[Date Index]
[Thread Index]
[Author Index]
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.
--
The Mathematica Wiki: http://www.mathematica-users.org/
Math for Comp Sci http://www.ifi.unizh.ch/math/bmwcs/master.html
Math for the WWW: http://www.w3.org/Math/
Prev by Date:
**Re: Timing of looping operators**
Next by Date:
**Re: Boolean Integral**
Previous by thread:
**Re: Re: How to View Mathematica and Hardcopy Books**
Next by thread:
**Re: Re: How to View Mathematica and Hardcopy Books**
| |