[Octave-bug-tracker] [bug #53991] Octave crashes using fsolve when x0 is a stationary point

[Rik]

Follow-up Comment #5, bug #53991 (project octave):

@Marco: Can you review this patch for fsolve?


diff -r b7db401e1a99 scripts/optimization/fsolve.m
--- a/scripts/optimization/fsolve.m     Tue Jun 19 09:18:44 2018 -0700
+++ b/scripts/optimization/fsolve.m     Tue Jun 19 14:23:19 2018 -0700
@@ -304,10 +304,18 @@ function [x, fvec, info, output, fjac] =
 
       ## Get trust-region model (dogleg) minimizer.
       if (useqr)
+        if (abs (r) < macheps)
+          info = -2;
+          break;
+        endif
         qtf = q'*fvec;
         s = - __dogleg__ (r, qtf, dg, delta);
         w = qtf + r * s;
       else
+        if (abs (fjac) < macheps)
+          info = -2;
+          break;
+        endif
         s = - __dogleg__ (fjac, fvec, dg, delta);
         w = fvec + fjac * s;
       endif


If the Jacobian is very small this stops fsolve before calling __dogleg__ with
a zero value for the first argument which would eventually lead to an
ill-conditioned matrix.

One question, should the test be for any component of fjac or should we be
taking the norm first?  In other words, this


if (any (abs (fjac(:)) < macheps))
  info = -2;
  break;
endif


OR


if (norm (fjac) < macheps)
  info = -2;
  break;
endif


I expect it is something like the latter.  The first thing that the
__dogleg__routine does is calculate


x = fjac \ fvec;


If fjac is a vector or matrix having a zero would be okay.  Only an all zero
array would be a problem.


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