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Bug 1018

Summary: blueNorm handles complex infinities wrong on some systems
Product: Eigen Reporter: Christoph Hertzberg <chtz>
Component: Core - generalAssignee: Nobody <eigen.nobody>
Status: CONFIRMED ---    
Severity: Wrong Result CC: chtz, gael.guennebaud, jacob.benoit.1
Priority: Normal    
Version: 3.3 (current stable)   
Hardware: All   
OS: All   
Bug Depends on: 1019    
Bug Blocks:    

Description Christoph Hertzberg 2015-05-20 12:53:53 UTC
This results in the stable_norm_5 unit test to fail on several systems (mostly clang, but I experienced it on g++4.9-cygwin, as well)

The problem is that sometimes abs for complex is implemented similar to this:

  template<typename _Tp>
    inline _Tp
    __complex_abs(const complex<_Tp>& __z)
      _Tp __x = __z.real();
      _Tp __y = __z.imag();
      const _Tp __s = std::max(abs(__x), abs(__y));
      if (__s == _Tp())  // well ...
        return __s;
      __x /= __s; 
      __y /= __s;
      return __s * sqrt(__x * __x + __y * __y);

This causes a division of Inf/Inf which results in NaN instead of Inf (which is a bug not caused by us). Nevertheless, even for working abs implementations, we could (actually for all *Norm implementations) increase stability and improve performance by computing the norm of a real-valued vector of twice the size (at least for Euclidean norm).

Related to that: Some of our decompositions (e.g. eigenvalue/svd) normalize the input matrix by dividing by .cwiseAbs().maxCoeff(). IMO it would make sense here to take use the max of (real().cwiseAbs(), imag().cwiseAbs()) here as well (no, need to compute any complex abs)
Comment 1 Gael Guennebaud 2015-06-05 13:03:56 UTC
Agree with both proposals.
Comment 2 Nobody 2019-12-04 14:39:12 UTC
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