Re: Re: finding out what Automatic was

*To*: mathgroup at smc.vnet.net*Subject*: [mg54290] Re: [mg54242] Re: finding out what Automatic was*From*: DrBob <drbob at bigfoot.com>*Date*: Wed, 16 Feb 2005 14:36:09 -0500 (EST)*References*: <200502140317.WAA14113@smc.vnet.net> <200502150250.VAA27243@smc.vnet.net>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

normdata = RandomArray[NormalDistribution[], 100]; hist = Histogram[normdata]; binLimits = Union@Flatten@Cases[hist, Rectangle[{left_, _}, {right_, _}] -> {left, right}, Infinity] {-3., -2.5, -2., -1.5, -1., -0.5, 0., 0.5, 1., 1.5, 2., 2.5} Bobby On Mon, 14 Feb 2005 21:50:35 -0500 (EST), Chris Chiasson <chris.chiasson at gmail.com> wrote: > Your question seems like a good one to me, probably because I don't > know the answer :] > > However, given that the category intervalas by the histogram command > are in the form of rectangles, one could just extract them. The first > three lines of the code that follow are directly from the help file > entry that contains the Histogram function description. Please accept > my apologies if you already understand the concepts involved in this > code. This code may be evaluated one line at a time for clarity. > > Needs["Statistics`NormalDistribution`"] > > normdata=RandomArray[NormalDistribution[],100] > > Needs["Graphics`Graphics`"] > > hist=Histogram[normdata] > > (*hist is a graphics object - the next line shows the internal > structure of hist*) > > hist//FullForm > > (*notice everything fis the form h[argument1,argument2,etc], which can > be thought of as functions*) > > {3,2,1}//FullForm > > List[3,2,1]//FullForm > > f[x,y,z]//FullForm > > (*notice the similarity between lists and everyday functions that have > not evaluated their parameters*) > > (*There are commands for extracting objects at different "depths" of > nested functions.*) > > (*the relevant objects we would like to extract are the rectangle > functions, which are located on level 4 of the hist graphics object*) > > Level[hist,{4}] > > (*note how the 4 is inisde brackets, just passing a plain 4 will give > everything down to that level, not just the level itself*) > > (*how many levels of nested functions are there in this graphics object*) > > Depth[hist] > > Level[hist,Depth[hist]] > > (*most commands have a parameter allowing one to specify the level at > which one wants to operate, rather than having to wrap the arguments > in Level functions*) > > (*the parameter we need to supply is the last argument in the case statement*) > > (*why would we need to use a case statement? well -- we need to > extract the rectangle functions and they happen to fit a pattern.case > statements extract objects that fit particular patterns from other > objects (heh,at least in mathematica:])*) > > (*so we first define the pattern*) > > Set[thepattern, > Rectangle[List[Pattern[xmin,Blank[]],Pattern[ymin,Blank[]]], > List[Pattern[xmax,Blank[]],Pattern[ymax,Blank[]]]]] > > (*note this could also be written thepattern= > Rectangle[{xmin_,ymin_},{xmax_,ymax_}]*) > > (*since we don't really care what level the rectangle functions are at > inside hist,,just supply the Depth[hist] for the level argument... > this will have the effect of searching for the rectangle pattern at > all levels*) > > Set[thecases,Cases[hist,thepattern,Depth[hist]]] > > (*note this could also be written Cases[hist,thepattern,Depth[hist]]*) > > Set[thesplits,ReplaceAll[thecases,Rule[thepattern,List[xmin,xmax]]]] > > thesplits//FullForm > > (*the above command gives you the list of bin splits-- it could also > be written as thesplits=thecases/.thepattern\[Rule]{xmin,xmax}*) > > Regards, > > On Sun, 13 Feb 2005 22:17:16 -0500 (EST), Curt Fischer > <tentrillion at gmail.nospam.com> wrote: >> Dear Group: >> >> How do you find out what value Mathematica has picked for an option set >> to "Automatic", especially when making graphs? >> >> For example, I want to access the frequency data for a Histogram[] I >> made from a list of 50000 integers. How do I figure out which bin sizes >> Histogram[] picked if I don't explicitly specify the bin sizes? >> >> Thanks. >> >> -- >> Curt Fischer >> >> > > -- DrBob at bigfoot.com www.eclecticdreams.net

**References**:**finding out what Automatic was***From:*Curt Fischer <tentrillion@gmail.NOSPAM.com>

**Re: finding out what Automatic was***From:*Chris Chiasson <chris.chiasson@gmail.com>