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[Octave-bug-tracker] [bug #45146] chol succeeds with incorrect factoriza


From: anonymous
Subject: [Octave-bug-tracker] [bug #45146] chol succeeds with incorrect factorization on non-hermitian complex inputs
Date: Tue, 19 May 2015 23:15:29 +0000
User-agent: Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Ubuntu Chromium/41.0.2272.76 Chrome/41.0.2272.76 Safari/537.36

URL:
  <http://savannah.gnu.org/bugs/?45146>

                 Summary: chol succeeds with incorrect factorization on
non-hermitian complex inputs
                 Project: GNU Octave
            Submitted by: None
            Submitted on: Tue 19 May 2015 11:15:27 PM UTC
                Category: Documentation
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Incorrect Documentation
                  Status: None
             Assigned to: None
         Originator Name: Nathan Whitehead
        Originator Email: address@hidden
             Open/Closed: Open
         Discussion Lock: Any
                 Release: 3.8.1
        Operating System: GNU/Linux

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Details:

The chol() function silently succeeds with non-intuitive results in the case
where the input matrix is complex and non-hermitian. 

The documentation states that the function fails if the input is not positive
definite, or that chol(A)' * chol(A) = A if it is positive definite. For the
case where A is complex but not hermitian, the function succeeds and returns a
value that does not satisfy chol(A)' * chol(A) = A.


A=[10,-i;-i,10;]; norm(A - chol(A)'*chol(A), Inf)


For this code I would expect either an error or a result that is close to
machine epsilon. I actually get the result:


ans =  2.0000


I believe the function is only looking at the upper triangular part and
assuming the lower triangular part is conjugate transpose; this should be
included in the documentation for the function.





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