@NasserM.Abbasi well, OK. without knowing anything else, and just looking at x'[t] and theta'[t], I'd we'd need to think about the physics of this, not NDSolve. but maybe I'm wrong
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@does it really not? I see to remember using it, and something like having to use normal (graphics, not logarithmic) coordinates, but right now can't check as my machines are busy and I am writing on an (apparently now ancient and obsolete) iPad
baah.. never mind. I figured it out. I assumed that using the original coordinates for a point in epilog would work because that's what's displayed on the axes, but I need to use the log10 coordinates
@acl Still not right though... the two coordinate systems differ by some scaling factor. i.e., I need to use k Log10@coord, where k is unknown (or some quirky hidden relation)
I was talking to Jarrod the other night about the early days of Stack Overflow. I then realized SO came out of private Beta three years ago.
What better way to celebrate this milestone than making a T-shirt for it?
I wanted to come up with a design that's interesting and regular SO users can r...
It was after the gaming shirt design, I realized the design isn't just about the community site itself. it's really a total branding package, from the site design, community blog, mod cards, user cards, tshirt, stickers, misc promos etc.
It might surprise you that finding the eigensystem of a banded matrix can be faster than performing Gram-Schmidt on a dense matrix of comparable size...
@J.M. Hmm. I'm just beginning to use numerical computation - most of my work until now was done analytically. I have no idea of the algorithms used in one case or another, so I'm not really surprised. Thanks though.
I'm actually puzzled by the behaviour in this question, which I've replicated. Is this just one of those fundamental calculus things that I've forgotten?
@Verbeia well, it doesn't always pull the constants out... try replacing q[t] with 1 or something, for example. It can't get more constanty than that! I think I might have seen a question somewhere on it. Maybe not. I think Mathematica figures out that it cannot proceed anywhere with this integral and doesn't bother pulling the constant out. This is reasonable, given that the general behaviour when it cannot do something is to return the input unevaluated
Recently, we received two project Euler questions:
How to find palindromic numbers (Project Euler #4)?
How to improve the performance of solutions to Project Euler (#39)？
I won't claim they are off-topic here. In fact, they often make exemplary Mathematica questions. However, I feel it goes a...
@J.M. Good question, "SunsetColors" seems to be closest, but I don't think it's any of the ColorData["Gradients"]. I would have expected AbsoluteOptions[MatrixPlot[mat], ColorFunction] to return something but it doesn't.
You should also be aware that MatrixPlot does some rescaling of the matrix entries internally, so plugging this into ArrayPlot wouldn't give the exact same answer unless the same rescaling is used
I tend to prefer ArrayPlot[] myself, since all I use it for is to look at sparsity patterns. It's just that the coloring by MatrixPlot[] got me curious, since I couldn't copy it...
@SjoerdC.deVries You know those code dumpers who pile pages of code upon us and say "it doesn't work"... I've always wanted to tell them to try On[] and look for messages and see where the error lies
@SjoerdC.deVries I don't think PE questions should be closed... we should evaluate it just like any other question — if it is about Mathematica and reasonably scoped (i.e. not 95% math, 5% basic mma type), then it should stay open
@J.M. according to the docs, the eigenvectors for degenerate eigenvalues are chosen to be linearly independent, not orthogonal. This applies to Hermitian matrices, too. This has bitten me fairly often, unfortunately.
In Stephen Wolfram’s personal analytics blog post, he showed a number of interesting plots of the steps he’s recorded on his pedometer over the past two years. Each plot highlighted a different feature of his activity. For example, this daily step distribution makes it clear that Stephen is typically most physically active around noon: In [...]
@ J.M quick question: do you know if there is a mathematica function, say Digitize[] which would behave like that: given tt = {5, 3, 1, 5, 5, 2, 1, 5} Digitize[tt, Range[1, 6]] would return {6, 4, 2, 6, 6, 3, 2, 6} i.e. return the index for each tt of the bin in which tt falls.
For instance 2 is the index of the second bin (1 being the index corresponding to tt<1).
@J.M. Not necessarily. The eigenspaces between different eigenvalues are orthogonal, but it is not necessary to have the vectors within an eigenspace be orthogonal as long as they span the space.
@R.M In gcc, -O3 is the highest level of optimization and the resulting machine code is usually incomprehensible to humans.
@rcollyer ah, you're here. About this... you suggest using LinearModelFit because of the complex numbers. Do you know how the *ModelFit functions handle complex-valued least squares? I couldn't work out how they would do it except in the (manual) way that I showed, but if they were doing that, we wouldn't have this problem in the first place...
@rcollyer yes, I would hope that too, but I don't really know if it's possible in general. The fact that it sometimes breaks down suggests that, if it is, it's not implemented that way in these functions.
Also, is the fact that they can (perhaps) manage complex valued data actually documented? I couldn't find a mention of it and assumed that they couldn't do it.
@rcollyer I know, but if memory serves the Hermitian QR algorithm is guaranteed to produce orthogonal vectors (since the eigenvectors are built from multiplication with various unitary matrices). Oh well...
@rcollyer if you assume the Euclidean norm, yes, I think so. But a priori, especially for nonlinear fits, I don't really see why one must choose that. What about the norm in the {Abs, Arg} space, for example? Maybe I'm missing something; I didn't work this through myself yet.
@chris, are you still here? I have an idea for your 3D critical points problem...
I realized you might be able to use the answers to this question; you can use the techniques there to find the curves of intersection of two of the partial derivatives, and then monitor where the sign of the other partial derivative changes at those points. Basically, a primitive curve-following method.
Once you locate where the sign changes, you have something to feed to FindRoot[] for subsequent polishing.
I know one method which would work called marching cube. My student implemented it in C. I was wondering if there was a nifty mathematica way of doing it differently.
Does anyone know how to backup a hsqldb database that I created from MMA? And how to move it to another PC? I tried what I found obvious but it didn't work
which if I understand you correctly would be a starting point to find the critical points while repeating the operation on {fx[x, y, z], fz[x, y, z]} say?
@balboa no problem, glad I could help! There are probably better or different ways to do this though, given how powerful Mathematica is. I'm a total newbie myself.
As a thank you for being awesome, if you have at least 730 reputation and are on page 1 or page 2 of …
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Recently, we received two project Euler questions:
How to find palindromic numbers (Project Euler #4)?
How to improve the performance of solutions to Project Euler (#39)？
I won't claim they are off-topic here. In fact, they often make exemplary Mathematica questions. However, I feel it goes a...
