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3:10 AM
FYI:
in Ask Ubuntu General Room, 3 mins ago, by halirutan
Hi. Quick question: In Ubuntu 14.04 with Unity, when a window becomes unresponsive, it is grayed out and a dialog appears that asks me whether I want to kill the process.
in Ask Ubuntu General Room, 3 mins ago, by halirutan
How can I turn this off?
in Ask Ubuntu General Room, 2 mins ago, by halirutan
(Reason: Mathematica seems to do something weird, because e.g. moving sliders will trigger this unresponsiveness warning after a few seconds. Very annoying)
 
 
1 hour later…
4:24 AM
@MichaelE2 Thank you for the very interesting answer. I did not manage to apply it yet to my problem (in dimension 7, with more complicated expressions). Anyway, my (basic) implementation of "pseudo arc-length continuation" works quite well. The initial point is found with FindRoot. For the initial direction, I do another FindRoot very close from the previous one. I am especially interested in getting all curves; your solution with NIntegrate seems smart.
It returned only a few point in my case. Btw, if think there's a typo in your answer: irst instead of First. Thank you again.
And if you have any ideas how to find efficiently the intersection of curves... That's probably the most tricky part with my algorithm (it cannot handle bifurcations).
 
 
9 hours later…
1:32 PM
@anderstood Thanks for pointing out the typo. I thought what might be helpful is that NDSolve already implements the projection/FindRoot step (in Method -> "Projection" and in solving DAEs). To get arc-length continuations, use x'[t].x'[t] == 1 and initialize x[0] == root, x'[0] == unittangent with the DAE method. One advantage ought to be that NDSolve will stop at a bifurcation, because the system should become stiff.
 
1:43 PM
At a bifurcation, the rank of the derivative will be less than $n-1$, if $f \colon R^n -> R^(n-1)$. These points will be where the determinants of the $n$ square $(n-1) \times (n-1)$ submatrices of the derivative simultaneously vanish. I don't know if that's a good way to find the bifurcation points or not.
 
1:54 PM
Searching for all roots in 7 dimensions is quite a task. One needs fine enough sampling to get a point in the basin of attraction for each solution. Increasing MaxRecursion might help.
 
2:30 PM
Could someone with appropriate versions work out which versions are affected by mathematica.stackexchange.com/questions/100139/… ?
 
@PatrickStevens Ok, I'll do so now
In version 10.0.1, which seems to be the earliest version I have, I get, with a fresh kernel
ClearSystemCache[]; a = 3/Sqrt[2] + 2 Sqrt[2];
Table[GroupBy[{a, a}, N[#, 3] &], {2}]
 
 
2 hours later…
4:13 PM
@halirutan Which room? :)
Hey guys, been a while :)
 
@Öskå This one :-)
Hi @Öskå
 
@halirutan Helloo hellooo
I deleted the comment
 
@Öskå So you want to start developing a language plugin?
Have you read any information on my site about it?
 
Well I've read what the Mathematica one can do, I'vent read anything about how you actually did it
 
@Öskå OK. So you have to write Java and there are many information available, but when it comes to specific details, you will always have to look at the IDEA code and how other plugins did it.
Let me give some links:
I wrote a pretty detailed article about how to set up you dev environment
 
4:27 PM
@halirutan To be honest I just thought your plugin was very well done so I directly thought about you without any first thought
 
You'll find two screencasts there, that should still work.
 
But I have to admit that I could have done some digging first
 
@Öskå No problem. I have stored most of the links.
A very basic tutorial that shows very many things can be found here
Although I have to say that there isn't much description about "why" you have to do something. It only shows you what you have to do to get basic functionality.
@Öskå What language do you try to support?
 
MAPDL, Ansys very basic language
padtinc.com/blog/tag/mapdl padtinc makes a texteditor for that language, but it's not free so I thought maybe I could give it a try
 
@Öskå Is there example code anywhere?
It seems a very specific language.
But it doesn't matter. The more structured and well defined the language is, the more awesome the IDEA support can be.
 
4:34 PM
It's a pretty weird language based on fortran
And here are all the commands: mostreal.sk/html/c-index.htm
 
@Öskå You will have to know it very well, because all the nice features, that separate IDEA from a texteditor, only work because IDEA really parses the language.
The hardest part is to write a lexer and a parser. For the last part you can use a parser-generator, that reads a BNF for your language.
 
@halirutan OK I'm lost already :)
 
@Öskå Lexical scanning separates a string into so-called token.
For instance
1+2
will become {Number, Plus, Number}.
 
I can understand that :P
 
@Öskå I used jflex for this. Since you know Mathematica, you could look at my definition of the language here.
Scroll down and you will understand how it is built up.
The parser is harder to implement compared to this.
 
4:45 PM
aaahhh that's like a million times harder than what I thought
 
@Öskå Yes, it's definitely a bit of work.
 
Well MAPDL is much less complicated that Mathematica so I guess it won't be as hard
 
@Öskå Ansys should be a simple enough language to support w/ just some regexes (if good highlighting is all you want). Intelligent suggestions... now that's a beast.
Are you a vim/emacs kind of person?
 
@R.M. I mostly want a good proposition system so I don't need to look in the docs all the time. And I'm more a vim than emacs )
 
@Öskå There is a difference between "autocompletion" and "intelligent autocompletion" :-)
 
4:53 PM
@Öskå Have you seen this?
 
@halirutan I would rather like the second :P
@R.M. No I did not, I definitely need to look into that
That's basically what I'm looking for so I need to test it :) Have you tried it yourself?
 
@Öskå Nope. Heh, I've only used Ansys for a semester some 10 years ago... Things were way shittier then :P
but I have used Sublime Text and can recommend it. It is a really good GUI text editor w/ good vim keybindings (optional)
 
@R.M. Well lets say that I'm stuck 10 years ago at work :P We are still using notepad++ to code on Ansys.. :)
2
 
😱
 
I do need to try it, in the example it seems to work for cylind but I wonder how good it is with *get :)
That might save me some headache thank you :P @halirutan plugin is fantastic but far from easy to do apparently )
 
5:10 PM
@Öskå Just shows you how much time and effort he has put into it :)
 
@R.M. I had no doubt it represented a lot of them :)
Well thanks a lot to you two, I will try Sublime Text and if it's not good enough for Ansys I will get into it and try a few things based on halirutan job :)
 
 
2 hours later…
6:55 PM
@MichaelE2 I see. I am trying to use NSolve to compare with my function. I am not sure what ImageColorOperationsDump$wavelengths is supposed to do. I will input values manually to try. Btw, I think there's another unimportant typo in domainEvt: it has two "StopIntegration" and no "StartIntegration".
 
@anderstood In that case, the guy was apparently trying to find the roots of a function constructed from CIE color matching functions.
 
@J.M. Shame on me. Thanks. (When I said numerical continuation was not so complicated to understand, I did not mean the whole topic was easy, of course. It's a research topic in itself. I meant that understanding the pseudo arc-length continuation as described in wikipedia is certainly possible for belisarius - in view of his answers here).
 
@anderstood There are a good number of algorithms that are easy to describe, but bitching hard to implement correctly. ;)
 
7:27 PM
@J.M. @MichaelE2 In this case, I can confirm that MichaelE2's suggestion is more efficient than my first implementation. I still have to work on it though. :)
 
@anderstood They're both supposed to be "StopIntegration". One of the things that confused me is that NDSolve "starts" integration at the initial condition, not at t1 in {t, t1, t2}, unless the initial condition happens to coincide with t1. When it the initial condition is in the middle, NDSolve does two integrations, one "Forward" and one "Backward". Basically I wanted NDSolve to stop integration whenever it exited the domain (out either side of the box).
@anderstood Just in case it's not clear: Image`ColorOperationsDump`$wavelengths[[{1,-1}]] are the limits {min, max} set by ChromaticityPloton the domain of the OP's interpolating functions. (The whole vector consists of the sample wavelengths used. I think I used it only for the endpoints, but I wrote some of the code so that the whole vector could be passed and only the endpoints would be used. Kinda sneaky, I suppose.)
 
@MichaelE2 "One of the things that confused me is that NDSolve "starts" integration at the initial condition" - yes, it's been a convenient feature for me thus far.
 
@J.M. It's perfectly fine, once I understood it. I think the docs assume it's obvious, but it's not the way ODEs are taught in a mathematical differential equations class (as opposed to a computational/numerical approach).
The most confusing thing is WhenEvent[x[t] < 0,...] in the backward vs. forward directions. They don't have the same meanings.
 
7:43 PM
@MichaelE2 Yes, event location can be confusing like that.
 
 
3 hours later…
10:33 PM
A quick math question, is this function continuous at the origin?
 
 
1 hour later…
11:38 PM
@xslittlegrass If $\delta$ is the Dirac "function" (distribution), the value in 0 is 0, while in the neighbourhood of 0 (excluding 0), you only get the cosine, which does not have any limit in $\infty$. So I don't think it is continuous. But that's not a proof.
 
@anderstood but the cos(1/w) is only discontinous at the point w=0
and that discontous point seems to be removed by the dirac delta function
 
@MichaelE2 I made a few experiments with NSolve and DAEs. I observed that sometimes, it founds solutions for the whole interval $[-500,500]$ (for example), and sometimes as expected it stops before reaching these values. I then calculate the rank of the derivatives (or the determinant of the jacobians or the square matrices) and it is sometimes less than n-1 (or =0), but usually not. I don't reasons for that. Would you?
@xslittlegrass "removing" w=0 is not enough: continuity implies that the function has to be equal to the limit of cos(1/w) in 0... but it does not have any limit. You might want to consider asking math.stackexchange.com.
 
@anderstood I actually did.
0
Q: Fourier transform of $e^{-\delta (x)} \cos\left(\frac{1}{x}\right)$

xslittlegrassI have a function $$ f(\omega) = \exp\left(-\frac{\gamma}{\gamma^2+\omega^2}\right)\cos\left(\frac{\gamma}{\gamma^2+\omega^2}\right), $$ and I'm trying to calculate its Fourier transform at the limit of $\gamma\rightarrow 0$: $$ \mathcal{F}\left[\lim_{\gamma\rightarrow 0} \, f(\omega)\right]....

 
This is what Mathematica says:
ff[t_] = Exp[-DiracDelta[t]]*Cos[1/t];
Limit[ff[t], t -> 0]
Interval[{-1, 1}]
 
@anderstood but consider the original function
it seems the limit at is 0 when gamma -> 0 and w->0
 
11:54 PM
@anderstood Being close to a singular point (of the derivative) might not be close enough to get the rank to drop. The size of the determinant is not necessarily a safe indicator. At this point though we begin to step outside my limited background in numerical linear algebra. The condition number might be the thing to consider; see mathematica.stackexchange.com/questions/11131/…
 
@MichaelE2 I'll investigate. Anyway you've been of great help, thank you very much!
 
@anderstood for example
 
@xslittlegrass I don't understand how f(delta(x)) is defined. I know delta(f(x)), but not the other way around.
 
@MichaelE2 I'm not sure of that either, I simply get from the limit of the function f(w)
for example
since
 

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