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MathGroup Archive 2004

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RE: Min[], Max[]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48326] RE: [mg48320] Min[], Max[]
  • From: David.Annetts at csiro.au
  • Date: Tue, 25 May 2004 07:16:41 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Frank,

> Dear newsgroup members,
> 
> can anyone explain me what´s the sense in the definition of
> 
> Min[{}]= Infinity and Max[{}]= -Infinity

Such definitions are often made before entering a loop (in say F90). They are designed to ensure that min & max are always one of your data points.  This is important if you want to normalise eg.
	data = data / max.
since if max is not an element of your data, you will divide by 0.  This is not usually what we want to do.

Consider the following.  

lst = Table[Random[Real, {-5, 5}], {10}]
mina = maxa = 0; (* this is one effect of not initialising ...*)
minb = Infinity; maxb = -minb;
Do[
    If[lst[[ji]] < mina, mina = lst[[ji]]];
    If[lst[[ji]] < minb, minb = lst[[ji]]];
    Print["mina = ", mina, "; minb = ", minb, "; lst[[ji]] = ", lst[[ji]]],
    {ji, 1, Length@lst}
    ];

Output will vary from run to run (because of Random[]), but for one run, I get 
	lst = {2.16401, 1.6797, 3.51037, -3.17384, -1.77294, 1.86815, 2.6709, 4.97422, \
-4.76049, -1.43248}.

This has outputs
Ji	minA		MinB
1	0		lst[[1]]
2	0		lst[[2]]
3	0		lst[[2]]
4	lst[[4]]	lst[[4]]
5 .....

Without the "minb" definition, you need to make an additional test that min != 0 (try it!), and this is not nearly as clear.  The 

Why do you want to initialise these (or any variable) in the first place?  So you know what you are dealing with.  Not initialising gives the compiler carte blanch to use what it likes, and this may not be what you need.

Regards,

Dave.
==========================================
  Dr. David Annetts
  EM Modelling Analyst
  CSIRO DEM            Tel: +612 9490 5416
  North Ryde           Fax: +612 9490 5467
  Australia         David.Annetts at csiro.au
===========================================


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