Re: [eigen] skipXxx / computeXxx parameters in Eigenvalues module

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On Sun, 30 May 2010, Benoit Jacob wrote:

I would like us to align everywhere on runtime computeXxx parameters,
not skipXxx parameters. In other words, 'true' means do compute. This
is so we can avoid a double negation ("do not not compute"). Do you

Yes, that makes sense.

Then a separate question is what the default should be. Initially I
thought default to true for ease of use. But actually, this makes it
easy to write slow code, even unbearingly slow (for 10000x10 matrices,
skipping the U computation is crucial...).

Currently, one can only compute the Schur (or Hessenberg or eigen-) decomposition of square matrices: given A, compute orthogonal U and a triangular T such that A = U T U^*. It is not clear to me what a Schur decomposition of a rectangular matrix is.

So perhaps default to false and make sure that the corresponding assertion messages make it very clear what's going on ("You tried accessing this but you didn't ask for it to be computed in this decomposition").

That raises another question. Some classes have an assert on an m_isInitialized member variable to guard against the user requesting the results before calling compute(). I guess all classes should have this. But in SelfAdjointEigenSolver, the member variable is only there if NDEBUG
is not defined:

   class SelfAdjointEigenSolver : ...
      #ifndef NDEBUG
      bool m_isInitialized;

That seems quite nice - it saves a few bytes if NDEBUG is defined, when the assert is not done anyway - but I haven't seen it elsewhere in Eigen. Are there problems with it?

Note that the Tridiagonalization and Hessenberg classes are special
since the Q can rather be returned as a householder sequence,
incurring no extra cost at the time of the decomposition.

That's a good point, thanks. I hadn't realized that.

These classes should be rewritten as trivial adaptations of, respectively, UpperBidiagonalization and HouseholderQR.

I don't understand this. If you know the QR decomposition, how does tat help you to compute the Hessenberg decomposition?


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