15,381 reputation
13088
bio website quantdec.com
location Northeastern US
age 14
visits member for 2 years, 11 months
seen 2 days ago

Consultant (environmental and spatial stats a specialty), expert witness, and teacher. I can be reached through (outdated but still valid) links posted on my web site.

Twitter: @WilliamAHuber // ASA-P website: http://amstatphilly.org/


Why waste time learning, when ignorance is instantaneous?

--T(iger) Hobbes.

For any complex problem there is a simple solution. And it's always wrong.

--[Mis?]attributed to H.L. Mencken by Dava Sobel, Longitude.


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
Jan
4
reviewed Close How to use the same color bar for different DensityPlot
Jan
4
comment How to get exact roots of this polynomial?
@minthao: Those roots are exact. What you seem to mean, then, is that you wish to identify some of the roots with some of the roots of another (unspecified) polynomial (which is how those cosines are defined).
Jan
4
revised How to get exact roots of this polynomial?
deleted 26 characters in body; edited title
Jan
4
comment How to get exact roots of this polynomial?
@b.gates And the next two steps are to let $x\to z/2$ to clear out powers of $2$ and then to take the big factor, $p(z)=1+3 z-3 z^2-4 z^3+z^4+z^5$ and symmetrize it via $p(z+1/z)z^5$: the primitive eleventh roots of unity pop right out.
Jan
2
comment Turn list of edges into a polygon function
@Daniel The example output is an intersection of half-planes, which can describe only a convex figure.
Jan
2
comment Turn list of edges into a polygon function
The type of example you give will work only for convex polygons. Is that a fair assumption to make in your application? If so, may we also assume the vertices have already been sorted in the order they appear around the polygon's boundary, and that the sorting follows a conventional orientation (such as keeping the interior of the polygon always to the left)? A solution for non-convex polygons can be obtained but would require more work (equivalent to triangulating them). Is it possible you only need some procedure to solve the point-in-polygon problem?
Jan
2
reviewed Leave Open Domain Coloring
Jan
2
reviewed Close Problem with SphericalPlot3D plotting
Dec
28
comment How to represent a list as a cycle
@Mr Very nice! I understand that your second method selects the lexicographically earliest representative of the class of all rotations of a list and then replaces any list by its representative. Because that is far superior in timing to the (quadratic) pattern-matching solution I posted, I'm deleting that solution.
Dec
28
comment How to visualize 3D fit
+1. It is useful at this stage to plot the residuals against the fit: that will make your comments more precise. BTW, fit["FitResiduals"] is a built-in way to obtain the residuals.
Dec
28
comment How to visualize 3D fit
A standard--and very effective--way to show the fit is to plot the residuals (equal to actual - estimated) against $x$ and $y$. For a good fit they should cluster evenly and randomly around the $xy$ plane. Because there's no question about where that plane lies, you don't even need the third dimension. For instance, many people map out the residuals in 2D using scaled and/or colored point symbols to represent their sizes and signs.
Dec
26
revised Define Log so that negative reals evaluate on lower edge of branch
added 154 characters in body
Dec
26
comment Using Transpose with a list as the second argument
+1 I am thinking the illustrations might work even better with some color coding. E.g., colors[1, 1] = Darker[Red]; colors[1, 2] = Darker[Green]; colors[1, 3] = Darker[Blue]; colors[2, 1] = Lighter[Red]; colors[2, 2] = Lighter[Green]; colors[2, 3] = Lighter[Blue]; f[x_] := Replace[MatrixForm[x], Subscript[a, i_, j_, k___] -> Style[Subscript[a, i, j, k], colors[i, j]], -1]; f[A], etc.
Dec
26
comment How do I expand a sum?
You are requesting two changes: first to Expand the products in the summation and second to Distribute the action of Sum over the addition. Consulting the help pages for Expand and Distribute will answer your question.