Formulas and/or algorithms for FFT's are available a zillion places
on
the net although I wouldn't bother with the one at numerical
recipes.
Formulas for MESA are also available on net although they
are a little
harder to find as I think someone who is probably the
best known for this
technique although not the originator of the
algorithm or even its use
with price data has done his best to
squelch a lot of what otherwise would
be available.
Writing efficient AFL for either is fairly straight
forward with no
need for extra hardware ( FFT Chips ?! ) or DLL's
...
--- In [EMAIL PROTECTED]ps.com,
"Ton Sieverding"
<ton.sieverding@...> wrote:
>
>
Thanks Tomasz. First I do not understand why it involves 3.000 * (
Bars# )
* ( Bars# ). Why not just 3.000 * ( Bars# ) ? I did the same
test in Excel
with 3.000 * ( Bars# ) and got no delay. After your
email I did it again
with 3.000 * ( Bars# ) * ( Bars# ) and got a
delay of several minutes. But
why two times 1.000 ?
> Secondly I just copied the code I got from Fred
and tried to speed
it up by removing the second and third harmonic
calculation. Of
course it was faster but still to slow for me. Frankly I
do not
understand how you can remove Cum() and LastValue() as the results
are being used for the calculation of the harmonic.
> Finally I
agree that Log calculations will speed up the process and
will look for
FFT code that does use Log's. I only have used full
Fourier Analysis in
electronics and have no experience with the Fast
Fourier Transform.
Although I agree with Ara that a FFT card is
probably needed for the real
good performance. Do you have any
experience with these goodies ?
>
> Ton.
>
> ----- Original Message -----
> From:
Tomasz Janeczko
> To: [EMAIL PROTECTED]ps.com
> Sent: Thursday, September 07, 2006 1:32 PM
> Subject: Re:
[amibroker] Re: Cycles and Mesa
>
>
>
>
Hello,
>
> You are doing 24 * 16 * 8 * (NUMBER OF BARS)
iterations per bar
(in the most inner loop you are using Cum() function
which is
cummulative
> sum over all bars). So entire execution
involves 24 * 16 * 8 *
(Number of bars) * (Number of bars). If you say
have 1000 bars you
end up with
> 3 billion operations.
> To
speed it up you would need to REMOVE Cum() and LastValue()
from inner loop
(they are not needed in fact).
>
> The code below is a sample of
very inefficient coding. Properly
coded FFT requires only N*logN
operations
>
> Best regards,
> Tomasz Janeczko
>
amibroker.com
> ----- Original Message -----
> From: Ton
Sieverding
> To: [EMAIL PROTECTED]ps.com
> Sent: Wednesday, September 06, 2006 12:16 PM
> Subject: Re:
[amibroker] Re: Cycles and Mesa
>
>
> Rakesh when talking
about the Fourier code ( Fred -> Ehler ? )
you sent me and looking for
what you want to get, why not just taking
the first harmonic and
forgetting the rest of the code. In this way
you have your current cycle
length - at least this is what I think
you want to get - and this will
also solve an important part of the
speed problem. So take Y01 and take
out the linear Y and you should
get the first harmonic. But as I already
told you, this is not what I
have in mind for the first harmonic
...
>
> Also I do not understand why this code is still so slow.
When
looking to the For Loops I am getting 24 * 16 * 8 being 3.072
iterations per Bar. So why is the code so slow ? Thomasz am I to
optimistic ? Dimitri do you have any idea ? You can speedup the
calculation by setting n = 6, g01=1.0 ( starting g=1 ) and stp0 = 200
( starting stp0 = 400 ). I do not see any difference in the graph and
the speed should be of course 12 * 8 * 4 = 384 or 8x the old
speed ...
>
> Ton.
>
>
>
>
_SECTION_BEGIN("Fourier Analysis Elementary");
> //
=============================================================
> // Elementary Fourier analysis, by D. Tsokakis, May 2004
> //
=============================================================
> t=Cum(1)-1;
> A=Param("Rsi",50,1,100,1);
>
B=Param("smooth",100,1,120,1);
> C1=MA(RSI(A),B);
> start=Cum(IsTrue(C1))==1;
> t1=ValueWhen(start,t);
>
> //
PlotShapes(shapeDownTriangle*start,colorYellow);
>
> //
C10=ValueWhen(start,C1);Plot(C1,"C1",colorBlack,8);
> GraphXSpace=2;
> x = Cum(1);
> lastx = LastValue(
x );
> Daysback = LastValue(Cum(IsTrue(C1)));
> aa =
LastValue( LinRegIntercept( C1, Daysback) );
> bb = LastValue(
LinRegSlope( C1, Daysback ) );
> yy = Aa + bb * ( x - (Lastx -
DaysBack) );
> yy=IIf( x >= (lastx - Daysback), yy, -1e10 );
>
> // Plot( yy, "yy", colorRed );
> detrend=C1-yy;
> new1=detrend;
>
Hor=LastValue(Cum(new1)/Cum(IsTrue(C1)));
>
pi=4*atan(1);
> n=12;
>
> //
===============================================
>
// Fundamental period, crude approximation
> //
===============================================
>
> error00=10000;
> per01=0;
> g01=0;
>
phi01=0;
> stg0=0.5;
> stp0=100;
>
>
for(phi=0;phi<2*pi;phi=phi+pi/n)
> {
>
for(g=0.5;g<=8;g=g+stg0)
> {
>
for(per=300;per<=1000;per=per+stp0)
> {
> f=1/per;
> y=Hor+g*sin(2*pi*f*(t-t1)+phi);
>
error=LastValue(Cum(abs(y-new1)));
> if(error<error00)
> {error00=error;per01=per;g01=g;phi01=phi;}
> }
> }
> }
>
> f01=1/per01;
>
y01=Hor+g01*sin(2*pi*f01*(t-t1)+phi01);
>
>
Plot(y01,"y01",colorRed,4);
>
> _SECTION_END();
>
>
> ----- Original Message -----
> From: Ara
Kaloustian
> To: [EMAIL PROTECTED]ps.com
> Sent: Wednesday, September 06, 2006 6:12 AM
> Subject: Re:
[amibroker] Re: Cycles and Mesa
>
>
>
>
Rakesh,
>
> John Ehler's code is quite usable with AB... it
produces the
dominant cycle value. It is a bit CPU intensive but I tried
using it
at the start of a new bar (instead of using it with every trade)
and
that made the CPU load quite acceptable.
>
> My issue
with both Ehler's code anf FFT is that I was not
satisfied with
either.
>
> Since you were getting good results with FFT, you
might try
Ehler's code.
>
> Theoretically ehler's code should
be better since it looks at
the most recent data, while FFT would need
much longer data to
produce usefuk cycle lengths.
>
> Good
luck
>
> Ara
> ----- Original Message -----
> From:
Rakesh Sahgal
> To: [EMAIL PROTECTED]ps.com
> Sent: Tuesday, September 05, 2006 5:33 PM
> Subject: Re:
[amibroker] Re: Cycles and Mesa
>
>
> Ton
>
>
Back in the old MetaStock days I had fiddled around with
using the
packaged FFT in MS. I had used it to extract the current
dominant cycle
length in a market and then used it to compute
studies. The results were
quite satisfactory. Then I changed
platforms to AB and the whole idea got
shelved. Subsequently I have
tried to find a way of extracting current
dominant cycle length in an
issue/market in AB but have not seen any way
of using it which my non-
engineering/mathmetician brain could
comprehend. It was in this
context I tried DT's code. Unfortunately (a) it
was computing power
intensive and (b) the results were beyond my
comprehension so I gave
up on it. I still would like to find a way of
ascertaining what the
current cycle length is in an issue but have not
been able to make
much progress. Perhaps someone on the list could throw
up some ideas
which are implementable on the AB platform.
>
>
> R
>
>
> On 9/6/06, Ton Sieverding
<ton.sieverding@...> wrote:
> Thanks Rakesh. I've tried
underneath mentioned AFL code
for Fourier analysis. It does something but
I have some questions :
>
> 1. I have the feeling that the code
uses a lot of
computer power. When modifying the parameters it takes
several
seconds ( about 5 sec ) before I have a result on the graph. I am
using a Ghz 2.6 CPU with 1GB internal and have never seen my computer
so slow. Do you have the same experience ?
> 2. What I would like
to see is a couple of sine waves
being the harmonics of the original time
series. So more or less the
same picture as Fred's Cycles. But that's not
what I get. Also the
calculations for the Fourier analysis does not look
familiar to me.
Where can I find the logical background behind these
formulas ?
>
> Ton.
>
>
> ----- Original
Message -----
> From: Rakesh Sahgal
> To: [EMAIL PROTECTED]ps.com
> Sent: Tuesday, September 05, 2006 2:12 PM
> Subject: Re:
[amibroker] Re: Cycles and Mesa
>
>
> If you are
interested in Fourier Analysis in AB
environment you should refer to the
work of Dmitris Tsokasis who
shared his work on Fourier Analysis with the
group. Am pasting below
his code. I have never used it and would not know
how to apply it in
a meaningful manner. Hope you find it useful.
>
>
> R
>
>
>
===============================
> // Elementary Fourier
analysis, by D. Tsokakis, May 2004
>
> t=Cum(1)-1;
>
> A=Param("Rsi",50,1,100,1);
>
>
B=Param("smooth",100,1,120,1);
>
>
C1=MA(RSI(A),B);
>
> start=Cum(IsTrue(C1))==1;
>
> t1=ValueWhen(start,t);
>
>
PlotShapes(shapeDownTriangle*start,colorYellow);
>
>
C10=ValueWhen(start,C1);Plot(C1,"C1",colorBlack,8);
>
> GraphXSpace=2;
>
> x = Cum(1);
>
>
lastx = LastValue( x );
>
> Daysback =
LastValue(Cum(IsTrue(C1)));
>
> aa = LastValue(
LinRegIntercept( C1, Daysback) );
>
> bb = LastValue(
LinRegSlope( C1, Daysback ) );
>
> yy = Aa + bb * ( x - (Lastx -
DaysBack) );
>
> yy=IIf( x >= (lastx - Daysback), yy, -1e10
);
>
> Plot( yy, "yy", colorRed );
>
>
detrend=C1-yy;
>
>
new1=detrend;Hor=LastValue(Cum(new1)/Cum(IsTrue(C1)));
>
> pi=4*atan(1);n=12;
>
> // Fundamental period, crude
approximation
>
>
error00=10000;per01=0;g01=0;phi01=0;stg0=0.5;stp0=100;
>
> for(phi=0;phi<2*pi;phi=phi+pi/n)
>
>
{
>
> for(g=0.5;g<=8;g=g+stg0)
>
> {
>
> for(per=300;per<=1000;per=per+stp0)
>
>
{f=1/per;
>
> y=Hor+g*sin(2*pi*f*(t-t1)+phi);
>
> error=LastValue(Cum(abs(y-new1)));
>
>
if(error<error00)
>
>
{error00=error;per01=per;g01=g;phi01=phi;}
>
>
}}}
>
>
f01=1/per01;y01=Hor+g01*sin(2*pi*f01*(t-t1)+phi01);
>
> Plot(y01+yy,"y01",colorSkyblue,4);
>
> Title=Name()+" [ Sample="+WriteVal(Daysback,1.0)+"
bars ]"+"\nyS0="+WriteVal(Hor,1.2)+
>
>
"\nyS01="+
>
>
WriteVal(g01,1.1)+"*sin(2*pi*(1/"+
>
>
WriteVal(per01,1.0)+")*(t-t1)+"+
>
>
WriteVal(12*phi01/pi,1.0)+"*pi/"+WriteVal(n, 1.0)+"),
Error1 ="+
>
>
WriteVal(LastValue(Cum(abs(y01-new1))),1.0)+", Error1/bar
="+
>
>
WriteVal(2*LastValue(Cum(abs(y01-new1)))/Daysback,1.2)+"
%";;
>
> // Fundamental period, detailed
approximation
>
>
error0=10000;per1=0;g1=0;phi1=0;stg=0.5;stp=10;
>
> for(phi=0;phi<2*pi;phi=phi+pi/n)
>
>
{
>
> for(g=0.5;g<=8;g=g+stg)
>
> {
>
> for(per=per01-stp0;per<=per01+stp0;per=per+stp)
>
> {f=1/per;
>
>
y=Hor+g*sin(2*pi*f*(t-t1)+phi);
>
>
error=LastValue(Cum(abs(y-new1)));
>
>
if(error<error0)
>
>
{error0=error;per1=per;g1=g;phi1=phi;}
>
>
}}}
>
>
f1=1/per1;y1=Hor+g1*sin(2*pi*f1*(t-t1)+phi1);
>
> Plot(y1+yy,"y1",colorBlue,4);
>
>
Title=Title+
>
> "\nyS1="+
>
>
WriteVal(g1,1.1)+"*sin(2*pi*(1/"+
>
>
WriteVal(per1,1.0)+")*(t-t1)+"+
>
>
WriteVal(12*phi1/pi, 1.0)+"*pi/"+WriteVal(n,1.0)+"),
Error1 ="+
>
>
WriteVal(LastValue(Cum(abs(y1-new1))),1.0)+", Error1/bar
="+
>
>
WriteVal(2*LastValue(Cum(abs(y1-new1)))/Daysback,1.2)+"
%";;
>
> // 2nd Harmonic
>
>
error0=10000;
>
>
for(phi=0;phi<2*pi;phi=phi+pi/n)
>
> {
>
> for(g=0;g<=8;g=g+0.1)
>
> {
>
>
per2=per1/2;f=1/per2;
>
>
y2=y1+g*sin(2*pi*f*(t-t1)+phi);
>
>
error2=LastValue(Cum(abs(y2-new1)));
>
>
if(error2<error0)
>
>
{error0=error2;g2=g;phi2=phi;}
>
> }}
>
>
f2=1/per2;y2=y1+g2*sin(2*pi*f2*(t-t1)+phi2);
>
> Plot(y2+yy,"y1",colorYellow,8);
>
>
Title=Title+
>
> "\nyS2="+
>
>
WriteVal(g2,1.1)+"*sin(2*pi*(1/"+
>
>
WriteVal(per2,1.0)+")*(t-t1)+"+
>
>
WriteVal(12*phi2/pi,1.0)+"*pi/"+WriteVal(n,1.0)+"),
Error2 ="+
>
>
WriteVal(LastValue(Cum(abs(y2-new1))),1.0)+", Error2/bar
="+
>
>
WriteVal(2*LastValue(Cum(abs(y2-new1)))/Daysback,1.2)+"
%";;
>
> // 3rd Harmonic
>
>
error0=10000;
>
>
for(phi=0;phi<2*pi;phi=phi+pi/n)
>
> {
>
> for(g=0;g<=8;g=g+0.1)
>
> {
>
>
per3=per2/2;f=1/per3;
>
>
y3=y2+g*sin(2*pi*f*(t-t1)+phi);
>
>
error3=LastValue(Cum(abs(y3-new1)));
>
>
if(error3<error0)
>
>
{error0=error3;g3=g;phi3=phi;}
>
> }}
>
>
f3=1/per3;y3=y2+g3*sin(2*pi*f3*(t-t1)+phi3);
>
> Plot(y3+yy,"y1",colorWhite,8);
>
>
Title=Title+
>
> "\nyS3="+
>
>
WriteVal(g3,1.1)+"*sin(2*pi*(1/"+
>
>
WriteVal(per3,1.0)+")*(t-t1)+"+
>
>
WriteVal(12*phi3/pi,1.0)+"*pi/"+WriteVal(n,1.0)+"),
Error3 ="+
>
>
WriteVal(LastValue(Cum(abs(y3-new1))),1.0)+", Error3/bar
="+
>
>
WriteVal(2*LastValue(Cum(abs(y3-new1)))/Daysback,1.2)+"
%";
>
> /*
>
>
===============================
>
>
>
> On 9/5/06, Ton Sieverding <ton.sieverding@...> wrote:
> I certainly like what I see Fred. But do you have the
AFL code
for this picture also ?
> Is this based on Fourier stuff ? I have tried
to find
the FTT instructions in AFL but cannot find them. Do they exist in
AFL or did you use some special DLL ?
>
> Kind
regards,
> Ton Sieverding.
>
> ----- Original Message -----
> From: Fred Tonetti
> To: [EMAIL PROTECTED]ps.com
> Sent: Tuesday, September 05, 2006 6:18 AM
> Subject:
[amibroker] Re: Cycles and Mesa
>
>
>
> For example
>
> <<...>>
>
>
>
>
------------------------------------------------