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Abort the extension. MatrixSquareRootTriangular only takes upper triangular matrices.
This commit is contained in:
Chen-Pang He
parent
067a5a98c8
commit
5814a5f1a0
@ -82,21 +82,21 @@ inline int matrix_power_get_pade_degree(double normIminusT)
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inline int matrix_power_get_pade_degree(long double normIminusT)
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{
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#if LDBL_MANT_DIG == 53
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enum { maxPadeDegree = 7 };
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const int maxPadeDegree = 7;
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const double maxNormForPade[] = { 1.884160592658218e-2L /* degree = 3 */ , 6.038881904059573e-2L, 1.239917516308172e-1L,
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1.999045567181744e-1L, 2.789358995219730e-1L };
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#elif LDBL_MANT_DIG <= 64
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enum { maxPadeDegree = 8 };
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const int maxPadeDegree = 8;
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const double maxNormForPade[] = { 6.3854693117491799460e-3L /* degree = 3 */ , 2.6394893435456973676e-2L,
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6.4216043030404063729e-2L, 1.1701165502926694307e-1L, 1.7904284231268670284e-1L, 2.4471944416607995472e-1L };
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#elif LDBL_MANT_DIG <= 106
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enum { maxPadeDegree = 10 };
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const int maxPadeDegree = 10;
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const double maxNormForPade[] = { 1.0007161601787493236741409687186e-4L /* degree = 3 */ ,
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1.0007161601787493236741409687186e-3L, 4.7069769360887572939882574746264e-3L, 1.3220386624169159689406653101695e-2L,
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2.8063482381631737920612944054906e-2L, 4.9625993951953473052385361085058e-2L, 7.7367040706027886224557538328171e-2L,
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1.1016843812851143391275867258512e-1L };
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#else
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enum { maxPadeDegree = 10 };
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const int maxPadeDegree = 10;
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const double maxNormForPade[] = { 5.524506147036624377378713555116378e-5L /* degree = 3 */ ,
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6.640600568157479679823602193345995e-4L, 3.227716520106894279249709728084626e-3L,
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9.619593944683432960546978734646284e-3L, 2.134595382433742403911124458161147e-2L,
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@ -111,36 +111,68 @@ inline int matrix_power_get_pade_degree(long double normIminusT)
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}
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} // namespace internal
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#define MATRIX_POWER_TRIANGULAR_2x2_SPECIALIZATION(Mode) \
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template<typename MatrixType> \
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class MatrixPowerTriangular2x2<MatrixType,Mode> \
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{ \
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private: \
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enum { \
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RowsAtCompileTime = MatrixType::RowsAtCompileTime, \
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MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime \
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}; \
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typedef typename MatrixType::Scalar Scalar; \
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typedef typename MatrixType::RealScalar RealScalar; \
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typedef Array<Scalar,RowsAtCompileTime,1,ColMajor,MaxRowsAtCompileTime> ArrayType; \
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const MatrixType& m_T; \
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public: \
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explicit MatrixPowerTriangular2x2(const MatrixType& T) : m_T(T) { } \
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void compute(MatrixType& res, RealScalar p) const; \
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};
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template<typename MatrixType>
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class MatrixPowerTriangularAtomic
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{
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private:
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enum {
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RowsAtCompileTime = MatrixType::RowsAtCompileTime,
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MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime
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};
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typedef typename MatrixType::Scalar Scalar;
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typedef typename MatrixType::RealScalar RealScalar;
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typedef Array<Scalar,RowsAtCompileTime,1,ColMajor,MaxRowsAtCompileTime> ArrayType;
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template<typename MatrixType, unsigned int Mode>
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class MatrixPowerTriangular2x2;
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const MatrixType& m_T;
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const MatrixType m_Id;
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MATRIX_POWER_TRIANGULAR_2x2_SPECIALIZATION(Upper)
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MATRIX_POWER_TRIANGULAR_2x2_SPECIALIZATION(Lower)
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MATRIX_POWER_TRIANGULAR_2x2_SPECIALIZATION(UnitUpper)
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MATRIX_POWER_TRIANGULAR_2x2_SPECIALIZATION(UnitLower)
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MATRIX_POWER_TRIANGULAR_2x2_SPECIALIZATION(StrictlyUpper)
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MATRIX_POWER_TRIANGULAR_2x2_SPECIALIZATION(StrictlyLower)
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void computePade(int degree, const MatrixType& IminusT, MatrixType& res, RealScalar p) const;
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void compute2x2(MatrixType& res, RealScalar p) const;
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void computeBig(MatrixType& res, RealScalar p) const;
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public:
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explicit MatrixPowerTriangularAtomic(const MatrixType& T);
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void compute(MatrixType& res, RealScalar p) const;
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};
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template<typename MatrixType>
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void MatrixPowerTriangular2x2<MatrixType,Upper>::compute(MatrixType& res, RealScalar p) const
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MatrixPowerTriangularAtomic<MatrixType>::MatrixPowerTriangularAtomic(const MatrixType& T) :
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m_T(T),
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m_Id(MatrixType::Identity(T.rows(), T.cols()))
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{ eigen_assert(T.rows() == T.cols()); }
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template<typename MatrixType>
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void MatrixPowerTriangularAtomic<MatrixType>::compute(MatrixType& res, RealScalar p) const
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{
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switch (m_T.rows()) {
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case 0:
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break;
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case 1:
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res(0,0) = std::pow(m_T(0,0), p);
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break;
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case 2:
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compute2x2(res, p);
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break;
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default:
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computeBig(res, p);
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}
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}
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template<typename MatrixType>
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void MatrixPowerTriangularAtomic<MatrixType>::computePade(int degree, const MatrixType& IminusT, MatrixType& res,
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RealScalar p) const
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{
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int i = degree<<1;
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res = (p-degree) / ((i-1)<<1) * IminusT;
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for (--i; i; --i) {
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res = (m_Id + res).template triangularView<Upper>().solve((i==1 ? -p : i&1 ? (-p-(i>>1))/(i<<1) :
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(p-(i>>1))/((i-1)<<1)) * IminusT).eval();
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}
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res += m_Id;
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}
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template<typename MatrixType>
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void MatrixPowerTriangularAtomic<MatrixType>::compute2x2(MatrixType& res, RealScalar p) const
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{
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using std::abs;
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using std::pow;
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@ -166,142 +198,18 @@ void MatrixPowerTriangular2x2<MatrixType,Upper>::compute(MatrixType& res, RealSc
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}
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template<typename MatrixType>
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void MatrixPowerTriangular2x2<MatrixType,Lower>::compute(MatrixType& res, RealScalar p) const
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void MatrixPowerTriangularAtomic<MatrixType>::computeBig(MatrixType& res, RealScalar p) const
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{
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using std::abs;
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using std::pow;
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ArrayType logTdiag = m_T.diagonal().array().log();
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res.coeffRef(0,0) = pow(m_T.coeff(0,0), p);
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for (int i=1; i < m_T.cols(); ++i) {
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res.coeffRef(i,i) = pow(m_T.coeff(i,i), p);
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if (m_T.coeff(i-1,i-1) == m_T.coeff(i,i)) {
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res.coeffRef(i,i-1) = p * pow(m_T.coeff(i,i-1), p-1);
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}
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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))) {
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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));
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}
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else {
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int unwindingNumber = std::ceil((internal::imag(logTdiag[i]-logTdiag[i-1]) - M_PI) / (2*M_PI));
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Scalar w = internal::matrix_power_unwinder<Scalar>::run(m_T.coeff(i,i), m_T.coeff(i-1,i-1), unwindingNumber);
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res.coeffRef(i,i-1) = m_T.coeff(i,i-1) * RealScalar(2) * std::exp(RealScalar(0.5)*p*(logTdiag[i]+logTdiag[i-1])) *
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std::sinh(p * w) / (m_T.coeff(i,i) - m_T.coeff(i-1,i-1));
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}
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}
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}
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template<typename MatrixType>
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void MatrixPowerTriangular2x2<MatrixType,UnitUpper>::compute(MatrixType& res, RealScalar p) const
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{
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for (int i=1; i < m_T.cols(); ++i)
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res.coeffRef(i-1,i) = p * std::pow(m_T.coeff(i-1,i), p-1);
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}
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template<typename MatrixType>
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void MatrixPowerTriangular2x2<MatrixType,UnitLower>::compute(MatrixType& res, RealScalar p) const
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{
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for (int i=1; i < m_T.cols(); ++i) {
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res.coeffRef(i,i-1) = p * std::pow(m_T.coeff(i,i-1), p-1);
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}
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}
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template<typename MatrixType>
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void MatrixPowerTriangular2x2<MatrixType,StrictlyUpper>::compute(MatrixType& res, RealScalar p) const
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{
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RealScalar diag = !p ? 1 : 0;
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res.coeffRef(0,0) = diag;
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for (int i=1; i < m_T.cols(); ++i) {
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res.coeffRef(i,i) = diag;
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res.coeffRef(i-1,i) = p * std::pow(m_T.coeff(i-1,i), p-1);
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}
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}
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template<typename MatrixType>
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void MatrixPowerTriangular2x2<MatrixType,StrictlyLower>::compute(MatrixType& res, RealScalar p) const
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{
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RealScalar diag = !p ? 1 : 0;
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res.coeffRef(0,0) = diag;
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for (int i=1; i < m_T.cols(); ++i) {
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res.coeffRef(i,i) = diag;
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res.coeffRef(i,i-1) = p * std::pow(m_T.coeff(i,i-1), p-1);
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}
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}
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template<typename MatrixType, unsigned int Mode=Upper>
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class MatrixPowerTriangularAtomic
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{
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private:
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enum {
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RowsAtCompileTime = MatrixType::RowsAtCompileTime,
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MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime
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};
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typedef typename MatrixType::Scalar Scalar;
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typedef typename MatrixType::RealScalar RealScalar;
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typedef Array<Scalar,RowsAtCompileTime,1,ColMajor,MaxRowsAtCompileTime> ArrayType;
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const MatrixType& m_T;
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const MatrixType m_Id;
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void computePade(int degree, const MatrixType& IminusT, MatrixType& res, RealScalar p) const;
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void computeBig(MatrixType& res, RealScalar p) const;
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public:
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explicit MatrixPowerTriangularAtomic(const MatrixType& T);
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void compute(MatrixType& res, RealScalar p) const;
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};
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template<typename MatrixType, unsigned int Mode>
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MatrixPowerTriangularAtomic<MatrixType,Mode>::MatrixPowerTriangularAtomic(const MatrixType& T) :
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m_T(T),
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m_Id(MatrixType::Identity(T.rows(), T.cols()))
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{ }
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template<typename MatrixType, unsigned int Mode>
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void MatrixPowerTriangularAtomic<MatrixType,Mode>::compute(MatrixType& res, RealScalar p) const
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{
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switch (m_T.rows()) {
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case 0:
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break;
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case 1:
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res(0,0) = std::pow(m_T(0,0), p);
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break;
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case 2:
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MatrixPowerTriangular2x2<MatrixType,Mode>(m_T).compute(res, p);
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break;
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default:
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computeBig(res, p);
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}
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}
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template<typename MatrixType, unsigned int Mode>
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void MatrixPowerTriangularAtomic<MatrixType,Mode>::computePade(int degree, const MatrixType& IminusT, MatrixType& res,
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RealScalar p) const
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{
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int i = degree<<1;
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res = (p-degree) / ((i-1)<<1) * IminusT;
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for (--i; i; --i) {
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res = (m_Id + res).template triangularView<Mode>().solve((i==1 ? -p : i&1 ? (-p-(i>>1))/(i<<1) :
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(p-(i>>1))/((i-1)<<1)) * IminusT).eval();
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}
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res += m_Id;
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}
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template<typename MatrixType, unsigned int Mode>
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void MatrixPowerTriangularAtomic<MatrixType,Mode>::computeBig(MatrixType& res, RealScalar p) const
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{
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enum { digits = std::numeric_limits<RealScalar>::digits };
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const int digits = std::numeric_limits<RealScalar>::digits;
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const RealScalar maxNormForPade = digits <= 24? 4.3386528e-1f: // sigle precision
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digits <= 53? 2.789358995219730e-1: // double precision
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digits <= 64? 2.4471944416607995472e-1L: // extended precision
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digits <= 106? 1.1016843812851143391275867258512e-1L: // double-double
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9.134603732914548552537150753385375e-2L; // quadruple precision
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const MatrixPowerTriangular2x2<MatrixType,Mode> atomic2x2(m_T);
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MatrixType IminusT, sqrtT, T=m_T;
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RealScalar normIminusT;
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int degree, degree2, numberOfSquareRoots=0, numberOfExtraSquareRoots=0;
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int degree, degree2, numberOfSquareRoots=0;
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bool hasExtraSquareRoot=false;
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while (true) {
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IminusT = MatrixType::Identity(m_T.rows(), m_T.cols()) - T;
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@ -309,9 +217,9 @@ void MatrixPowerTriangularAtomic<MatrixType,Mode>::computeBig(MatrixType& res, R
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if (normIminusT < maxNormForPade) {
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degree = internal::matrix_power_get_pade_degree(normIminusT);
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degree2 = internal::matrix_power_get_pade_degree(normIminusT/2);
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if (degree - degree2 <= 1 || numberOfExtraSquareRoots)
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if (degree - degree2 <= 1 || hasExtraSquareRoot)
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break;
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++numberOfExtraSquareRoots;
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hasExtraSquareRoot = true;
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}
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MatrixSquareRootTriangular<MatrixType>(T).compute(sqrtT);
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T = sqrtT;
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@ -320,10 +228,10 @@ void MatrixPowerTriangularAtomic<MatrixType,Mode>::computeBig(MatrixType& res, R
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computePade(degree, IminusT, res, p);
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for (; numberOfSquareRoots; --numberOfSquareRoots) {
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atomic2x2.compute(res, std::ldexp(p,-numberOfSquareRoots));
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compute2x2(res, std::ldexp(p,-numberOfSquareRoots));
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res *= res;
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}
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atomic2x2.compute(res, p);
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compute2x2(res, p);
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}
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#define EIGEN_MATRIX_POWER_PUBLIC_INTERFACE(Derived) \
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@ -391,11 +299,6 @@ class MatrixPowerBase
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explicit MatrixPowerBase(const MatrixType& A, RealScalar cond);
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template<typename OtherDerived>
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explicit MatrixPowerBase(const MatrixBase<OtherDerived>& A, RealScalar cond);
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~MatrixPowerBase();
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void compute(MatrixType& res, RealScalar p);
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template<typename OtherDerived, typename ResultType>
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@ -411,31 +314,14 @@ class MatrixPowerBase
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const MatrixType m_Id;
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MatrixType m_tmp1, m_tmp2;
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RealScalar m_conditionNumber;
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private:
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const bool m_del; // whether to delete the pointer at destruction
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};
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template<typename Derived, typename MatrixType>
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MatrixPowerBase<Derived,MatrixType>::MatrixPowerBase(const MatrixType& A, RealScalar cond) :
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m_A(A),
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m_Id(MatrixType::Identity(A.rows(),A.cols())),
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m_conditionNumber(cond),
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m_del(false)
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{ }
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template<typename Derived, typename MatrixType>
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template<typename OtherDerived>
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MatrixPowerBase<Derived,MatrixType>::MatrixPowerBase(const MatrixBase<OtherDerived>& A, RealScalar cond) :
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m_A(*new MatrixType(A)),
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m_Id(MatrixType::Identity(A.rows(),A.cols())),
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m_conditionNumber(cond),
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m_del(true)
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{ }
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template<typename Derived, typename MatrixType>
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MatrixPowerBase<Derived,MatrixType>::~MatrixPowerBase()
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{ if (m_del) delete &m_A; }
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m_conditionNumber(cond)
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{ eigen_assert(A.rows() == A.cols()); }
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template<typename Derived, typename MatrixType>
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void MatrixPowerBase<Derived,MatrixType>::compute(MatrixType& res, RealScalar p)
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