Class 7

Review from previous class

Fixed points and recursion

Fixed point algorithms are naturally expressed recursively.

Generic versus special case

Its only a little harder (and in some ways easier) to write a function that solves a generic fixed point problem rather than worrying about the details of solving a specific fixed-point problem (like Newton's method).

Functions that build functions

In Lisp, it is no harder to return a function than it is to return a list or other value. The abilities to pass functions as arguments and return functions as results together simplify the task of building generic tools in Lisp, like our fixed-point program or implementations of Newton's method.

Tools for the Day

Unfortunately, you cannot just "cut and paste" graphics produced in a program like Mathematica or S into another application. Instead, you will typically need to save them as a Postscript file. Today, we will see how to save Mathematica plots as Postscript files that become part of a Latex document.

Saving Mathematica plots

The notebook postscript.nb defines a function to make this chore pretty easy.

Showing plots in Latex

We will use the psfig options to import graphics into Latex documents, viewing the results with ghostview. The small Tex file myPlot.tex gives a very basic illustration of the use of the psfig extensions.

Status of Projects

Your page with a filling bibliography needs to be available. Be sure to e-mail me the URL (http://...) for your pages today if you have not done so already.
My page is at steady small state.

Recursion and Searching, with local variables and functions

Iterative programs

For many reasons, many of us tend to think of programs consisting of lots and lots of possibly nested "do loops". Though I am trying to make recursion seem natural (as well as computationally efficient through the use of compilation and tail recursion), Lisp also supports this more traditional style of programming.

Macros

Some of Lisp's iteration constructs (like the "do" form) seem pretty unnatural without a lot of practice and are often more general than what is needed. Macros allow you to make your own "language" for iteration. We will use a simple one that provides a "while loop".

Comparisons

Often, the built-in functions are the last word in a problem. Use them when they are available --- unless you have to construct special things (like lists of values) that are not needed than for using the built-in functions. Even though the built-in functions are fast, the overhead of list construction can make this approach inferior to iterative or recursive programs.

Lisp script for today's class.

class7.lsp

Next time

We take a special look at the simulation capabilities of Lisp-Stat and use them to explore some of the basic properties and capabilities of Gibbs sampling.