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Hello,
Actual code can be in fact even shorter:
function fN( N, x )
{
for( i = 0; i < N; i++ )
{
x= x^2-3/4;
}
return x;
}
Title = "";
for(i=-1.75;i<2;i=i+0.25)
{
Title=Title+
StrFormat("i=%6.2f %6.3f %6.3f %6.3f %6.3f %6.3f %6.3f %6.3f\n",
i,
fN( 1, i), fN( 5, i), fN( 10, i), fN( 50, i), fN( 100, i), fN( 500, i), fN( 1000, i));
}
Best regards,
Tomasz Janeczko
amibroker.com
----- Original Message -----
From: "Tomasz Janeczko" <amibroker@xxxxxx>
To: <amibroker@xxxxxxxxxxxxxxx>
Sent: Wednesday, October 06, 2004 9:22 AM
Subject: Re: [amibroker] Chaos:Introductory AFL notes
> Hello,
>
> You can also use iterative execution (results in shorter code)
>
> function fN( N, x )
> {
> for( i = 0; i < N; i++ )
> {
> x= x^2+1/4;
> }
>
> return x;
> }
>
> and call it
> fN( 1000, 0.75 ); // this is equivalent to f1000( 0.75 )
>
> Also to reduce time needed to compute you should avoid calling
> the same function with the same parameters twice (1st time in WriteIf and
> 2nd time in WriteVal) when it is only necessary to call it once:
>
> function fN( N, x )
> {
> for( i = 0; i < N; i++ )
> {
> x= x^2-3/4;
> }
>
> return x;
> }
>
> Title = "";
> for(i=-1.75;i<2;i=i+0.25)
> {
> Title=Title+"\ni="+
> WriteIf(i>=0," ","")+WriteVal(i,1.2)+
> StrFormat("%6.2f %6.3f %6.3f %6.3f %6.3f %6.3f %6.3f %6.3f",
> i,
> fN( 1, i), fN( 5, i), fN( 10, i), fN( 50, i), fN( 100, i), fN( 500, i), fN( 1000, i));
> }
>
>
> This code executes in 0.5 second or less (4 times faster).
> This simple example shows the how much speed can be gained by making the code
> optimal.
>
> Best regards,
> Tomasz Janeczko
> amibroker.com
> ----- Original Message -----
> From: "DIMITRIS TSOKAKIS" <TSOKAKIS@xxxxxxxxx>
> To: <amibroker@xxxxxxxxxxxxxxx>
> Sent: Wednesday, October 06, 2004 8:52 AM
> Subject: [amibroker] Chaos:Introductory AFL notes
>
>
>>
>>
>> AFL structure helps to reproduce the tables of
>> http://www.hypertextbook.com/chaos/11.shtml
>> The initial function is applied 1, 5, 10, 50, 100, 500 and 1000 times
>> [!!]
>> In an Indicator builder window paste the
>>
>> Title="The orbits of 9 seeds of the f(x)=x^2+1/4";
>> function f1(x)
>> {return x^2+1/4;}
>> function f5(x)
>> {return f1(f1(f1(f1(f1(x)))));}
>> function f10(x)
>> {return f5(f5(x));}
>> function f50(x)
>> {return f10(f10(f10(f10(f10(x)))));}
>> function f100(x)
>> {return f50(f50(x));}
>> function f500(x)
>> {return f100(f100(f100(f100(f100(x)))));}
>> function f1000(x)
>> {return f500(f500(x));}
>> for(i=-1;i<=1;i=i+0.25)
>> {
>> Title=Title+"\ni="+
>> WriteIf(i>=0," ","")+WriteVal(i,1.2)+
>> WriteIf(f1(i)>0," "," ")+WriteVal(f1(i),1.3)+
>> WriteIf(f5(i)>0," "," ")+WriteVal(f5(i),1.3)+
>> WriteIf(f10(i)>0," "," ")+WriteVal(f10(i),1.3)+
>> WriteIf(f50(i)>0," "," ")+WriteVal(f50(i),1.3)+
>> WriteIf(f100(i)>0," "," ")+WriteVal(f100(i),1.3)+
>> WriteIf(f500(i)>0," "," ")+WriteVal(f500(i),1.3)+
>> WriteIf(f1000(i)>0," "," ")+WriteVal(f1000(i),1.3);
>> }
>>
>> and, with a few changes, in a new IB window, paste the
>>
>> Title="The orbits of 15 seeds of the f(x)=x^2-3/4";
>> function f1(x)
>> {return x^2-3/4;}
>> function f5(x)
>> {return f1(f1(f1(f1(f1(x)))));}
>> function f10(x)
>> {return f5(f5(x));}
>> function f50(x)
>> {return f10(f10(f10(f10(f10(x)))));}
>> function f100(x)
>> {return f50(f50(x));}
>> function f500(x)
>> {return f100(f100(f100(f100(f100(x)))));}
>> function f1000(x)
>> {return f500(f500(x));}
>> for(i=-1.75;i<2;i=i+0.25)
>> {
>> Title=Title+"\ni="+
>> WriteIf(i>=0," ","")+WriteVal(i,1.2)+
>> WriteIf(f1(i)>0," "," ")+WriteVal(f1(i),1.3)+
>> WriteIf(f5(i)>0," "," ")+WriteVal(f5(i),1.3)+
>> WriteIf(f10(i)>0," "," ")+WriteVal(f10(i),1.3)+
>> WriteIf(f50(i)>0," "," ")+WriteVal(f50(i),1.3)+
>> WriteIf(f100(i)>0," "," ")+WriteVal(f100(i),1.3)+
>> WriteIf(f500(i)>0," "," ")+WriteVal(f500(i),1.3)+
>> WriteIf(f1000(i)>0," "," ")+WriteVal(f1000(i),1.3);
>> }
>>
>> Glenn Elert, the author of this interesting book, writes :"...if you
>> wait long enough..."
>> The AFL time is ~2sec and it is not bad at all !!
>>
>> Dimitris
>>
>>
>>
>>
>>
>>
>>
>> Check AmiBroker web page at:
>> http://www.amibroker.com/
>>
>> Check group FAQ at: http://groups.yahoo.com/group/amibroker/files/groupfaq.html
>> Yahoo! Groups Links
>>
>>
>>
>>
>>
>>
>>
>>
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