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I always have had the impression that you're a math professor from
all the codes you wrote. Why so humble? :-)
--- In amibroker@xxxxxxxxxxxxxxx, "DIMITRIS TSOKAKIS"
<TSOKAKIS@xxxx> wrote:
>
> If we use strict math terms, f[g(x)] is a composite function.
> [2-11 Definition in Tom Apostol, Mathematical Analysis, Addison-
> Wesley. I did not use it to avoid confusion with the AFL
composites
> and the AddToComposite() function]
> The function g is applied on x and then the function f is applied
on g
> (x).
> If f=g then f[g(x)] becomes f[f(x)].
> Example:
> If f(x)=sinx and g(x)=cosx, then we speak for
> f[g(x)]=sin(cosx)
> and
> f[f(x)]=sin(sinx)
> A power form is used in printed formulas. Since it is not easy to
use
> exponents here, I decided to use f2(x) for f(f(x)) and f5(x) for
> f(f(f(f(f(x))))).
> According to the http://www.hypertextbook.com/chaos/11.shtml we
may
> speak for iterated mapping, the symbol fn(x) will represent
the "nth
> iterate" of x and, finally, the series
> x, f(x), f2(x), f3(x),...,fn(x),...
> will form the "orbit" of the function f. The initial value x is
> called the "seed" of the orbit.
> I hope it is more clear now.
> I also hope the math educated will excuse the naive style of my
title.
> Dimitris
> --- In amibroker@xxxxxxxxxxxxxxx, "dingo" <dingo@xxxx> wrote:
> > no - recursive is when you call the function f1 from within the
> function f1.
> > all of these calls to f1 were from outside the function - in f10.
> >
> > d
> >
> >
> > _____
> >
> > From: mmqp [mailto:mmqp@x...]
> > Sent: Tuesday, October 05, 2004 12:14 PM
> > To: amibroker@xxxxxxxxxxxxxxx
> > Subject: [amibroker] Re: The function of a function of a function
> >
> >
> >
> > Is this equivalent to recursive function call?
> >
> > --- In amibroker@xxxxxxxxxxxxxxx, "DIMITRIS TSOKAKIS"
> > <TSOKAKIS@xxxx> wrote:
> > >
> > > The function f1 returns the sin of x.
> > > The function f10 returns the sin of the sin of the sin...10
> > times...
> > > of x.
> > > The f10(f10(f10(x))) applies the sin transformation 1000 times
> > over
> > > the result of sin(x).
> > > The respective AFL would be
> > >
> > > //The function of a function
> > > function f1(x)
> > > {
> > > return sin(x);
> > > }
> > > function f10(x)
> > > {
> > > return f1(f1(f1(f1(f1(f1(f1(f1(f1(f1(x))))))))));
> > > }
> > > x=2*3.14*10*Cum(1);
> > > Plot(f1(x),"f1",colorBlack,1);
> > > Plot(f10(x),"f10",colorWhite,1);
> > > Plot(f10(f10(f10(x))),"f1000",colorRed,1);
> > >
> > > Dimitris
> >
> >
> >
> >
> >
> > Check AmiBroker web page at:
> > http://www.amibroker.com/
> >
> > Check group FAQ at:
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> >
> >
> >
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