In this chapter, we describe some of the finer points of MATLAB and review in more detail some of the concepts introduced in Chapter 2. We explore enough of MATLAB's internal structure to improve your ability to work with complicated functions, expressions, and commands. At the end of this chapter, we introduce some of the MATLAB commands for doing calculus.

Suppressing Output

Some MATLAB commands produce output that is superfluous. For example, when you assign a value to a variable, MATLAB echoes the value. You can suppress the output of a command by putting a semicolon after the command. Here is an example:

The semicolon does not affect the way MATLAB processes the command internally, as you can see from its response to the command z.

You can also use semicolons to separate a string of commands when you are interested only in the output of the final command (several examples appear later in the chapter). Commas can also be used to separate commands without suppressing output. If you use a semicolon after a graphics command, it will not suppress the graphic.

⇒ The most common use of the semicolon is to suppress the printing of a long vector, as indicated in Chapter 2.

Another object that you may want to suppress is MATLAB's label for the output of a command. The command disp is designed to achieve that; typing disp(x) will print the value of the variable x without printing the label and the equal sign.

In this chapter, we discuss a number of interrelated subjects: how to use the Internet to get additional help with MATLAB and to find MATLAB programs for certain specific applications, how to disseminate MATLAB programs over the Internet, and how to use MATLAB to prepare documents for posting on the World Wide Web.

MATLAB Help on the Internet

For answers to a variety of questions about MATLAB, it pays to visit the web site for The MathWorks,

(In MATLAB 6, the Web menu on the Desktop menu bar can take you there automatically.) Since files on this site are moved around periodically, we won't tell you precisely what is located where, but we will point out a few things to look for. First, you can find complete documentation sets for MATLAB and all the toolboxes. This is particularly useful if you didn't install all the documentation locally in order to save space. Second, there are lists of frequently asked questions about MATLAB, bug reports and bug fixes, etc. Third, there is an index of MATLAB-based books (including this one), with descriptions and ordering information. And finally, there are libraries of M-files, developed both by The MathWorks and by various MATLAB users, which you can download for free. These are especially useful if you need to do a standard sort of calculation for which there are established algorithms but for which MATLAB has no built-in M-file; in all probability, someone has written an M-file for it and made it available.

In this chapter we describe SIMULINK, a MATLAB accessory for simulating dynamical processes, and GUIDE, a built-in tool for creating your own graphical user interfaces. These brief introductions are not comprehensive, but together with the online documentation they should be enough to get you started.

SIMULINK

If you want to learn about SIMULINK in depth, you can read the massive PDF document SIMULINK: Dynamic System Simulation for MATLAB that comes with the software. Here we give a brief introduction for the casual user who wants to get going with SIMULINK quickly. You start SIMULINK by doubleclicking on SIMULINK in the Launch Pad, by clicking on the SIMULINK button on the MATLAB Desktop tool bar, or simply by typing simulink in the Command Window. This opens the SIMULINK library window, which is shown for UNIX systems in Figure 8-1. On Windows systems, you see instead the SIMULINK Library Browser, shown in Figure 8-2.

To begin to use SIMULINK, click New: Model from the File menu. This opens a blank model window. You create a SIMULINK model by copying units, called blocks, from the various SIMULINK libraries into the model window. We will explain how to use this procedure to model the homogeneous linear ordinary differential equation u″ + 2u′ + 5u = 0, which represents a damped harmonic oscillator.

First we have to figure out how to represent the equation in a way that SIMULINK can understand. One way to do this is as follows.

That statement encapsulates the view of The Math Works, Inc., the developer of MATLAB®. MATLAB 6 is an ambitious program. It contains hundreds of commands to do mathematics. You can use it to graph functions, solve equations, perform statistical tests, and do much more. It is a high-level programming language that can communicate with its cousins, e.g., FORTRAN and C. You can produce sound and animate graphics. You can do simulations and modeling (especially if you have access not just to basic MATLAB but also to its accessory SIMULINK®). You can prepare materials for export to the World Wide Web. In addition, you can use MATLAB, in conjunction with the word processing and desktop publishing features of Microsoft Word®, to combine mathematical computations with text and graphics to produce a polished, integrated, and interactive document.

A program this sophisticated contains many features and options. There are literally hundreds of useful commands at your disposal. The MATLAB help documentation contains thousands of entries. The standard references, whether the MathWorks User's Guide for the product, or any of our competitors, contain myriad tables describing an endless stream of commands, options, and features that the user might be expected to learn or access.

MATLAB is more than a fancy calculator; it is an extremely useful and versatile tool.

In this chapter, we present examples showing you how to apply MATLAB to problems in several different disciplines. Each example is presented as a MATLAB M-book. These M-books are illustrations of the kinds of polished, integrated, interactive documents that you can create with MATLAB, as augmented by the Word interface. The M-books are:

• Illuminating a Room

• Mortgage Payments

• Monte Carlo Simulation

• Population Dynamics

• Linear Economic Models

• Linear Programming

• The 360° Pendulum

• Numerical Solution of the Heat Equation

• A Model of Traffic Flow

We have not explained all the MATLAB commands that we use; you can learn about the new commands from the online help. SIMULINK is used in A Model of Traffic Flow and as an optional accessory in Population Dynamics and Numerical Solution of the Heat Equation. Running the M-book on Linear Programming also requires an M-file found (in slightly different forms) in the SIMULINK and Optimization toolboxes.

The M-books require different levels of mathematical background and expertise in other subjects. Illuminating a Room, Mortgage Payments, and Population Dynamics use only high school mathematics. Monte Carlo Simulation uses some probability and statistics; Linear Economic Models and Linear Programming, some linear algebra; The 360° Pendulum, some ordinary differential equations; Numerical Solution of the Heat Equation, some partial differential equations; and A Model of Traffic Flow, differential equations, linear algebra, and familiarity with the function ez for z a complex number.

In this chapter we describe more of MATLAB's graphics commands and the most common ways of manipulating and customizing them. You can get a list of MATLAB graphics commands by typing help graphics (for general graphics commands), help graph2d (for two-dimensional graphing), help graph3d (for three-dimensional graphing), or help specgraph (for specialized graphing commands).

We have already discussed the commands plot and ezplot in Chapter 2. We will begin this chapter by discussing more uses of these commands, as well as the other most commonly used plotting commands in two and three dimensions. Then we will discuss some techniques for customizing and manipulating graphics.

Two-Dimensional Plots

Often one wants to draw a curve in the x-y plane, but with y not given explicitly as a function of x. There are two main techniques for plotting such curves: parametric plotting and contour or implicit plotting. We discuss these in turn in the next two subsections.

Parametric Plots

Sometimes x and y are both given as functions of some parameter. For example, the circle of radius 1 centered at (0,0) can be expressed in parametric form as x = cos(2πt), y = sin(2πt) where t runs from 0 to 1. Though y is not expressed as a function of x, you can easily graph this curve with plot, as follows:

The output is shown in Figure 5.1.

Every time you create an M-file, you are writing a computer program using the MATLAB programming language. You can do quite a lot in MATLAB using no more than the most basic programming techniques that we have already introduced. In particular, we discussed simple loops (using for) and a rudimentary approach to debugging in Chapter 3. In this chapter, we will cover some further programming commands and techniques that are useful for attacking more complicated problems with MATLAB. If you are already familiar with another programming language, much of this material will be quite easy for you to pick up!

√ Many MATLAB commands are themselves M-files, which you can examine using type or edit (for example, enter type isprime to see the M-file for the command isprime). You can learn a lot about MATLAB programming techniques by inspecting the built-in M-files.

Branching

For many user-defined functions, you can use a function M-file that executes the same sequence of commands for each input. However, one often wants a function to perform a different sequence of commands in different cases, depending on the input. You can accomplish this with a branching command, and as in many other programming languages, branching in MATLAB is usually done with the command if, which we will discuss now. Later we will describe the other main branching command, switch.

MATLAB is exceptionally strong in linear algebra, numerical methods, and graphical interpretation of data. It is easily programmed and relatively easy to learn to use. As suchit has proven invaluable to engineers and scientists who are working on problems that rely on scientific techniques and methods at which MATLAB excels. Very often the individuals and groups that so employ MATLAB are primarily interested in the numbers and graphs that emerge from MATLAB commands, processes, and programs. Therefore, it is enough for them to work in a MATLAB Command Window, from which they can easily print or export their desired output. At most, the production technique described in Chapter 3 involving diary files is sufficient for their presentation needs.

However, other practitioners of mathematical software find themselves with two additional requirements. They need a mathematical software package embedded in an interactive environment — one in which the output is not necessarily “linear”, that is, one that they can manipulate and massage without regard to chronology or geographical location. Second, they need a higher-level presentation mode, which affords graphics integrated with text, with different formats for input and output, and one that can communicate effortlessly with other software applications. Some of MATLAB's competitors have focused on such needs in designing the interfaces (or front ends) behind which their mathematical software runs. MATLAB has decided to concentrate on the software rather than the interface — and for the reasons and purposes outlined above, that is clearly a wise decision.

In this chapter we describe an effective procedure for working with MATLAB, and for preparing and presenting the results of a MATLAB session. In particular we will discuss some features of the MATLAB interface and the use of script M-files, function M-files, and diary files. We also give some simple hints for debugging your M-files.

The MATLAB Interface

MATLAB 6 has a new interface called the MATLAB Desktop. Embedded inside it is the Command Window that we described in Chapter 2. If you are using MATLAB 5, then you will only see the Command Window. In that case you should skip the next subsection and proceed directly to the Menu and Tool Bars subsection below.

The Desktop

By default, the MATLAB Desktop (Figure 1-1 in Chapter 1) contains five windows inside it, the Command Window on the right, the Launch Pad and the Workspace browser in the upper left, and the Command History window and Current Directory browser in the lower left. Note that there are tabs for alternating between the Launch Pad and the Workspace browser, or between the Command History window and Current Directory browser. Which of the five windows are currently visible can be adjusted with the View: Desktop Layout menu at the top of the Desktop. (For example, with the Simple option, you see only the Command History and Command Window, side-by-side.) The sizes of the windows can be adjusted by dragging their edges with the mouse.

Following Shapiro and Varian (1999), I contend that the Internet does not so much change the fundamental characteristics of the general negotiation process, as the economic principles behind negotiations are still valid. Yet it does enable trading mechanisms to be implemented that were previously unknown or infeasible. This book has analyzed a broad range of negotiation protocols for electronic markets while focusing largely on auction mechanisms.

Auctions have proven to be very effcient negotiation protocols that converge to an equilibrium very quickly, which is important in situations where transactions need to occur at a rapid rate. Considering political contexts, auctions are also widely perceived as fair. In fact, they reflect the general shift of power towards the consumer, as sellers who do not offer some form of negotiation might be in danger of falling behind or being considered consumer-unfriendly. Aside from theoretical arguments, auctions have a number of practical advantages for both seller and buyer:

• An auction mechanism releases the bid taker from having to negotiate with several bidders individually, thus saving time.

Electronic markets are breaking new ground in old industries by providing them with a wealth of supply chain information via the Internet. The way that net market makers match buyers and sellers is key to the success of a marketplace and the design of electronic marketplaces has become a million-dollar business. This is a challenging field for both the business and the academic community.

This book introduces a framework of negotiation protocols for electronic markets. In particular, I will focus on multi-dimensional auction mechanisms which allow automated negotiation on multiple attributes and/or multiple units of a product. The findings and analyses should be useful to an audience of scholars as well as practitioners involved in the business of electronic market design. Through this book a reader should be able to understand the multitude of technical and economic issues involved in the design of electronic marketplaces. In contrast to purely economic treatments of this topic, the book combines aspects of both economics andcomputer science. The book provides a detailed description of the various negotiation protocols, which will be a valuable resource for systems engineers and designers. It also covers the relevant theoretical concepts in this multi-disciplinary field and should, therefore, be of interest to the wider academic community.

Information systems and their application play a major role in today's business. In addition to the introduction of new technologies which help to streamline processes within companies, electronic commerce has become the most recent trend. Electronic commerce has been described as “commercial transactions occurring over open networks, such as the Internet” (OECD, 1997). These new information technologies provide new opportunities and mechanisms to cooperate or to compete, taking advantage of computer power, the communication possibilities of the network, and the fact that millions of people and businesses are simultaneously online.

Though only a few years old, electronic commerce (e-commerce) has the potential to radically alter business-to-business, business-to-consumer as well as consumer-to-consumer transactions. For instance, electronic communication between businesses and suppliers via Electronic Data Interchange (EDI) has recently been enhanced by web-based front-ends for the placement of customer orders. Inter-organizational systems, efficient consumer response, and supply chain management are only a few of the challenges that future businesses will have to meet.

The current success of electronic commerce and the creation of billions in market capitalization and revenue is based on fundamental work done in the past in various disciplines.

This book analyzes a variety of market mechanisms for electronic marketplaces. “Electronic brokerage” is a metaphor for information systems facilitating the matching of buyers and suppliers in an electronic market; and, therefore, these mechanisms are key to the success of an electronic brokerage system. Before market mechanisms are analyzed, this chapter will give an overview of electronic brokerage systems on the Internet, and classify the various services being provided by electronic brokerages.

The Role of Electronic Brokers

The current state of Internet commerce is a far cry from what an electronic marketplace is envisioned to be. Although a growing number of suppliers, manufacturers and retailers offer their goods and services, in many markets there are no scalable and integrated methods for

• suppliers to reach customers

• customers to reach suppliers

• introducing new products, services, and offers efficiently

• negotiating, billing, and accounting

• creating limited, structured electronic marketplaces.

Electronic commerce depends on the emergence of capabilities that empower buyers to obtain all the product data they need to make informed purchase decisions quickly and easily.