Basics of MATLAB and Beyond

Andrew Knight

• Publisher: Chapman and Hall/CRC
• Year: 2019
• ISBN:
  9780429525186
• Edition: 1
• Topic: Matemáticas
• Subtopic: Matemáticas general

MATLAB The tremendously popular computation, numerical analysis, signal processing, data analysis, and graphical software package-allows virtually every scientist and engineer to make better and faster progress. As MATLAB's world-wide sales approach a half-million with an estimated four million users, it becomes a near necessity that professionals a

Beyond the Basics

Prelude

This part of the book assumes that you already have some competency with MATLAB. You may have been using it for a while and you find you want to do more with it. Perhaps you have seen what other people do and are wondering how it is done. Well, read on.

This part of the book follows an introductory course in MATLAB (Part I) that covered the basics: matrices, typing shortcuts, basic graphics, basic algebra and data analysis, basics of m-files and data files, and a few simple applications, such as curve fitting, FFTs, and sound. Basic handle graphics were introduced using set and get.

We begin by looking at sparse matrices and strings, go on to deal with some of the data types that are new to MATLAB version 5: cell arrays, multidimensional arrays and structures, then deal with a variety of topics that you will probably have to deal with at some stage if you are a frequent user of MATLAB. The book can be worked through from start to finish, but if you are not interested in a particular topic, you can skip over it without affecting your understanding of later topics. Exercises are given throughout the book, and answers to most of them are given at the end. We start by introducing some new variable types that go beyond the functionality of a rectangular matrix.

25 Sparse Arrays

In some applications, matrices have only a few non-zero elements. Such matrices might arise, for example, when analysing communication networks or when performing finite element modelling. MATLAB provides sparse arrays for dealing with such cases. Sparse arrays take up much less storage space and calculation time than full arrays.

25.1 Example: Airfoil

Suppose we are doing some finite element modelling of the airflow over an aeroplane wing. In finite element modelling you set up a calculation grid whose points are more densely spaced where the solution has high gradients. A suitable set of points is contained in the file airfoil:

There are 4253 points distributed around the main wing and the two flaps. In carrying out the calculation, we need to define the network of interrelationships among the points; that is, which group of points will be influenced by each point on the grid. We restrict the influence of a given point to the points nearby. This information is stored in the vectors i and j, included in the loaded data. Suppose all the points are numbered 1, 2, …, 4253. The i and j vectors describe the links between point i and point j. For example, if we look at the first five elements:

≫ [i(1:5) j(1:5]’

ans =

1	2	3	5	4
2	3	10	10	11

The interpretation is that point 1 is connected to point 2, point 2 is connected to point 3, points 3 and 5 are connected to point 10, and so on. We create a sparse adjacency matrix, A, by using i and j as inputs to the sparse function:

The spy function plots a sparse matrix with a dot at the positions of all the non-zero entries, which number 12,289 here (the length of the Ni and j vectors). The concentration of non-zero elements near the diagonal reflects the local nature of the interaction (given a reasonable numbering scheme). To plot the geometry of the interactions we can use the gplot function:

(Try zooming in on this plo...