[ http://issues.apache.org/jira/browse/MATH-157?page=all ]
Remi Arntzen updated MATH-157:
------------------------------
Attachment: svd.tar.gz
This is just a preliminary implementation.
Seeing as how I have not taken a course in linear algebra as of yet, I would
appreciate having some test cases to verify my code against. In particular any
special cases involved in the algorithm, e.g. singular square non-square, as
far as I can tell my method should work on all matrix inputs, but no guarantees.
My method involves finding the eigen values by using the QR algorithm, taking
the square roots of these values and placing them along the diagonal of Σ.
Then I compute the eigen vectors of mTm and mmT by computing the null space of
these matrices ( with the difference of the Identity*eigen value), and in
calculating the null space I used the reduced row echelon form via the Gaussian
algorithm.
This is just a start, still needs provide more documentation, and test cases.
> Add support for SVD.
> --------------------
>
> Key: MATH-157
> URL: http://issues.apache.org/jira/browse/MATH-157
> Project: Commons Math
> Issue Type: New Feature
> Reporter: Tyler Ward
> Attachments: svd.tar.gz
>
>
> SVD is probably the most important feature in any linear algebra package,
> though also one of the more difficult.
> In general, SVD is needed because very often real systems end up being
> singular (which can be handled by QR), or nearly singular (which can't). A
> good example is a nonlinear root finder. Often the jacobian will be nearly
> singular, but it is VERY rare for it to be exactly singular. Consequently, LU
> or QR produces really bad results, because they are dominated by rounding
> error. What is needed is a way to throw out the insignificant parts of the
> solution, and take what improvements we can get. That is what SVD provides.
> The colt SVD algorithm has a serious infinite loop bug, caused primarily by
> Double.NaN in the inputs, but also by underflow and overflow, which really
> can't be prevented.
> If worried about patents and such, SVD can be derrived from first principals
> very easily with the acceptance of two postulates.
> 1) That an SVD always exists.
> 2) That Jacobi reduction works.
> Both are very basic results from linear algebra, available in nearly any text
> book. Once that's accepted, then the rest of the algorithm falls into place
> in a very simple manner.
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