diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h b/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h
index 12322a256..e8069154c 100644
--- a/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h
+++ b/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h
@@ -178,9 +178,9 @@ class MatrixFunction<MatrixType, 1>
       *
       * This is morally a \c static \c const \c Scalar, but only
       * integers can be static constant class members in C++. The
-      * separation constant is set to 0.01, a value taken from the
+      * separation constant is set to 0.1, a value taken from the
       * paper by Davies and Higham. */
-    static const RealScalar separation() { return static_cast<RealScalar>(0.01); }
+    static const RealScalar separation() { return static_cast<RealScalar>(0.1); }
 };
 
 /** \brief Constructor. 
@@ -492,14 +492,12 @@ typename MatrixFunction<MatrixType,1>::DynMatrixType MatrixFunction<MatrixType,1
 template<typename Derived> class MatrixFunctionReturnValue
 : public ReturnByValue<MatrixFunctionReturnValue<Derived> >
 {
-  private:
+  public:
 
     typedef typename ei_traits<Derived>::Scalar Scalar;
     typedef typename ei_stem_function<Scalar>::type StemFunction;
 
-  public:
-
-    /** \brief Constructor.
+   /** \brief Constructor.
       *
       * \param[in] A  %Matrix (expression) forming the argument of the
       * matrix function.
diff --git a/unsupported/test/matrix_function.cpp b/unsupported/test/matrix_function.cpp
index 4ff6d7f1e..7a1501da2 100644
--- a/unsupported/test/matrix_function.cpp
+++ b/unsupported/test/matrix_function.cpp
@@ -109,11 +109,10 @@ template<typename MatrixType>
 void testHyperbolicFunctions(const MatrixType& A)
 {
   for (int i = 0; i < g_repeat; i++) {
-    MatrixType sinhA = ei_matrix_sinh(A);
-    MatrixType coshA = ei_matrix_cosh(A);
     MatrixType expA = ei_matrix_exponential(A);
-    VERIFY_IS_APPROX(sinhA, (expA - expA.inverse())/2);
-    VERIFY_IS_APPROX(coshA, (expA + expA.inverse())/2);
+    MatrixType expmA = ei_matrix_exponential(-A);
+    VERIFY_IS_APPROX(ei_matrix_sinh(A), (expA - expmA) / 2);
+    VERIFY_IS_APPROX(ei_matrix_cosh(A), (expA + expmA) / 2);
   }
 }
 
@@ -134,14 +133,15 @@ void testGonioFunctions(const MatrixType& A)
     ComplexMatrix Ac = A.template cast<ComplexScalar>();
 
     ComplexMatrix exp_iA = ei_matrix_exponential(imagUnit * Ac);
+    ComplexMatrix exp_miA = ei_matrix_exponential(-imagUnit * Ac);
 
     MatrixType sinA = ei_matrix_sin(A);
     ComplexMatrix sinAc = sinA.template cast<ComplexScalar>();
-    VERIFY_IS_APPROX(sinAc, (exp_iA - exp_iA.inverse()) / (two*imagUnit));
+    VERIFY_IS_APPROX(sinAc, (exp_iA - exp_miA) / (two*imagUnit));
 
     MatrixType cosA = ei_matrix_cos(A);
     ComplexMatrix cosAc = cosA.template cast<ComplexScalar>();
-    VERIFY_IS_APPROX(cosAc, (exp_iA + exp_iA.inverse()) / 2);
+    VERIFY_IS_APPROX(cosAc, (exp_iA + exp_miA) / 2);
   }
 }