Abort the extension. MatrixSquareRootTriangular only takes upper triangular matrices.

1 files changed, 51 insertions, 165 deletions

diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixPowerBase.h b/unsupported/Eigen/src/MatrixFunctions/MatrixPowerBase.h
index e83d4abfd..9616659ca 100644
--- a/unsupported/Eigen/src/MatrixFunctions/MatrixPowerBase.h
+++ b/unsupported/Eigen/src/MatrixFunctions/MatrixPowerBase.h
@@ -82,21 +82,21 @@ inline int matrix_power_get_pade_degree(double normIminusT)
 inline int matrix_power_get_pade_degree(long double normIminusT)
 {
 #if   LDBL_MANT_DIG == 53
-  enum { maxPadeDegree = 7 };
+  const int maxPadeDegree = 7;
   const double maxNormForPade[] = { 1.884160592658218e-2L /* degree = 3 */ , 6.038881904059573e-2L, 1.239917516308172e-1L,
       1.999045567181744e-1L, 2.789358995219730e-1L };
 #elif LDBL_MANT_DIG <= 64
-  enum { maxPadeDegree = 8 };
+  const int maxPadeDegree = 8;
   const double maxNormForPade[] = { 6.3854693117491799460e-3L /* degree = 3 */ , 2.6394893435456973676e-2L,
       6.4216043030404063729e-2L, 1.1701165502926694307e-1L, 1.7904284231268670284e-1L, 2.4471944416607995472e-1L };
 #elif LDBL_MANT_DIG <= 106
-  enum { maxPadeDegree = 10 };
+  const int maxPadeDegree = 10;
   const double maxNormForPade[] = { 1.0007161601787493236741409687186e-4L /* degree = 3 */ ,
       1.0007161601787493236741409687186e-3L, 4.7069769360887572939882574746264e-3L, 1.3220386624169159689406653101695e-2L,
       2.8063482381631737920612944054906e-2L, 4.9625993951953473052385361085058e-2L, 7.7367040706027886224557538328171e-2L,
       1.1016843812851143391275867258512e-1L };
 #else
-  enum { maxPadeDegree = 10 };
+  const int maxPadeDegree = 10;
   const double maxNormForPade[] = { 5.524506147036624377378713555116378e-5L /* degree = 3 */ ,
       6.640600568157479679823602193345995e-4L, 3.227716520106894279249709728084626e-3L,
       9.619593944683432960546978734646284e-3L, 2.134595382433742403911124458161147e-2L,
@@ -111,126 +111,7 @@ inline int matrix_power_get_pade_degree(long double normIminusT)
 }
 } // namespace internal
 
-#define MATRIX_POWER_TRIANGULAR_2x2_SPECIALIZATION(Mode) \
-  template<typename MatrixType> \
-  class MatrixPowerTriangular2x2<MatrixType,Mode> \
-  { \
-    private: \
-      enum { \
-	RowsAtCompileTime = MatrixType::RowsAtCompileTime, \
-	MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime \
-      }; \
-      typedef typename MatrixType::Scalar Scalar; \
-      typedef typename MatrixType::RealScalar RealScalar; \
-      typedef Array<Scalar,RowsAtCompileTime,1,ColMajor,MaxRowsAtCompileTime> ArrayType; \
-      const MatrixType& m_T; \
-    public: \
-      explicit MatrixPowerTriangular2x2(const MatrixType& T) : m_T(T) { } \
-      void compute(MatrixType& res, RealScalar p) const; \
-  };
-
-template<typename MatrixType, unsigned int Mode>
-class MatrixPowerTriangular2x2;
-
-MATRIX_POWER_TRIANGULAR_2x2_SPECIALIZATION(Upper)
-MATRIX_POWER_TRIANGULAR_2x2_SPECIALIZATION(Lower)
-MATRIX_POWER_TRIANGULAR_2x2_SPECIALIZATION(UnitUpper)
-MATRIX_POWER_TRIANGULAR_2x2_SPECIALIZATION(UnitLower)
-MATRIX_POWER_TRIANGULAR_2x2_SPECIALIZATION(StrictlyUpper)
-MATRIX_POWER_TRIANGULAR_2x2_SPECIALIZATION(StrictlyLower)
-
-template<typename MatrixType>
-void MatrixPowerTriangular2x2<MatrixType,Upper>::compute(MatrixType& res, RealScalar p) const
-{
-  using std::abs;
-  using std::pow;
-  
-  ArrayType logTdiag = m_T.diagonal().array().log();
-  res.coeffRef(0,0) = pow(m_T.coeff(0,0), p);
-
-  for (int i=1; i < m_T.cols(); ++i) {
-    res.coeffRef(i,i) = pow(m_T.coeff(i,i), p);
-    if (m_T.coeff(i-1,i-1) == m_T.coeff(i,i)) {
-      res.coeffRef(i-1,i) = p * pow(m_T.coeff(i-1,i), p-1);
-    }
-    else if (2*abs(m_T.coeff(i-1,i-1)) < abs(m_T.coeff(i,i)) || 2*abs(m_T.coeff(i,i)) < abs(m_T.coeff(i-1,i-1))) {
-      res.coeffRef(i-1,i) = m_T.coeff(i-1,i) * (res.coeff(i,i)-res.coeff(i-1,i-1)) / (m_T.coeff(i,i)-m_T.coeff(i-1,i-1));
-    }
-    else {
-      int unwindingNumber = std::ceil((internal::imag(logTdiag[i]-logTdiag[i-1]) - M_PI) / (2*M_PI));
-      Scalar w = internal::matrix_power_unwinder<Scalar>::run(m_T.coeff(i,i), m_T.coeff(i-1,i-1), unwindingNumber);
-      res.coeffRef(i-1,i) = m_T.coeff(i-1,i) * RealScalar(2) * std::exp(RealScalar(0.5)*p*(logTdiag[i]+logTdiag[i-1])) *
-	  std::sinh(p * w) / (m_T.coeff(i,i) - m_T.coeff(i-1,i-1));
-    }
-  }
-}
-
-template<typename MatrixType>
-void MatrixPowerTriangular2x2<MatrixType,Lower>::compute(MatrixType& res, RealScalar p) const
-{
-  using std::abs;
-  using std::pow;
-  
-  ArrayType logTdiag = m_T.diagonal().array().log();
-  res.coeffRef(0,0) = pow(m_T.coeff(0,0), p);
-
-  for (int i=1; i < m_T.cols(); ++i) {
-    res.coeffRef(i,i) = pow(m_T.coeff(i,i), p);
-    if (m_T.coeff(i-1,i-1) == m_T.coeff(i,i)) {
-      res.coeffRef(i,i-1) = p * pow(m_T.coeff(i,i-1), p-1);
-    }
-    else if (2*abs(m_T.coeff(i-1,i-1)) < abs(m_T.coeff(i,i)) || 2*abs(m_T.coeff(i,i)) < abs(m_T.coeff(i-1,i-1))) {
-      res.coeffRef(i,i-1) = m_T.coeff(i,i-1) * (res.coeff(i,i)-res.coeff(i-1,i-1)) / (m_T.coeff(i,i)-m_T.coeff(i-1,i-1));
-    }
-    else {
-      int unwindingNumber = std::ceil((internal::imag(logTdiag[i]-logTdiag[i-1]) - M_PI) / (2*M_PI));
-      Scalar w = internal::matrix_power_unwinder<Scalar>::run(m_T.coeff(i,i), m_T.coeff(i-1,i-1), unwindingNumber);
-      res.coeffRef(i,i-1) = m_T.coeff(i,i-1) * RealScalar(2) * std::exp(RealScalar(0.5)*p*(logTdiag[i]+logTdiag[i-1])) *
-	  std::sinh(p * w) / (m_T.coeff(i,i) - m_T.coeff(i-1,i-1));
-    }
-  }
-}
-
-template<typename MatrixType>
-void MatrixPowerTriangular2x2<MatrixType,UnitUpper>::compute(MatrixType& res, RealScalar p) const
-{
-  for (int i=1; i < m_T.cols(); ++i)
-    res.coeffRef(i-1,i) = p * std::pow(m_T.coeff(i-1,i), p-1);
-}
-
-template<typename MatrixType>
-void MatrixPowerTriangular2x2<MatrixType,UnitLower>::compute(MatrixType& res, RealScalar p) const
-{
-  for (int i=1; i < m_T.cols(); ++i) {
-    res.coeffRef(i,i-1) = p * std::pow(m_T.coeff(i,i-1), p-1);
-  }
-}
-
-template<typename MatrixType>
-void MatrixPowerTriangular2x2<MatrixType,StrictlyUpper>::compute(MatrixType& res, RealScalar p) const
-{
-  RealScalar diag   = !p ? 1 : 0;
-  res.coeffRef(0,0) = diag;
-
-  for (int i=1; i < m_T.cols(); ++i) {
-    res.coeffRef(i,i)   = diag;
-    res.coeffRef(i-1,i) = p * std::pow(m_T.coeff(i-1,i), p-1);
-  }
-}
-
 template<typename MatrixType>
-void MatrixPowerTriangular2x2<MatrixType,StrictlyLower>::compute(MatrixType& res, RealScalar p) const
-{
-  RealScalar diag   = !p ? 1 : 0;
-  res.coeffRef(0,0) = diag;
-
-  for (int i=1; i < m_T.cols(); ++i) {
-    res.coeffRef(i,i)   = diag;
-    res.coeffRef(i,i-1) = p * std::pow(m_T.coeff(i,i-1), p-1);
-  }
-}
-
-template<typename MatrixType, unsigned int Mode=Upper>
 class MatrixPowerTriangularAtomic
 {
   private:
@@ -246,6 +127,7 @@ class MatrixPowerTriangularAtomic
     const MatrixType m_Id;
 
     void computePade(int degree, const MatrixType& IminusT, MatrixType& res, RealScalar p) const;
+    void compute2x2(MatrixType& res, RealScalar p) const;
     void computeBig(MatrixType& res, RealScalar p) const;
 
   public:
@@ -253,14 +135,14 @@ class MatrixPowerTriangularAtomic
     void compute(MatrixType& res, RealScalar p) const;
 };
 
-template<typename MatrixType, unsigned int Mode>
-MatrixPowerTriangularAtomic<MatrixType,Mode>::MatrixPowerTriangularAtomic(const MatrixType& T) :
+template<typename MatrixType>
+MatrixPowerTriangularAtomic<MatrixType>::MatrixPowerTriangularAtomic(const MatrixType& T) :
   m_T(T),
   m_Id(MatrixType::Identity(T.rows(), T.cols()))
-{ }
+{ eigen_assert(T.rows() == T.cols()); }
 
-template<typename MatrixType, unsigned int Mode>
-void MatrixPowerTriangularAtomic<MatrixType,Mode>::compute(MatrixType& res, RealScalar p) const
+template<typename MatrixType>
+void MatrixPowerTriangularAtomic<MatrixType>::compute(MatrixType& res, RealScalar p) const
 {
   switch (m_T.rows()) {
     case 0:
@@ -269,39 +151,65 @@ void MatrixPowerTriangularAtomic<MatrixType,Mode>::compute(MatrixType& res, Real
       res(0,0) = std::pow(m_T(0,0), p);
       break;
     case 2:
-      MatrixPowerTriangular2x2<MatrixType,Mode>(m_T).compute(res, p);
+      compute2x2(res, p);
       break;
     default:
       computeBig(res, p);
   }
 }
 
-template<typename MatrixType, unsigned int Mode>
-void MatrixPowerTriangularAtomic<MatrixType,Mode>::computePade(int degree, const MatrixType& IminusT, MatrixType& res,
+template<typename MatrixType>
+void MatrixPowerTriangularAtomic<MatrixType>::computePade(int degree, const MatrixType& IminusT, MatrixType& res,
   RealScalar p) const
 {
   int i = degree<<1;
   res = (p-degree) / ((i-1)<<1) * IminusT;
   for (--i; i; --i) {
-    res = (m_Id + res).template triangularView<Mode>().solve((i==1 ? -p : i&1 ? (-p-(i>>1))/(i<<1) :
+    res = (m_Id + res).template triangularView<Upper>().solve((i==1 ? -p : i&1 ? (-p-(i>>1))/(i<<1) :
 	(p-(i>>1))/((i-1)<<1)) * IminusT).eval();
   }
   res += m_Id;
 }
 
-template<typename MatrixType, unsigned int Mode>
-void MatrixPowerTriangularAtomic<MatrixType,Mode>::computeBig(MatrixType& res, RealScalar p) const
+template<typename MatrixType>
+void MatrixPowerTriangularAtomic<MatrixType>::compute2x2(MatrixType& res, RealScalar p) const
+{
+  using std::abs;
+  using std::pow;
+  
+  ArrayType logTdiag = m_T.diagonal().array().log();
+  res.coeffRef(0,0) = pow(m_T.coeff(0,0), p);
+
+  for (int i=1; i < m_T.cols(); ++i) {
+    res.coeffRef(i,i) = pow(m_T.coeff(i,i), p);
+    if (m_T.coeff(i-1,i-1) == m_T.coeff(i,i)) {
+      res.coeffRef(i-1,i) = p * pow(m_T.coeff(i-1,i), p-1);
+    }
+    else if (2*abs(m_T.coeff(i-1,i-1)) < abs(m_T.coeff(i,i)) || 2*abs(m_T.coeff(i,i)) < abs(m_T.coeff(i-1,i-1))) {
+      res.coeffRef(i-1,i) = m_T.coeff(i-1,i) * (res.coeff(i,i)-res.coeff(i-1,i-1)) / (m_T.coeff(i,i)-m_T.coeff(i-1,i-1));
+    }
+    else {
+      int unwindingNumber = std::ceil((internal::imag(logTdiag[i]-logTdiag[i-1]) - M_PI) / (2*M_PI));
+      Scalar w = internal::matrix_power_unwinder<Scalar>::run(m_T.coeff(i,i), m_T.coeff(i-1,i-1), unwindingNumber);
+      res.coeffRef(i-1,i) = m_T.coeff(i-1,i) * RealScalar(2) * std::exp(RealScalar(0.5)*p*(logTdiag[i]+logTdiag[i-1])) *
+	  std::sinh(p * w) / (m_T.coeff(i,i) - m_T.coeff(i-1,i-1));
+    }
+  }
+}
+
+template<typename MatrixType>
+void MatrixPowerTriangularAtomic<MatrixType>::computeBig(MatrixType& res, RealScalar p) const
 {
-  enum { digits = std::numeric_limits<RealScalar>::digits };
+  const int digits = std::numeric_limits<RealScalar>::digits;
   const RealScalar maxNormForPade = digits <=  24? 4.3386528e-1f:                           // sigle precision
 				    digits <=  53? 2.789358995219730e-1:                    // double precision
 				    digits <=  64? 2.4471944416607995472e-1L:               // extended precision
 				    digits <= 106? 1.1016843812851143391275867258512e-1L:   // double-double
 						   9.134603732914548552537150753385375e-2L; // quadruple precision
-  const MatrixPowerTriangular2x2<MatrixType,Mode> atomic2x2(m_T);
   MatrixType IminusT, sqrtT, T=m_T;
   RealScalar normIminusT;
-  int degree, degree2, numberOfSquareRoots=0, numberOfExtraSquareRoots=0;
+  int degree, degree2, numberOfSquareRoots=0;
+  bool hasExtraSquareRoot=false;
 
   while (true) {
     IminusT = MatrixType::Identity(m_T.rows(), m_T.cols()) - T;
@@ -309,9 +217,9 @@ void MatrixPowerTriangularAtomic<MatrixType,Mode>::computeBig(MatrixType& res, R
     if (normIminusT < maxNormForPade) {
       degree = internal::matrix_power_get_pade_degree(normIminusT);
       degree2 = internal::matrix_power_get_pade_degree(normIminusT/2);
-      if (degree - degree2 <= 1 || numberOfExtraSquareRoots)
+      if (degree - degree2 <= 1 || hasExtraSquareRoot)
 	break;
-      ++numberOfExtraSquareRoots;
+      hasExtraSquareRoot = true;
     }
     MatrixSquareRootTriangular<MatrixType>(T).compute(sqrtT);
     T = sqrtT;
@@ -320,10 +228,10 @@ void MatrixPowerTriangularAtomic<MatrixType,Mode>::computeBig(MatrixType& res, R
   computePade(degree, IminusT, res, p);
 
   for (; numberOfSquareRoots; --numberOfSquareRoots) {
-    atomic2x2.compute(res, std::ldexp(p,-numberOfSquareRoots));
+    compute2x2(res, std::ldexp(p,-numberOfSquareRoots));
     res *= res;
   }
-  atomic2x2.compute(res, p);
+  compute2x2(res, p);
 }
 
 #define EIGEN_MATRIX_POWER_PUBLIC_INTERFACE(Derived) \
@@ -391,11 +299,6 @@ class MatrixPowerBase
 
     explicit MatrixPowerBase(const MatrixType& A, RealScalar cond);
 
-    template<typename OtherDerived>
-    explicit MatrixPowerBase(const MatrixBase<OtherDerived>& A, RealScalar cond);
-
-    ~MatrixPowerBase();
-
     void compute(MatrixType& res, RealScalar p);
 
     template<typename OtherDerived, typename ResultType>
@@ -411,31 +314,14 @@ class MatrixPowerBase
     const MatrixType m_Id;
     MatrixType m_tmp1, m_tmp2;
     RealScalar m_conditionNumber;
-
-  private:
-    const bool m_del;  // whether to delete the pointer at destruction
 };
 
 template<typename Derived, typename MatrixType>
 MatrixPowerBase<Derived,MatrixType>::MatrixPowerBase(const MatrixType& A, RealScalar cond) :
   m_A(A),
   m_Id(MatrixType::Identity(A.rows(),A.cols())),
-  m_conditionNumber(cond),
-  m_del(false)
-{ }
-
-template<typename Derived, typename MatrixType>
-template<typename OtherDerived>
-MatrixPowerBase<Derived,MatrixType>::MatrixPowerBase(const MatrixBase<OtherDerived>& A, RealScalar cond) :
-  m_A(*new MatrixType(A)),
-  m_Id(MatrixType::Identity(A.rows(),A.cols())),
-  m_conditionNumber(cond),
-  m_del(true)
-{ }
-
-template<typename Derived, typename MatrixType>
-MatrixPowerBase<Derived,MatrixType>::~MatrixPowerBase()
-{ if (m_del)  delete &m_A; }
+  m_conditionNumber(cond)
+{ eigen_assert(A.rows() == A.cols()); }
 
 template<typename Derived, typename MatrixType>
 void MatrixPowerBase<Derived,MatrixType>::compute(MatrixType& res, RealScalar p)