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Consultant (environmental stats a specialty) and teacher.


Jan
8
comment Define an 'inner product' with AngleBracket
@Rojo That's a good point. Although the OP hasn't asked for it, in general an inner product is sesquilinear, not bilinear, so it may be of use to illustrate a solution--as here--that would apply in full generality.
Jan
8
comment Define an 'inner product' with AngleBracket
By definition, the arguments of an inner product have to be elements of the same vector space. Because 0 is not the same as {0} which is not the same as {0,0}, which is not the same as (say) an $L^2$ integrable complex-valued function on a space--all of which could be considered vectors--it should not be the case that $\langle 0,v\rangle = 0$: that expression is, in general, nonsensical. To avoid hidden surprises, consider creating an appropriate vector type and defining AngleBracket as a (sesquilinear) bivariate function of vectors.
Jan
8
comment How to convert from and to UTM coordinates in Mathematica?
The output of GeoProjectionData is not correct for the UTM system: the value of GridOrigin is wrong (it should be {500000,0} and so is the value of CentralScaleFactor (it should be 0.9996).
Jan
8
reviewed Leave Open How do I plot a 3D vector field using a data file with three x y z columns?
Jan
8
comment How do I plot a 3D vector field using a data file with three x y z columns?
@user That was such a substantial change that you should roll this question back to its original and post your modification as a new question. Please consider upvoting and accepting this reply, too, because you have acknowledged that it answers your original question.
Jan
8
reviewed Close Coding mistake?
Jan
8
comment Correct way to populate a DiagonalMatrix?
(1) The SparseArray solution is a lot faster--a couple orders of magnitude. (2) It does not necessarily take much RAM. E.g., making an ArrayPlot with dimensions $10^5$ (involving $10^{10}$ floating point entries) required only about $70$ Mb. (3) If you don't want true zeros or ones at the end of the range, just use Range[0.0, 1.0, 0.1]. If you're concerned about floating point imprecision, Range[0,10]/10.0 should do fine.
Jan
7
comment xkcd-style graphs
Mathematica 9 users please see the follow-up post at mathematica.stackexchange.com/questions/17272/… concerning slower speeds.
Jan
7
comment Correct way to populate a DiagonalMatrix?
+1 for the edit. But have you honestly compared the timing by forcing an evaluation of both results, such as with an ArrayPlot? When I do that, I find the compiled solution is only 25% faster. That's a nice achievement, but because it is so little, I would in many cases prefer a clear simple native Mathematica solution to a compiled (and perhaps obscure) solution. As you hinted, speed isn't everything!
Jan
7
comment Correct way to populate a DiagonalMatrix?
+1 Given that the final matrix is not sparse, it is noteworthy that the SparseArray representation of the diagonal matrix gives a faster calculation.
Jan
7
comment Efficient code for the Ten True Sentences puzzle
@Silvia Thank you--it seems like almost any one-line function I can write has already been incorporated in the software somewhere :-).
Jan
7
answered Efficient code for the Ten True Sentences puzzle
Jan
7
reviewed Close How to search for initialization cells?
Jan
7
comment How to get exact roots of this polynomial?
+1 Example of another way: the output of MinimalPolynomial[ Root[1 + 6 #1 - 12 #1^2 - 32 #1^3 + 16 #1^4 + 32 #1^5 &, 1] - Cos[10 \[Pi]/11]] is #1 &.
Jan
6
comment How to get exact roots of this polynomial?
@Artes Thank you for the suggestion. I posted them as comments because I don't think they actually answer the question: they require one to anticipate that the root really is a trigonometric value and will not work in general.
Jan
6
answered Correct way to populate a DiagonalMatrix?
Jan
5
comment Can some one explain perplexing behavior of arbitrary precision arithmetic?
It may be of interest that MMA can recognize the equivalence of Root[1] and Root[1 + 6 #1 - ... &, 5]: applying MinimalPolynomial to both of these yields the same expression. Equivalently, applying Root[MinimalPolynomial[#], 1]& to their difference--rather than N--produces $0$ (and you can just as easily check that this is the only root).
Jan
5
comment How to obtain a smaller-sized output from Solve
Because these are linear equations, why aren't you using LinearSolve?
Jan
5
reviewed Close Sharing an axis between two plots
Jan
4
reviewed Leave Open Lorenz map for the Rössler system