Clean-up of MatrixSquareRoot.

unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h

@@ -141,7 +141,7 @@ void MatrixLogarithmAtomic<MatrixType>::computeBig(const MatrixType& A, MatrixTy
         break;
       ++numberOfExtraSquareRoots;
     }
-    MatrixSquareRootTriangular<MatrixType>(T).compute(sqrtT);
+    matrix_sqrt_triangular(T, sqrtT);
     T = sqrtT.template triangularView<Upper>();
     ++numberOfSquareRoots;
   }

unsupported/Eigen/src/MatrixFunctions/MatrixPower.h

@@ -219,7 +219,7 @@ void MatrixPowerAtomic<MatrixType>::computeBig(ResultType& res) const
 	break;
       hasExtraSquareRoot = true;
     }
-    MatrixSquareRootTriangular<MatrixType>(T).compute(sqrtT);
+    matrix_sqrt_triangular(T, sqrtT);
     T = sqrtT.template triangularView<Upper>();
     ++numberOfSquareRoots;
   }

unsupported/Eigen/src/MatrixFunctions/MatrixSquareRoot.h

@@ -12,133 +12,16 @@
 
 namespace Eigen { 
 
-/** \ingroup MatrixFunctions_Module
+namespace internal {
-  * \brief Class for computing matrix square roots of upper quasi-triangular matrices.
-  * \tparam  MatrixType  type of the argument of the matrix square root,
-  *                      expected to be an instantiation of the Matrix class template.
-  *
-  * This class computes the square root of the upper quasi-triangular
-  * matrix stored in the upper Hessenberg part of the matrix passed to
-  * the constructor.
-  *
-  * \sa MatrixSquareRoot, MatrixSquareRootTriangular
-  */
-template <typename MatrixType>
-class MatrixSquareRootQuasiTriangular : internal::noncopyable
-{
-  public:
-
-    /** \brief Constructor. 
-      *
-      * \param[in]  A  upper quasi-triangular matrix whose square root 
-      *                is to be computed.
-      *
-      * The class stores a reference to \p A, so it should not be
-      * changed (or destroyed) before compute() is called.
-      */
-    explicit MatrixSquareRootQuasiTriangular(const MatrixType& A) 
-      : m_A(A) 
-    {
-      eigen_assert(A.rows() == A.cols());
-    }
-    
-    /** \brief Compute the matrix square root
-      *
-      * \param[out] result  square root of \p A, as specified in the constructor.
-      *
-      * Only the upper Hessenberg part of \p result is updated, the
-      * rest is not touched.  See MatrixBase::sqrt() for details on
-      * how this computation is implemented.
-      */
-    template <typename ResultType> void compute(ResultType &result);    
-    
-  private:
-    typedef typename MatrixType::Index Index;
-    typedef typename MatrixType::Scalar Scalar;
-    
-    void computeDiagonalPartOfSqrt(MatrixType& sqrtT, const MatrixType& T);
-    void computeOffDiagonalPartOfSqrt(MatrixType& sqrtT, const MatrixType& T);
-    void compute2x2diagonalBlock(MatrixType& sqrtT, const MatrixType& T, typename MatrixType::Index i);
-    void compute1x1offDiagonalBlock(MatrixType& sqrtT, const MatrixType& T, 
-				  typename MatrixType::Index i, typename MatrixType::Index j);
-    void compute1x2offDiagonalBlock(MatrixType& sqrtT, const MatrixType& T, 
-				  typename MatrixType::Index i, typename MatrixType::Index j);
-    void compute2x1offDiagonalBlock(MatrixType& sqrtT, const MatrixType& T, 
-				  typename MatrixType::Index i, typename MatrixType::Index j);
-    void compute2x2offDiagonalBlock(MatrixType& sqrtT, const MatrixType& T, 
-				  typename MatrixType::Index i, typename MatrixType::Index j);
-  
-    template <typename SmallMatrixType>
-    static void solveAuxiliaryEquation(SmallMatrixType& X, const SmallMatrixType& A, 
-				     const SmallMatrixType& B, const SmallMatrixType& C);
-  
-    const MatrixType& m_A;
-};
-
-template <typename MatrixType>
-template <typename ResultType> 
-void MatrixSquareRootQuasiTriangular<MatrixType>::compute(ResultType &result)
-{
-  result.resize(m_A.rows(), m_A.cols());
-  computeDiagonalPartOfSqrt(result, m_A);
-  computeOffDiagonalPartOfSqrt(result, m_A);
-}
-
-// pre:  T is quasi-upper-triangular and sqrtT is a zero matrix of the same size
-// post: the diagonal blocks of sqrtT are the square roots of the diagonal blocks of T
-template <typename MatrixType>
-void MatrixSquareRootQuasiTriangular<MatrixType>::computeDiagonalPartOfSqrt(MatrixType& sqrtT, 
-									  const MatrixType& T)
-{
-  using std::sqrt;
-  const Index size = m_A.rows();
-  for (Index i = 0; i < size; i++) {
-    if (i == size - 1 || T.coeff(i+1, i) == 0) {
-      eigen_assert(T(i,i) >= 0);
-      sqrtT.coeffRef(i,i) = sqrt(T.coeff(i,i));
-    }
-    else {
-      compute2x2diagonalBlock(sqrtT, T, i);
-      ++i;
-    }
-  }
-}
-
-// pre:  T is quasi-upper-triangular and diagonal blocks of sqrtT are square root of diagonal blocks of T.
-// post: sqrtT is the square root of T.
-template <typename MatrixType>
-void MatrixSquareRootQuasiTriangular<MatrixType>::computeOffDiagonalPartOfSqrt(MatrixType& sqrtT, 
-									     const MatrixType& T)
-{
-  const Index size = m_A.rows();
-  for (Index j = 1; j < size; j++) {
-      if (T.coeff(j, j-1) != 0)  // if T(j-1:j, j-1:j) is a 2-by-2 block
-	continue;
-    for (Index i = j-1; i >= 0; i--) {
-      if (i > 0 && T.coeff(i, i-1) != 0)  // if T(i-1:i, i-1:i) is a 2-by-2 block
-	continue;
-      bool iBlockIs2x2 = (i < size - 1) && (T.coeff(i+1, i) != 0);
-      bool jBlockIs2x2 = (j < size - 1) && (T.coeff(j+1, j) != 0);
-      if (iBlockIs2x2 && jBlockIs2x2) 
-	compute2x2offDiagonalBlock(sqrtT, T, i, j);
-      else if (iBlockIs2x2 && !jBlockIs2x2) 
-	compute2x1offDiagonalBlock(sqrtT, T, i, j);
-      else if (!iBlockIs2x2 && jBlockIs2x2) 
-	compute1x2offDiagonalBlock(sqrtT, T, i, j);
-      else if (!iBlockIs2x2 && !jBlockIs2x2) 
-	compute1x1offDiagonalBlock(sqrtT, T, i, j);
-    }
-  }
-}
 
 // pre:  T.block(i,i,2,2) has complex conjugate eigenvalues
 // post: sqrtT.block(i,i,2,2) is square root of T.block(i,i,2,2)
-template <typename MatrixType>
+template <typename MatrixType, typename ResultType>
-void MatrixSquareRootQuasiTriangular<MatrixType>
+void matrix_sqrt_quasi_triangular_2x2_diagonal_block(const MatrixType& T, typename MatrixType::Index i, ResultType& sqrtT)
-     ::compute2x2diagonalBlock(MatrixType& sqrtT, const MatrixType& T, typename MatrixType::Index i)
 {
   // TODO: This case (2-by-2 blocks with complex conjugate eigenvalues) is probably hidden somewhere
   //       in EigenSolver. If we expose it, we could call it directly from here.
+  typedef typename traits<MatrixType>::Scalar Scalar;
   Matrix<Scalar,2,2> block = T.template block<2,2>(i,i);
   EigenSolver<Matrix<Scalar,2,2> > es(block);
   sqrtT.template block<2,2>(i,i)
@@ -148,21 +31,19 @@ void MatrixSquareRootQuasiTriangular<MatrixType>
 // pre:  block structure of T is such that (i,j) is a 1x1 block,
 //       all blocks of sqrtT to left of and below (i,j) are correct
 // post: sqrtT(i,j) has the correct value
-template <typename MatrixType>
+template <typename MatrixType, typename ResultType>
-void MatrixSquareRootQuasiTriangular<MatrixType>
+void matrix_sqrt_quasi_triangular_1x1_off_diagonal_block(const MatrixType& T, typename MatrixType::Index i, typename MatrixType::Index j, ResultType& sqrtT)
-     ::compute1x1offDiagonalBlock(MatrixType& sqrtT, const MatrixType& T, 
-				  typename MatrixType::Index i, typename MatrixType::Index j)
 {
+  typedef typename traits<MatrixType>::Scalar Scalar;
   Scalar tmp = (sqrtT.row(i).segment(i+1,j-i-1) * sqrtT.col(j).segment(i+1,j-i-1)).value();
   sqrtT.coeffRef(i,j) = (T.coeff(i,j) - tmp) / (sqrtT.coeff(i,i) + sqrtT.coeff(j,j));
 }
 
 // similar to compute1x1offDiagonalBlock()
-template <typename MatrixType>
+template <typename MatrixType, typename ResultType>
-void MatrixSquareRootQuasiTriangular<MatrixType>
+void matrix_sqrt_quasi_triangular_1x2_off_diagonal_block(const MatrixType& T, typename MatrixType::Index i, typename MatrixType::Index j, ResultType& sqrtT)
-     ::compute1x2offDiagonalBlock(MatrixType& sqrtT, const MatrixType& T, 
-				  typename MatrixType::Index i, typename MatrixType::Index j)
 {
+  typedef typename traits<MatrixType>::Scalar Scalar;
   Matrix<Scalar,1,2> rhs = T.template block<1,2>(i,j);
   if (j-i > 1)
     rhs -= sqrtT.block(i, i+1, 1, j-i-1) * sqrtT.block(i+1, j, j-i-1, 2);
@@ -172,11 +53,10 @@ void MatrixSquareRootQuasiTriangular<MatrixType>
 }
 
 // similar to compute1x1offDiagonalBlock()
-template <typename MatrixType>
+template <typename MatrixType, typename ResultType>
-void MatrixSquareRootQuasiTriangular<MatrixType>
+void matrix_sqrt_quasi_triangular_2x1_off_diagonal_block(const MatrixType& T, typename MatrixType::Index i, typename MatrixType::Index j, ResultType& sqrtT)
-     ::compute2x1offDiagonalBlock(MatrixType& sqrtT, const MatrixType& T, 
-				  typename MatrixType::Index i, typename MatrixType::Index j)
 {
+  typedef typename traits<MatrixType>::Scalar Scalar;
   Matrix<Scalar,2,1> rhs = T.template block<2,1>(i,j);
   if (j-i > 2)
     rhs -= sqrtT.block(i, i+2, 2, j-i-2) * sqrtT.block(i+2, j, j-i-2, 1);
@@ -186,31 +66,25 @@ void MatrixSquareRootQuasiTriangular<MatrixType>
 }
 
 // similar to compute1x1offDiagonalBlock()
-template <typename MatrixType>
+template <typename MatrixType, typename ResultType>
-void MatrixSquareRootQuasiTriangular<MatrixType>
+void matrix_sqrt_quasi_triangular_2x2_off_diagonal_block(const MatrixType& T, typename MatrixType::Index i, typename MatrixType::Index j, ResultType& sqrtT)
-     ::compute2x2offDiagonalBlock(MatrixType& sqrtT, const MatrixType& T, 
-				  typename MatrixType::Index i, typename MatrixType::Index j)
 {
+  typedef typename traits<MatrixType>::Scalar Scalar;
   Matrix<Scalar,2,2> A = sqrtT.template block<2,2>(i,i);
   Matrix<Scalar,2,2> B = sqrtT.template block<2,2>(j,j);
   Matrix<Scalar,2,2> C = T.template block<2,2>(i,j);
   if (j-i > 2)
     C -= sqrtT.block(i, i+2, 2, j-i-2) * sqrtT.block(i+2, j, j-i-2, 2);
   Matrix<Scalar,2,2> X;
-  solveAuxiliaryEquation(X, A, B, C);
+  matrix_sqrt_quasi_triangular_solve_auxiliary_equation(X, A, B, C);
   sqrtT.template block<2,2>(i,j) = X;
 }
 
 // solves the equation A X + X B = C where all matrices are 2-by-2
 template <typename MatrixType>
-template <typename SmallMatrixType>
+void matrix_sqrt_quasi_triangular_solve_auxiliary_equation(MatrixType& X, const MatrixType& A, const MatrixType& B, const MatrixType& C)
-void MatrixSquareRootQuasiTriangular<MatrixType>
-     ::solveAuxiliaryEquation(SmallMatrixType& X, const SmallMatrixType& A,
-			      const SmallMatrixType& B, const SmallMatrixType& C)
 {
-  EIGEN_STATIC_ASSERT((internal::is_same<SmallMatrixType, Matrix<Scalar,2,2> >::value),
+  typedef typename traits<MatrixType>::Scalar Scalar;
-		      EIGEN_INTERNAL_ERROR_PLEASE_FILE_A_BUG_REPORT);
-
   Matrix<Scalar,4,4> coeffMatrix = Matrix<Scalar,4,4>::Zero();
   coeffMatrix.coeffRef(0,0) = A.coeff(0,0) + B.coeff(0,0);
   coeffMatrix.coeffRef(1,1) = A.coeff(0,0) + B.coeff(1,1);
@@ -241,164 +115,193 @@ void MatrixSquareRootQuasiTriangular<MatrixType>
 }
 
 
+// pre:  T is quasi-upper-triangular and sqrtT is a zero matrix of the same size
+// post: the diagonal blocks of sqrtT are the square roots of the diagonal blocks of T
+template <typename MatrixType, typename ResultType>
+void matrix_sqrt_quasi_triangular_diagonal(const MatrixType& T, ResultType& sqrtT)
+{
+  using std::sqrt;
+  typedef typename MatrixType::Index Index;
+  const Index size = T.rows();
+  for (Index i = 0; i < size; i++) {
+    if (i == size - 1 || T.coeff(i+1, i) == 0) {
+      eigen_assert(T(i,i) >= 0);
+      sqrtT.coeffRef(i,i) = sqrt(T.coeff(i,i));
+    }
+    else {
+      matrix_sqrt_quasi_triangular_2x2_diagonal_block(T, i, sqrtT);
+      ++i;
+    }
+  }
+}
+
+// pre:  T is quasi-upper-triangular and diagonal blocks of sqrtT are square root of diagonal blocks of T.
+// post: sqrtT is the square root of T.
+template <typename MatrixType, typename ResultType>
+void matrix_sqrt_quasi_triangular_off_diagonal(const MatrixType& T, ResultType& sqrtT)
+{
+  typedef typename MatrixType::Index Index;
+  const Index size = T.rows();
+  for (Index j = 1; j < size; j++) {
+      if (T.coeff(j, j-1) != 0)  // if T(j-1:j, j-1:j) is a 2-by-2 block
+	continue;
+    for (Index i = j-1; i >= 0; i--) {
+      if (i > 0 && T.coeff(i, i-1) != 0)  // if T(i-1:i, i-1:i) is a 2-by-2 block
+	continue;
+      bool iBlockIs2x2 = (i < size - 1) && (T.coeff(i+1, i) != 0);
+      bool jBlockIs2x2 = (j < size - 1) && (T.coeff(j+1, j) != 0);
+      if (iBlockIs2x2 && jBlockIs2x2) 
+        matrix_sqrt_quasi_triangular_2x2_off_diagonal_block(T, i, j, sqrtT);
+      else if (iBlockIs2x2 && !jBlockIs2x2) 
+        matrix_sqrt_quasi_triangular_2x1_off_diagonal_block(T, i, j, sqrtT);
+      else if (!iBlockIs2x2 && jBlockIs2x2) 
+        matrix_sqrt_quasi_triangular_1x2_off_diagonal_block(T, i, j, sqrtT);
+      else if (!iBlockIs2x2 && !jBlockIs2x2) 
+        matrix_sqrt_quasi_triangular_1x1_off_diagonal_block(T, i, j, sqrtT);
+    }
+  }
+}
+
+} // end of namespace internal
+
 /** \ingroup MatrixFunctions_Module
-  * \brief Class for computing matrix square roots of upper triangular matrices.
+  * \brief Compute matrix square root of quasi-triangular matrix.
-  * \tparam  MatrixType  type of the argument of the matrix square root,
-  *                      expected to be an instantiation of the Matrix class template.
   *
-  * This class computes the square root of the upper triangular matrix
+  * \tparam  MatrixType  type of \p arg, the argument of matrix square root,
-  * stored in the upper triangular part (including the diagonal) of
+  *                      expected to be an instantiation of the Matrix class template.
-  * the matrix passed to the constructor.
+  * \tparam  ResultType  type of \p result, where result is to be stored.
+  * \param[in]  arg      argument of matrix square root.
+  * \param[out] result   matrix square root of upper Hessenberg part of \p arg.
+  *
+  * This function computes the square root of the upper quasi-triangular matrix stored in the upper
+  * Hessenberg part of \p arg.  Only the upper Hessenberg part of \p result is updated, the rest is
+  * not touched.  See MatrixBase::sqrt() for details on how this computation is implemented.
   *
   * \sa MatrixSquareRoot, MatrixSquareRootQuasiTriangular
   */
-template <typename MatrixType>
+template <typename MatrixType, typename ResultType> 
-class MatrixSquareRootTriangular : internal::noncopyable
+void matrix_sqrt_quasi_triangular(const MatrixType &arg, ResultType &result)
 {
-  public:
+  eigen_assert(arg.rows() == arg.cols());
-    explicit MatrixSquareRootTriangular(const MatrixType& A) 
+  result.resize(arg.rows(), arg.cols());
-      : m_A(A) 
+  internal::matrix_sqrt_quasi_triangular_diagonal(arg, result);
-    {
+  internal::matrix_sqrt_quasi_triangular_off_diagonal(arg, result);
-      eigen_assert(A.rows() == A.cols());
+}
-    }
 
-    /** \brief Compute the matrix square root
-      *
-      * \param[out] result  square root of \p A, as specified in the constructor.
-      *
-      * Only the upper triangular part (including the diagonal) of 
-      * \p result is updated, the rest is not touched.  See
-      * MatrixBase::sqrt() for details on how this computation is
-      * implemented.
-      */
-    template <typename ResultType> void compute(ResultType &result);    
 
- private:
+/** \ingroup MatrixFunctions_Module
-    const MatrixType& m_A;
+  * \brief Compute matrix square root of triangular matrix.
-};
+  *
-
+  * \tparam  MatrixType  type of \p arg, the argument of matrix square root,
-template <typename MatrixType>
+  *                      expected to be an instantiation of the Matrix class template.
-template <typename ResultType> 
+  * \tparam  ResultType  type of \p result, where result is to be stored.
-void MatrixSquareRootTriangular<MatrixType>::compute(ResultType &result)
+  * \param[in]  arg      argument of matrix square root.
+  * \param[out] result   matrix square root of upper triangular part of \p arg.
+  *
+  * Only the upper triangular part (including the diagonal) of \p result is updated, the rest is not
+  * touched.  See MatrixBase::sqrt() for details on how this computation is implemented.
+  *
+  * \sa MatrixSquareRoot, MatrixSquareRootQuasiTriangular
+  */
+template <typename MatrixType, typename ResultType> 
+void matrix_sqrt_triangular(const MatrixType &arg, ResultType &result)
 {
   using std::sqrt;
-
-  // Compute square root of m_A and store it in upper triangular part of result
-  // This uses that the square root of triangular matrices can be computed directly.
-  result.resize(m_A.rows(), m_A.cols());
   typedef typename MatrixType::Index Index;
-  for (Index i = 0; i < m_A.rows(); i++) {
-    result.coeffRef(i,i) = sqrt(m_A.coeff(i,i));
-  }
-  for (Index j = 1; j < m_A.cols(); j++) {
-    for (Index i = j-1; i >= 0; i--) {
       typedef typename MatrixType::Scalar Scalar;
+
+  eigen_assert(arg.rows() == arg.cols());
+
+  // Compute square root of arg and store it in upper triangular part of result
+  // This uses that the square root of triangular matrices can be computed directly.
+  result.resize(arg.rows(), arg.cols());
+  for (Index i = 0; i < arg.rows(); i++) {
+    result.coeffRef(i,i) = sqrt(arg.coeff(i,i));
+  }
+  for (Index j = 1; j < arg.cols(); j++) {
+    for (Index i = j-1; i >= 0; i--) {
       // if i = j-1, then segment has length 0 so tmp = 0
       Scalar tmp = (result.row(i).segment(i+1,j-i-1) * result.col(j).segment(i+1,j-i-1)).value();
       // denominator may be zero if original matrix is singular
-      result.coeffRef(i,j) = (m_A.coeff(i,j) - tmp) / (result.coeff(i,i) + result.coeff(j,j));
+      result.coeffRef(i,j) = (arg.coeff(i,j) - tmp) / (result.coeff(i,i) + result.coeff(j,j));
     }
   }
 }
 
 
+namespace internal {
+
 /** \ingroup MatrixFunctions_Module
-  * \brief Class for computing matrix square roots of general matrices.
+  * \brief Helper struct for computing matrix square roots of general matrices.
   * \tparam  MatrixType  type of the argument of the matrix square root,
   *                      expected to be an instantiation of the Matrix class template.
   *
   * \sa MatrixSquareRootTriangular, MatrixSquareRootQuasiTriangular, MatrixBase::sqrt()
   */
 template <typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex>
-class MatrixSquareRoot
+struct matrix_sqrt_compute
 {
-  public:
+  /** \brief Compute the matrix square root
-
+    *
-    /** \brief Constructor. 
+    * \param[in]  arg     matrix whose square root is to be computed.
-      *
+    * \param[out] result  square root of \p arg.
-      * \param[in]  A  matrix whose square root is to be computed.
+    *
-      *
+    * See MatrixBase::sqrt() for details on how this computation is implemented.
-      * The class stores a reference to \p A, so it should not be
+    */
-      * changed (or destroyed) before compute() is called.
+  template <typename ResultType> static void run(const MatrixType &arg, ResultType &result);    
-      */
-    explicit MatrixSquareRoot(const MatrixType& A); 
-    
-    /** \brief Compute the matrix square root
-      *
-      * \param[out] result  square root of \p A, as specified in the constructor.
-      *
-      * See MatrixBase::sqrt() for details on how this computation is
-      * implemented.
-      */
-    template <typename ResultType> void compute(ResultType &result);    
 };
 
 
 // ********** Partial specialization for real matrices **********
 
 template <typename MatrixType>
-class MatrixSquareRoot<MatrixType, 0>
+struct matrix_sqrt_compute<MatrixType, 0>
 {
-  public:
+  template <typename ResultType>
+  static void run(const MatrixType &arg, ResultType &result)
+  {
+    eigen_assert(arg.rows() == arg.cols());
 
-    explicit MatrixSquareRoot(const MatrixType& A) 
+    // Compute Schur decomposition of arg
-      : m_A(A) 
+    const RealSchur<MatrixType> schurOfA(arg);  
-    {  
+    const MatrixType& T = schurOfA.matrixT();
-      eigen_assert(A.rows() == A.cols());
+    const MatrixType& U = schurOfA.matrixU();
-    }
     
-    template <typename ResultType> void compute(ResultType &result)
+    // Compute square root of T
-    {
+    MatrixType sqrtT = MatrixType::Zero(arg.rows(), arg.cols());
-      // Compute Schur decomposition of m_A
+    matrix_sqrt_quasi_triangular(T, sqrtT);
-      const RealSchur<MatrixType> schurOfA(m_A);  
-      const MatrixType& T = schurOfA.matrixT();
-      const MatrixType& U = schurOfA.matrixU();
     
-      // Compute square root of T
+    // Compute square root of arg
-      MatrixType sqrtT = MatrixType::Zero(m_A.rows(), m_A.cols());
+    result = U * sqrtT * U.adjoint();
-      MatrixSquareRootQuasiTriangular<MatrixType>(T).compute(sqrtT);
+  }
-    
-      // Compute square root of m_A
-      result = U * sqrtT * U.adjoint();
-    }
-    
-  private:
-    const MatrixType& m_A;
 };
 
 
 // ********** Partial specialization for complex matrices **********
 
 template <typename MatrixType>
-class MatrixSquareRoot<MatrixType, 1> : internal::noncopyable
+struct matrix_sqrt_compute<MatrixType, 1>
 {
-  public:
+  template <typename ResultType>
+  static void run(const MatrixType &arg, ResultType &result)
+  {
+    eigen_assert(arg.rows() == arg.cols());
 
-    explicit MatrixSquareRoot(const MatrixType& A) 
+    // Compute Schur decomposition of arg
-      : m_A(A) 
+    const ComplexSchur<MatrixType> schurOfA(arg);  
-    {  
+    const MatrixType& T = schurOfA.matrixT();
-      eigen_assert(A.rows() == A.cols());
+    const MatrixType& U = schurOfA.matrixU();
-    }
     
-    template <typename ResultType> void compute(ResultType &result)
+    // Compute square root of T
-    {
+    MatrixType sqrtT;
-      // Compute Schur decomposition of m_A
+    matrix_sqrt_triangular(T, sqrtT);
-      const ComplexSchur<MatrixType> schurOfA(m_A);  
-      const MatrixType& T = schurOfA.matrixT();
-      const MatrixType& U = schurOfA.matrixU();
     
-      // Compute square root of T
+    // Compute square root of arg
-      MatrixType sqrtT;
+    result = U * (sqrtT.template triangularView<Upper>() * U.adjoint());
-      MatrixSquareRootTriangular<MatrixType>(T).compute(sqrtT);
+  }
-    
-      // Compute square root of m_A
-      result = U * (sqrtT.template triangularView<Upper>() * U.adjoint());
-    }
-    
-  private:
-    const MatrixType& m_A;
 };
 
+} // end namespace internal
 
 /** \ingroup MatrixFunctions_Module
   *
@@ -432,9 +335,9 @@ template<typename Derived> class MatrixSquareRootReturnValue
     template <typename ResultType>
     inline void evalTo(ResultType& result) const
     {
-      const typename Derived::PlainObject srcEvaluated = m_src.eval();
+      typedef typename Derived::PlainObject PlainObject;
-      MatrixSquareRoot<typename Derived::PlainObject> me(srcEvaluated);
+      const PlainObject srcEvaluated = m_src.eval();
-      me.compute(result);
+      internal::matrix_sqrt_compute<PlainObject>::run(srcEvaluated, result);
     }
 
     Index rows() const { return m_src.rows(); }

unsupported/test/matrix_power.cpp

@@ -100,8 +100,6 @@ template<typename MatrixType>
 void testSingular(MatrixType m, double tol)
 {
   const int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex;
-  typedef typename internal::conditional< IsComplex, MatrixSquareRootTriangular<MatrixType>,
-          MatrixSquareRootQuasiTriangular<MatrixType> >::type SquareRootType;
   typedef typename internal::conditional<IsComplex, TriangularView<MatrixType,Upper>, const MatrixType&>::type TriangularType;
   typename internal::conditional< IsComplex, ComplexSchur<MatrixType>, RealSchur<MatrixType> >::type schur;
   MatrixType T;
@@ -116,13 +114,13 @@ void testSingular(MatrixType m, double tol)
     processTriangularMatrix<MatrixType>::run(m, T, U);
     MatrixPower<MatrixType> mpow(m);
 
-    SquareRootType(T).compute(T);
+    T = T.sqrt();
     VERIFY(mpow(0.5).isApprox(U * (TriangularType(T) * U.adjoint()), tol));
 
-    SquareRootType(T).compute(T);
+    T = T.sqrt();
     VERIFY(mpow(0.25).isApprox(U * (TriangularType(T) * U.adjoint()), tol));
 
-    SquareRootType(T).compute(T);
+    T = T.sqrt();
     VERIFY(mpow(0.125).isApprox(U * (TriangularType(T) * U.adjoint()), tol));
   }
 }