On 2012-07-27, at 3:39 AM, Evgeny Kurbatov wrote: > On Thu, 26 Jul 2012 14:39:21 -0400 > Jens Chluba <[email protected]> wrote: > >> Hi there, >> >> just a comment on the new convention for interpolation. Round-off >> error lead to problems with >> >> if (x < interp->xmin || x > interp->xmax) >> { >> GSL_ERROR_VAL("interpolation error", GSL_EDOM, GSL_NAN); >> } >> >> if indeed x very close to the boundaries but within the interval >> [xmin, xmax]. It is probably better to put something like >> >> if (x < interp->xmin*(1.0-1.0e-14) || x > >> interp->xmax*(1.0+1.0e-14)) { >> GSL_ERROR_VAL("interpolation error", GSL_EDOM, GSL_NAN); >> } >> >> This allows for a tiny range of extrapolation but fixes the round-off >> error problem. > > Hi, Jens! > > I was the one who proposed a patch for interpolation routines > toughening control to the boundary violation. There was times when I > was sorry about that, but now the belief rises that this was right. The > control forces you to think deeper and be more accurate. > So hold on, be man!
It certainly is very important to make sure extrapolation is not mistaken for interpolation. I absolutely agree that this is a good move! Still, [platform & compiler flag (fast-math) dependent] round off errors should not be making you have to dig into things. Certainly fixed this by manning up ;-) >> In addition, I was wondering if the GSL team could be interested in >> some pretty fast and accurate integration schemes based on the >> Patterson quadrature rules? These are fully nested and converge very >> rapidly. I have the required c++ code and will be happy to provide >> them. Certainly, this can only be a base for GSL, since you guys have >> much higher coding standards... > > I don't mind. It is not my invention (just like Gauss-Kronrod is not yours), but it beats almost any quadrature rule! NAG uses it, and it is one of the most efficient algorithms I have come across. Just take a look. Even for me as an amateur programmer it did not take a lot to beat your integration routines & those of scipy in most cases [still getting precision to all digits]. It would be foolish not to consider these impressive methods. I am sure you will find all you need digging yourself then. > Best witches, > Evgeny Kurbatov All the best & many thanks for your kind response, Jens ------------------------------------------------------------------------------------------------------------- Jens Chluba Tel. ++1 416 978 5946 or ++1 416 262 8224 Senior Research Associate Fax ++1 416 978 3921 CITA, University of Toronto .+'''+. .+'''+. 60 St. George Street mailto:[email protected] Toronto, Ontario M5S 3H8 '+...+' '+...+' Canada http://www.cita.utoronto.ca/~jchluba/ -------------------------------------------------------------------------------------------------------------
