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Replace atanh with atanh2

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Chen-Pang He
2012-08-27 21:43:41 +01:00
parent ebe511334f
commit b55d260ada
3 changed files with 79 additions and 72 deletions
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18
unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h
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@@ -51,7 +51,7 @@ private:
void compute2x2(const MatrixType& A, MatrixType& result);
void computeBig(const MatrixType& A, MatrixType& result);
static Scalar atanh(Scalar x);
static Scalar atanh2(Scalar y, Scalar x);
int getPadeDegree(float normTminusI);
int getPadeDegree(double normTminusI);
int getPadeDegree(long double normTminusI);
@@ -93,16 +93,18 @@ MatrixType MatrixLogarithmAtomic<MatrixType>::compute(const MatrixType& A)
return result;
}
/** \brief Compute atanh (inverse hyperbolic tangent). */
/** \brief Compute atanh (inverse hyperbolic tangent) for \f$ y / x \f$. */
template <typename MatrixType>
typename MatrixType::Scalar MatrixLogarithmAtomic<MatrixType>::atanh(typename MatrixType::Scalar x)
typename MatrixType::Scalar MatrixLogarithmAtomic<MatrixType>::atanh2(Scalar y, Scalar x)
{
using std::abs;
using std::sqrt;
if (abs(x) > sqrt(NumTraits<Scalar>::epsilon()))
return Scalar(0.5) * log((Scalar(1) + x) / (Scalar(1) - x));
Scalar z = y / x;
if (abs(z) > sqrt(NumTraits<Scalar>::epsilon()))
return Scalar(0.5) * log((x + y) / (x - y));
else
return x + x*x*x / Scalar(3);
return z + z*z*z / Scalar(3);
}
/** \brief Compute logarithm of 2x2 triangular matrix. */
@@ -128,8 +130,8 @@ void MatrixLogarithmAtomic<MatrixType>::compute2x2(const MatrixType& A, MatrixTy
} else {
// 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 z = (A(1,1) - A(0,0)) / (A(1,1) + A(0,0));
result(0,1) = A(0,1) * (Scalar(2) * atanh(z) + Scalar(0,2*M_PI*unwindingNumber)) / (A(1,1) - A(0,0));
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;
}
}