Eigen 3.2.2, Mac OSX El Capitan.

Hi. As part of a large robotics project, I wrote this function:

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template<typename Derived>
inline Eigen::Matrix<typename Derived::Scalar, 3, 1> log_q(const Eigen::QuaternionBase<Derived>& _q)
{
    typedef typename Derived::Scalar T;
    Eigen::AngleAxis<T> aa(_q);
    return aa.angle() * aa.axis();
}


which pretends to use Eigen's ability to convert from different rotation representations to write the logarithm of a quaternion via AngleAxis.

When using a Quaternion<ceres::Jet> type, we have Derived::Scalar = ceres::Jet<double, 7> and the following error occurs at compile time:

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In file included from /usr/local/include/eigen3/Eigen/Geometry:43:
/usr/local/include/eigen3/Eigen/src/Geometry/AngleAxis.h:181:14: error: invalid operands to binary expression ('Scalar' (aka 'ceres::Jet<double, 7>') and 'int')
    if(q.w() < 0)
       ~~~~~ ^ ~


which refers to line 181 in AngleAxis.h, with the operator=,

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template<typename Scalar>
template<typename QuatDerived>
EIGEN_DEVICE_FUNC AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const QuaternionBase<QuatDerived>& q)
{
  EIGEN_USING_STD_MATH(atan2)
  EIGEN_USING_STD_MATH(abs)
  Scalar n = q.vec().norm();
  if(n<NumTraits<Scalar>::epsilon())
    n = q.vec().stableNorm();

  if (n != Scalar(0))
  {
    m_angle = Scalar(2)*atan2(n, abs(q.w()));
    if(q.w() < 0)
      n = -n;
    m_axis  = q.vec() / n;
  }
  else
  {
    m_angle = Scalar(0);
    m_axis << Scalar(1), Scalar(0), Scalar(0);
  }
  return *this;
}


In this line 181, we see:

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    if(q.w() < 0)


which is comparing a ceres::Jet q.w() against an 'int' scalar (not even a double!).

Usually, we would rather cast the plain scalar for Jet compatibility (ceres::Jet is very picky with these otherwise obvious binary operators)

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    if( q.w() < Scalar(0) )


being Scalar precisely the ceres::Jet type, through the template definition (or at least I assume so).

I tried to alter this line as suggested above, and other errors then followed, like this:

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In file included from /usr/local/include/eigen3/Eigen/Core:446:
/usr/local/include/eigen3/Eigen/src/Core/StableNorm.h:26:33: error: no member named 'highest' in 'Eigen::NumTraits<ceres::Jet<double, 7> >'
    if(tmp > NumTraits<Scalar>::highest())
             ~~~~~~~~~~~~~~~~~~~^


This second error is now cryptic to me. So I stopped my investigation and reverted to a custom implementation of my log_q function (which is not very complicated anyway).

Am I doing anything wrong? Could I expect Eigen's AngleAxis to accept a Quaternion<Jet> and work at all? Is this a minor Eigen bug, or would this fix require major redesign efforts?

Thank you.

Please check with a recent version of Eigen first.

Sorry for the old version. Just tried with Eigen 3.3.4. The issue remains exactly the same as explained in the original post.

In order to narrow the issue, I have edited the 'AngleAxis::operator=' function to:

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template<typename Scalar>
template<typename QuatDerived>
EIGEN_DEVICE_FUNC AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const QuaternionBase<QuatDerived>& q)
{
  EIGEN_USING_STD_MATH(atan2)
  EIGEN_USING_STD_MATH(abs)
  Scalar n = q.vec().norm();
 // if(n<NumTraits<Scalar>::epsilon())   // <-- edited here
  //  n = q.vec().stableNorm();          // <-- edited here

  if (n != Scalar(0))
  {
    m_angle = Scalar(2)*atan2(n, abs(q.w()));
    if(q.w() < Scalar(0))                // <-- edited here
      n = -n;
    m_axis  = q.vec() / n;
  }
  else
  {
    m_angle = Scalar(0);
    m_axis << Scalar(1), Scalar(0), Scalar(0);
  }
  return *this;
}


that is, I casted the lonely '0' value, and commented out the 'stableNorm()' call, which was giving problems.

My 'log_q' function now compiles and executes correctly.

I checked and both problems have been fixed a while ago. For "highest" you need to update ceres. For Scalar(0), you need the head of the 3.3 branch (will be 3.3.5).

Thanks for this answer. Success required both HEAD versions of eigen and ceres-solver. In this order:

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brew install --HEAD eigen
brew install --build-from-source --HEAD ceres-solver