On 11/27, Oleg Nesterov wrote:
>
> On 11/25, Julius Smith wrote:
> >
> > I would expect ba.tabulate() to be unbeatable when the function being
> > sampled is actually linear, quadratic, or cubic,
>
> Well ;) If the function is cubic then chebtab() will win even with NX=1.
> Ignoring the floating point issues, chebtab() will be simply equal to
> the approximated function. If the function is "nearly cubic", chebtab()
> should likely win anyway, I guess, but this depends.
Let me provide a couple of stupid test-cases just in case ;)
CK = 1;
FX(x) = x^3 - 2*x^2 - 100* x - 1;
X0 = 0;
X1 = 10;
NX = 50;
CD = 3;
// Both ch() and tb() create rdtable of size=200 and both use cubic
// polynomial, so this comparison is more or less fair.
ch(x) = chebtab(CK, FX, NX, CD, X0,X1, x);
tb(x) = ba.tabulate(CK, FX, NX*(CD+1), X0,X1, x).cub;
maxerr = abs : max ~ _;
line(n, x0,x1) = x0 + (ba.time%n)/n * (x1-x0);
process = line(50000, X0,X1) <: FX-tb,FX-ch : par(i,2,maxerr);
compiled with -a plot.cpp
$ /tmp/c-plot -n 50000 | tail -1
0.600803971 5.68434189e-13
e-13 is just the floating point errors. The close result if I change ch(x)
to use NX=1.
Lets add some "noise" to FX,
FX(x) = x^3 - 2*x^2 - 100* x - 1 + sin(x); // sin(x) is small compared
to poly
Now,
$ /tmp/c-plot -n 50000 | tail -1
0.59773165 5.20619665e-07
OK, lets recall that ba.tabulate() doesn't play well near X0, X1, lets help
tabulate() to be more accurate:
// ensure that ba.tabulate() always have at least 4 valid points
offs = 4 * (X1-X0) / (NX*(CD+1));
process = line(50000, X0+offs,X1-offs) <: FX-tb,FX-ch : par(i,2,maxerr);
now ba.tabulate() works MUCH better but chebtab() still wins:
$ /tmp/c-plot -n 50000 | tail -1
1.42467743e-05 5.20622848e-07
Oleg.
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