Re: [boost] Re: Numerical Integration - continued

From: Victor A. Wagner, Jr. (vawjr_at_[hidden])
Date: 2002-10-23 11:58:47

At Wednesday 2002/10/23 03:23, Martin Weiser <weiser_at_[hidden]> wrote:
>On Mittwoch, 23. Oktober 2002 11:34, Victor A. Wagner, Jr. wrote:

[deleted]

> > >It seems as if given only dx and dt, the only possibility to implement
> > >such a function is the explicit Euler scheme, i.e. rectangular
> > >integration - unless you store computed points and perform some
> > > multistep method. But I gather this would require an interface
> > > change.
> >
> > I can't see why, method can include the information
>
>Let me be more detailed in order to ensure we're talking about the same
>things. Omitting genericity,
>
>double integrate_step(double dx, double dt) {
>         // compute increment from dx and dt. Only possibility:
>         return dx*dt;
//not really.... for example (delete the previous line (return dx*dt;))

static double x = 0.0;
static double old_x, old_dt;
static int step = 0;
static bool first_time = true;
double new_x;

         if (first_time) {
                 new_x = dx * dt;
                 first_time = false;
         } else {
                 //perform some multistep method
                 new_x = multistep(old_x,old_dt,x,dt);
         }
         old_x = x;
         old_dt = dt;
         ++step;  // not sure what this does
         return x += new_x;

>}

Now, I've made NO changes to what was in the header file describing the 
function.
I don't see how one could say the "interface" changed.
Of course, I prefer the function object idea as you show below, but I don't 
follow your comment about "changing the interface".
Unless you're referring to the obvious change from a free function to a 
member function, but somehow I don't think that's what you meant.

>Or, the more sophisticated version:
>
>class integrator {
>         double x;
>         double old_x, old_dt;
>         int step;
>public:
>         integrator(): x(0), step(0) {}
>         double integrate_step(double dx, double dt) {
>                 if (n==0) {
>                         x = dt*dx;
>                         old_x = 0;
>                         old_dt = dt;
>                 } else {
>                         // perform some second order multistep method
>                         double DX = multistep(old_x,old_dt,x,dt,dx/dt);
>                         old_dt = dt;
>                         old_x = x;
>                         x += DX;
>                 }
>                 ++step;
>                 return x;
>         }
>};
>
>Is that what you mean? I'd call that different interfaces, even though
>"integrate_step" has the same signature.
>
>Yours,
>Martin
>
>--
>Dr. Martin Weiser            Zuse Institute Berlin
>weiser_at_[hidden]                Scientific Computing
>http://www.zib.de/weiser     Numerical Analysis and Modelling
>
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Victor A. Wagner Jr.      http://rudbek.com
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