MATLAB Basics

Perhaps the first thing to do when first using MATLAB is to set the Path. The Path is a list of directories that MATLAB searches for files. The default Path is where users usually want to store files and recover them later. A usual place for file storage might be on a thumb drive. Assume that the directory of interest is F MyDocuments MATLAB. To put this directory into the Path and to make it the default directory, go to the File menu and click on Set Path—the following window appears  

Click on Add Folder, Save, and then Close. Next, at the Command prompt, issue the following command (cd stands for change directory). 

From this point forward, any file that is saved is deposited in the selected directory, and when opening a file, this directory will be searched first. 

A unique thing about MATLAB is that all variables are matrices. For example, the command shown in the Command Window below creates a variable named x (see that name having been added to the Workspace). Following the command, the current value of x is listed. To avoid having the value of x printed following the command, simply add a semicolon at the end of the command. It is important to note that all MATLAB identifiers are case sensitive. 

ONew to MATLABi Watch thlsMdaa. see Bemos. or read Carting Started. 

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Figure 7.4 Time versus ln[3p -p,J plot generated in MATLAB basic fitting option to determine the rate constant /rat 154.6°C.

The set of differential equations written above were solved numerical by the finite difference method of Runge-Kutta (Ode23tb of Matlab). Basically, a polymer sample is discretized into N knots equally spaced with a distance Ax ... 

Versions of Volume I exist for C, Basic, and Pascal. Matlab enthusiasts will find some coverage of optimization (and nonlinear regression) techniques in... 

Basically two search procedures for non-linear parameter estimation applications apply. (Nash and Walker-Smith, 1987). The first of these is derived from Newton s gradient method and numerous improvements on this method have been developed. The second method uses direct search techniques, one of which, the Nelder-Mead search algorithm, is derived from a simplex-like approach. Many of these methods are part of important mathematical computer-based program packages (e.g., IMSL, BMDP, MATLAB) or are available through other important mathematical program packages (e.g., IMSL). 

Non-linear parameter estimation is far from a trivial task, even though it is greatly simplified by the availability of user-friendly program packages such as a) SIMUSOLV (Steiner et al., 1986), b) ESL, c) a set of BASIC programs (supplied with the book of Nash and Walker-Smith, 1987) or d) by mathematical software (MATLAB). ISIM itself does not supply these advanced features, but ISIM programs can easily be translated into other more powerful languages. 

The basic statements are provided already in the example. For more details, see our Web Support for the MATLAB statements and plots. 

MATLAB is a formidable mathematics analysis package. We provide an introduction to the most basic commands that are needed for our use. We make no attempts to be comprehensive. We do not want a big, intimidating manual. The beauty of MATLAB is that we only need to know a tiny bit to get going and be productive. Once we get started, we can pick up new skills quickly with MATLAB s excellent on-line help features. We can only learn with hands-on work these notes are written as a "walk-through" tutorial—you are expected to enter the commands into MATLAB as you read along. 

For each session, we put the most important functions in a table for easy reference or review. The first one is on the basic commands and plotting. Try the commands as you read. You do not have to enter any text after the "%" sign. Any text behind a "%" is considered a comment and is ignored. We will save some paper and omit the results generated by MATLAB. If you need to see that for help, they are provided on our Web Support. There is also where we post any new MATLAB changes and upgrades. Features in our tutorial sessions are based on MATLAB Version 6.1, and Control System Toolbox 5.1. 

The help features and the Command Window interface tend to evolve quickly. For that reason, we use our Web Support to provide additional hints and tidbits so we can keep you update of the latest MATLAB changes. For now, we will introduce a few more basic commands ... 

If basic assumptions concerning the error structure are incorrect (e.g., non-Gaussian distribution) or cannot be specified, more robust estimation techniques may be necessary, e.g., Maria and Heinzle (1998). In addition to the above considerations, it is often important to introduce constraints on the estimated parameters (e.g., the parameters can only be positive). Such constraints are included in the simulation and parameter estimation package ACSL-OPTIMIZE and in the MATLAB Optimisation Toolbox. Because of numerical inaccuracy, scaling of parameters and data may be necessary if the numerical values are of greatly differing order. Plots of the residuals, difference between model and measurement value, are very useful in identifying systematic or model errors. 

Of course parts of, or the whole chapter can be skipped by those readers who are already proficient in the basics of matrix algebra and the implementation in Matlab and Excel. 

Excel does not provide functions for the factor analysis of matrices. Further, Excel does not support iterative processes. Consequently, there are no Excel examples in Chapter 5, Model-Free Analyses. There are vast numbers of free add-ins available on the internet, e.g. for the Singular Value Decomposition. Alternatively, it is possible to write Visual Basic programs for the task and link them to Excel. We strongly believe that such algorithms are much better written in Matlab and decided not to include such options in our Excel collection. 

In this chapter, we present the basic matrix mathematics that is required for understanding the methods introduced later in the book. In line with the philosophy that all concepts are immediately implemented in Matlab and/or Excel, this will be done here as well. This way, Chapter 2 not only revises the basic mathematics, it also serves as a very short introduction to the Matlab and Excel languages. It is not meant to be a manual on Matlab or Excel the reader will need to refer to more specialised texts and proper manuals. Several more advanced features of both languages are not covered at this introductory stage but will be explained as they emerge in later chapters. 

As mentioned before, this chapter has two goals, (a) to refresh some basic matrix mathematics and (b) to familiarise the reader with the essentials of both Matlab and Excel, particularly with respect to multivariate data... 

As stated earlier, Matlab s philosophy is to read everything as a matrix. Consequently, the basic operators for multiplication, right division, left division, power (, /,, A) automatically perform corresponding matrix operations (A will be introduced shortly in the context of square matrices, / and will be discussed later, in the context of linear regression and the calculation of a pseudo inverse, see The Pseudo-Inverse, p.117). 

In contrast to Matlab, where the defaults are the matrix operators, in Excel the default is the element-wise operation. In fact, all basic operations (e-g- 0, 0> 0> 0> Q) and functions (e.g. EXP, LN, LOG) work element-wise in Excel. All... 

While there is an analytical solution for this mechanism, the formula for the calculation of the concentration profiles for A and B is fairly complex, involving the tan and atan functions (according to Matlab s symbolic toolbox). We use it to demonstrate the basic ideas of numerical integration. 

In contrast to our preferred standard mode in this book, we do not develop a Matlab function for the task of numerical integration of the differential equations pertinent to chemical kinetics. While it would be fairly easy to develop basic functions that work reliably and efficiently with most mechanisms, it was decided not to include such functions since Matlab, in its basic edition, supplies a good suite of fully fledged ODE solvers. ODE solvers play a very important role in many applications outside chemistry and thus high level routines are readily available. An important aspect for fast computation is the automatic adjustment of the step-size, depending on the required accuracy. Also, it is important to differentiate between stiff and non-stiff problems. Proper discussion of the difference between the two is clearly outside the scope of this book, however, we indicate the stiffness of problems in a series of examples discussed later. So, instead of developing our own ODE solver in Matlab, we will learn how to use the routines supplied by Matlab. This will be done in a quite extensive series of examples. 

These simplifications in the parameter handling are best organised by using structures and cell arrays, as provided by Matlab to supplement the matrix as a basic data type. We introduce both, beginning with structures. 

Usually, imaging workstations and luminometers include proprietary software to operate the devices and allow the direct export of raw data and basic measurements to common spreadsheet software, including Microsoft Excel. More complex image analyses can be successfully performed with ImageJ or Matlab software packages. 

Simulations of three-component time-dependent diffusion were made based on two slightly different models using Matlab software [33]. Basically, fluid layer thicknesses are predicted, which determine diffusion distances. In this way, the H+ and OH- concentrations are revealed which can be related back to the pH. By the known fluorescence intensity-pH relationship, the quantum yield is thus given. 

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