[Bug-gsl] gsl BFGS multimin bug

[Carl Glen Henshaw]

All:

I believe I have located a bug in the bfgs multivariate minimization 
routine. Specifically, in some circumstances it is possible for the 
vector returned by the bfgs minimization routine to contain NaN 
elements. This is because in the file vector_bfgs.c, in the routine 
vector_bfgs_iterate, starting on or near line 289, it is possible for 
dxdg to be uniformly equal to zero. When the BFGS update is calculated, 
dxg/dxdg and dgg/dxdg are then undefined.

In tracing the bug back further, I *think* this is because in line 263, 
which reads:

 if (stepb == 0.0)
    {
      return GSL_ENOPROG;
    }

it is possible for stepb to be very very small (on my machine around 
1e-18) but nonzero, which leaves the intermediate point unchanged from 
the initial point. Changing the line to read something like:

if (fabs(stepb) <5e-18)
    {
      return GSL_ENOPROG;
    }

appears to fix the problem. I'm not as up on my machine computation 
definitions as I should be, but shouldn't the line really be something 
like

if (gsl_fcmp(stepb, 0.0, DBL_EPS))
  {
    return GSL_ENOPROG;
  }

Thanks,
Glen

--------------------------------------------------------

Dr. Glen Henshaw
Attitude Control Systems Branch
Naval Center for Space Technology
U.S. Naval Research Laboratory