result accumulation - Monitoring progress of long calculations

I've came upon a few methods of how to display "processing" information while Mathematica is running. But, from what I've understood, this only works in between lines of codes. Is it possible to display a "how far is something being processed"-information during a line of code?

For example, I wish to Map a function g over a very large list, for example:

Map[ g , Sort[Apply[Join, Table[Range[1000000], {1000}]]] ],

which will take quite some time. Now, because the list consists of 1000 times every number between 1 and 1000000, could it be possible do display (as a temporary display), which number is being processed?

I have thought of using Print and changing the function being mapped to

Map[ (Print[#]; g[#]) &, Sort[Apply[Join, Table[Range[1000000], {1000}]]] ],

but I was wondering if there was any "faster" method, which wouldn't print out every number of the list, but for example every 1000th number. I have thought about If before Print, but I think this method would take too much extra time.

Answer

Or you can use something like this:

Monitor[
    Table[Length@FactorInteger[2^n - 1], {n, 50, 500, 50}], 
    Grid[{{Text[Style["Integer Factorization :", Darker[Blue, 0.66]]],
        ProgressIndicator[n, {50, 500}]},

    {Text[Style["Factoring 2^n-1 with n : ", Darker[Blue, 0.66]]], n}},
Alignment -> Left, Dividers -> Center]]

enter image description here

Sorry for not using your computation, since it did not make sense to me, which is my fault. That's why I've chosen another, just to display my approach.

Comments

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 - 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 - 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....

Blog

Search This Blog