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MATLAB Usage and Computational Errors

Chapter Outline

• 1.1 Basic Operations of MATLAB
  • 1.1.1 Input/Output of Data from MATLAB Command Window
  • 1.1.2 Input/Output of Data Through Files
  • 1.1.3 Input/Output of Data Using Keyboard
  • 1.1.4 Two-Dimensional (2D) Graphic Input/Output
  • 1.1.5 Three Dimensional (3D) Graphic Output
  • 1.1.6 Mathematical Functions
  • 1.1.7 Operations on Vectors and Matrices
  • 1.1.8 Random Number Generators
  • 1.1.9 Flow Control
• 1.2 Computer Errors vs. Human Mistakes
  • 1.2.1 IEEE 64-bit Floating-Point Number Representation
  • 1.2.2 Various Kinds of Computing Errors
  • 1.2.3 Absolute/Relative Computing Errors
  • 1.2.4 Error Propagation
  • 1.2.5 Tips for Avoiding Large Errors
• 1.3 Toward Good Program
  • 1.3.1 Nested Computing for Computational Efficiency
  • 1.3.2 Vector Operation vs. Loop Iteration
  • 1.3.3 Iterative Routine vs. Recursive Routine
  • 1.3.4 To Avoid Runtime Error
  • 1.3.5 Parameter Sharing via GLOBAL Variables
  • 1.3.6 Parameter Passing Through VARARGIN
  • 1.3.7 Adaptive Input Argument List
  • Problems

1.1 Basic Operations of MATLAB

MATLAB is a high-level software package with many built-in functions that make the learning of numerical methods much easier and more interesting. In this section, we will introduce some basic operations that will enable you to learn the software and build your own programs for problem solving. In the workstation environment, you type "matlab" to start the program, while in the PC environment, you simply double-click the MATLAB icon.

Once you start the MATLAB program, a Command window will open with the MATLAB prompt ». On the command line, you can type MATLAB commands, functions together with their input/output arguments, the names of script files containing a block of statements to be executed at a time or functions defined by users. The MATLAB program files must have the extension name ***.m to be executed in the MATLAB environment. If you want to create a new M-file or edit an existing file, you click File/New/M-file or File/Open in the top left corner of the main menu, find/select/load the file by double-clicking it, and then begin editing it in the Editor window. If the path of the file you want to run is not listed in the MATLAB search path, the file name will not be recognized by MATLAB. In such cases, you need to add the path to the MATLAB-path list by clicking the menu 'Set_Path' in the Command window, clicking the 'Add_Folder' button, browsing/clicking the folder name and finally clicking the SAVE button and the Close button. The lookfor command is available to help you find the MATLAB commands/functions that are related with a job you want to be done. The help command helps you know the usage of a particular command/function. You may type directly in the Command window

to find the MATLAB commands in connection with 'repeat' or to find information about the 'for loop'

1.1.1 Input/Output of Data from MATLAB Command Window

MATLAB remembers all input data in a session (anything entered through direct keyboard input or running a script file) until the command ' clear()' is given or you exit MATLAB.

One of the many features of MATLAB is that it enables us to deal with the vectors/matrices in the same way as scalars. For instance, to input the matrices/vectors,

type the following statements in the MATLAB Command window:

At the end of the statement, press <Enter> key if you want to check the result of executing the statement immediately. Otherwise, type a semicolon ';' before pressing <Enter> key so that the Command window will not be overloaded by a long display of results.

1.1.2 Input/Output of Data Through Files

MATLAB can handle two types of data files. One is the binary format mat-files named ***.mat. This kind of files can preserve the values of more than one variable, but will be handled only in the MATLAB environment and cannot be shared with other programming environments. The other is the ASCII dat-files named ***.txt, which can be shared with other programming environments, but preserve the values of only one variable.

Beneath are a few sample statements for storing some data into a mat-file in the current directory and reading the data back from the mat-file.

If you want to store the data into an ASCII dat-file (in the current directory), make the filename the same as the name of the data and type ' -ascii' at the end of the save statement.

However, with the save/load commands into/from a dat-file, the value of only one variable having the lowercase name can be saved/loaded, a scalar or a vector/matrix. Besides, nonnumeric data cannot be handled by using a dat-file. If you save a string data into a dat-file, its ASCII code will be saved. If a dat-file is constructed to have a data matrix in other environments than MATLAB, every line (row) of the file must have the same number of columns. If you want to read the data from the dat-file in MATLAB, just type the (lowercase) filename ***.txt after ' load', which will also be recognized as the name of the data contained in the dat-file.

At the MATLAB prompt, you can type 'nm112' (the filename excluding the extension name part ".m") and <Enter> key to run the following M-file "nm112.m" consisting of several file input(save)/output(load) statements. Then you will see the effects of the individual statements from the running results appearing on the screen.

1.1.3 Input/Output of Data Using Keyboard

The command 'input' enables the user to input some data via the keyboard. For example,

Note that the fraction 1/3 is a nonterminating decimal number, but only four digits after the decimal point is displayed as the result of executing the above command. This is a choice of formatting in MATLAB. One may choose to display more decimal places by using the command ' format', which can make a fraction show up as a fraction, as a decimal number with more digits, or even in an exponential form of a normalized number times 10 to the power of some integer. For instance:

Note that the number of displayed digits is not the actual number of significant digits of the value stored in computer memory. This point will be made clear in Section 1.2.1.

There are other ways of displaying the value of a variable and a string on the screen than typing the name of the...