[PYTHON MATRIX-SIG] LAPACK module questions

[Konrad HINSEN]

   I assume that the caller knows the structure of the storage methods and
   packs it into an python array object.  I have not used these functions

Yes, that's a reasonable assumption. After all, it's low level. A
good interface can always be added later by defining a Python class
representing e.g. a packed symmetric matrix.

   What is a "generalized inverse"?  If I remember correctly, the generalized 
   eigenvalue problem is (A - lambda C)x = 0 where C is a matrix.  But I don't
   remember running across a generalized inverse.

It's also known as a pseudoinverse or Moore-Penrose-inverse. There is
a uniquely defined generalized inverse for any matrix, and in the case
of a square non-singular matrix it is equal to the ordinary inverse.
Generalized inverses can be used to express the solution of over- or
underdetermined (or both) systems of linear equations conveniently,
and they are very useful in least-squares problems. The preferred way
to calculate the generalized inverse uses SVD: take the original
matrix, do SVD, invert all the non-zero singular values, multiply the
three matrices again, and return the transpose. Trivial to code in
Python based on low-level SVD calls.

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Konrad Hinsen                     | E-Mail: hinsenk@ere.umontreal.ca
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