Date: Apr 11, 2013 4:10 AM
Author: Albert Retey
Subject: Re: Timing puzzle
Hi,

> I am writing a graphics package that often creates objects with

> thousands of polygons, possibly up to 10^5. Out of curiosity I

> tested 5 ways of dynamically creating a plot list, using AppendTo,

> Append, Join, etc., and did the following timing test of 5 ways to do

> it:

>

> ClearAll[poly,p,n]; poly={}; n00; p[arg_]:=

> {mygraphic[mycolor[Random[],Random[],Random[]]],

> mygraphic[mypoly[{{Random[],Random[]},

> {Random[],Random[]},{Random[],Random[]}}]]};

> Print[Timing[Do[AppendTo[poly,p[i]],{i,1,n}]][[1]]]; ClearAll[poly];

> poly={}; Print[Timing[Do[poly=Append[poly,p[i]],{i,1,n}]][[1]]];

> ClearAll[poly]; poly={};

> Print[Timing[Do[poly=Join[poly,{p[i]}],{i,1,n}]][[1]]];

> ClearAll[poly]; poly={};

> Print[Timing[Do[poly={poly,{p[i]}},{i,1,n}];poly=Flatten[poly]][[1]]];

>

>

>

ClearAll[poly]; poly=Table[0,{n}];

> Print[Timing[Do[poly[[i]]=p[i],{i,1,n}]][[1]]];

>

> Running with n00 on a MacPro under Mac OSX 10.6.8 gives these times:

>

> 0.911327 Second 0.891656 Second 0.927267 Second 0.504454 Second

> 0.009575 Second

>

> Question: why is the last method much faster? I thought that

> appending an object to a list should take about the same time as

> storing an array entry. When I worked with linked lists several

> decades ago (using assembly code on a CDC 7600) all I had to do is

> retrieve the object address, manipulate registers, store in a

> pointer array, and presto! it was done.

the answer is pretty obvious: Lists in Mathematica are - despite their

name - not linked lists but arrays. It can be argued whether that was a

good decision or not, but you certainly have to live with that fact and

remember it if efficiency matters...

You should check your results of case 4, this is a well known

"Mathematica emulation" of linked lists and should be much faster: on my

computer (Windows 7, Mathematica 9) with n=10000 it is just as fast as the Do

loop which sets the preallocated table entries...

hth,

albert