diff options
author | Chen-Pang He <jdh8@ms63.hinet.net> | 2012-08-30 23:40:30 +0800 |
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committer | Chen-Pang He <jdh8@ms63.hinet.net> | 2012-08-30 23:40:30 +0800 |
commit | d23134e4a7d689431a717a1ecf376b12b01afa24 (patch) | |
tree | d28a79e969a31a2bf70549d11b1a5938fdbd7828 /unsupported | |
parent | 9da41cc527ec595feb3377d089db6cd3adc9a5c8 (diff) |
Avoid inefficient 2x2 LU. Move atanh to internal for maintainability.
Diffstat (limited to 'unsupported')
-rw-r--r-- | unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h | 17 | ||||
-rw-r--r-- | unsupported/Eigen/src/MatrixFunctions/MatrixPower.h | 22 |
2 files changed, 3 insertions, 36 deletions
diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h b/unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h index 18bcf3d0d..e1e5b770c 100644 --- a/unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h +++ b/unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h @@ -51,7 +51,6 @@ private: void compute2x2(const MatrixType& A, MatrixType& result); void computeBig(const MatrixType& A, MatrixType& result); - static Scalar atanh2(Scalar y, Scalar x); int getPadeDegree(float normTminusI); int getPadeDegree(double normTminusI); int getPadeDegree(long double normTminusI); @@ -93,20 +92,6 @@ MatrixType MatrixLogarithmAtomic<MatrixType>::compute(const MatrixType& A) return result; } -/** \brief Compute atanh (inverse hyperbolic tangent) for \f$ y / x \f$. */ -template <typename MatrixType> -typename MatrixType::Scalar MatrixLogarithmAtomic<MatrixType>::atanh2(Scalar y, Scalar x) -{ - using std::abs; - using std::sqrt; - - Scalar z = y / x; - if (abs(z) > sqrt(NumTraits<Scalar>::epsilon())) - return Scalar(0.5) * log((x + y) / (x - y)); - else - return z + z*z*z / Scalar(3); -} - /** \brief Compute logarithm of 2x2 triangular matrix. */ template <typename MatrixType> void MatrixLogarithmAtomic<MatrixType>::compute2x2(const MatrixType& A, MatrixType& result) @@ -131,7 +116,7 @@ void MatrixLogarithmAtomic<MatrixType>::compute2x2(const MatrixType& A, MatrixTy // computation in previous branch is inaccurate if A(1,1) \approx A(0,0) int unwindingNumber = static_cast<int>(ceil((imag(logA11 - logA00) - M_PI) / (2*M_PI))); Scalar y = A(1,1) - A(0,0), x = A(1,1) + A(0,0); - result(0,1) = A(0,1) * (Scalar(2) * atanh2(y,x) + Scalar(0,2*M_PI*unwindingNumber)) / y; + result(0,1) = A(0,1) * (Scalar(2) * internal::atanh2(y,x) + Scalar(0,2*M_PI*unwindingNumber)) / y; } } diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixPower.h b/unsupported/Eigen/src/MatrixFunctions/MatrixPower.h index 2a46d2cc0..7238501ed 100644 --- a/unsupported/Eigen/src/MatrixFunctions/MatrixPower.h +++ b/unsupported/Eigen/src/MatrixFunctions/MatrixPower.h @@ -111,9 +111,6 @@ class MatrixPower */ void getFractionalExponent(); - /** \brief Compute atanh (inverse hyperbolic tangent) for \f$ y / x \f$. */ - static ComplexScalar atanh2(const ComplexScalar& y, const ComplexScalar& x); - /** \brief Compute power of 2x2 triangular matrix. */ void compute2x2(RealScalar p); @@ -223,7 +220,7 @@ void MatrixPower<MatrixType,PlainObject>::computeChainProduct(ResultType& result int cost = computeCost(p); if (m_pInt < RealScalar(0)) { - if (p * m_dimb <= cost * m_dimA) { + if (p * m_dimb <= cost * m_dimA && m_dimA > 2) { partialPivLuSolve(result, p); return; } else { @@ -297,21 +294,6 @@ void MatrixPower<MatrixType,PlainObject>::getFractionalExponent() } template<typename MatrixType, typename PlainObject> -std::complex<typename MatrixType::RealScalar> -MatrixPower<MatrixType,PlainObject>::atanh2(const ComplexScalar& y, const ComplexScalar& x) -{ - using std::abs; - using std::log; - using std::sqrt; - const ComplexScalar z = y / x; - - if (abs(z) > sqrt(NumTraits<RealScalar>::epsilon())) - return RealScalar(0.5) * log((x + y) / (x - y)); - else - return z + z*z*z / RealScalar(3); -} - -template<typename MatrixType, typename PlainObject> void MatrixPower<MatrixType,PlainObject>::compute2x2(RealScalar p) { using std::abs; @@ -337,7 +319,7 @@ void MatrixPower<MatrixType,PlainObject>::compute2x2(RealScalar p) } else { // computation in previous branch is inaccurate if abs(m_T(j,j)) \approx abs(m_T(i,i)) unwindingNumber = ceil((imag(m_logTdiag[j] - m_logTdiag[i]) - M_PI) / (2 * M_PI)); - w = atanh2(m_T(j,j) - m_T(i,i), m_T(j,j) + m_T(i,i)) + ComplexScalar(0, M_PI * unwindingNumber); + w = internal::atanh2(m_T(j,j) - m_T(i,i), m_T(j,j) + m_T(i,i)) + ComplexScalar(0, M_PI * unwindingNumber); m_fT(i,j) = m_T(i,j) * RealScalar(2) * exp(RealScalar(0.5) * p * (m_logTdiag[j] + m_logTdiag[i])) * sinh(p * w) / (m_T(j,j) - m_T(i,i)); } |