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* do without an empirical homemade formula that i wasn't comfortable about...Gravatar Benoit Jacob2009-08-12
| | | | turns out it's not needed anymore and removing it seems to only increase the precision
* make jacobi SVD more robust after experimenting with very nasty matrices...Gravatar Benoit Jacob2009-08-12
| | | | | | | it turns out to be better to repeat the jacobi steps on a given (p,q) pair until it is diagonal to machine precision, before going to the next (p,q) pair. it's also an optimization as experiments show that in a majority of cases this allows to find out that the (p,q) pair is already diagonal to machine precision.
* finally, the good approach was two-sided Jacobi. Indeed, it allowsGravatar Benoit Jacob2009-08-12
| | | | | | | | | | to guarantee the precision of the output, which is very valuable. Here, we guarantee that the diagonal matrix returned by the SVD is actually diagonal, to machine precision. Performance isn't bad at all at 50% of the current householder SVD performance for a 200x200 matrix (no vectorization) and we have lots of room for improvement.
* * add Jacobi transformationsGravatar Benoit Jacob2009-08-09
* add Jacobi (Hestenes) SVD decomposition for square matrices * add function for trivial Householder