So if you use it only for Mathematica, that you can basically turn off almost everything. If this doesn't improve performance, then I have no idea what you are doing wrong.

Except for the startup, IDEA has always great performance on all machines I'm using it on.

@Rojo, if all the off-diagonal entries are positive, then your matrix is similar to a symmetric tridiagonal matrix, and you can use the usual methods. If there are negative entries… that family of problems is known to have a number of members that are ill-conditioned with respect to the eigenproblem.

@Guesswhoitis. Still around and do you have Mathematica 10 and can test something?

Why does this work

Plot[EllipticTheta[4, 0, E^(-2*x^2)], {x, 0, 3}]

while this here does not

Plot[1 - EllipticTheta[4, 0, E^(-2*x^2)], {x, 0, 3}]

Btw, the problem is the 0 in the plotrange. Additionally, changing the 1-... to 1.0-... makes it work.

In version 9 this runs without problems

Sorry, @hal, back to gedanken for me. :( But that seems like a nasty bug.

But EllipticTheta[4, 0, 1] ought to remain unevaluated (it's precisely at the edge of the analyticity domain).

@Guesswhoitis. wonderful, thanks. They are all positive (actually negative but its the same)

@Rojo, yes, that's okay; should have been "all off-diagonal entries are of the same sign".

Here is the classical EISPACK implementation, it's FORTRAN, but it should be readable.

This was noted in Wilkinson's book; but I forgot which page and I'm far away from my copy.

Anyway, you are lucky. The tridiagonal matrices that are not similar to symmetric ones are often ill-conditioned.

@halirutan Plot[1. - EllipticTheta[4, 0, E^(-2*x^2)], {x, 0, 3}] works

@RolfMertig It's what I wrote in the last line here:

I'm having a brain freeze that is in need of thawing. I'd like to get a polygon from this image, which is a set of points which I've Dilated in order to get a thick line. Is there a ComponentMeasurements argument that returns a better polygon than "ConvexVertices"?

I have a non-convex but single connected polygon. Imagine a "blob" (whatever comes up when you google for that word). Now I want to "blow up" this blob, in a way similar to what Dilate does. What's the simplest way to do this?

Ultimately I will need to parametrize this blown up outline to place equidistant points on it. I'm mentioning this only to give an idea of what sorts of output formats are useful. Images are not really useful for this (which is why I want to avoid Dilate). An ordered list of points (like in Polygon) is very useful.

Ideas?

*singly connected (i.e. no holes)

To explain even more why I want this: I have some sort of map. Imagine e.g. Australia divided into counties. I will have a line drawn from the centre of each county to the outside of the map and put a label there. The location of the labels will be on this "blown up" outline.

In my application most labels simply don't fit inside their areas, this is why I need the connector lines.

Does anyone know of an elegant way to use NestList so that it only stores every, say other element? e.g. it might return {x, f[f[x]], f[f[f[f[x]]]], f[f[f[f[f[f[f[f[x]]]]]]]]} etc.

@blochwave probably not ... [[;; ;; 2]] would filter it though

indeed, but that doesn't keep memory use down :-(

may have to sacrifice elegance in that case

@blochwave Not very elegant: NestList[Nest[f, #, 2] &, x, 3].

@Szabolcs ah, ineresting!

@halirutan forgot to scroll ... sorry.

@SquareOne Indeed, just received the usual email:

@Guesswhoitis. Very helpful, thanks!

@blochwave Thanks for letting us know! You're always the first one.

@blochwave

@Szabolcs :-D

@Guesswhoitis. thanks!!!

@blochwave -enhanced by over 100 new functions-- . That's frightening

@belisarius I want to know what they are! Nothing here yet: wolfram.com/mathematica/quick-revision-history.html

@bel, TweetToCloud[]?

@Guesswhoitis. EmbarrassYourselfByNotBeingAbleToKeepWithAllFunctionNames[]

@blochwave Now, that frightens me more :)

Somehow I'm pessimistic; likely less than a quarter of them will be mathematical, and a good amount of that would be syntactical diabetes.

Quick question: am I missing anything by not being a member of Wolfram Community?

"Increasing cloud operations" == a permanent supercell will form in your server room, causing havoc and spreading despair.

BTW: does Wolfram Data Drop have some sort of published pricing structure? At least they have hid it well enough I've pretty much lost interest...

…your cables will be even more entangled than they already are!

@Guesswhoitis. @kirma I believe that WR is setting a course for the No-Users' land. They weren't able to compete (for example with the overrated Matlab) in a narrow field so they are trying to broaden their scope. But way toooo much

I'm sort of interested of IoT data collection, now that things like this (dx.com/p/…) are available at such prices. It's really a microcontroller with sufficient capacity to run TCP/IP stack, connect to remote servers over (integrated!) wifi, and of course, read data from your sensors.

@belisarius Yes, sadly I feel the same.

@kirma That's really cheap

Well feck, MATLAB's another one slowly being barnacled. Yeesh.

Runs stuff like nodemcu.com/index_en.html

Ever noticed that there aren't any new Standard Packages anymore? Anything new is instantly a kernel function (that is actually being loaded from a dump file BTS)…

@Guesswhoitis. I wonder from where are they envisioning their future revenues to come

I'd say the cloud push by WRI might make a bit more sense if they would package their cloud-oriented offerings to clearly productized and licensed virtual appliances which you can drop on your private or cloud service provider infrastructure with ease. And offer the same service and migration paths between Wolfram-provided and customer-controlled clouds.

@Guesswhoitis. I gave up my past efforts to induce others to use Mma. The learning curve is now both too steep and too high

(I don't want to use the term "IoT", even as a joke.)

@bel, I can understand. A shame…

For instance, that "data drop" could make sense if I'd know I can migrate those datasets to my own virtual appliance system trivially, instead of needing to be a government lab to turn their head.

"government lab" - it's already passing through the NSA already, tho. :D

@Guesswhoitis. Like any other thing being transmitted over the inet

Heh. I was thinking more of places like LLNL which could speculatively be the rare customers that actually buy these private cloud offerings from WRI.

@kirma i wouldn't trust nuclear security issues to Mma code :)

Because they probably can't let people use things like WolframAlpha even casually, in their paranoia and bureaucratic preventive measures...

I wonder where's the agreement I have to click every time I upgrade my license. It has stuff about nuclear and chemical weapons design being a no-no... at least if you do it abroad in selected countries.

Well, maybe CERN… but as @bel says, would you trust Mathematica with your smashed particles?

Eh...

As it looks to me, they have as many bugs as there are features now. It's either haste or hubris; I can't tell.

@Guesswhoitis. I don't think CERN has any sort of secrecy concerns regarding use of cloud services, though.

@Guesswhoitis. plus CERN have a lot of C++ code already...

@Guesswhoitis. I believe they started to change their revenue model on V9, heading for somewhere I can't discern. It's not haste, but internal pressure to arrive at a certain port, I believe.

@bloch, right, their software library. It would now not be shocking if something in there does a better job than the corresponding Mathematica command. :)

@kirma, right, so they "might" have more reason to "go cloud" than Livermore or Los Alamos or Oak Ridge.

@Guesswhoitis. Welll. I think if they actually want that stuff (cloud, instead of, say, clusters), they would want to run their own, or on their chosen infrastructure provider which they can change. I also bet there are many other potential customers that would want that to be a possibility. Marketing materials I've found are not very strongly indicative WRI would have taken the hint, though. Hint being: people don't want to get trapped to SaaS model when there are no alternatives to ...

the software vendor.

SaaS for mail is pretty OK, but if your only SaaS provider and installation model for software is buying it from WRI, you have trapped yourself.

@kirma WRI was never good at "open" anything

I don't think it would need to be open. It would need to be deployable, and have clear pricing models for different alternatives.

Hi, I have a quick question. I'm trying to plot multiple graphs using Show[p1,p2,p3,p4], however, I would like to increase the window for the y-values, is there any way that I can do this?

@Jun-GooKwak What do you mean by "increase"?

@belisarius So when I use the Show[] function, it automatically restricts my window from y=[-1,15]

@belisarius I would like for the show function to extend the y window, say from [-10,10]

You can use PlotRange either with Plot, or Show around it.

Without explicitly setting the PlotRange, the setting of the first plot is inherited.

See "Possible Issues" section on Show manual page, and PlotRange in general (and for Plot).

@kirma PlotRange resolved it. Thank you.

@Guesswhoitis. You were right in that it was the settings of the first plot, thanks.

Depending on type of your graph, PlotRange -> All on Show may be the simplest solution.

I'm a bit worried about WRI in the sense that if 10.2 is coming soon and it'll have bunch of new functions again, they are probably going to charge a full upgrade price from home users again.

Are they running out of income?

~100 euros for major-version upgrade is OK, but not two times a year for increments with somewhat questionable quality measures.

"If you're going to make me an unwitting alpha tester, at least have the decency to give me bugfixes for free. :P"

@kirma That was what I was trying to say above. Where they believe their income is going to come from? I don't understand their business model

For that 100 euros, I essentially got some helper functions and new forms, and DimensionReduce/DimensionReduction (which are marked experimental, by the way). Nothing else is either useful or usable in my experience.

@belisarius I feel it has been pretty opaque even on the old times regarding who their money-making customers actually are. Are they private businesses? Is there lot of them? Are they government organizations? Universities? If universities, how large portion of license income comes from users that are only theoretical in existence?

I recall they boasted "million users" or something way back. That was definitely theoretical number of students using the product.

Or even "students over the years."

If so, broadening their base is not too good a method for their "millions of users".

(FWIW: most of the time I used Mathematica, it was at some university installation.)

Well, they have acquired that with WolframAlpha, but turning them to good profitable customers... well, I would actually want to pay for them for useful products. Sadly their focus spread all over hasn't produced any products other than Mathematica that I see point paying for.

Speaking of… I'm missing the logic of their Alpha smartphone app not being free, when you can use Alpha from within the phone's browser…

I have used Mathematica since '95, but it was first university installation, then a student license... and there was probably a gap of several years during which I just occassionally logged in in the university systems for it and didn't really develop my skills... but then when Home Edition came around, I got more active again, and especially with Mma.SE, much more so.

(A proper laptop three years ago might have affected this, too. I actually sit in bars and tinker with Mma large portion of the time with it.)

I really think that it's a bit sad that Mma.SE is probably best promotion they have for their product at the moment.

Haha, when I still had my notebook, I got gawkers at coffeeshops while I was doing my artwork.

Not that Mma.SE would be bad by any measure, but... usually it's companies that do it on their own.

Ouch. :)

@kirma And instead of giving momentum to us ... they are competing!

Personality of a certain guy naming products and a language after himself might be a bit to blame. :I

It was in all likelihood automated, but SW just sent me an e-mail asking me to use his cloud… :D

something about it being "the start of his dream" or somesuch.

Heh.

@Guesswhoitis. A New Kind of Dream, for sure

In Finnish, selling "cloud" can mean either cloud services, or weed. Constant source of puns...

That meme is not going to go stale anytime soon with their fine work… :P

The weed can sometimes be more useful than the cloud, tho. One of the two can relieve headaches. ;)

I wish WRI could actually make a responsive modern Web technologies based FE replacement, including rendering more or less entirely. I wonder if we are going to see it eventually.

Until that happens, cloud UI offerings are a bit meagre.

An FE implemented as Ajax… hmm…

Is ParallelTable somewhat faster alternative to Table?

@psimeson It attempts to run the code on multiple kernels, in practice multiple CPU cores in parallel.

All code doesn't want to parallelize, and some code with side effect dependencies may produce unexpected or non-repeatable results, though. Before you use it, you should have an idea what's good for it.

Like always, if you have a chance, you should write your code running inside ParallelTable purely functionally, without side effects outside single invocation of table item computation.

@Guesswhoitis. Yes! The awesome experience to wait 30 seconds until a simple webpage is loaded... It's like in 1995.

@psimeson Documentation is your friend. :)

@halirutan What sort of page?

Ah... :)

:22479681

(first posted by our toad)

I'd say modern browsers could easily run the whole FE nowadays, if WRI just had sufficient interest to make that happen. Initial load time might not be small, but modern web applications can also tell the browser to permanently cache considerable portions of content.

Then again, I have watched a web UI being crafted for a highly professional system, using modern Web standards. I think these people have now spent at least 20 man-years on it, and it's still not a replacement of any kind (well, it's not yet meant to be) for desktop UI.

And these people are not amateurs by any means.

So, it takes a bit of time.

@kirma I had problem with it. I am trying to do this: mathematica.stackexchange.com/questions/9004/… but for multiple chain so I had to use ParallelTable for multiple chain and it was too slow compared to Table

@psimeson What's the "problem" there?

@hal, alright, better to not spread myself thin, then. :)

It's not the same tho; no modem sounds. ;)

@kirma That animation is from this morning, I was actually a bit surprised at how fast it is. I had a different recollection of it...

…I notice that the predictive interface is also on while all that was happening. Wow.

@kirma For many purposes it seems to be ready I think, certainly for those who use Mathematica for math.

@Pickett So, they have made it client(browser)-side?

I did some programming cloud stuff some weeks ago when not next to my laptop, and I think it was snappier than before. Not graphics, though.

@kirma oh, you think we need that too?

@kirma I don't understand how that would work really. You need a server of some kind.

@Pickett Looks like client-side to me. Modern browsers have pretty much everything you need for dynamic 3D graphics.

@kirma Yeah, I mean certainly the Mathematica FE can be ported to the browser and that's what they've done. The kernel is still on their servers though, and I don't think that can change.

@Pickett They could translate that to asm.js or future wasm quite easily, but that wouldn't be a small thing to load. Nothing preventing it, though.

Have to take a look at Manipulate on it.

Now there's a challenge…

I'm preeetty convinced graphics frontend has been reimplemented on browser entirely. Manipulate responsiveness is still tuned down, though. Maybe to save back-end capacity?

could be

@kirma I don't know if you've seen this but I made some experiments with cloud APIs and posted them here. The servers do respond veyr quickly, so that's not the problem anyhow.

Also, of course, arbitrary Manipulate might generate quite an amount of data per frame, even if it's symbolic data for the rendering front-end.

f.e. when I use the arrows in the BMI calculator form.

Ah, also that increasing trouble running CDF plugin on browsers. I see two necessary components for this: efficient Javascript-based rendering on browser, and ability to deploy corresponding kernel content also somewhere else than "Wolfram Cloud". That is, servers you control yourself.

FE part seems to be done to an extent, but the other one...

@kirma Concerning CDF plugin, if I understand well John Fultz (wolfram.com/broadcast/video.php?v=1246, see min. 41'55) "the future of the web browser plugin does not look good, ... the end is on the horizon !"

Flatten[Outer[
   Plus,
   CirclePoints[1, 100],
   {{0, 0}, {1, 0}}
   ], 2] // ListPlot

Why are they lines and not circles?!