Skip to main content

list manipulation - Threading behavior of SameQ vs Equals


I ran into a bug in my code today based on an errant assumption. Namely, I thought that:


Thread[Equal[{aa, bb, cc}, {dd, ee, ff}]]
Thread[SameQ[{aa, bb, cc}, {dd, ee, ff}]]

Would



{aa == dd, bb == ee, cc == ff}
{False,False,False}

Respectively (variables are undefined). What I get instead is


{aa == dd, bb == ee, cc == ff}
False

Which I can argue makes sense, since the lists aren't equivalent. But why doesn't Thread work? What's the precedence argument here? How can I get the answer I want ({False,False,False}) from a similar construct?



Answer



Thread doesn't hold its arguments. You can check its attributes.



So, before doing any threading, it evaluates its arguments.


Now, understanding the behaviour you describe requires understanding the difference between Equal and SameQ. Equal is meant for math reasoning. For expressing an equality, which might involve a variable that at the time you don't yet know it's value. So, for example, x==8 returns unevaluated if x isn't defined.


SameQ however is a predicate. It will always return either True or False if the constructs are exactly the same (after evaluation).


So, Thread[SameQ[{aa, bb, cc}, {dd, ee, ff}]] -> Thread[False]-> False


One can see this by running (thanks @rcollyer)


Trace[Thread[SameQ[{aa, bb, cc}, {dd, ee, ff}]], 
TraceInternal -> True]

Out[1] = {{{aa, bb, cc} === {dd, ee, ff}, False}, Thread[False], False}


If you want to thread SameQ without evaluation, just use Unevaluated


Thread[Unevaluated@SameQ[{aa, bb, cc}, {dd, ee, ff}]]

{False, False, False}

Another construction that gives the result you want is the one suggested by @kguler in his comment and supported by @rcoller and his upvoters: MapThread. I'd suggest you search the docs if you don't know it


MapThread[SameQ, {{aa, bb, cc}, {dd, ee, ff}}]

Comments

Popular posts from this blog

plotting - Filling between two spheres in SphericalPlot3D

Manipulate[ SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, Mesh -> None, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], {n, 0, 1}] I cant' seem to be able to make a filling between two spheres. I've already tried the obvious Filling -> {1 -> {2}} but Mathematica doesn't seem to like that option. Is there any easy way around this or ... Answer There is no built-in filling in SphericalPlot3D . One option is to use ParametricPlot3D to draw the surfaces between the two shells: Manipulate[ Show[SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], ParametricPlot3D[{ r {Sin[t] Cos[1.5 Pi], Sin[t] Sin[1.5 Pi], Cos[t]}, r {Sin[t] Cos[0 Pi], Sin[t] Sin[0 Pi], Cos[t]}}, {r, 1, 2 - n}, {t, 0, Pi}, PlotStyle -> Yellow, Mesh -> {2, 15}]], {n, 0, 1}]

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]

plotting - Mathematica: 3D plot based on combined 2D graphs

I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1.