+            for( size_type k = 0; k < n; ++k )
+                ret[ i ][ j ] += A[ i ][ k ] * B[ k ][ j ];
+        }
+    }
+    return ret;
+}
+
+template< int m, int n, int p >
+auto operator* ( const Dune::FieldMatrix< double, m, n > &A, const Dune::FieldMatrix< adouble, n, p > &B)
+  -> Dune::FieldMatrix<adouble, m, p>
+{
+    typedef typename Dune::FieldMatrix< adouble, m, p > :: size_type size_type;
+    Dune::FieldMatrix< adouble, m, p > ret;
+
+    for( size_type i = 0; i < m; ++i ) {
+
+        for( size_type j = 0; j < p; ++j ) {
+            ret[ i ][ j ] = 0.0;
+            for( size_type k = 0; k < n; ++k )
+                ret[ i ][ j ] += A[ i ][ k ] * B[ k ][ j ];
+        }
+    }
+    return ret;
+}
+
+//! calculates ret = A + B
 template< class K, int m, int n>
-Dune::FieldMatrix<K,m,n> operator- ( const Dune::FieldMatrix<K, m, n> &A, const Dune::FieldMatrix<K,m,n> &B)
+Dune::FieldMatrix<K,m,n> operator+ ( const Dune::FieldMatrix<K, m, n> &A, const Dune::FieldMatrix<K,m,n> &B)
 {
     typedef typename Dune::FieldMatrix<K,m,n> :: size_type size_type;
     Dune::FieldMatrix<K,m,n> ret;
 
     for( size_type i = 0; i < m; ++i )
         for( size_type j = 0; j < n; ++j )
-            ret[i][j] = A[i][j] - B[i][j];
+            ret[i][j] = A[i][j] + B[i][j];
 
     return ret;
 }
 
+//! calculates ret = A - B
+template <int m, int n>
+auto operator- ( const Dune::FieldMatrix< adouble, m, n > &A, const Dune::FieldMatrix< double, m, n > &B)
+  -> Dune::FieldMatrix<adouble, m, n>
+{
+    Dune::FieldMatrix<adouble,m,n> result;
+    typedef typename decltype(result)::size_type size_type;
+
+    for( size_type i = 0; i < m; ++i )
+        for( size_type j = 0; j < n; ++j )
+            result[i][j] = A[i][j] - B[i][j];
+
+    return result;
+}
+
+//! calculates ret = A - B
+template <int m, int n>
+auto operator- ( const Dune::FieldMatrix< adouble, m, n > &A, const Dune::FieldMatrix< adouble, m, n > &B)
+  -> Dune::FieldMatrix<adouble, m, n>
+{
+    Dune::FieldMatrix<adouble,m,n> result;
+    typedef typename decltype(result)::size_type size_type;
+
+    for( size_type i = 0; i < m; ++i )
+        for( size_type j = 0; j < n; ++j )
+            result[i][j] = A[i][j] - B[i][j];
+
+    return result;
+}
+
+//! calculates ret = s*A
+template< int m, int n>
+auto operator* ( const double& s, const Dune::FieldMatrix<adouble, m, n> &A)
+  -> Dune::FieldMatrix<adouble,m,n>
+{
+    typedef typename Dune::FieldMatrix<adouble,m,n> :: size_type size_type;
+    Dune::FieldMatrix<adouble,m,n> ret;
+
+    for( size_type i = 0; i < m; ++i )
+        for( size_type j = 0; j < n; ++j )
+            ret[i][j] = s * A[i][j];
+
+    return ret;
+}
+
+//! calculates ret = s*A
+template< int m, int n>
+auto operator* ( const double& s, const Dune::FieldMatrix<double, m, n> &A)
+  -> Dune::FieldMatrix<double,m,n>
+{
+    typedef typename Dune::FieldMatrix<double,m,n> :: size_type size_type;
+    Dune::FieldMatrix<double,m,n> ret;
+
+    for( size_type i = 0; i < m; ++i )
+        for( size_type j = 0; j < n; ++j )
+            ret[i][j] = s * A[i][j];
+
+    return ret;
+}
 
 //! calculates ret = A/s
 template< class K, int m, int n>
@@ -50,4 +145,17 @@ Dune::FieldMatrix<K,m,n> operator/ ( const Dune::FieldMatrix<K, m, n> &A, const
     return ret;
 }
 
+//! calculates ret = A/s
+template< class K, int m>
+Dune::FieldVector<K,m> operator/ ( const Dune::FieldVector<K, m> &A, const K& s)
+{
+    typedef typename Dune::FieldVector<K,m> :: size_type size_type;
+    Dune::FieldVector<K,m> result;
+
+    for( size_type i = 0; i < m; ++i )
+        result[i] = A[i] / s;
+
+    return result;
+}
+
 #endif