Menu
▾
▴
gnuplot-beta
|
From: <pl...@pi...> - 2013-10-20 23:48:20
Attachments:
gnuplot-oops.png
|
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
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
|
|
From: sfeam <sf...@us...> - 2013-10-21 00:40:08
|
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 > > |
|
From: <pl...@pi...> - 2013-10-21 09:23:24
|
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, |
|
From: Hans-Bernhard B. <HBB...@t-...> - 2013-10-21 15:49:01
|
[Ooops, forgot to CC the list.] On 21.10.2013 02:40, sfeam wrote: > 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. The setting of "set samples" has no effect on this plot, because the plot is made from data: plot datafile u (($1)/365.25+1945):(f3($1)) w l But neither the current CVS version nor 4.6.2 shows the problem here. The reason for that may very well be that the subset of the data presented to us is missing one data point (at 22671, transformed x value 2007.07), which might be just where that "peak" is. |
