On Thu, Nov 16, 2006 at 04:21:46PM -0600, Seb wrote:
> On Thu, 16 Nov 2006 13:35:15 -0800,
> Daniel Lakeland <dlakelan at street-artists.org> wrote:
>
> [...]
>
> > As for the computational issues, maxima has looping constructs so you
> > could create an array of numbers. Are you trying to create a 3D surface
> > graph, or perhaps you only need to solve for some specific subset of the
> > values in the region x in (.1,3) and t in (0,300)? ie. those values
> > given by some real-world data or whatever?
>
> Exactly! I wanted to plot my real-world u vs t, and then plot several
> curves on top of that showing the estimated u for a few selected x.
> However, I got to Raymond's message too late, after having found function
> uniroot() in GNU R, where I'm doing the rest of my work. It wasn't hard
> to create a loop (as you suggested) there that applied uniroot() to those
> specific subsets. Next time I'll try doing this all in maxima as I become
> more familiar with it.
>
> Thanks to all those who provided some input.
I often find that when dealing with "real world" or numerical data, R
is the way to go. Maxima I find helpful for discovering mathematical
theory to support real-world modelling. For example I recently used
maxima to solve a differential equation which gave a solution for t
(time) in terms of y (height). Of course this is backwards from what
was desired, but it was similar to your situation, impossible to
reverse the result except by taylor expansion with limited
convergence. However, it was very useful to take the maxima result and
hand it to uniroot in R to create a computational function y(t). I was
then able to fit the 2 parameters in the differential equation model
to my data using "nls" in R (nonlinear least squares).
Although maxima can do many of these things, R is primarily a
numerical and data analysis package and I find it more satisfying for
the numerical and data analysis portions of my work. I believe it is
often faster for numerical work as well.
The combination of R and maxima is unbelievably useful and I only wish
that they were available when I was in school in the mid 1990's.
When I recently returned to school to study Civil Engineering I tried
to encourage all the students I met to learn these and other
computational tools. Unfortunately I had little effect compared to the
extremely common and baroque use of Excel.
One application I was particularly proud of was the use of Maxima to
perform lagrange multiplier minimization of the weighted errors in a
particularly baroque survey traverse (ie. surveying instruments for
measuring the ground). Let's just say that we were confident in there
having been mistakes, but we wanted to get a best estimate of the
location of control points given our estimates of where and how big
the mistakes were.
I hope you enjoy using these tools for your work.
--
Daniel Lakeland
dlakelan at street-artists.org
http://www.street-artists.org/~dlakelan