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MathGroup Archive 2005

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Re: Re: How to View Mathematica and Hardcopy Books

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62451] Re: Re: How to View Mathematica and Hardcopy Books
  • From: "Steven T. Hatton" <hattons at globalsymmetry.com>
  • Date: Thu, 24 Nov 2005 06:33:51 -0500 (EST)
  • References: <dls5ig$qn1$1@smc.vnet.net> <200511220942.EAA23713@smc.vnet.net> <dm1abe$hr1$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Andrzej Kozlowski wrote:

> On 22 Nov 2005, at 18:42, Steven T. Hatton wrote:
> 
>> For purposes of number crunching Mathematica is quite often the
>> wrong tool
>> for the job.  If you are doing things which involve very intensive
>> mumeric
>> calculation which are likely to be repeated in form, you are
>> probably much
>> better off translating your work to something like C++, or
>> FORTRAN.  My
>> understanding is that MathCode C++ can produce executables which
>> run orders
>> of magnitude faster than the Mathematica implementation of the same
>> algorithm
> 
> 
> This is of course true in some cases. For example, if you are working
> on simulations in molecular biology then Mathematica would normally
> not be the right tool for the job.

I suspect Mathematica can play a significant role in designing programs that
perform specialized highperformance calculations.  I've often turned to
Mathematica as a means of exploring the mathematics behind 3D (OpenGL)
graphics.

> But the situation is quite 
> different when what might be called "mathematical number crunching"
> is involved. First of all, the speed advantage of C++ usually
> disappears in cases when Mathematica has a built-in function that by
> itself does the job (and often the advantage lies with Mathematica
> since such functions tend to use the best known algorithms and are
> already highly optimised).

There are some very good numerics libraries written in C++ (according to
what others have told me.)  I'm trust there are many cases in which both
C++ and Mathematica provide comerable solutions.  The question then becomes
which is more convenient.  If a person is already working with Mathematica,
there is probably little reason to bother with the comparable C++ solution.

> But more importantly, in problems in 
> numerical mathematics accuracy and the ability to keep track of
> errors is much more important than speed. There is no great advantage 
> in getting a wrong answer several orders of magnitude faster.
> Mathematica offers pretty sophisticated tools that help with this
> task, which as far as I know no calculator does, nor is there, to my
> knowledge, anything comparable available in C++.

I can't claim expertise in either C++, nor Mathematica highperformance
numerical calculations.  I will say this - and the folks at WRI may want to
take notice - the C++ Technical Report 1 (TR1) adds many specialized math
functions to the C++ Standard Library.

One gap I would like to bridge is between 3D graphics and Mathematica.  I am
aware that Mathematica produces graphics using 3-dimensional mathematical
space, but it does not use specialized 3D libraries such as OpenGL.  I
suspect there is much improvement possible in how Mathematica handles
graphics.  I also suspect such improvements will be non-trivial to
implement.

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