Re: glitch in cosine

[<pl...@pi...>]

On 10/21/13 02:40, sfeam wrote:
> On Sunday, 20 October 2013 08:22:51 PM you wrote:
>> Hi,
>>
>> I have a curious glitch in plotting the sum of three cosines.
>>
>> set samples 1700
>>
>>              twopi=2*pi
>>             c1(x)=a1*cos(twopi*(x-yz+ph1)/p1)
>>             c2(x)=a2*cos(twopi*(x-yz+ph2)/p2)
>>             c3(x)=a3*cos(twopi*(x-yz+ph3)/p3)
>>             f3(x)=c1(x)+c2(x)+c0+c3(x)
>>
>>    a1=a2=a3=1; c0=3.; yz=1958; p1=1.0;p2=0.5;p3=.25; ph1=ph2=ph3=.1
>>    a3=1;ph3=0.1;p3=0.25
>>
>> fit f3(x) datafile   u (($1)/365.25+1945):2 via
>> a1,a2,c0,ph1,ph2,p2,p3,a3,ph3
>>
>>    plot  datafile u (($1)/365.25+1945):(f3($1)) w l
>
> I suspect that despite your large value for "set sample"
> you are still sampling too coarsely by a factor of a thousand or so.
> The smooth curve you see is probably an aliasing artifact.
>
> 	Ethan
>
>
>
>
>>
>> data either side of that point seem fine and if I use it directly with
>> plot "-" I don't get the glitch.
>>
>>
>> Closing gnuplot session and repeating the plot from file gives same
>> result seen in attached png flie.
>>
>> For the benefit of the list that don't see the file, it looks like a
>> cosine ranging -0.07 and + 0.014 pk to pk with some small ripple with
>> sporadic spikes ranging from 0.025 to 0.075 , glitches are just single
>> points.
>>
>> Irrespective of the actual data fed in , I fail to see how the sum of
>> cosines can have such glitches.
>>
>>
>> If anyone can explain how that could happen I'd like to know, otherwise
>> it looks like a bug.
>>
>> Thanks, Peter.
>>
>>
>>
>>
>>
>>     plot  "-" u (($1)/365.25+1945):(f3($1)) w l
>>
>> 22629  381.81
>> 22636  381.88
>> 22643  381.65
>> 22650  382.62
>> 22657  382.25
>> 22664  381.37
>> 22678  383.09
>> 22685  383.59
>> 22692  384.19
>> 22699  383.76
>> 22706  383.71
>> 22713  383.64
>> 22720  384.28
>> e
>>
>>
>>
>>
>> Final set of parameters            Asymptotic Standard Error
>> =======================            ==========================
>>
>> a1              = 0.0486237        +/- 0.001654     (3.402%)
>> a2              = 0.0265777        +/- 0.001788     (6.728%)
>> c0              = 0.00416031       +/- 0.001169     (28.1%)
>> ph1             = -0.0557476       +/- 0.005409     (9.703%)
>> ph2             = 0.163801         +/- 0.009924     (6.059%)
>> p2              = 0.49982          +/- 0.0001585    (0.03171%)
>> p3              = 0.258274         +/- 0.0005954    (0.2305%)
>> a3              = -0.00192983      +/- 0.00202      (104.7%)
>> ph3             = -0.923156        +/- 0.06458      (6.996%)
>>
>>    G N U P L O T
>>           Version 4.7 patchlevel 0    last modified 2012-10-16
>>           Build System: Linux i686
>>
>>
>

HI,

aliasing was my first thought too but
  set samples 1700000; replot

same thing.


what I intend to be plotting is

  plot  datafile u (($1)/365.25+1945):(f3($1/365.25+1945)) w l

That works. but while fiddling I saw these glitches and went to see 
where they were coming from.

What looks buggy to me is that _whatever_ numbers I throw at it , the 
sum of three cosines should never have spikes.

Is this some internal underflow/overflow problem?

Thanks Ethan,