Skip to main content

list manipulation - How to randomly select subsets


I have a list of around 300 elements. I want to sample subsets of length 25 such that my samples are all distinct. My first inclination was to use something like RandomSample[Subsets[list, {25}], 1000], but the problem is the number of subsets of length 25 out of a 300 element set is way to big for the computer to deal with. Anyone have a nice way to do this?



Answer



This question may be a duplicate but for the time being:



list = Range[300];

The number of subsets length 25:


n = Binomial[300, 25]


1953265141442868389822364184842211512

Five samples:


samp = RandomInteger[{1, n}, 5]



{1097179597483122074395819626389736050,
 1278400886908268917844987164926797363,
 1855898035549513136165016617586671669,
 1005956584417012779260052361741534263,
 1845054078551378518016127833496347335}

Your subsets:


 Subsets[list, {25}, {#}][[1]] & /@ samp



{{10,15,57,64,65,73,82,115,120,130,133,160,161,164,178,192,196,218,223,235,238,240,267,271,290},
{12,54,58,81,90,91,115,130,146,181,189,204,205,218,222,230,233,234,235,254,256,268,281,283,284},
{33,42,45,65,78,81,85,118,151,167,172,174,202,203,207,208,211,212,223,239,246,251,254,262,267},
{9,12,35,69,72,77,79,109,113,116,141,144,158,163,195,202,221,228,230,231,254,259,267,280,292},
{32,39,49,53,62,102,104,132,135,159,164,167,169,172,191,211,244,245,253,263,265,271,282,283,286}}

Be aware that RandomInteger could produce duplicate samples however for the example given it is extremely unlikely. You can produce more an use DeleteDuplicates and Take as needed.




I think kguler's answer is the better method, and I wish I had had the insight to realize it myself, however there is still some value in the method above. Referring to subsets by a single number can make them easier to handle.



  • They take less space.

  • Comparison (e.g. for removing duplicates) requires a single numeric comparison rather than a list comparison.

  • A given subset is independent of the input list; only length of input and subset matter.


One can "unrank" them at any time using the third parameter of Subsets as shown above.


Comments

Post a Comment

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[ ...
Post a Comment
Read more

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?
Post a Comment
Read more

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...
Post a Comment
Read more