Le 13/09/2012 19:10, Thomas Neidhart a écrit : > On 09/13/2012 05:13 PM, l...@apache.org wrote: >> Author: luc >> Date: Thu Sep 13 15:13:03 2012 >> New Revision: 1384363 >> >> URL: http://svn.apache.org/viewvc?rev=1384363&view=rev >> Log: >> Fixed an error in rectangular Cholesky decomposition. >> >> JIRA: MATH-789 > > Hi Luc, > > thanks for looking into this. > > I think that there is still an error in the way the rank is calculated > in case diagonal values are below the threshold: > > //all remaining diagonal elements are close to zero, we consider we have > // found the rank of the symmetric positive semidefinite matrix > //++r; <- commented out > loop = false; > > Otherwise the resulting root Matrix may be rank deficient as can be seen > in the examples below.
You are right. Could you make the change? In fact, I wonder if we should test for values <=0 instead of using a "small" parameter. Here is what Nicholas J. Higham writes in the discussion section of his 1990 paper "Analysis of the Cholesky Decomposition of a Semi-definite Matrix" (<http://eprints.ma.man.ac.uk/1193/>), about the SCHDC function in Linpack. "Consequently, SCHDC proceeds with the Cholesky algorithm until a nonpositive pivot is encountered, that is, up to and including stage k − 1, where k is the smallest integer for which aii ≤ 0, i = k, ..., n" Of course, users can set "small" to 0 themselves... Luc > > Actually there is a unit test (CorrelatedRandomVectorGeneratorTest) that > tests for a wrong rank: > > @Test > public void testRank() { > Assert.assertEquals(3, generator.getRank()); > } > > Should be 2, see the resulting root Matrix: > > Array2DRowRealMatrix{ > {2.0823861495,0.0605633926,0.0}, > {2.6016090812,0.0403755951,0.0}, > {3.1208320129,0.0201877975,0.0}, > {3.6400549446,0.0,0.0}} > > with the fix the result is the following: > > Array2DRowRealMatrix{ > {2.0823861495,0.0605633926}, > {2.6016090812,0.0403755951}, > {3.1208320129,0.0201877975}, > {3.6400549446,0.0}} > > Thomas > > --------------------------------------------------------------------- > To unsubscribe, e-mail: dev-unsubscr...@commons.apache.org > For additional commands, e-mail: dev-h...@commons.apache.org > > --------------------------------------------------------------------- To unsubscribe, e-mail: dev-unsubscr...@commons.apache.org For additional commands, e-mail: dev-h...@commons.apache.org
