[eigen] Student contribution

[BRUN Gauthier <brunga@xxxxxxxxxxxxxx>]

Hello,

At the moment, the two first steps of our algorithm are working well on 
dynamic defined matrices of double and float.
Sadly, it still doesn't work for matrices of complex.

For matrices of int, it returns a matrix of zero in order to match the 
behaviour of jacobi algorithm (although using SVD on such matrices is 
irrelevant)

We are sorry, we couldn't finish the third and last step, but our 
algorithm in its current state is already significantly increasing the 
performances of the singular value decomposition on big matrices (more 
than around 200 rows and columns)
Thus we would like to submit the two first parts, the tests and the 
benchmark to you in order to validate an important step in our school 
project.
Indeed, although the work is not entirely finished, we believe that it 
can be useful to Eigen in its current state.

Despite the fact that our main work is supposed to be finished today, 
we can still work on it until next wednesday, so we will be able to make 
modifications on our code if you ask for it. Our final code has not been 
commited yet on our bitbucket

https://bitbucket.org/gl27/eigen-bdcsvd


Performance analysis: We joined to this mail graphs of the performances 
analysis
                      (in red JacobiSVD times and in blue BDCSVD times)
        - Measures are not accurate since we run each test only one 
time
        - Time was measure with ctime (clock_gettime REALTIME) on the 
compute part of the algorithm
        - We compiled with " icpc -O3 -xhost "
        - The test machine is an Intel Ivy Bridge (i5 3570k)

On the graph largMatrixTime we can suppose our version improve the 
complexity of the SVD, but on the largeMatrixRatio, we can noticed that 
the performance boost is stuck at x1,7. This because we still use a 
JacobiSVD in the third part, instead of using a SVD algorithm of the 
special matrix.



Best regards,

Team GL27
Jean Ceccato, Pierre Zoppitelli, Gauthier Brun, Nicolas Carre

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