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Avoid inefficient 2x2 LU. Move atanh to internal for maintainability.

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This commit is contained in:
Chen-Pang He
2012-08-30 23:40:30 +08:00
parent 9da41cc527
commit d23134e4a7
4 changed files with 51 additions and 37 deletions
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17
unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h
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@@ -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;
}
}

22
unsupported/Eigen/src/MatrixFunctions/MatrixPower.h
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@@ -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 {
@@ -296,21 +293,6 @@ 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)
{
@@ -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));
}