Skip to main content

programming - Is this the most efficient way to round approximate integers to integers while leaving other Reals untouched?


This might seem like an overly simple question, but I need to specify custom plot tick marks as integers (no trailing decimal point) if they are approximately integers, but not if they are not. Using Rationalize on all the tick values won't work because I don't want ticks in the form of $\frac{3}{2}$.


Consider:


roundif = If[Chop[# - Floor[#]] == 0, Rationalize[#], #] & 

Some tests to show it works as intended:



roundif /@ {-1., -1, 0, 0.5,  1500, 1501., 1501.2}

(* {-1, -1, 0, 0.5, 1500, 1501, 1501.2} *)

roundif /@ Range[-3, 3, 0.5]

(* {-3, -2.5, -2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2, 2.5, 3} *)

(Of course, I could make it a normal SetDelayed function and make its Attributes include Listable.)


Timing seems to be linear in the length of the list and the number of times it is performed.



testdata = Range[-30, 30, 0.5];   
Do[roundif /@ testdata, {10000}]; // AbsoluteTiming
{5.8656000, Null}

Is this the most efficient way to do this? Have I missed some subtlety?



Answer



Stan Wagon presents a little utility function in his book Mathematica in Action called IntegerChop[]. Here's a slightly wrinkled version:


IntegerChop = With[{r = Round[#]}, r + Chop[# - r]] &;

You might wish to do comparisons yourself (the computer I am using does not have Mathematica).





Here are some benchmarks:


Do[roundif /@ testdata, {10000}]; // AbsoluteTiming  
(* ==> {4.7382710, Null} *)

Do[IntegerChop /@ testdata, {10000}]; // AbsoluteTiming
(* ==> {4.6512660, Null} *)

So basically no difference.


Comments

Popular posts from this blog

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...

equation solving - Invert and fit implicitly defined curve

I need to fit an implicitly defined curve. I thought I could get some data out of Solve , and then using FindFit . Therefore, I would like to find the relation the parametric curve defined by $F(x,y)=0$: Solve[-(1/2) + 1/2 (0.41202 BesselK[0, 0.1 Sqrt[x^2 + y^2]] + (0.101483 x BesselK[1, 0.1 Sqrt[x^2 + y^2]])/Sqrt[x^2 + y^2]) == 0, y] But I can't get an output: Solve was unable to solve the system with inexact coefficients or the system obtained by direct rationalization of inexact numbers present in the system. Since many of the methods used by Solve require exact input, providing Solve with an exact version of the system may help. >> Edit: In particular, I would like to fit the data coming from the curve with the expression of another curve, and not with a function $f(x)$. In particular, since this clearly looks like a cardioid , I would like it to fit to something like it. What other strategies could I try?

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...