Skip to main content

programming - Are there any cases when For[] loops are reasonable?


To my mind the only reason for the existence of For[] loops in Mathematica is to allow new users with some experience in procedural programming languages to write simple Mathematica programs. The real problem is that sometimes such a user do not dive deeper and as a consequence he has 1) ugly and unreliable code and 2) a belief that "Mathematica has a C-like syntax".


It is hard for me to imagine a situation when For[] cannot be effectively and more cleanly replaced by Table, Map, anything else or Do at least. Am I wrong? Should we really recommend beginners to avoid For[] loops?





SUMMARY


There are actually two great answers. The first answer is the accepted one and the second answer is this question. I wish I could accept it as well.



Answer



To my mind, there are at least two cases when For loops are ok:



  • Inside Compile, or in code which is being written with Compile in mind

  • When your inner loops are vectorized or made efficient by some other means, so that each iteration of the For loop is sufficiently intensive computationally


Many efficient algorithms are procedural by nature and gain their efficiency by side effects and local mutations. When those algorithms contain nested loops, what matters the most is to speed up innermost loop(s). While we mostly tend to move away from For loops, I have no problem with a For loop being an outer loop in a program, as long as innermost loops are optimized. Also, For loops are more flexible than Map or Scan because you can use Break and Continue, and generally are not forced to iterate over all of the elements in a list in a prescribed order.


That said, I think we should recommend beginners to avoid For loops, just because this would allow them to change their mindset and get to the better understanding of Mathematica programming sooner. I'd say, it is ok to occasionally use For loops for experienced users, but beginners would be better off avoiding them entirely, until they get more experience with the language.



Comments

Popular posts from this blog

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....