MATLAB | POLYSPACE RELEASE NOTES | Getting Started with MATLAB 7

Getting Started with MATLAB 7
Getting Started with MATLAB® 7
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Getting Started with MATLAB
© COPYRIGHT 1984–2007 by The MathWorks, Inc.
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Revision History
December 1996
May 1997
September 1998
September 2000
June 2001
July 2002
August 2002
June 2004
October 2004
March 2005
June 2005
September 2005
March 2006
September 2006
March 2007
September 2007
First printing
Second printing
Third printing
Fourth printing
Online only
Online only
Fifth printing
Sixth printing
Online only
Online only
Seventh printing
Online only
Online only
Eighth printing
Ninth printing
Tenth printing
For MATLAB 5
For MATLAB 5.1
For MATLAB 5.3
Revised for MATLAB 6 (Release 12)
Revised for MATLAB 6.1 (Release 12.1)
Revised for MATLAB 6.5 (Release 13)
Revised for MATLAB 6.5
Revised for MATLAB 7.0 (Release 14)
Revised for MATLAB 7.0.1 (Release 14SP1)
Revised for MATLAB 7.0.4 (Release 14SP2)
Minor revision for MATLAB 7.0.4 (Release 14SP2)
Minor revision for MATLAB 7.1 (Release 14SP3)
Minor revision for MATLAB 7.2 (Release 2006a)
Minor revision for MATLAB 7.3 (Release 2006b)
Minor revision for MATLAB 7.4 (Release 2007a)
Minor revision for MATLAB 7.5 (Release 2007b)
Contents
Introduction
1
What Is MATLAB? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Overview of MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The MATLAB System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1-2
1-2
1-3
MATLAB Documentation . . . . . . . . . . . . . . . . . . . . . . . . . . .
1-5
Starting and Quitting MATLAB . . . . . . . . . . . . . . . . . . . . .
Starting MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Quitting MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1-7
1-7
1-8
Matrices and Arrays
2
Matrices and Magic Squares . . . . . . . . . . . . . . . . . . . . . . . .
About Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Entering Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
sum, transpose, and diag . . . . . . . . . . . . . . . . . . . . . . . . . . .
Subscripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Colon Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The magic Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-2
2-2
2-4
2-5
2-7
2-8
2-9
Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Examples of Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-11
2-11
2-12
2-12
2-13
2-14
Working with Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Generating Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The load Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-16
2-16
2-17
v
M-Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Concatenation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Deleting Rows and Columns . . . . . . . . . . . . . . . . . . . . . . . . .
2-17
2-18
2-19
More About Matrices and Arrays . . . . . . . . . . . . . . . . . . . .
Linear Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Multivariate Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scalar Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Logical Subscripting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The find Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-20
2-20
2-24
2-26
2-27
2-27
2-28
Controlling Command Window Input and Output . . . .
The format Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Suppressing Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Entering Long Statements . . . . . . . . . . . . . . . . . . . . . . . . . .
Command Line Editing . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-30
2-30
2-31
2-32
2-32
Graphics
3
vi
Contents
Overview of MATLAB Plotting . . . . . . . . . . . . . . . . . . . . . .
Plotting Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Graph Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Figure Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Arranging Graphs Within a Figure . . . . . . . . . . . . . . . . . . .
Choosing a Type of Graph to Plot . . . . . . . . . . . . . . . . . . . . .
3-2
3-2
3-5
3-6
3-12
3-13
Editing Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Plot Edit Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Using Functions to Edit Graphs . . . . . . . . . . . . . . . . . . . . . .
3-17
3-17
3-22
Some Ways to Use MATLAB Plotting Tools . . . . . . . . . . .
Plotting Two Variables with Plotting Tools . . . . . . . . . . . . .
Changing the Appearance of Lines and Markers . . . . . . . .
Adding More Data to the Graph . . . . . . . . . . . . . . . . . . . . . .
Changing the Type of Graph . . . . . . . . . . . . . . . . . . . . . . . .
Modifying the Graph Data Source . . . . . . . . . . . . . . . . . . . .
3-23
3-23
3-26
3-27
3-30
3-32
Preparing Graphs for Presentation . . . . . . . . . . . . . . . . .
Annotating Graphs for Presentation . . . . . . . . . . . . . . . . . .
Printing the Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Exporting the Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-37
3-37
3-42
3-46
Using Basic Plotting Functions . . . . . . . . . . . . . . . . . . . . .
Creating a Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Plotting Multiple Data Sets in One Graph . . . . . . . . . . . . .
Specifying Line Styles and Colors . . . . . . . . . . . . . . . . . . . .
Plotting Lines and Markers . . . . . . . . . . . . . . . . . . . . . . . . .
Graphing Imaginary and Complex Data . . . . . . . . . . . . . . .
Adding Plots to an Existing Graph . . . . . . . . . . . . . . . . . . .
Figure Windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Displaying Multiple Plots in One Figure . . . . . . . . . . . . . . .
Controlling the Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Adding Axis Labels and Titles . . . . . . . . . . . . . . . . . . . . . . .
Saving Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-49
3-49
3-50
3-51
3-52
3-53
3-54
3-55
3-56
3-58
3-59
3-61
Creating Mesh and Surface Plots . . . . . . . . . . . . . . . . . . . .
About Mesh and Surface Plots . . . . . . . . . . . . . . . . . . . . . . .
Visualizing Functions of Two Variables . . . . . . . . . . . . . . . .
3-63
3-63
3-63
Plotting Image Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
About Plotting Image Data . . . . . . . . . . . . . . . . . . . . . . . . . .
Reading and Writing Images . . . . . . . . . . . . . . . . . . . . . . . .
3-69
3-69
3-70
Printing Graphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Overview of Printing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Printing from the File Menu . . . . . . . . . . . . . . . . . . . . . . . . .
Exporting the Figure to a Graphics File . . . . . . . . . . . . . . .
Using the Print Command . . . . . . . . . . . . . . . . . . . . . . . . . .
3-71
3-71
3-71
3-72
3-72
Handle Graphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Using the Handle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Graphics Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Setting Object Properties . . . . . . . . . . . . . . . . . . . . . . . . . . .
Specifying the Axes or Figure . . . . . . . . . . . . . . . . . . . . . . . .
Finding the Handles of Existing Objects . . . . . . . . . . . . . . .
3-74
3-74
3-75
3-77
3-80
3-81
vii
Programming
4
Flow Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conditional Control – if, else, switch . . . . . . . . . . . . . . . . . .
Loop Control – for, while, continue, break . . . . . . . . . . . . . .
Error Control – try, catch . . . . . . . . . . . . . . . . . . . . . . . . . . .
Program Termination – return . . . . . . . . . . . . . . . . . . . . . . .
4-2
4-2
4-5
4-7
4-8
Other Data Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Multidimensional Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cell Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Characters and Text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-9
4-9
4-11
4-13
4-16
Scripts and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Types of Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Global Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Passing String Arguments to Functions . . . . . . . . . . . . . . .
The eval Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Function Handles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Function Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Vectorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Preallocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-20
4-20
4-21
4-22
4-24
4-26
4-27
4-28
4-28
4-29
4-31
4-32
Data Analysis
5
viii
Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-2
Preprocessing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Loading the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Missing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Outliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-3
5-3
5-3
5-4
5-4
Smoothing and Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-6
Summarizing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Measures of Location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Measures of Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Shape of a Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-10
5-10
5-10
5-11
5-11
Visualizing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-D Scatter Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-D Scatter Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scatter Plot Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-14
5-14
5-14
5-16
5-18
Modeling Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Polynomial Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
General Linear Regression . . . . . . . . . . . . . . . . . . . . . . . . . .
5-19
5-19
5-19
5-20
Creating Graphical User Interfaces
6
What Is GUIDE? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6-2
Laying Out a GUI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Starting GUIDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Layout Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6-3
6-3
6-4
Programming a GUI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6-6
Desktop Tools and Development Environment
7
Desktop Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Introduction to the Desktop . . . . . . . . . . . . . . . . . . . . . . . . .
7-2
7-2
ix
Arranging the Desktop . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Start Button . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7-4
7-4
Command Window and Command History . . . . . . . . . . .
Command Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Command History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7-6
7-6
7-7
Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Help Browser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Other Forms of Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Typographical Conventions . . . . . . . . . . . . . . . . . . . . . . . . .
7-8
7-8
7-11
7-12
Current Directory Browser and Search Path . . . . . . . . .
Running Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Current Directory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Search Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7-14
7-14
7-14
7-15
Workspace Browser and Array Editor . . . . . . . . . . . . . . .
Workspace Browser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Array Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7-17
7-17
7-18
Editor/Debugger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7-20
M-Lint Code Check and Profiler Reports . . . . . . . . . . . .
M-Lint Code Check Report . . . . . . . . . . . . . . . . . . . . . . . . . .
Profiler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7-23
7-23
7-26
Other Development Environment Features . . . . . . . . . .
7-28
External Interfaces
8
Programming Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . .
Call MATLAB from C and Fortran Programs . . . . . . . . . . .
Call C and Fortran Programs from MATLAB . . . . . . . . . . .
Call Java from MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . . .
Call Functions in Shared Libraries . . . . . . . . . . . . . . . . . . .
Import and Export Data . . . . . . . . . . . . . . . . . . . . . . . . . . . .
x
Contents
8-2
8-2
8-2
8-3
8-3
8-3
Component Object Model Interface . . . . . . . . . . . . . . . . . .
8-4
Web Services . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8-5
Serial Port Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8-6
Index
xi
xii
Contents
1
Introduction
What Is MATLAB? (p. 1-2)
See how MATLAB® can provide
solutions for you in technical
computing, what are some of
the common applications of
MATLAB, and what types of add-on
application-specific solutions are
available in MATLAB toolboxes.
MATLAB Documentation (p. 1-5)
Find out where to look for instruction
on how to use each component of
MATLAB, and where to find help
when you need it.
Starting and Quitting MATLAB
(p. 1-7)
Start a new MATLAB session,
use the desktop environment, and
terminate the session.
1
Introduction
What Is MATLAB?
In this section...
“Overview of MATLAB” on page 1-2
“The MATLAB System” on page 1-3
Overview of MATLAB
MATLAB is a high-performance language for technical computing. It
integrates computation, visualization, and programming in an easy-to-use
environment where problems and solutions are expressed in familiar
mathematical notation. Typical uses include
• Math and computation
• Algorithm development
• Data acquisition
• Modeling, simulation, and prototyping
• Data analysis, exploration, and visualization
• Scientific and engineering graphics
• Application development, including graphical user interface building
MATLAB is an interactive system whose basic data element is an array that
does not require dimensioning. This allows you to solve many technical
computing problems, especially those with matrix and vector formulations,
in a fraction of the time it would take to write a program in a scalar
noninteractive language such as C or Fortran.
The name MATLAB stands for matrix laboratory. MATLAB was originally
written to provide easy access to matrix software developed by the LINPACK
and EISPACK projects. Today, MATLAB engines incorporate the LAPACK
and BLAS libraries, embedding the state of the art in software for matrix
computation.
MATLAB has evolved over a period of years with input from many users. In
university environments, it is the standard instructional tool for introductory
1-2
What Is MATLAB?
and advanced courses in mathematics, engineering, and science. In industry,
MATLAB is the tool of choice for high-productivity research, development,
and analysis.
MATLAB features a family of add-on application-specific solutions called
toolboxes. Very important to most users of MATLAB, toolboxes allow you
to learn and apply specialized technology. Toolboxes are comprehensive
collections of MATLAB functions (M-files) that extend the MATLAB
environment to solve particular classes of problems. Areas in which toolboxes
are available include signal processing, control systems, neural networks,
fuzzy logic, wavelets, simulation, and many others.
The MATLAB System
The MATLAB system consists of these main parts:
Desktop Tools and Development Environment
This is the set of tools and facilities that help you use MATLAB functions
and files. Many of these tools are graphical user interfaces. It includes the
MATLAB desktop and Command Window, a command history, an editor and
debugger, a code analyzer and other reports, and browsers for viewing help,
the workspace, files, and the search path.
The MATLAB Mathematical Function Library
This is a vast collection of computational algorithms ranging from elementary
functions, like sum, sine, cosine, and complex arithmetic, to more sophisticated
functions like matrix inverse, matrix eigenvalues, Bessel functions, and fast
Fourier transforms.
The MATLAB Language
This is a high-level matrix/array language with control flow statements,
functions, data structures, input/output, and object-oriented programming
features. It allows both “programming in the small” to rapidly create quick
and dirty throw-away programs, and “programming in the large” to create
large and complex application programs.
1-3
1
Introduction
Graphics
MATLAB has extensive facilities for displaying vectors and matrices as
graphs, as well as annotating and printing these graphs. It includes high-level
functions for two-dimensional and three-dimensional data visualization,
image processing, animation, and presentation graphics. It also includes
low-level functions that allow you to fully customize the appearance of
graphics as well as to build complete graphical user interfaces on your
MATLAB applications.
MATLAB External Interfaces
This is a library that allows you to write C and Fortran programs that interact
with MATLAB. It includes facilities for calling routines from MATLAB
(dynamic linking), calling MATLAB as a computational engine, and for
reading and writing MAT-files.
1-4
MATLAB Documentation
MATLAB Documentation
MATLAB provides extensive documentation, in both printable and HTML
format, to help you learn about and use all of its features. If you are a new
user, start with this Getting Started book. It covers all the primary MATLAB
features at a high level, including many examples.
To view the online documentation, select MATLAB Help from the Help menu
in MATLAB. Online help appears in the Help browser, providing task-oriented
and reference information about MATLAB features. For more information
about using the Help browser, including typographical conventions used in
the documentation, see “Help” on page 7-8.
The MATLAB documentation is organized into these main topics:
• Desktop Tools and Development Environment — Startup and shutdown,
the desktop, and other tools that help you use MATLAB
• Mathematics — Mathematical operations
• Data Analysis — Data analysis, including data fitting, Fourier analysis,
and time-series tools
• Programming — The MATLAB language and how to develop MATLAB
applications
• Graphics — Tools and techniques for plotting, graph annotation, printing,
and programming with Handle Graphics®
• 3-D Visualization — Visualizing surface and volume data, transparency,
and viewing and lighting techniques
• Creating Graphical User Interfaces — GUI-building tools and how to write
callback functions
• External Interfaces — MEX-files, the MATLAB engine, and interfacing
to Java, COM, and the serial port
1-5
1
Introduction
MATLAB also includes reference documentation for all MATLAB functions:
• “Functions — By Category” — Lists all MATLAB functions grouped into
categories
• Handle Graphics Property Browser — Provides easy access to descriptions
of graphics object properties
• C and Fortran API Reference — Covers those functions used by the
MATLAB external interfaces, providing information on syntax in the
calling language, description, arguments, return values, and examples
The MATLAB online documentation also includes
• Examples — An index of examples included in the documentation
• Release Notes — New features, compatibility considerations, and bug
reports
• Printable Documentation — PDF versions of the documentation suitable
for printing
In addition to the documentation, you can access demos from the Help browser
by clicking the Demos tab. Run demos to learn about key functionality of
MathWorks products and tools.
1-6
Starting and Quitting MATLAB
Starting and Quitting MATLAB
In this section...
“Starting MATLAB” on page 1-7
“Quitting MATLAB” on page 1-8
Starting MATLAB
On Windows platforms, start MATLAB by double-clicking the MATLAB
shortcut icon
on your Windows desktop.
On UNIX platforms, start MATLAB by typing matlab at the operating system
prompt.
You can customize MATLAB startup. For example, you can change the
directory in which MATLAB starts or automatically execute MATLAB
statements in a script file named startup.m.
For More Information See “Starting MATLAB on Windows Platforms”
and “Starting MATLAB on UNIX Platforms” in the Desktop Tools and
Development Environment documentation.
MATLAB Desktop
When you start MATLAB, the MATLAB desktop appears, containing tools
(graphical user interfaces) for managing files, variables, and applications
associated with MATLAB.
The following illustration shows the default desktop. You can customize the
arrangement of tools and documents to suit your needs. For more information
about the desktop tools, see Chapter 7, “Desktop Tools and Development
Environment”.
1-7
1
Introduction
Menus change,
depending on the
tool you are using.
Enter MATLAB
statements at the
prompt.
View or change the
current directory.
Move or resize the
Command Window.
Quitting MATLAB
To end your MATLAB session, select File > Exit MATLAB in the desktop,
or type quit in the Command Window. You can run a script file named
1-8
Starting and Quitting MATLAB
finish.m each time MATLAB quits that, for example, executes functions to
save the workspace.
Confirm Quitting
MATLAB can display a confirmation dialog box before quitting. To set this
option, select File > Preferences > General > Confirmation Dialogs, and
select the check box for Confirm before exiting MATLAB.
For More Information See “Quitting MATLAB” in the Desktop Tools and
Development Environment documentation.
1-9
1
1-10
Introduction
2
Matrices and Arrays
You can watch the Getting Started with MATLAB video demo for an overview
of the major functionality.
Matrices and Magic Squares (p. 2-2)
Enter matrices, perform matrix
operations, and access matrix
elements.
Expressions (p. 2-11)
Work with variables, numbers,
operators, functions, and
expressions.
Working with Matrices (p. 2-16)
Generate matrices, load matrices,
create matrices from M-files and
concatenation, and delete matrix
rows and columns.
More About Matrices and Arrays
(p. 2-20)
Use matrices for linear algebra,
work with arrays, multivariate
data, scalar expansion, and logical
subscripting, and use the find
function.
Controlling Command Window
Input and Output (p. 2-30)
Change output format, suppress
output, enter long lines, and edit at
the command line.
2
Matrices and Arrays
Matrices and Magic Squares
In this section...
“About Matrices” on page 2-2
“Entering Matrices” on page 2-4
“sum, transpose, and diag” on page 2-5
“Subscripts” on page 2-7
“The Colon Operator” on page 2-8
“The magic Function” on page 2-9
About Matrices
In MATLAB, a matrix is a rectangular array of numbers. Special meaning
is sometimes attached to 1-by-1 matrices, which are scalars, and to matrices
with only one row or column, which are vectors. MATLAB has other ways of
storing both numeric and nonnumeric data, but in the beginning, it is usually
best to think of everything as a matrix. The operations in MATLAB are
designed to be as natural as possible. Where other programming languages
work with numbers one at a time, MATLAB allows you to work with entire
matrices quickly and easily. A good example matrix, used throughout this
book, appears in the Renaissance engraving Melencolia I by the German
artist and amateur mathematician Albrecht Dürer.
2-2
Matrices and Magic Squares
This image is filled with mathematical symbolism, and if you look carefully,
you will see a matrix in the upper right corner. This matrix is known as a
magic square and was believed by many in Dürer’s time to have genuinely
magical properties. It does turn out to have some fascinating characteristics
worth exploring.
2-3
2
Matrices and Arrays
Entering Matrices
The best way for you to get started with MATLAB is to learn how to handle
matrices. Start MATLAB and follow along with each example.
You can enter matrices into MATLAB in several different ways:
• Enter an explicit list of elements.
• Load matrices from external data files.
• Generate matrices using built-in functions.
• Create matrices with your own functions in M-files.
Start by entering Dürer’s matrix as a list of its elements. You only have to
follow a few basic conventions:
• Separate the elements of a row with blanks or commas.
• Use a semicolon, ; , to indicate the end of each row.
• Surround the entire list of elements with square brackets, [ ].
To enter Dürer’s matrix, simply type in the Command Window
A = [16 3 2 13; 5 10 11 8; 9 6 7 12; 4 15 14 1]
2-4
Matrices and Magic Squares
MATLAB displays the matrix you just entered:
A =
16
5
9
4
3
10
6
15
2
11
7
14
13
8
12
1
This matrix matches the numbers in the engraving. Once you have entered
the matrix, it is automatically remembered in the MATLAB workspace. You
can refer to it simply as A. Now that you have A in the workspace, take a look
at what makes it so interesting. Why is it magic?
sum, transpose, and diag
You are probably already aware that the special properties of a magic square
have to do with the various ways of summing its elements. If you take the
sum along any row or column, or along either of the two main diagonals,
you will always get the same number. Let us verify that using MATLAB.
The first statement to try is
sum(A)
MATLAB replies with
ans =
34
34
34
34
When you do not specify an output variable, MATLAB uses the variable ans,
short for answer, to store the results of a calculation. You have computed a
row vector containing the sums of the columns of A. Sure enough, each of the
columns has the same sum, the magic sum, 34.
How about the row sums? MATLAB has a preference for working with the
columns of a matrix, so one way to get the row sums is to transpose the
matrix, compute the column sums of the transpose, and then transpose the
result. For an additional way that avoids the double transpose use the
dimension argument for the sum function.
MATLAB has two transpose operators. The apostrophe operator (e.g., A')
performs a complex conjugate transposition. It flips a matrix about its main
2-5
2
Matrices and Arrays
diagonal, and also changes the sign of the imaginary component of any
complex elements of the matrix. The dot-apostrophe operator (e.g., A.'),
transposes without affecting the sign of complex elements. For matrices
containing all real elements, the two operators return the same result.
So
A'
produces
ans =
16
3
2
13
5
10
11
8
9
6
7
12
4
15
14
1
and
sum(A')'
produces a column vector containing the row sums
ans =
34
34
34
34
The sum of the elements on the main diagonal is obtained with the sum and
the diag functions:
diag(A)
produces
ans =
16
10
7
1
2-6
Matrices and Magic Squares
and
sum(diag(A))
produces
ans =
34
The other diagonal, the so-called antidiagonal, is not so important
mathematically, so MATLAB does not have a ready-made function for it.
But a function originally intended for use in graphics, fliplr, flips a matrix
from left to right:
sum(diag(fliplr(A)))
ans =
34
You have verified that the matrix in Dürer’s engraving is indeed a magic
square and, in the process, have sampled a few MATLAB matrix operations.
The following sections continue to use this matrix to illustrate additional
MATLAB capabilities.
Subscripts
The element in row i and column j of A is denoted by A(i,j). For example,
A(4,2) is the number in the fourth row and second column. For our magic
square, A(4,2) is 15. So to compute the sum of the elements in the fourth
column of A, type
A(1,4) + A(2,4) + A(3,4) + A(4,4)
This produces
ans =
34
but is not the most elegant way of summing a single column.
It is also possible to refer to the elements of a matrix with a single subscript,
A(k). This is the usual way of referencing row and column vectors. But it
can also apply to a fully two-dimensional matrix, in which case the array is
2-7
2
Matrices and Arrays
regarded as one long column vector formed from the columns of the original
matrix. So, for our magic square, A(8) is another way of referring to the
value 15 stored in A(4,2).
If you try to use the value of an element outside of the matrix, it is an error:
t = A(4,5)
Index exceeds matrix dimensions.
On the other hand, if you store a value in an element outside of the matrix,
the size increases to accommodate the newcomer:
X = A;
X(4,5) = 17
X =
16
5
9
4
3
10
6
15
2
11
7
14
13
8
12
1
0
0
0
17
The Colon Operator
The colon, :, is one of the most important MATLAB operators. It occurs in
several different forms. The expression
1:10
is a row vector containing the integers from 1 to 10:
1
2
3
4
5
6
7
8
9
To obtain nonunit spacing, specify an increment. For example,
100:-7:50
is
100
93
and
0:pi/4:pi
2-8
86
79
72
65
58
51
10
Matrices and Magic Squares
is
0
0.7854
1.5708
2.3562
3.1416
Subscript expressions involving colons refer to portions of a matrix:
A(1:k,j)
is the first k elements of the jth column of A. So
sum(A(1:4,4))
computes the sum of the fourth column. But there is a better way. The colon
by itself refers to all the elements in a row or column of a matrix and the
keyword end refers to the last row or column. So
sum(A(:,end))
computes the sum of the elements in the last column of A:
ans =
34
Why is the magic sum for a 4-by-4 square equal to 34? If the integers from 1
to 16 are sorted into four groups with equal sums, that sum must be
sum(1:16)/4
which, of course, is
ans =
34
The magic Function
MATLAB actually has a built-in function that creates magic squares of almost
any size. Not surprisingly, this function is named magic:
B = magic(4)
B =
16
2
5
11
9
7
4
14
3
10
6
15
13
8
12
1
2-9
2
Matrices and Arrays
This matrix is almost the same as the one in the Dürer engraving and has
all the same “magic” properties; the only difference is that the two middle
columns are exchanged.
To make this B into Dürer’s A, swap the two middle columns:
A = B(:,[1 3 2 4])
This says, for each of the rows of matrix B, reorder the elements in the order
1, 3, 2, 4. It produces
A =
16
5
9
4
3
10
6
15
2
11
7
14
13
8
12
1
Why would Dürer go to the trouble of rearranging the columns when he could
have used MATLAB ordering? No doubt he wanted to include the date of the
engraving, 1514, at the bottom of his magic square.
2-10
Expressions
Expressions
In this section...
“Variables” on page 2-11
“Numbers” on page 2-12
“Operators” on page 2-12
“Functions” on page 2-13
“Examples of Expressions” on page 2-14
Variables
Like most other programming languages, MATLAB provides mathematical
expressions, but unlike most programming languages, these expressions
involve entire matrices.
MATLAB does not require any type declarations or dimension statements.
When MATLAB encounters a new variable name, it automatically creates the
variable and allocates the appropriate amount of storage. If the variable
already exists, MATLAB changes its contents and, if necessary, allocates
new storage. For example,
num_students = 25
creates a 1-by-1 matrix named num_students and stores the value 25 in its
single element. To view the matrix assigned to any variable, simply enter
the variable name.
Variable names consist of a letter, followed by any number of letters, digits, or
underscores. MATLAB is case sensitive; it distinguishes between uppercase
and lowercase letters. A and a are not the same variable.
Although variable names can be of any length, MATLAB uses only the first
N characters of the name, (where N is the number returned by the function
namelengthmax), and ignores the rest. Hence, it is important to make
each variable name unique in the first N characters to enable MATLAB to
distinguish variables.
N = namelengthmax
2-11
2
Matrices and Arrays
N =
63
The genvarname function can be useful in creating variable names that are
both valid and unique.
Numbers
MATLAB uses conventional decimal notation, with an optional decimal point
and leading plus or minus sign, for numbers. Scientific notation uses the
letter e to specify a power-of-ten scale factor. Imaginary numbers use either i
or j as a suffix. Some examples of legal numbers are
3
9.6397238
1i
-99
1.60210e-20
-3.14159j
0.0001
6.02252e23
3e5i
All numbers are stored internally using the long format specified by the IEEE
floating-point standard. Floating-point numbers have a finite precision of
roughly 16 significant decimal digits and a finite range of roughly 10-308
to 10+308.
The section “Avoiding Common Problems with Floating-Point Arithmetic”
gives a few of the examples showing how IEEE floating-point arithmetic
affects computations in MATLAB. For more examples and information, see
Technical Note 1108 — Common Problems with Floating-Point Arithmetic.
Operators
Expressions use familiar arithmetic operators and precedence rules.
2-12
+
Addition
-
Subtraction
*
Multiplication
/
Division
\
Left division (described in “Matrices and Linear Algebra”
in the MATLAB documentation)
^
Power
Expressions
'
Complex conjugate transpose
( )
Specify evaluation order
Functions
MATLAB provides a large number of standard elementary mathematical
functions, including abs, sqrt, exp, and sin. Taking the square root or
logarithm of a negative number is not an error; the appropriate complex result
is produced automatically. MATLAB also provides many more advanced
mathematical functions, including Bessel and gamma functions. Most of
these functions accept complex arguments. For a list of the elementary
mathematical functions, type
help elfun
For a list of more advanced mathematical and matrix functions, type
help specfun
help elmat
Some of the functions, like sqrt and sin, are built in. Built-in functions are
part of the MATLAB core so they are very efficient, but the computational
details are not readily accessible. Other functions, like gamma and sinh, are
implemented in M-files.
There are some differences between built-in functions and other functions. For
example, for built-in functions, you cannot see the code. For other functions,
you can see the code and even modify it if you want.
Several special functions provide values of useful constants.
pi
3.14159265...
i
Imaginary unit,
j
Same as i
eps
Floating-point relative precision,
realmin
Smallest floating-point number,
2-13
2
Matrices and Arrays
realmax
Largest floating-point number,
Inf
Infinity
NaN
Not-a-number
Infinity is generated by dividing a nonzero value by zero, or by evaluating
well defined mathematical expressions that overflow, i.e., exceed realmax.
Not-a-number is generated by trying to evaluate expressions like 0/0 or
Inf-Inf that do not have well defined mathematical values.
The function names are not reserved. It is possible to overwrite any of them
with a new variable, such as
eps = 1.e-6
and then use that value in subsequent calculations. The original function
can be restored with
clear eps
Examples of Expressions
You have already seen several examples of MATLAB expressions. Here are a
few more examples, and the resulting values:
rho = (1+sqrt(5))/2
rho =
1.6180
a = abs(3+4i)
a =
5
z = sqrt(besselk(4/3,rho-i))
z =
0.3730+ 0.3214i
huge = exp(log(realmax))
huge =
1.7977e+308
2-14
Expressions
toobig = pi*huge
toobig =
Inf
2-15
2
Matrices and Arrays
Working with Matrices
In this section...
“Generating Matrices” on page 2-16
“The load Function” on page 2-17
“M-Files” on page 2-17
“Concatenation” on page 2-18
“Deleting Rows and Columns” on page 2-19
Generating Matrices
MATLAB provides four functions that generate basic matrices.
zeros
All zeros
ones
All ones
rand
Uniformly distributed random elements
randn
Normally distributed random elements
Here are some examples:
Z = zeros(2,4)
Z =
0
0
0
0
0
0
F = 5*ones(3,3)
F =
5
5
5
5
5
5
5
5
5
0
0
N = fix(10*rand(1,10))
N =
9
2
6
4
2-16
8
7
4
0
8
4
Working with Matrices
R = randn(4,4)
R =
0.6353
0.0860
-0.6014
-2.0046
0.5512
-0.4931
-1.0998
0.4620
-0.3210
1.2366
-0.6313
-2.3252
-1.2316
1.0556
-0.1132
0.3792
The load Function
The load function reads binary files containing matrices generated by earlier
MATLAB sessions, or reads text files containing numeric data. The text file
should be organized as a rectangular table of numbers, separated by blanks,
with one row per line, and an equal number of elements in each row. For
example, outside of MATLAB, create a text file containing these four lines:
16.0
5.0
9.0
4.0
3.0
10.0
6.0
15.0
2.0
11.0
7.0
14.0
13.0
8.0
12.0
1.0
Save the file as magik.dat in the current directory. The statement
load magik.dat
reads the file and creates a variable, magik, containing the example matrix.
An easy way to read data into MATLAB in many text or binary formats is to
use the Import Wizard.
M-Files
You can create your own matrices using M-files, which are text files containing
MATLAB code. Use the MATLAB Editor or another text editor to create a file
containing the same statements you would type at the MATLAB command
line. Save the file under a name that ends in .m.
For example, create a file in the current directory named magik.m containing
these five lines:
A = [16.0
5.0
3.0
10.0
2.0
11.0
13.0
8.0
2-17
2
Matrices and Arrays
9.0
4.0
6.0
15.0
7.0
14.0
12.0
1.0 ];
The statement
magik
reads the file and creates a variable, A, containing the example matrix.
Concatenation
Concatenation is the process of joining small matrices to make bigger ones. In
fact, you made your first matrix by concatenating its individual elements. The
pair of square brackets, [], is the concatenation operator. For an example,
start with the 4-by-4 magic square, A, and form
B = [A
A+32; A+48
A+16]
The result is an 8-by-8 matrix, obtained by joining the four submatrices:
B =
16
5
9
4
64
53
57
52
3
10
6
15
51
58
54
63
2
11
7
14
50
59
55
62
13
8
12
1
61
56
60
49
48
37
41
36
32
21
25
20
35
42
38
47
19
26
22
31
34
43
39
46
18
27
23
30
45
40
44
33
29
24
28
17
This matrix is halfway to being another magic square. Its elements are a
rearrangement of the integers 1:64. Its column sums are the correct value
for an 8-by-8 magic square:
sum(B)
ans =
260
260
260
260
260
260
260
260
But its row sums, sum(B')', are not all the same. Further manipulation is
necessary to make this a valid 8-by-8 magic square.
2-18
Working with Matrices
Deleting Rows and Columns
You can delete rows and columns from a matrix using just a pair of square
brackets. Start with
X = A;
Then, to delete the second column of X, use
X(:,2) = []
This changes X to
X =
16
5
9
4
2
11
7
14
13
8
12
1
If you delete a single element from a matrix, the result is not a matrix
anymore. So, expressions like
X(1,2) = []
result in an error. However, using a single subscript deletes a single element,
or sequence of elements, and reshapes the remaining elements into a row
vector. So
X(2:2:10) = []
results in
X =
16
9
2
7
13
12
1
2-19
2
Matrices and Arrays
More About Matrices and Arrays
In this section...
“Linear Algebra” on page 2-20
“Arrays” on page 2-24
“Multivariate Data” on page 2-26
“Scalar Expansion” on page 2-27
“Logical Subscripting” on page 2-27
“The find Function” on page 2-28
Linear Algebra
Informally, the terms matrix and array are often used interchangeably. More
precisely, a matrix is a two-dimensional numeric array that represents a
linear transformation. The mathematical operations defined on matrices are
the subject of linear algebra.
Dürer’s magic square
A = [16
5
9
4
3
10
6
15
2
11
7
14
13
8
12
1 ]
provides several examples that give a taste of MATLAB matrix operations.
You have already seen the matrix transpose, A'. Adding a matrix to its
transpose produces a symmetric matrix:
A + A'
ans =
32
8
11
17
2-20
8
20
17
23
11
17
14
26
17
23
26
2
More About Matrices and Arrays
The multiplication symbol, *, denotes the matrix multiplication involving
inner products between rows and columns. Multiplying the transpose of a
matrix by the original matrix also produces a symmetric matrix:
A'*A
ans =
378
212
206
360
212
370
368
206
206
368
370
212
360
206
212
378
The determinant of this particular matrix happens to be zero, indicating
that the matrix is singular:
d = det(A)
d =
0
The reduced row echelon form of A is not the identity:
R = rref(A)
R =
1
0
0
0
0
1
0
0
0
0
1
0
1
-3
3
0
Since the matrix is singular, it does not have an inverse. If you try to compute
the inverse with
X = inv(A)
you will get a warning message:
Warning: Matrix is close to singular or badly scaled.
Results may be inaccurate. RCOND = 9.796086e-018.
Roundoff error has prevented the matrix inversion algorithm from detecting
exact singularity. But the value of rcond, which stands for reciprocal
2-21
2
Matrices and Arrays
condition estimate, is on the order of eps, the floating-point relative precision,
so the computed inverse is unlikely to be of much use.
The eigenvalues of the magic square are interesting:
e = eig(A)
e =
34.0000
8.0000
0.0000
-8.0000
One of the eigenvalues is zero, which is another consequence of singularity.
The largest eigenvalue is 34, the magic sum. That is because the vector of all
ones is an eigenvector:
v = ones(4,1)
v =
1
1
1
1
A*v
ans =
34
34
34
34
When a magic square is scaled by its magic sum,
P = A/34
the result is a doubly stochastic matrix whose row and column sums are all 1:
P =
0.4706
2-22
0.0882
0.0588
0.3824
More About Matrices and Arrays
0.1471
0.2647
0.1176
0.2941
0.1765
0.4412
0.3235
0.2059
0.4118
0.2353
0.3529
0.0294
Such matrices represent the transition probabilities in a Markov process.
Repeated powers of the matrix represent repeated steps of the process. For
our example, the fifth power
P^5
is
0.2507
0.2497
0.2500
0.2496
0.2495
0.2501
0.2498
0.2506
This shows that as
, approach
0.2494
0.2502
0.2499
0.2505
0.2504
0.2500
0.2503
0.2493
approaches infinity, all the elements in the th power,
.
Finally, the coefficients in the characteristic polynomial
poly(A)
are
1
-34
-64
2176
0
This indicates that the characteristic polynomial
is
The constant term is zero, because the matrix is singular, and the coefficient
of the cubic term is -34, because the matrix is magic!
2-23
2
Matrices and Arrays
Arrays
When they are taken away from the world of linear algebra, matrices become
two-dimensional numeric arrays. Arithmetic operations on arrays are
done element by element. This means that addition and subtraction are
the same for arrays and matrices, but that multiplicative operations are
different. MATLAB uses a dot, or decimal point, as part of the notation for
multiplicative array operations.
The list of operators includes
+
Addition
-
Subtraction
.*
Element-by-element multiplication
./
Element-by-element division
.\
Element-by-element left division
.^
Element-by-element power
.'
Unconjugated array transpose
If the Dürer magic square is multiplied by itself with array multiplication
A.*A
the result is an array containing the squares of the integers from 1 to 16,
in an unusual order:
ans =
256
25
81
16
9
100
36
225
4
121
49
196
169
64
144
1
Building Tables
Array operations are useful for building tables. Suppose n is the column vector
n = (0:9)';
2-24
More About Matrices and Arrays
Then
pows = [n
n.^2
2.^n]
builds a table of squares and powers of 2:
pows =
0
1
2
3
4
5
6
7
8
9
0
1
4
9
16
25
36
49
64
81
1
2
4
8
16
32
64
128
256
512
The elementary math functions operate on arrays element by element. So
format short g
x = (1:0.1:2)';
logs = [x log10(x)]
builds a table of logarithms.
logs =
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
0
0.04139
0.07918
0.11394
0.14613
0.17609
0.20412
0.23045
0.25527
0.27875
0.30103
2-25
2
Matrices and Arrays
Multivariate Data
MATLAB uses column-oriented analysis for multivariate statistical data.
Each column in a data set represents a variable and each row an observation.
The (i,j)th element is the ith observation of the jth variable.
As an example, consider a data set with three variables:
• Heart rate
• Weight
• Hours of exercise per week
For five observations, the resulting array might look like
D = [ 72
81
69
82
75
134
201
156
148
170
3.2
3.5
7.1
2.4
1.2 ]
The first row contains the heart rate, weight, and exercise hours for patient
1, the second row contains the data for patient 2, and so on. Now you can
apply many MATLAB data analysis functions to this data set. For example, to
obtain the mean and standard deviation of each column, use
mu = mean(D), sigma = std(D)
mu =
75.8
161.8
3.48
sigma =
5.6303
25.499
2.2107
For a list of the data analysis functions available in MATLAB, type
help datafun
If you have access to Statistics Toolbox, type
help stats
2-26
More About Matrices and Arrays
Scalar Expansion
Matrices and scalars can be combined in several different ways. For example,
a scalar is subtracted from a matrix by subtracting it from each element. The
average value of the elements in our magic square is 8.5, so
B = A - 8.5
forms a matrix whose column sums are zero:
B =
7.5
-3.5
0.5
-4.5
-5.5
1.5
-2.5
6.5
-6.5
2.5
-1.5
5.5
4.5
-0.5
3.5
-7.5
sum(B)
ans =
0
0
0
0
With scalar expansion, MATLAB assigns a specified scalar to all indices in a
range. For example,
B(1:2,2:3) = 0
zeroes out a portion of B:
B =
7.5
-3.5
0.5
-4.5
0
0
-2.5
6.5
0
0
-1.5
5.5
4.5
-0.5
3.5
-7.5
Logical Subscripting
The logical vectors created from logical and relational operations can be used
to reference subarrays. Suppose X is an ordinary matrix and L is a matrix of
the same size that is the result of some logical operation. Then X(L) specifies
the elements of X where the elements of L are nonzero.
2-27
2
Matrices and Arrays
This kind of subscripting can be done in one step by specifying the logical
operation as the subscripting expression. Suppose you have the following
set of data:
x = [2.1 1.7 1.6 1.5 NaN 1.9 1.8 1.5 5.1 1.8 1.4 2.2 1.6 1.8];
The NaN is a marker for a missing observation, such as a failure to respond to
an item on a questionnaire. To remove the missing data with logical indexing,
use isfinite(x), which is true for all finite numerical values and false for
NaN and Inf:
x = x(isfinite(x))
x =
2.1 1.7 1.6 1.5 1.9 1.8 1.5 5.1 1.8 1.4 2.2 1.6 1.8
Now there is one observation, 5.1, which seems to be very different from the
others. It is an outlier. The following statement removes outliers, in this case
those elements more than three standard deviations from the mean:
x = x(abs(x-mean(x)) <= 3*std(x))
x =
2.1 1.7 1.6 1.5 1.9 1.8 1.5 1.8 1.4 2.2 1.6 1.8
For another example, highlight the location of the prime numbers in Dürer’s
magic square by using logical indexing and scalar expansion to set the
nonprimes to 0. (See “The magic Function” on page 2-9.)
A(~isprime(A)) = 0
A =
0
5
0
0
3
0
0
0
2
11
7
0
13
0
0
0
The find Function
The find function determines the indices of array elements that meet a given
logical condition. In its simplest form, find returns a column vector of indices.
Transpose that vector to obtain a row vector of indices. For example, start
again with Dürer’s magic square. (See “The magic Function” on page 2-9.)
2-28
More About Matrices and Arrays
k = find(isprime(A))'
picks out the locations, using one-dimensional indexing, of the primes in the
magic square:
k =
2
5
9
10
11
13
Display those primes, as a row vector in the order determined by k, with
A(k)
ans =
5
3
2
11
7
13
When you use k as a left-hand-side index in an assignment statement, the
matrix structure is preserved:
A(k) = NaN
A =
16
NaN
9
4
NaN
10
6
15
NaN
NaN
NaN
14
NaN
8
12
1
2-29
2
Matrices and Arrays
Controlling Command Window Input and Output
In this section...
“The format Function” on page 2-30
“Suppressing Output” on page 2-31
“Entering Long Statements” on page 2-32
“Command Line Editing” on page 2-32
The format Function
The format function controls the numeric format of the values displayed by
MATLAB. The function affects only how numbers are displayed, not how
MATLAB computes or saves them. Here are the different formats, together
with the resulting output produced from a vector x with components of
different magnitudes.
Note To ensure proper spacing, use a fixed-width font, such as Courier.
x = [4/3 1.2345e-6]
format short
1.3333
0.0000
format short e
1.3333e+000
1.2345e-006
format short g
1.3333
1.2345e-006
format long
1.33333333333333
2-30
0.00000123450000
Controlling Command Window Input and Output
format long e
1.333333333333333e+000
1.234500000000000e-006
format long g
1.33333333333333
1.2345e-006
format bank
1.33
0.00
format rat
4/3
1/810045
format hex
3ff5555555555555
3eb4b6231abfd271
If the largest element of a matrix is larger than 103 or smaller than 10-3,
MATLAB applies a common scale factor for the short and long formats.
In addition to the format functions shown above
format compact
suppresses many of the blank lines that appear in the output. This lets you
view more information on a screen or window. If you want more control over
the output format, use the sprintf and fprintf functions.
Suppressing Output
If you simply type a statement and press Return or Enter, MATLAB
automatically displays the results on screen. However, if you end the line
with a semicolon, MATLAB performs the computation but does not display
any output. This is particularly useful when you generate large matrices.
For example,
A = magic(100);
2-31
2
Matrices and Arrays
Entering Long Statements
If a statement does not fit on one line, use an ellipsis (three periods), ...,
followed by Return or Enter to indicate that the statement continues on
the next line. For example,
s = 1 -1/2 + 1/3 -1/4 + 1/5 - 1/6 + 1/7 ...
- 1/8 + 1/9 - 1/10 + 1/11 - 1/12;
Blank spaces around the =, +, and - signs are optional, but they improve
readability.
Command Line Editing
Various arrow and control keys on your keyboard allow you to recall, edit,
and reuse statements you have typed earlier. For example, suppose you
mistakenly enter
rho = (1 + sqt(5))/2
You have misspelled sqrt. MATLAB responds with
Undefined function or variable 'sqt'.
Instead of retyping the entire line, simply press the key. The statement
you typed is redisplayed. Use the
key to move the cursor over and insert
the missing r. Repeated use of the key recalls earlier lines. Typing a few
characters and then the key finds a previous line that begins with those
characters. You can also copy previously executed statements from the
Command History. For more information, see “Command History” on page 7-7.
Following is the list of arrow and control keys you can use in the Command
Window. If the preference you select for “Command Window Key Bindings”
is MATLAB standard (Emacs), you can also use the Ctrl+key combinations
shown. See also general keyboard shortcuts for desktop tools in the MATLAB
Desktop Tools and Development Environment documentation.
2-32
Controlling Command Window Input and Output
Control Key for
MATLAB Standard
(Emacs) Preference
Operation
Ctrl+P
Recall previous line. Works only at command line.
Ctrl+N
Recall next line. Works only at the prompt if you
previously used the up arrow or Ctrl+P.
Ctrl+B
Move back one character.
Ctrl+F
Move forward one character.
Ctrl+
None
Move right one word.
Ctrl+
None
Move left one word.
Home
Ctrl+A
Move to beginning of current statement.
End
Ctrl+E
Move to end of current statement.
Ctrl+Home
None
Move to top of Command Window.
Ctrl+End
None
Move to end of Command Window.
Esc
Ctrl+U
Clear command line when cursor is at the prompt.
Otherwise, move cursor to the prompt.
Delete
Ctrl+D
Delete character after cursor.
Backspace
Ctrl+H
Delete character before cursor.
None
Ctrl+K
Cut contents (kill) to end of command line.
Shift+Home
None
Select from cursor to beginning of statement.
Shift+End
None
Select from cursor to end of statement.
Key
2-33
2
2-34
Matrices and Arrays
3
Graphics
Overview of MATLAB Plotting
(p. 3-2)
Create plots, include multiple data
sets, specify property values, and
save figures.
Editing Plots (p. 3-17)
Edit plots interactively and using
functions, and use the property
editor.
Some Ways to Use MATLAB Plotting
Tools (p. 3-23)
Edit plots interactively with
graphical plotting tools.
Preparing Graphs for Presentation
(p. 3-37)
Use plotting tools to modify graphs,
add explanatory information, and
print for presentation.
Using Basic Plotting Functions
(p. 3-49)
Use MATLAB plotting functions to
create and modify plots.
Creating Mesh and Surface Plots
(p. 3-63)
Visualize functions of two variables.
Plotting Image Data (p. 3-69)
Work with images.
Printing Graphics (p. 3-71)
Print and export figures.
Handle Graphics (p. 3-74)
Visualize functions of two variables.
3
Graphics
Overview of MATLAB Plotting
In this section...
“Plotting Process” on page 3-2
“Graph Components” on page 3-5
“Figure Tools” on page 3-6
“Arranging Graphs Within a Figure” on page 3-12
“Choosing a Type of Graph to Plot” on page 3-13
For More Information MATLAB Graphics and 3-D Visualization in the
MATLAB documentation provide in-depth coverage of MATLAB graphics and
visualization tools. Access these topics from the Help browser.
Plotting Process
MATLAB provides a wide variety of techniques to display data graphically.
Interactive tools enable you to manipulate graphs to achieve results that
reveal the most information about your data. You can also annotate and print
graphs for presentations, or export graphs to standard graphics formats for
presentation in web browsers or other media.
The process of visualizing data typically involves a series of operations. This
section provides a “big picture” view of the plotting process and contains
links to sections that have examples and specific details about performing
each operation.
Creating a Graph
The type of graph you choose to create depends on the nature of your data and
what you want to reveal about the data. MATLAB predefines many graph
types, such as line, bar, histogram, and pie graphs. There are also 3-D graphs,
such as surfaces, slice planes, and streamlines.
There are two basic ways to create graphs in MATLAB:
• Use plotting tools to create graphs interactively.
3-2
Overview of MATLAB Plotting
See “Some Ways to Use MATLAB Plotting Tools” on page 3-23.
• Use the command interface to enter commands in the Command Window
or create plotting programs.
See “Using Basic Plotting Functions” on page 3-49.
You might find it useful to combine both approaches. For example, you might
issue a plotting command to create a graph and then modify the graph using
one of the interactive tools.
Exploring Data
Once you create a graph, you can extract specific information about the data,
such as the numeric value of a peak in a plot, the average value of a series of
data, or you can perform data fitting.
For More Information See “Data Exploration Tools” in the MATLAB
Graphics documentation and “Opening the Basic Fitting GUI” in the MATLAB
Data Analysis documentation.
Editing the Graph Components
Graphs are composed of objects, which have properties you can change. These
properties affect the way the various graph components look and behave.
For example, the axes used to define the coordinate system of the graph has
properties that define the limits of each axis, the scale, color, etc. The line
used to create a line graph has properties such as color, type of marker used
at each data point (if any), line style, etc.
Note that the data used to create a line graph are properties of the line. You
can, therefore, change the data without actually creating a new graph.
See “Editing Plots” on page 3-17.
Annotating Graphs
Annotations are the text, arrows, callouts, and other labels added to graphs
to help viewers see what is important about the data. You typically add
3-3
3
Graphics
annotations to graphs when you want to show them to other people or when
you want to save them for later reference.
For More Information See “Annotating Graphs” in the MATLAB Graphics
documentation or select Annotating Graphs from the figure Help menu.
Printing and Exporting Graphs
You can print your graph on any printer connected to your computer. The
print previewer enables you to view how your graph will look when printed.
It enables you to add headers, footers, a date, and so on. The print preview
dialog lets you control the size, layout, and other characteristics of the graph
(select Print Preview from the figure File menu).
Exporting a graph means creating a copy of it in a standard graphics file
format, such as TIFF, JPEG, or EPS. You can then import the file into a word
processor, include it in an HTML document, or edit it in a drawing package
(select Export Setup from the figure File menu).
Adding and Removing Figure Content
By default, when you create a new graph in the same figure window, its data
replaces that of the graph that is currently displayed, if any. You can add
new data to a graph in several ways; see “Adding More Data to the Graph”
on page 3-27 for how to do this using a GUI. You can manually remove all
data, graphics and annotations from the current figure by typing CLF in the
Command Window or by selecting Clear Figure from the figure’s Edit menu.
For More Information See the print command reference page and “Printing
and Exporting” in the MATLAB Graphics documentation or select Printing
and Exporting from the figure Help menu.
Saving Graphs to Reload into MATLAB
There are two ways to save graphs that enable you to save the work you have
invested in their preparation:
3-4
Overview of MATLAB Plotting
• Save the graph as a FIG-file (select Save from the figure File menu).
• Generate MATLAB code that can recreate the graph (select Generate
M-File from the figure File menu).
FIG-Files. FIG-files are a binary format that saves a figure in its current
state. This means that all graphics objects and property settings are stored in
the file when you create it. You can reload the file into a different MATLAB
session, even if you are running MATLAB on a different type of computer.
When you load a FIG-file, MATLAB creates a new figure in the same state
as the one you saved.
Note that the states of any figure tools (i.e., any items on the toolbars) are not
saved in a FIG-file; only the contents of the graph are saved.
Generated Code. You can use the MATLAB M-code generator to create
code that recreates the graph. Unlike a FIG-file, the generated code does not
contain any data. You must pass appropriate data to the generated function
when you run the code.
Studying the generated code for a graph is a good way to learn how to
program with MATLAB.
For More Information See the print command reference page and “Saving
Your Work” in the MATLAB Graphics documentation.
Graph Components
MATLAB displays graphs in a special window known as a figure. To create
a graph, you need to define a coordinate system. Therefore every graph is
placed within axes, which are contained by the figure.
The actual visual representation of the data is achieved with graphics objects
like lines and surfaces. These objects are drawn within the coordinate system
defined by the axes, which MATLAB automatically creates specifically to
accommodate the range of the data. The actual data is stored as properties of
the graphics objects.
3-5
3
Graphics
See “Handle Graphics” on page 3-74 for more information about graphics
object properties.
The following picture shows the basic components of a typical graph. You can
find commands for plotting this graph in “Preparing Graphs for Presentation”
on page 3-37.
Figure window displays graphs.
Axes define
a coordinate
system for
the graph.
Line plot
represents
data.
Figure Tools
The figure is equipped with sets of tools that operate on graphs. The figure
Tools menu provides access to many graph tools, as this view of the Options
submenu illustrates. Many of the options shown here are also present as
3-6
Overview of MATLAB Plotting
context menu items for individual tools such as zoom and pan. The figure also
shows three figure toolbars, discussed in “Figure Toolbars” on page 3-8.
For More Information See “Plots and Plotting Tools” in the MATLAB
Graphics documentation or select Plotting Tools from the figure Help menu.
3-7
3
Graphics
Accessing the Tools
You can access or remove the figure toolbars and the plotting tools from the
View menu, as shown in the following picture. Toggle on and off the toolbars
you need. Adding a toolbar stacks it beneath the lowest one.
Figure Toolbars
Figure toolbars provide easy access to many graph modification features.
There are three toolbars. When you place the cursor over a particular tool, a
text box pops up with the tool name. The following picture shows the three
toolbars displayed with the cursor over the Data Cursor tool.
For More Information See “Anatomy of a Graph” in the MATLAB Graphics
documentation.
3-8
Overview of MATLAB Plotting
Plotting Tools
Plotting tools are attached to figures and create an environment for creating
graphs. These tools enable you to do the following:
• Select from a wide variety of graph types.
• Change the type of graph that represents a variable.
• See and set the properties of graphics objects.
• Annotate graphs with text, arrows, etc.
• Create and arrange subplots in the figure.
• Drag and drop data into graphs.
Display the plotting tools from the View menu or by clicking the Show Plot
Tools icon in the figure toolbar, as shown in the following picture.
Enable plotting tools from
the View menu or toolbar
You can also start the plotting tools from the MATLAB prompt:
plottools
The plotting tools are made up of three independent GUI components:
• Figure Palette — Specify and arrange subplots, access workspace variables
for plotting or editing, and add annotations.
• Plot Browser — Select objects in the graphics hierarchy, control visibility,
and add data to axes.
• Property Editor — Change key properties of the selected object. Click More
Properties to access all object properties with the Property Inspector.
3-9
3
Graphics
You can also control these components from the MATLAB Command Window,
by typing the following:
figurepalette
plotbrowser
propertyeditor
See the reference pages for plottools, figurepalette, plotbrowser, and
propertyeditor for information on syntax and options.
The following picture shows a figure with all three plotting tools enabled.
3-10
Overview of MATLAB Plotting
Using Plotting Tools and MATLAB Code
You can enable the plotting tools for any graph, even one created using
MATLAB commands. For example, suppose you type the following code
to create a graph:
t = 0:pi/20:2*pi;
y = exp(sin(t));
plotyy(t,y,t,y,'plot','stem')
xlabel('X Axis')
ylabel('Plot Y Axis')
title('Two Y Axes')
This graph contains two y-axes, one for each plot type (a lineseries and a
stemseries). The plotting tools make it easy to select any of the objects that
the graph contains and modify their properties.
3-11
3
Graphics
For example, adding a label for the y-axis that corresponds to the stem plot
is easily accomplished by selecting that axes in the Plot Browser and setting
the Y Label property in the Property Editor (if you do not see that text field,
stretch the Figures window to make it taller).
Arranging Graphs Within a Figure
You can place a number of axes within a figure by selecting the layout you
want from the Figure Palette. For example, the following picture shows how
to specify four 2-D axes in the figure.
3-12
Overview of MATLAB Plotting
Click to add one axes to bottom
of current layout
Click and drag right to specify
axes layout.
Select the axes you want to target for plotting. You can also use the subplot
function to create multiple axes.
Choosing a Type of Graph to Plot
The many kinds of 2-D and 3-D graphs that MATLAB can make are
described in “Types of Plots Available in MATLAB” in the MATLAB Graphics
documentation. Almost all plot types are itemized, described, and illustrated
by a tool called the Plot Catalog. You can use the Plot Catalog to browse
graph types, choose one to visualize your selected variables, and then create
it in the current or a new figure window. You can access the Plot Catalog by
selecting one or more variables, as follows:
3-13
3
Graphics
• In the Figure Palette, right-click a selected variable and choose More
Plots from the context menu
• In the Workspace Browser, right-click a selected variable and choose More
Plots from the context menu, or click the plot selector
choose More Plots from its menu
tool and
• In the Array Editor, select the values you want to graph, click the plot
selector
tool and choose More Plots from its menu
The icon on the plot selector tool represents a graph type, and changes
depending on the type and dimensionality of the data you select. It is disabled
if no data or non-numeric data is selected.
The following illustration shows how you can open the plot catalog from the
Figure Palette:
3-14
Overview of MATLAB Plotting
MATLAB displays the Plot Catalog in a new, undocked window with the
selected variables ready to plot, after you select a plot type and click Plot or
Plot in New Figure. You can override the selected variables by typing other
variable names or MATLAB expressions in the Plotted Variables edit field.
3-15
3
Graphics
Specify variables to plot.
See a description of each plot type.
Select a category of graphs and then choose a specific type.
3-16
Editing Plots
Editing Plots
In this section...
“Plot Edit Mode” on page 3-17
“Using Functions to Edit Graphs” on page 3-22
Plot Edit Mode
Plot edit mode lets you select specific objects in a graph and enables you to
perform point-and-click editing of most of them.
Enabling Plot Edit Mode
To enable plot edit mode, click the arrowhead in the figure toolbar:
Plot edit mode enabled
You can also select Edit Plot from the figure Tools menu.
Setting Object Properties
After you have enabled plot edit mode, you can select objects by clicking them
in the graph. Selection handles appear and indicate that the object is selected.
Select multiple objects using Shift+click.
Right-click with the pointer over the selected object to display the object’s
context menu:
3-17
3
Graphics
The context menu provides quick access to the most commonly used operations
and properties.
Using the Property Editor
In plot edit mode, double-clicking an object in a graph opens the Property
Editor GUI with that object’s major properties displayed. The Property Editor
provides access to the most used object properties. It is updated to display the
properties of whatever object you select.
3-18
Editing Plots
Click to display Property Inspector
Accessing Properties with the Property Inspector
The Property Inspector is a tool that enables you to access most of the
properties of Handle Graphics and other MATLAB objects. If you do not
find the property you want to set in the Property Editor, click the More
Properties button to display the Property Inspector. You can also use the
inspect command to start the Property Inspector. For example, to inspect the
properties of the current axes, type
inspect(gca)
3-19
3
Graphics
The following picture shows the Property Inspector displaying the properties
of a graph’s axes. It lists each property and provides a text field or other
appropriate device (such as a color picker) from which you can set the value
of the property.
As you select different objects, the Property Inspector is updated to display
the properties of the current object.
3-20
Editing Plots
The Property Inspector lists properties alphabetically by default. However,
you can group Handle Graphics objects, such as axes, by categories which you
can reveal or close in the Property Inspector. To do this, click the
icon
at the upper left, then click the + next to the category you want to expand.
For example, to see the position-related properties, click the + to the left of
the Position category.
The Position category opens and the + changes to a - to indicate that you can
collapse the category by clicking it.
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Using Functions to Edit Graphs
If you prefer to work from the MATLAB command line, or if you are creating
an M-file, you can use MATLAB commands to edit the graphs you create. You
can use the set and get commands to change the properties of the objects in a
graph. For more information about using graphics commands, see “Handle
Graphics” on page 3-74.
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Some Ways to Use MATLAB Plotting Tools
Some Ways to Use MATLAB Plotting Tools
In this section...
“Plotting Two Variables with Plotting Tools” on page 3-23
“Changing the Appearance of Lines and Markers” on page 3-26
“Adding More Data to the Graph” on page 3-27
“Changing the Type of Graph” on page 3-30
“Modifying the Graph Data Source” on page 3-32
Plotting Two Variables with Plotting Tools
Suppose you want to graph the function y = x3 over the x domain -1 to 1. The
first step is to generate the data to plot.
It is simple to evaluate a function because MATLAB can distribute arithmetic
operations over all elements of a multivalued variable.
For example, the following statement creates a variable x that contains values
ranging from -1 to 1 in increments of 0.1 (you could also use the linspace
function to generate data for x). The second statement raises each value in
x to the third power and stores these values in y:
x = -1:.1:1; % Define the range of x
y = x.^3;
% Raise each element in x to the third power
Now that you have generated some data, you can plot it using the MATLAB
plotting tools. To start the plotting tools, type
plottools
MATLAB displays a figure with plotting tools attached.
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Variables in workspace
3-24
Figure plotting area
Some Ways to Use MATLAB Plotting Tools
Note When you invoke plottools, the set of plotting tools you see and their
relative positions depend on how they were configured the last time you used
them. Also, sometimes when you dock and undock figures with plotting tools
attached, the size or proportions of the various components can change, and
you may need to resize one or more of the tool panes.
A simple line graph is a suitable way to display x as the independent variable
and y as the dependent variable. To do this, select both variables (click to
select, and then Shift+click to select again), and then right-click to display
the context menu.
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Select plot(x, y) from the menu. MATLAB creates the line graph in the figure
area. The black squares indicate that the line is selected and you can edit its
properties with the Property Editor.
Changing the Appearance of Lines and Markers
Next change the line properties so that the graph displays only the data point.
Use the Property Editor to set following properties:
• Line to no line
• Marker to o (circle)
• Marker size to 4.0
• Marker fill color to red
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Some Ways to Use MATLAB Plotting Tools
Set line to no line.
Set Marker to O.
Set Marker fill color to red.
Set Marker size to 4.0.
Adding More Data to the Graph
You can add more data to the graph by defining more variables or by specifying
an expression that MATLAB uses to generate data for the plot. This second
approach makes it easy to explore variations of the data already plotted.
To add data to the graph, select the axes in the Plot Browser and click the
Add Data button. When you are using the plotting tools, MATLAB always
adds data to the existing graph, instead of replacing the graph, as it would
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if you issued repeated plotting commands. That is, the plotting tools are in
a hold on state.
To add data using the Plot Browser:
1 Click the Edit Plot tool
.
2 Select the axes to which you wish to add data; handles appear around it.
3 Click the Add Data button in the Plot Browser; the Add Data to Axes
dialog box opens.
4 Select a plot type from the Plot Type drop-down menu.
5 Select a variable or type an expression for X Data Source.
6 Select a variable or type an expression for Y Data Source.
7 Click OK; a plot of the data you specified is added to the axes.
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Some Ways to Use MATLAB Plotting Tools
1. Select axes.
3. Enter expression.
2. Click Add Data.
The picture above shows how to use the Add Data to Axes dialog box to create
a line plot of y = x4, which is added to the existing plot of y = x3. The resulting
plot is shown as follows with the Plot Browser:
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Changing the Type of Graph
The plotting tools enable you to easily view your data with a variety of plot
types. The following picture shows the same data as above converted to stem
plots. To change the plot type,
1 Select both plotted series in the Plot Browser or Shift+click to select them
in the plot itself.
2 Select short dashes from the Line drop-down menu in the Property
Inspector; the line type of both series changes.
3 Select Stem from the Plot Type menu.
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Some Ways to Use MATLAB Plotting Tools
Select both sets of data.
Select Stem as the Plot Type.
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Modifying the Graph Data Source
You can link graph data to variables in your workspace. When you change
the values contained in the variables, you can then update the graph to use
the new data without having to create a new graph. (See also the refresh
function.)
1 Define 50 points between -3π and 3π and compute their sines and cosines:
x = linspace(-3*pi,3*pi,50);
ys = sin(x);
yc = cos(x);
2 Using the plotting tools, create a graph of ys = sin(x):
figure
plottools
3 In the Figure Palette, alternate-click to select x and ys in the Variable pane.
4 Right-click either selected variable and choose plot(x, ys) from the context
menu, as shown below.
The resulting plot looks like this.
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Some Ways to Use MATLAB Plotting Tools
You can use the Property Editor to change the data that this plot displays:
1 Select the line ys vs x in the Plot Browser or by clicking it.
2 In the Property Editor, select yc in the Y Data Source drop-down menu.
3 Click the Refresh Data button; the plot will change to display a plot of
yc vs x.
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Providing New Values for the Data Source
MATLAB copies the data that defines the graph from variables in the base
workspace (for example, x and y) to the XData and YData properties of the
plot object (for example, a lineseries). Therefore, in addition to being able to
choose new data sources, you can assign new values to workspace variables
in the Command Window and click the Refresh Data button to update a
graph to use the new data.
x = linspace(-pi,pi,50); % Define 50 points between -π and π
y = sin(x);
area(x,y) % Make an area plot of x and y
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Some Ways to Use MATLAB Plotting Tools
Now recalculate y at the command line:
y = cos(x)
Select the blue line on the plot. Select, x as the X Data Source, y as the Y
Data Source, and click Refresh Data. The graph’s XData and YData are
replaced, making the plot look like this.
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Graphics
Preparing Graphs for Presentation
Preparing Graphs for Presentation
In this section...
“Annotating Graphs for Presentation” on page 3-37
“Printing the Graph” on page 3-42
“Exporting the Graph” on page 3-46
Annotating Graphs for Presentation
Suppose you plot the following data and want to create a graph that presents
certain information about the data:
x = -10:.005:40;
y = [1.5*cos(x)+4*exp(-.01*x).*cos(x)+exp(.07*x).*sin(3*x)];
plot(x,y)
This picture shows the graph created by the previous code.
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Now suppose you want to save copies of the graph by
• Printing the graph on a local printer so you have a copy for your notebook
• Exporting the graph to an Encapsulated PostScript (EPS) file to incorporate
into a word processor document
To obtain a better view, zoom in on the graph using horizontal zoom.
Enable zoom mode by clicking the Zoom tool
on the figure toolbar, and
then right-click to display the context menu. Select Horizontal Zoom (2-D
Plots Only) from Zoom Options. Notice that you can reverse your zoom
direction by Shift+left-clicking, or using the context menu.
Left-click to zoom in on a region of the graph and use the Pan tool
position the points of interest where you want them on the graph.
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to
Preparing Graphs for Presentation
Label some key points with data tips using the Data Cursor tool
. Notice
that left-clicking the line moves the last datatip you created to where you just
clicked. To create a new datatip, press Alt+click or use the tool’s context
menu. See “Data Cursor — Displaying Data Values Interactively” in the
MATLAB Graphics documentation for more information on using datatips.
Next use the Figure Palette to annotate the plot. Choose the Double arrow
tool in the Annotations section to draw a line between two datatips, as shown
below:
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Now add a text box, also using the Figure Palette. You may have to scroll to
see the text box icon. Drag out a box, and then type into it. You can stretch
or shrink the box with its handles, and center the text with the Property
Editor while the text box is selected. You can also use the Property Editor to
change the text font, size, style, and color, as well as the text box line and
background colors.
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Preparing Graphs for Presentation
Finally, add text annotations, axis labels, and a title. You can add the title and
axis labels using the following commands:
title ('y = 1.5cos(x) + 4e^{-0.01x}cos(x) + e^{0.07x}sin(3x)')
xlabel('X Axis')
ylabel('Y Axis')
Note that the text string passed to the title command uses TEX syntax
to produce the exponents. See “Information About Using TEX” in the Text
Properties page in the MATLAB Function Reference documentation about
using TEX syntax to produce mathematical symbols.
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You can also add these annotations by selecting the axes and typing the above
strings into their respective fields in the Property Editor. The graph is now
ready to print and export.
Printing the Graph
Before printing the graph, select Print Preview from the figure File menu
to see and modify how the graph will be laid out on the page. The Print
Preview window opens, containing a tabbed control panel on its left side and a
page image on its right side.
• Click the Lines/Text tab, and enter a line of text in the Header Text edit
field that you want to place at the top of the page. You can change the font,
style, and size of the header by clicking the Font button beneath the text
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Preparing Graphs for Presentation
field, and also use the Date Style drop-down list to specify a date format to
add the current date/time to the header.
• Notice the three black handlebars in the rulers along the left and top sides
of the preview pane. The outside handlebars let you stretch one edge of the
plot, leaving the other edges in place. The inner handlebars let you move
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the plot up and down or left and right without stretching it. Using them
does not affect the figure itself, only the printed version of it.
• You can also change the size and position of the plot on the page using the
buttons and edit boxes on the Layout tab. You can revert to the original
configuration by clicking the Auto (Actual Size, Centered) option button,
and correct stretching and shrinking by clicking Fix Aspect Ratio. The
following picture shows the Layout tab in Auto configuration.
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Preparing Graphs for Presentation
• By default, MATLAB recalculates the locations of the axes tick marks
because a printed graph is normally larger than the one displayed on your
monitor. However, you can keep your graph’s tick marks and limits when
printing it by clicking the Advanced tab and selecting Keep screen
limits and ticks.
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• When you are ready to print your plot, click Print in the right pane. You
can also click Close to accept the settings and dismiss the dialog box.
Later, you can print the figure as you previewed it using Print on the
figure’s File menu. Both methods will open a standard Print dialog box,
and will produce the same printed results.
Note There is no way to cancel a print preview; any changes you make
will take effect if you print the figure. If you want to revert to a default
page layout, you can generally accomplish this by selecting either the Use
Defaults button or the Auto (Actual Size, Centered) option button on the
Layout tab, although this will not affect every setting you can make.
The Print Preview dialog box provides many other options for controlling how
printed graphs look. Click its Help button for more information.
Exporting the Graph
Exporting a graph is the process of creating a standard graphics file format
of the graph (such as EPS or TIFF), which you can then import into other
applications like word processors, drawing packages, etc.
This example exports the graph as an EPS file with the following
requirements:
• The size of the picture when imported into the word processor document
should be 4 inches wide and 3 inches high.
• All the text in the figure should have a size of 8 points.
Specifying the Size of the Graph
To set the size, use the Export Setup dialog box (select Export Setup from
the figure File menu). Then select 4 from the Width list and 3 from the
Height list.
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Preparing Graphs for Presentation
Set the size at which to
export the graph to a file.
Specifying the Font Size
To set the font size of all the text in the graph, select Fonts in the Export
Setup dialog box Properties selector. Then click Use fixed font size and
enter 8 in the text box.
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Selecting the File Format
After you finish setting options for the exported graph, click the Export
button. MATLAB displays a standard Save As dialog box that enables you
to specify a name for the file as well as select the type of file format you
want to use.
The Save as type drop-down menu lists a number of other options for file
formats. For this example, select EPS (*.eps) from the Save as type menu.
You can import the saved file into any application that supports EPS files.
You can also use the print command to print figures on your local printer or
to export graphs to standard file types.
For More Information See the print command reference page and “Printing
and Exporting” in the MATLAB Graphics documentation or select Printing
and Exporting from the figure Help menu.
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Using Basic Plotting Functions
Using Basic Plotting Functions
In this section...
“Creating a Plot” on page 3-49
“Plotting Multiple Data Sets in One Graph” on page 3-50
“Specifying Line Styles and Colors” on page 3-51
“Plotting Lines and Markers” on page 3-52
“Graphing Imaginary and Complex Data” on page 3-53
“Adding Plots to an Existing Graph” on page 3-54
“Figure Windows” on page 3-55
“Displaying Multiple Plots in One Figure” on page 3-56
“Controlling the Axes” on page 3-58
“Adding Axis Labels and Titles” on page 3-59
“Saving Figures” on page 3-61
Creating a Plot
The plot function has different forms, depending on the input arguments. If
y is a vector, plot(y) produces a piecewise linear graph of the elements of y
versus the index of the elements of y. If you specify two vectors as arguments,
plot(x,y) produces a graph of y versus x.
For example, these statements use the colon operator to create a vector of
x values ranging from 0 to 2π, compute the sine of these values, and plot
the result:
x = 0:pi/100:2*pi;
y = sin(x);
plot(x,y)
Now label the axes and add a title. The characters \pi create the symbol π.
See “text strings” in the MATLAB Reference documentation for more symbols:
xlabel('x = 0:2\pi')
ylabel('Sine of x')
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title('Plot of the Sine Function','FontSize',12)
Plotting Multiple Data Sets in One Graph
Multiple x-y pair arguments create multiple graphs with a single call to plot.
MATLAB automatically cycles through a predefined (but user settable) list of
colors to allow discrimination among sets of data. See the axes ColorOrder
and LineStyleOrder properties.
For example, these statements plot three related functions of x, with each
curve in a separate distinguishing color:
x = 0:pi/100:2*pi;
y = sin(x);
y2 = sin(x-.25);
y3 = sin(x-.5);
plot(x,y,x,y2,x,y3)
The legend command provides an easy way to identify the individual plots:
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Using Basic Plotting Functions
legend('sin(x)','sin(x-.25)','sin(x-.5)')
For More Information See “Defining the Color of Lines for Plotting” in the
MATLAB Graphics documentation.
Specifying Line Styles and Colors
It is possible to specify color, line styles, and markers (such as plus signs or
circles) when you plot your data using the plot command:
plot(x,y,'color_style_marker')
color_style_marker is a string containing from one to four characters
(enclosed in single quotation marks) constructed from a color, a line style,
and a marker type:
• Color strings are 'c', 'm', 'y', 'r', 'g', 'b', 'w', and 'k'. These
correspond to cyan, magenta, yellow, red, green, blue, white, and black.
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• Line style strings are '-' for solid, '--' for dashed, ':' for dotted, and
'-.' for dash-dot. Omit the line style for no line.
• The marker types are '+', 'o', '*', and 'x', and the filled marker types
are 's' for square, 'd' for diamond, '^' for up triangle, 'v' for down
triangle, '>' for right triangle, '<' for left triangle, 'p' for pentagram, 'h'
for hexagram, and none for no marker.
You can also edit color, line style, and markers interactively. See “Editing
Plots” on page 3-17 for more information.
Plotting Lines and Markers
If you specify a marker type but not a line style, MATLAB draws only the
marker. For example,
plot(x,y,'ks')
plots black squares at each data point, but does not connect the markers
with a line.
The statement
plot(x,y,'r:+')
plots a red dotted line and places plus sign markers at each data point.
Placing Markers at Every Tenth Data Point
You might want to use fewer data points to plot the markers than you use to
plot the lines. This example plots the data twice using a different number of
points for the dotted line and marker plots:
x1 = 0:pi/100:2*pi;
x2 = 0:pi/10:2*pi;
plot(x1,sin(x1),'r:',x2,sin(x2),'r+')
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Using Basic Plotting Functions
Graphing Imaginary and Complex Data
When the arguments to plot are complex, the imaginary part is ignored
except when you pass plot a single complex argument. For this special case,
the command is a shortcut for a graph of the real part versus the imaginary
part. Therefore,
plot(Z)
where Z is a complex vector or matrix, is equivalent to
plot(real(Z),imag(Z))
For example,
t = 0:pi/10:2*pi;
plot(exp(i*t),'-o')
axis equal
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draws a 20-sided polygon with little circles at the vertices. The axis equal
command makes the individual tick-mark increments on the x- and y-axes the
same length, which makes this plot more circular in appearance.
Adding Plots to an Existing Graph
The hold command enables you to add plots to an existing graph. When
you type
hold on
MATLAB does not replace the existing graph when you issue another plotting
command; it adds the new data to the current graph, rescaling the axes
if necessary.
For example, these statements first create a contour plot of the peaks
function, then superimpose a pseudocolor plot of the same function:
[x,y,z] = peaks;
pcolor(x,y,z)
shading interp
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Using Basic Plotting Functions
hold on
contour(x,y,z,20,'k')
hold off
The hold on command combines the pcolor plot with the contour plot in
one figure.
For More Information See “Creating Specialized Plots” in the MATLAB
Graphics documentation for details about a variety of graph types.
Figure Windows
Graphing functions automatically open a new figure window if there are no
figure windows already on the screen. If a figure window exists, MATLAB
uses that window for graphics output. If there are multiple figure windows
open, MATLAB targets the one that is designated the “current figure” (the
last figure used or clicked in).
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To make an existing figure window the current figure, you can click the mouse
while the pointer is in that window or you can type
figure(n)
where n is the number in the figure title bar. The results of subsequent
graphics commands are displayed in this window.
To open a new figure window and make it the current figure, type
figure
Clearing the Figure for a New Plot
When a figure already exists, most plotting commands clear the axes and use
this figure to create the new plot. However, these commands do not reset
figure properties, such as the background color or the colormap. If you have
set any figure properties in the previous plot, you might want to use the clf
command with the reset option,
clf reset
before creating your new plot to restore the figure’s properties to their defaults.
For More Information See “Figure Properties” and “Graphics Windows —
the Figure” in the MATLAB Graphics documentation for details about figures.
Displaying Multiple Plots in One Figure
The subplot command enables you to display multiple plots in the same
window or print them on the same piece of paper. Typing
subplot(m,n,p)
partitions the figure window into an m-by-n matrix of small subplots and
selects the pth subplot for the current plot. The plots are numbered along the
first row of the figure window, then the second row, and so on. For example,
these statements plot data in four different subregions of the figure window:
t = 0:pi/10:2*pi;
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Using Basic Plotting Functions
[X,Y,Z] = cylinder(4*cos(t));
subplot(2,2,1); mesh(X)
subplot(2,2,2); mesh(Y)
subplot(2,2,3); mesh(Z)
subplot(2,2,4); mesh(X,Y,Z)
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You can add subplots to GUIs as well as to figures. For details about creating
subplots in a GUIDE-generated GUI, see “Creating Subplots” in the MATLAB
Creating Graphical User Interfaces documentation.
Controlling the Axes
The axis command provides a number of options for setting the scaling,
orientation, and aspect ratio of graphs. You can also set these options
interactively. See “Editing Plots” on page 3-17 for more information.
Setting Axis Limits
By default, MATLAB finds the maxima and minima of the data and chooses
the axis limits to span this range. The axis command enables you to specify
your own limits:
axis([xmin xmax ymin ymax])
or for three-dimensional graphs,
axis([xmin xmax ymin ymax zmin zmax])
Use the command
axis auto
to reenable MATLAB automatic limit selection.
Setting the Axis Aspect Ratio
The axis command also enables you to specify a number of predefined modes.
For example,
axis square
makes the x-axis and y-axis the same length.
axis equal
makes the individual tick mark increments on the x-axes and y-axes the same
length. This means
plot(exp(i*[0:pi/10:2*pi]))
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Using Basic Plotting Functions
followed by either axis square or axis equal turns the oval into a proper
circle:
axis auto normal
returns the axis scaling to its default automatic mode.
Setting Axis Visibility
You can use the axis command to make the axis visible or invisible.
axis on
makes the axes visible. This is the default.
axis off
makes the axes invisible.
Setting Grid Lines
The grid command toggles grid lines on and off. The statement
grid on
turns the grid lines on, and
grid off
turns them back off again.
For More Information See the axis and axes reference pages and “Axes
Properties” in the MATLAB Graphics documentation.
Adding Axis Labels and Titles
The xlabel, ylabel, and zlabel commands add x-, y-, and z-axis labels. The
title command adds a title at the top of the figure and the text function
inserts text anywhere in the figure.
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You can produce mathematical symbols using LaTeX notation in the text
string, as the following example illustrates:
t = -pi:pi/100:pi;
y = sin(t);
plot(t,y)
axis([-pi pi -1 1])
xlabel('-\pi \leq {\itt} \leq \pi')
ylabel('sin(t)')
title('Graph of the sine function')
text(1,-1/3,'{\itNote the odd symmetry.}')
You can also set these options interactively. See “Editing Plots” on page 3-17
for more information.
Note that the location of the text string is defined in axes units (i.e., the
same units as the data). See the annotation function for a way to place text
in normalized figure units.
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Using Basic Plotting Functions
Saving Figures
Save a figure by selecting Save from the File menu to display a Save dialog
box. MATLAB saves the data it needs to recreate the figure and its contents
(i.e., the entire graph) in a file with a .fig extension.
To save a figure using a standard graphics format, such as TIFF, for use
with other applications, select Export Setup from the File menu. You can
also save from the command line—use the saveas command, including any
options to save the figure in a different format. The more restricted hgexport
command, which saves figures to either bitmap or metafile files, depending on
the rendering method in effect, is also available.
See “Exporting the Graph” on page 3-46 for an example.
Saving Workspace Data
You can save the variables in your workspace by selecting Save Workspace
As from the figure File menu. You can reload saved data using the Import
Data item in the figure File menu. MATLAB supports a variety of data file
formats, including MATLAB data files, which have a .mat extension.
Generating M-Code to Recreate a Figure
You can generate MATLAB code that recreates a figure and the graph it
contains by selecting Generate M-File from the figure File menu. This
option is particularly useful if you have developed a graph using plotting tools
and want to create a similar graph using the same or different data.
Saving Figures That Are Compatible with the Previous Version
of MATLAB
Create backward-compatible FIG-files by following these two steps:
1 Ensure that any plotting functions used to create the contents of the figure
are called with the 'v6' argument, where applicable.
2 Use the '-v6' option with the hgsave command.
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Note The v6 option enables users of Version 7.x of MATLAB to create
FIG-files that previous versions can open. It is obsolete and will be removed
in a future version of MATLAB. For more information, see “Plot Objects and
Backward Compatibility” in the MATLAB Graphics documentation.
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Creating Mesh and Surface Plots
Creating Mesh and Surface Plots
In this section...
“About Mesh and Surface Plots” on page 3-63
“Visualizing Functions of Two Variables” on page 3-63
About Mesh and Surface Plots
MATLAB defines a surface by the z-coordinates of points above a grid in the
x-y plane, using straight lines to connect adjacent points. The mesh and
surf plotting functions display surfaces in three dimensions. mesh produces
wireframe surfaces that color only the lines connecting the defining points.
surf displays both the connecting lines and the faces of the surface in color.
The figure colormap and figure properties determine how MATLAB colors
the surface.
Visualizing Functions of Two Variables
To display a function of two variables, z = f (x,y),
1 Generate X and Y matrices consisting of repeated rows and columns,
respectively, over the domain of the function.
2 Use X and Y to evaluate and graph the function.
The meshgrid function transforms the domain specified by a single vector or
two vectors x and y into matrices X and Y for use in evaluating functions of
two variables. The rows of X are copies of the vector x and the columns of
Y are copies of the vector y.
Example — Graphing the sinc Function
This example evaluates and graphs the two-dimensional sinc function,
sin(r)/r, between the x and y directions. R is the distance from the origin, which
is at the center of the matrix. Adding eps (a MATLAB command that returns
a small floating-point number) avoids the indeterminate 0/0 at the origin:
[X,Y] = meshgrid(-8:.5:8);
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R = sqrt(X.^2 + Y.^2) + eps;
Z = sin(R)./R;
mesh(X,Y,Z,'EdgeColor','black')
By default, MATLAB colors the mesh using the current colormap. However,
this example uses a single-colored mesh by specifying the EdgeColor surface
property. See the surface reference page for a list of all surface properties.
You can create a mesh with see-through faces by disabling hidden line
removal:
hidden off
See the hidden reference page for more information on this option.
Example — Colored Surface Plots
A surface plot is similar to a mesh plot except that MATLAB colors the
rectangular faces of the surface. The color of each face is determined by the
values of Z and the colormap (a colormap is an ordered list of colors). These
statements graph the sinc function as a surface plot, specify a colormap, and
add a color bar to show the mapping of data to color:
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Creating Mesh and Surface Plots
surf(X,Y,Z)
colormap hsv
colorbar
See the colormap reference page for information on colormaps.
For More Information See “Creating 3-D Graphs” in the MATLAB 3-D
Visualization documentation for more information on surface plots.
Making Surfaces Transparent
You can make the faces of a surface transparent to a varying degree.
Transparency (referred to as the alpha value) can be specified for the whole
object or can be based on an alphamap, which behaves similarly to colormaps.
For example,
surf(X,Y,Z)
colormap hsv
alpha(.4)
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3
Graphics
produces a surface with a face alpha value of 0.4. Alpha values range from 0
(completely transparent) to 1 (not transparent).
For More Information See “Transparency” in the MATLAB 3-D
Visualization documentation for details about using this feature.
Illuminating Surface Plots with Lights
Lighting is the technique of illuminating an object with a directional light
source. In certain cases, this technique can make subtle differences in
surface shape easier to see. Lighting can also be used to add realism to
three-dimensional graphs.
This example uses the same surface as the previous examples, but colors it
red and removes the mesh lines. A light object is then added to the left of the
“camera” (the camera is the location in space from where you are viewing
the surface):
3-66
Creating Mesh and Surface Plots
surf(X,Y,Z,'FaceColor','red','EdgeColor','none')
camlight left; lighting phong
Manipulating the Surface
The figure toolbar and the camera toolbar provide ways to explore 3-D
graphics interactively. Display the camera toolbar by selecting Camera
Toolbar from the figure View menu.
The following picture shows both toolbars with the Rotate 3D tool selected.
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Graphics
These tools enable you to move the camera around the surface object,
zoom, add lighting, and perform other viewing operations without issuing
commands.
The following picture shows the surface viewed by orbiting the camera toward
the bottom using Rotate 3D. A scene light has been added to illuminate the
underside of the surface, which is not lit by the light added in the previous
section.
For More Information See “Lighting as a Visualization Tool” and “View
Control with the Camera Toolbar” in the MATLAB 3-D Visualization
documentation for details about these techniques.
3-68
Plotting Image Data
Plotting Image Data
In this section...
“About Plotting Image Data” on page 3-69
“Reading and Writing Images” on page 3-70
About Plotting Image Data
Two-dimensional arrays can be displayed as images, where the array elements
determine brightness or color of the images. For example, the statements
load durer
whos
Name
X
caption
map
Size
Bytes
648x509
2x28
128x3
2638656
112
3072
Class
double array
char array
double array
load the file durer.mat, adding three variables to the workspace. The matrix
X is a 648-by-509 matrix and map is a 128-by-3 matrix that is the colormap
for this image.
MAT-files, such as durer.mat, are binary files that can be created on one
platform and later read by MATLAB on a different platform.
The elements of X are integers between 1 and 128, which serve as indices
into the colormap, map. Then
image(X)
colormap(map)
axis image
reproduces Albrecht Dürer’s etching shown in “Matrices and Magic Squares”
on page 2-2. A high-resolution scan of the magic square in the upper-right
corner is available in another file. Type
load detail
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3
Graphics
and then use the up arrow key on your keyboard to reexecute the image,
colormap, and axis commands. The statement
colormap(hot)
adds some 21st century colorization to the 16th century etching. The function
hot generates a colormap containing shades of reds, oranges, and yellows.
Typically, a given image matrix has a specific colormap associated with it. See
the colormap reference page for a list of other predefined colormaps.
Reading and Writing Images
You can read standard image files (TIFF, JPEG, BMP, etc.) into MATLAB
using the imread function. The type of data returned by imread depends on
the type of image you are reading.
You can write MATLAB data to a variety of standard image formats using
the imwrite function. See the MATLAB reference pages for these functions
for more information and examples.
For More Information See “Displaying Bit-Mapped Images” in the MATLAB
Graphics documentation for details about the image processing capabilities
of MATLAB.
3-70
Printing Graphics
Printing Graphics
In this section...
“Overview of Printing” on page 3-71
“Printing from the File Menu” on page 3-71
“Exporting the Figure to a Graphics File” on page 3-72
“Using the Print Command” on page 3-72
Overview of Printing
You can print a MATLAB figure directly on a printer connected to your
computer or you can export the figure to one of the standard graphics file
formats supported by MATLAB. There are two ways to print and export
figures:
• Use the Print, Print Preview, or Export Setup GUI options under the
File menu; see “Preparing Graphs for Presentation” on page 3-37 for an
example.
• Use the print command to print or export the figure from the command
line.
The print command provides greater control over drivers and file formats.
The Print Preview dialog box gives you greater control over figure size,
proportions, placement, and page headers. You can sometimes notice
differences in output as printed from a GUI and as printed from the command
line.
Printing from the File Menu
There are two menu options under the File menu that pertain to printing:
• The Print Preview option displays a dialog box that lets you lay out and
style figures for printing while previewing the output page, and from which
you can print the figure. It includes options that formerly were part of
the Page Setup dialog box.
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Graphics
• The Print option displays a dialog box that lets you choose a printer, select
standard printing options, and print the figure.
Use Print Preview to determine whether the printed output is what you
want. Click the Print Preview dialog box Help button to display information
on how to set up the page.
See “Printing the Graph” on page 3-42 for an example of printing from
the Print Preview dialog. For details on printing from GUIs and from the
Command Window, see “Printing and Exporting” in the MATLAB Graphics
documentation.
Exporting the Figure to a Graphics File
The Export Setup option in the File menu opens a GUI that enables you
to set graphic characteristics, such as text size, font, and style, for figures
you save as graphics files. The Export Setup GUI lets you define and apply
templates to customize and standardize output. After setup, you can export
the figure to a number of standard graphics file formats such as EPS, PNG,
and TIFF.
See “Exporting the Graph” on page 3-46 for an example of exporting a figure
to a graphics file.
Using the Print Command
The print command provides more flexibility in the type of output sent to the
printer and allows you to control printing from M-files. The result can be sent
directly to your default printer or stored in a specified file. A wide variety of
output formats, including TIFF, JPEG, and PostScript, is available.
For example, this statement saves the contents of the current figure window
as color Encapsulated Level 2 PostScript in the file called magicsquare.eps.
It also includes a TIFF preview, which enables most word processors to
display the picture.
print -depsc2 -tiff magicsquare.eps
To save the same figure as a TIFF file with a resolution of 200 dpi, use the
following command:
3-72
Printing Graphics
print -dtiff -r200 magicsquare.tiff
If you type print on the command line,
print
MATLAB prints the current figure on your default printer.
For More Information See the print reference page and “Printing and
Exporting” in the MATLAB Graphics documentation for details about
printing.
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3
Graphics
Handle Graphics
In this section...
“Using the Handle” on page 3-74
“Graphics Objects” on page 3-75
“Setting Object Properties” on page 3-77
“Specifying the Axes or Figure” on page 3-80
“Finding the Handles of Existing Objects” on page 3-81
Handle Graphics refers to a system of graphics objects that MATLAB uses to
implement graphing and visualization functions. Each object created has a
fixed set of properties. You can use these properties to control the behavior
and appearance of your graph.
When you call a plotting function, MATLAB creates the graph using various
graphics objects, such as a figure window, axes, lines, text, and so on.
MATLAB enables you to query the value of each property and set the values
of most properties.
For example, the following statement creates a figure with a white background
color and without displaying the figure toolbar:
figure('Color','white','Toolbar','none')
Using the Handle
Whenever MATLAB creates a graphics object, it assigns an identifier (called a
handle) to the object. You can use this handle to access the object’s properties
with the set and get functions. For example, the following statements create
a graph and return a handle to a lineseries object in h:
x = 1:10;
y = x.^3;
h = plot(x,y);
You can use the handle h to set the properties of the lineseries object. For
example, you can set its Color property:
3-74
Handle Graphics
set(h,'Color','red')
You can also specify properties when you call the plotting function:
h = plot(x,y,'Color','red');
When you query the lineseries properties,
get(h,'LineWidth')
MATLAB returns the answer:
ans =
0.5000
Use the handle to see what properties a particular object contains:
get(h)
Graphics Objects
Graphics objects are the basic elements used to display graphs and user
interface components. These objects are organized into a hierarchy, as shown
by the following diagram.
Key Graphics Objects
When you call a function to create a graph, MATLAB creates a hierarchy of
graphics objects. For example, calling the plot function creates the following
graphics objects:
• Lineseries plot objects — Represent the data passed to the plot function.
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Graphics
• Axes — Provide a frame of reference and scaling for the plotted lineseries.
• Text — Label the axes tick marks and are used for titles and annotations.
• Figures — Are the windows that contain axes toolbars, menus, etc.
Different types of graphs use different objects to represent data; however, all
data objects are contained in axes and all objects (except root) are contained
in figures.
The root is an abstract object that primarily stores information about your
computer or MATLAB state. You cannot create an instance of the root object.
For More Information See “Handle Graphics Objects” in the MATLAB
Graphics documentation for details about graphics objects.
User interface objects are used to create graphical user interfaces (GUIs).
These objects include components like push buttons, editable text boxes, and
list boxes.
For More Information See Chapter 6, “Creating Graphical User Interfaces”
for details about user interface objects.
Creating Objects
Plotting functions (like plot and surf) call the appropriate low-level function
to draw their respective graph. For information about an object’s properties,
you can use the Handle Graphics Property Browser in the MATLAB online
Graphics documentation.
Functions for Working with Objects
This table lists functions commonly used when working with objects.
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Handle Graphics
Function
Purpose
allchild
Find all children of specified objects.
ancestor
Find ancestor of graphics object.
copyobj
Copy graphics object.
delete
Delete an object.
findall
Find all graphics objects (including hidden handles).
findobj
Find the handles of objects having specified property
values.
gca
Return the handle of the current axes.
gcf
Return the handle of the current figure.
gco
Return the handle of the current object.
get
Query the values of an object’s properties.
ishandle
True if the value is a valid object handle.
set
Set the values of an object’s properties.
Setting Object Properties
All object properties have default values. However, you might find it useful
to change the settings of some properties to customize your graph. There
are two ways to set object properties:
• Specify values for properties when you create the object.
• Set the property value on an object that already exists.
Setting Properties from Plotting Commands
You can specify object property value pairs as arguments to many plotting
functions, such as plot, mesh, and surf.
For example, plotting commands that create lineseries or surfaceplot objects
enable you to specify property name/property value pairs as arguments. The
command
3-77
3
Graphics
surf(x,y,z,'FaceColor','interp',...
'FaceLighting','gouraud')
plots the data in the variables x, y, and z using a surfaceplot object with
interpolated face color and employing the Gouraud face light technique. You
can set any of the object’s properties this way.
Setting Properties of Existing Objects
To modify the property values of existing objects, you can use the set
command or the Property Editor. This section describes how to use the set
command. See “Using the Property Editor” on page 3-18 for more information.
Most plotting functions return the handles of the objects that they create
so you can modify the objects using the set command. For example, these
statements plot a 5-by-5 matrix (creating five lineseries, one per column), and
then set the Marker property to a square and the MarkerFaceColor property
to green:
h = plot(magic(5));
set(h,'Marker','s','MarkerFaceColor','g')
In this case, h is a vector containing five handles, one for each of the
five lineseries in the graph. The set statement sets the Marker and
MarkerFaceColor properties of all lineseries to the same values.
Setting Multiple Property Values
If you want to set the properties of each lineseries to a different value, you
can use cell arrays to store all the data and pass it to the set command. For
example, create a plot and save the lineseries handles:
h = plot(magic(5));
Suppose you want to add different markers to each lineseries and color the
marker’s face color the same color as the lineseries. You need to define two
cell arrays—one containing the property names and the other containing
the desired values of the properties.
The prop_name cell array contains two elements:
prop_name(1) = {'Marker'};
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Handle Graphics
prop_name(2) = {'MarkerFaceColor'};
The prop_values cell array contains 10 values: five values for the Marker
property and five values for the MarkerFaceColor property. Notice that
prop_values is a two-dimensional cell array. The first dimension indicates
which handle in h the values apply to and the second dimension indicates
which property the value is assigned to:
prop_values(1,1)
prop_values(1,2)
prop_values(2,1)
prop_values(2,2)
prop_values(3,1)
prop_values(3,2)
prop_values(4,1)
prop_values(4,2)
prop_values(5,1)
prop_values(5,2)
=
=
=
=
=
=
=
=
=
=
{'s'};
{get(h(1),'Color')};
{'d'};
{get(h(2),'Color')};
{'o'};
{get(h(3),'Color')};
{'p'};
{get(h(4),'Color')};
{'h'};
{get(h(5),'Color')};
The MarkerFaceColor is always assigned the value of the corresponding
line’s color (obtained by getting the lineseries Color property with the get
command).
After defining the cell arrays, call set to specify the new property values:
set(h,prop_name,prop_values)
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3
Graphics
Specifying the Axes or Figure
MATLAB always creates an axes or figure if one does not exist when you
issue a plotting command. However, when you are creating a graphics M-file,
it is good practice to explicitly create and specify the parent axes and figure,
particularly if others will use your program. Specifying the parent prevents
the following problems:
• Your M-file overwrites the graph in the current figure. Note that a figure
becomes the current figure whenever a user clicks it.
• The current figure might be in an unexpected state and not behave as
your program expects.
The following example shows a simple M-file that plots a function and the
mean of the function over the specified range:
function myfunc(x)
% x = -10:.005:40; Here's a value you can use for x
y = [1.5*cos(x) + 6*exp(-.1*x) + exp(.07*x).*sin(3*x)];
ym = mean(y);
3-80
Handle Graphics
hfig = figure('Name','Function and Mean',...
'Pointer','fullcrosshair');
hax = axes('Parent',hfig);
plot(hax,x,y)
hold on
plot(hax,[min(x) max(x)],[ym ym],'Color','red')
hold off
ylab = get(hax,'YTick');
set(hax,'YTick',sort([ylab ym]))
title ('y = 1.5cos(x) + 6e^{-0.1x} + e^{0.07x}sin(3x)')
xlabel('X Axis'); ylabel('Y Axis')
Finding the Handles of Existing Objects
The findobj function enables you to obtain the handles of graphics objects
by searching for objects with particular property values. With findobj you
can specify the values of any combination of properties, which makes it easy
to pick one object out of many. findobj also recognizes regular expressions
(regexp).
For example, you might want to find the blue line with square marker having
blue face color. You can also specify which figures or axes to search, if there
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3
Graphics
are more than one. The following four sections provide examples illustrating
how to use findobj.
Finding All Objects of a Certain Type
Because all objects have a Type property that identifies the type of object,
you can find the handles of all occurrences of a particular type of object. For
example,
h = findobj('Type','patch');
finds the handles of all patch objects.
Finding Objects with a Particular Property
You can specify multiple properties to narrow the search. For example,
h = findobj('Type','line','Color','r','LineStyle',':');
finds the handles of all red dotted lines.
Limiting the Scope of the Search
You can specify the starting point in the object hierarchy by passing the
handle of the starting figure or axes as the first argument. For example,
h = findobj(gca,'Type','text','String','\pi/2');
finds the string π/2 only within the current axes.
Using findobj as an Argument
Because findobj returns the handles it finds, you can use it in place of the
handle argument. For example,
set(findobj('Type','line','Color','red'),'LineStyle',':')
finds all red lines and sets their line style to dotted.
3-82
4
Programming
If you have an active Internet connection, you can watch the Writing a
MATLAB Program video demo for an overview of the major functionality.
Flow Control (p. 4-2)
Use flow control constructs,
including if, switch and case, for,
while, continue, and break.
Other Data Structures (p. 4-9)
Work with multidimensional arrays,
cell arrays, character and text data,
and structures.
Scripts and Functions (p. 4-20)
Write scripts and functions, use
global variables, pass string
arguments to functions, use eval to
evaluate text expressions, vectorize
code, preallocate arrays, reference
functions using handles, and use
functions that operate on functions.
4
Programming
Flow Control
In this section...
“Conditional Control – if, else, switch” on page 4-2
“Loop Control – for, while, continue, break” on page 4-5
“Error Control – try, catch” on page 4-7
“Program Termination – return” on page 4-8
Conditional Control – if, else, switch
This section covers those MATLAB functions that provide conditional
program control.
if, else, and elseif
The if statement evaluates a logical expression and executes a group of
statements when the expression is true. The optional elseif and else
keywords provide for the execution of alternate groups of statements. An end
keyword, which matches the if, terminates the last group of statements.
The groups of statements are delineated by the four keywords—no braces or
brackets are involved.
The MATLAB algorithm for generating a magic square of order n involves
three different cases: when n is odd, when n is even but not divisible by 4,
or when n is divisible by 4. This is described by
if rem(n,2) ~= 0
M = odd_magic(n)
elseif rem(n,4) ~= 0
M = single_even_magic(n)
else
M = double_even_magic(n)
end
For most values of n in this example, the three cases are mutually exclusive.
For values that are not mutually exclusive, such as n=5, the first true
condition is executed.
4-2
Flow Control
It is important to understand how relational operators and if statements
work with matrices. When you want to check for equality between two
variables, you might use
if A == B, ...
This is valid MATLAB code, and does what you expect when A and B are
scalars. But when A and B are matrices, A == B does not test if they are
equal, it tests where they are equal; the result is another matrix of 0’s and
1’s showing element-by-element equality. (In fact, if A and B are not the same
size, then A == B is an error.)
A = magic(4);
A == B
ans =
0
1
1
1
1
1
1
1
B = A;
1
1
1
1
B(1,1) = 0;
1
1
1
1
The proper way to check for equality between two variables is to use the
isequal function:
if isequal(A, B), ...
isequal returns a scalar logical value of 1 (representing true) or 0 (false),
instead of a matrix, as the expression to be evaluated by the if function.
Using the A and B matrices from above, you get
isequal(A, B)
ans =
0
Here is another example to emphasize this point. If A and B are scalars, the
following program will never reach the “unexpected situation”. But for most
pairs of matrices, including our magic squares with interchanged columns,
none of the matrix conditions A > B, A < B, or A == B is true for all elements
and so the else clause is executed:
if A > B
'greater'
4-3
4
Programming
elseif A < B
'less'
elseif A == B
'equal'
else
error('Unexpected situation')
end
Several functions are helpful for reducing the results of matrix comparisons
to scalar conditions for use with if, including
isequal
isempty
all
any
switch and case
The switch statement executes groups of statements based on the value of
a variable or expression. The keywords case and otherwise delineate the
groups. Only the first matching case is executed. There must always be an
end to match the switch.
The logic of the magic squares algorithm can also be described by
switch (rem(n,4)==0) + (rem(n,2)==0)
case 0
M = odd_magic(n)
case 1
M = single_even_magic(n)
case 2
M = double_even_magic(n)
otherwise
error('This is impossible')
end
Note Unlike the C language switch statement, MATLAB switch does not
fall through. If the first case statement is true, the other case statements do
not execute. So, break statements are not required.
4-4
Flow Control
Loop Control – for, while, continue, break
This section covers those MATLAB functions that provide control over
program loops.
for
The for loop repeats a group of statements a fixed, predetermined number of
times. A matching end delineates the statements:
for n = 3:32
r(n) = rank(magic(n));
end
r
The semicolon terminating the inner statement suppresses repeated printing,
and the r after the loop displays the final result.
It is a good idea to indent the loops for readability, especially when they are
nested:
for i = 1:m
for j = 1:n
H(i,j) = 1/(i+j);
end
end
while
The while loop repeats a group of statements an indefinite number of times
under control of a logical condition. A matching end delineates the statements.
Here is a complete program, illustrating while, if, else, and end, that uses
interval bisection to find a zero of a polynomial:
a = 0; fa = -Inf;
b = 3; fb = Inf;
while b-a > eps*b
x = (a+b)/2;
fx = x^3-2*x-5;
if sign(fx) == sign(fa)
a = x; fa = fx;
4-5
4
Programming
else
b = x; fb = fx;
end
end
x
The result is a root of the polynomial x3 - 2x - 5, namely
x =
2.09455148154233
The cautions involving matrix comparisons that are discussed in the section
on the if statement also apply to the while statement.
continue
The continue statement passes control to the next iteration of the for loop
or while loop in which it appears, skipping any remaining statements in the
body of the loop. The same holds true for continue statements in nested
loops. That is, execution continues at the beginning of the loop in which the
continue statement was encountered.
The example below shows a continue loop that counts the lines of code in the
file magic.m, skipping all blank lines and comments. A continue statement is
used to advance to the next line in magic.m without incrementing the count
whenever a blank line or comment line is encountered:
fid = fopen('magic.m','r');
count = 0;
while ~feof(fid)
line = fgetl(fid);
if isempty(line) | strncmp(line,'%',1)
continue
end
count = count + 1;
end
disp(sprintf('%d lines',count));
4-6
Flow Control
break
The break statement lets you exit early from a for loop or while loop. In
nested loops, break exits from the innermost loop only.
Here is an improvement on the example from the previous section. Why is
this use of break a good idea?
a = 0; fa = -Inf;
b = 3; fb = Inf;
while b-a > eps*b
x = (a+b)/2;
fx = x^3-2*x-5;
if fx == 0
break
elseif sign(fx) == sign(fa)
a = x; fa = fx;
else
b = x; fb = fx;
end
end
x
Error Control – try, catch
This section covers those MATLAB functions that provide error handling
control.
try
The general form of a try-catch statement sequence is
try
statement
...
statement
catch
statement
...
statement
end
4-7
4
Programming
In this sequence the statements between try and catch are executed until
an error occurs. The statements between catch and end are then executed.
Use lasterr to see the cause of the error. If an error occurs between catch
and end, MATLAB terminates execution unless another try-catch sequence
has been established.
Program Termination – return
This section covers the MATLAB return function that enables you to
terminate your program before it runs to completion.
return
return terminates the current sequence of commands and returns control to
the invoking function or to the keyboard. return is also used to terminate
keyboard mode. A called function normally transfers control to the function
that invoked it when it reaches the end of the function. You can insert a
return statement within the called function to force an early termination and
to transfer control to the invoking function.
4-8
Other Data Structures
Other Data Structures
In this section...
“Multidimensional Arrays” on page 4-9
“Cell Arrays” on page 4-11
“Characters and Text” on page 4-13
“Structures” on page 4-16
Multidimensional Arrays
Multidimensional arrays in MATLAB are arrays with more than two
subscripts. One way of creating a multidimensional array is by calling zeros,
ones, rand, or randn with more than two arguments. For example,
R = randn(3,4,5);
creates a 3-by-4-by-5 array with a total of 3*4*5 = 60 normally distributed
random elements.
A three-dimensional array might represent three-dimensional physical data,
say the temperature in a room, sampled on a rectangular grid. Or it might
represent a sequence of matrices, A(k), or samples of a time-dependent matrix,
A(t). In these latter cases, the (i, j)th element of the kth matrix, or the tkth
matrix, is denoted by A(i,j,k).
MATLAB and Dürer’s versions of the magic square of order 4 differ by an
interchange of two columns. Many different magic squares can be generated
by interchanging columns. The statement
p = perms(1:4);
generates the 4! = 24 permutations of 1:4. The kth permutation is the row
vector p(k,:). Then
A = magic(4);
M = zeros(4,4,24);
for k = 1:24
4-9
4
Programming
M(:,:,k) = A(:,p(k,:));
end
stores the sequence of 24 magic squares in a three-dimensional array, M. The
size of M is
size(M)
ans =
4
4
24
Note The order of the matrices shown in this illustration might differ from
your results. The perms function always returns all permutations of the input
vector, but the order of the permutations might be different for different
MATLAB versions.
The statement
sum(M,d)
computes sums by varying the dth subscript. So
sum(M,1)
is a 1-by-4-by-24 array containing 24 copies of the row vector
4-10
Other Data Structures
34
34
34
34
and
sum(M,2)
is a 4-by-1-by-24 array containing 24 copies of the column vector
34
34
34
34
Finally,
S = sum(M,3)
adds the 24 matrices in the sequence. The result has size 4-by-4-by-1, so
it looks like a 4-by-4 array:
S =
204
204
204
204
204
204
204
204
204
204
204
204
204
204
204
204
Cell Arrays
Cell arrays in MATLAB are multidimensional arrays whose elements are
copies of other arrays. A cell array of empty matrices can be created with
the cell function. But, more often, cell arrays are created by enclosing a
miscellaneous collection of things in curly braces, {}. The curly braces are
also used with subscripts to access the contents of various cells. For example,
C = {A sum(A) prod(prod(A))}
produces a 1-by-3 cell array. The three cells contain the magic square, the
row vector of column sums, and the product of all its elements. When C
is displayed, you see
C =
[4x4 double]
[1x4 double]
[20922789888000]
4-11
4
Programming
This is because the first two cells are too large to print in this limited space,
but the third cell contains only a single number, 16!, so there is room to print it.
Here are two important points to remember. First, to retrieve the contents of
one of the cells, use subscripts in curly braces. For example, C{1} retrieves
the magic square and C{3} is 16!. Second, cell arrays contain copies of other
arrays, not pointers to those arrays. If you subsequently change A, nothing
happens to C.
You can use three-dimensional arrays to store a sequence of matrices of the
same size. Cell arrays can be used to store a sequence of matrices of different
sizes. For example,
M = cell(8,1);
for n = 1:8
M{n} = magic(n);
end
M
produces a sequence of magic squares of different order:
M =
[
[
[
[
[
[
[
[
4-12
2x2
3x3
4x4
5x5
6x6
7x7
8x8
1]
double]
double]
double]
double]
double]
double]
double]
Other Data Structures
You can retrieve the 4-by-4 magic square matrix with
M{4}
Characters and Text
Enter text into MATLAB using single quotes. For example,
s = 'Hello'
The result is not the same kind of numeric matrix or array you have been
dealing with up to now. It is a 1-by-5 character array.
4-13
4
Programming
Internally, the characters are stored as numbers, but not in floating-point
format. The statement
a = double(s)
converts the character array to a numeric matrix containing floating-point
representations of the ASCII codes for each character. The result is
a =
72
101
108
108
111
The statement
s = char(a)
reverses the conversion.
Converting numbers to characters makes it possible to investigate the various
fonts available on your computer. The printable characters in the basic ASCII
character set are represented by the integers 32:127. (The integers less than
32 represent nonprintable control characters.) These integers are arranged in
an appropriate 6-by-16 array with
F = reshape(32:127,16,6)';
The printable characters in the extended ASCII character set are represented
by F+128. When these integers are interpreted as characters, the result
depends on the font currently being used. Type the statements
char(F)
char(F+128)
and then vary the font being used for the Command Window. Select
Preferences from the File menu to change the font. If you include tabs in
lines of code, use a fixed-width font, such as Monospaced, to align the tab
positions on different lines.
Concatenation with square brackets joins text variables together into larger
strings. The statement
h = [s, ' world']
4-14
Other Data Structures
joins the strings horizontally and produces
h =
Hello world
The statement
v = [s; 'world']
joins the strings vertically and produces
v =
Hello
world
Note that a blank has to be inserted before the 'w' in h and that both words
in v have to have the same length. The resulting arrays are both character
arrays; h is 1-by-11 and v is 2-by-5.
To manipulate a body of text containing lines of different lengths, you have
two choices—a padded character array or a cell array of strings. When
creating a character array, you must make each row of the array the same
length. (Pad the ends of the shorter rows with spaces.) The char function does
this padding for you. For example,
S = char('A','rolling','stone','gathers','momentum.')
produces a 5-by-9 character array:
S =
A
rolling
stone
gathers
momentum.
Alternatively, you can store the text in a cell array. For example,
C = {'A';'rolling';'stone';'gathers';'momentum.'}
creates a 5-by-1 cell array that requires no padding because each row of the
array can have a different length:
4-15
4
Programming
C =
'A'
'rolling'
'stone'
'gathers'
'momentum.'
You can convert a padded character array to a cell array of strings with
C = cellstr(S)
and reverse the process with
S = char(C)
Structures
Structures are multidimensional MATLAB arrays with elements accessed by
textual field designators. For example,
S.name = 'Ed Plum';
S.score = 83;
S.grade = 'B+'
creates a scalar structure with three fields:
S =
name: 'Ed Plum'
score: 83
grade: 'B+'
Like everything else in MATLAB, structures are arrays, so you can insert
additional elements. In this case, each element of the array is a structure with
several fields. The fields can be added one at a time,
S(2).name = 'Toni Miller';
S(2).score = 91;
S(2).grade = 'A-';
or an entire element can be added with a single statement:
S(3) = struct('name','Jerry Garcia',...
'score',70,'grade','C')
4-16
Other Data Structures
Now the structure is large enough that only a summary is printed:
S =
1x3 struct array with fields:
name
score
grade
There are several ways to reassemble the various fields into other MATLAB
arrays. They are mostly based on the notation of a comma-separated list. If
you type
S.score
it is the same as typing
S(1).score, S(2).score, S(3).score
which is a comma-separated list.
If you enclose the expression that generates such a list within square
brackets, MATLAB stores each item from the list in an array. In this example,
MATLAB creates a numeric row vector containing the score field of each
element of structure array S:
scores = [S.score]
scores =
83
91
70
avg_score = sum(scores)/length(scores)
avg_score =
81.3333
To create a character array from one of the text fields (name, for example), call
the char function on the comma-separated list produced by S.name:
names = char(S.name)
names =
Ed Plum
Toni Miller
Jerry Garcia
4-17
4
Programming
Similarly, you can create a cell array from the name fields by enclosing the
list-generating expression within curly braces:
names = {S.name}
names =
'Ed Plum'
'Toni Miller'
'Jerry Garcia'
To assign the fields of each element of a structure array to separate variables
outside of the structure, specify each output to the left of the equals sign,
enclosing them all within square brackets:
[N1 N2 N3] = S.name
N1 =
Ed Plum
N2 =
Toni Miller
N3 =
Jerry Garcia
Dynamic Field Names
The most common way to access the data in a structure is by specifying the
name of the field that you want to reference. Another means of accessing
structure data is to use dynamic field names. These names express the
field as a variable expression that MATLAB evaluates at run-time. The
dot-parentheses syntax shown here makes expression a dynamic field name:
structName.(expression)
Index into this field using the standard MATLAB indexing syntax. For
example, to evaluate expression into a field name and obtain the values of
that field at columns 1 through 25 of row 7, use
structName.(expression)(7,1:25)
Dynamic Field Names Example. The avgscore function shown below
computes an average test score, retrieving information from the testscores
structure using dynamic field names:
function avg = avgscore(testscores, student, first, last)
for k = first:last
scores(k) = testscores.(student).week(k);
4-18
Other Data Structures
end
avg = sum(scores)/(last - first + 1);
You can run this function using different values for the dynamic field student.
First, initialize the structure that contains scores for a 25-week period:
testscores.Ann_Lane.week(1:25) = ...
[95 89 76 82 79 92 94 92 89 81 75 93 ...
85 84 83 86 85 90 82 82 84 79 96 88 98];
testscores.William_King.week(1:25) = ...
[87 80 91 84 99 87 93 87 97 87 82 89 ...
86 82 90 98 75 79 92 84 90 93 84 78 81];
Now run avgscore, supplying the students name fields for the testscores
structure at runtime using dynamic field names:
avgscore(testscores, 'Ann_Lane', 7, 22)
ans =
85.2500
avgscore(testscores, 'William_King', 7, 22)
ans =
87.7500
4-19
4
Programming
Scripts and Functions
In this section...
“Overview” on page 4-20
“Scripts” on page 4-21
“Functions” on page 4-22
“Types of Functions” on page 4-24
“Global Variables” on page 4-26
“Passing String Arguments to Functions” on page 4-27
“The eval Function” on page 4-28
“Function Handles” on page 4-28
“Function Functions” on page 4-29
“Vectorization” on page 4-31
“Preallocation” on page 4-32
Overview
MATLAB is a powerful programming language as well as an interactive
computational environment. Files that contain code in the MATLAB language
are called M-files. You create M-files using a text editor, then use them as you
would any other MATLAB function or command.
There are two kinds of M-files:
• Scripts, which do not accept input arguments or return output arguments.
They operate on data in the workspace.
• Functions, which can accept input arguments and return output arguments.
Internal variables are local to the function.
If you’re a new MATLAB programmer, just create the M-files that you want
to try out in the current directory. As you develop more of your own M-files,
you will want to organize them into other directories and personal toolboxes
that you can add to your MATLAB search path.
4-20
Scripts and Functions
If you duplicate function names, MATLAB executes the one that occurs first
in the search path.
To view the contents of an M-file, for example, myfunction.m, use
type myfunction
Scripts
When you invoke a script, MATLAB simply executes the commands found in
the file. Scripts can operate on existing data in the workspace, or they can
create new data on which to operate. Although scripts do not return output
arguments, any variables that they create remain in the workspace, to be
used in subsequent computations. In addition, scripts can produce graphical
output using functions like plot.
For example, create a file called magicrank.m that contains these MATLAB
commands:
% Investigate the rank of magic squares
r = zeros(1,32);
for n = 3:32
r(n) = rank(magic(n));
end
r
bar(r)
Typing the statement
magicrank
causes MATLAB to execute the commands, compute the rank of the first 30
magic squares, and plot a bar graph of the result. After execution of the file is
complete, the variables n and r remain in the workspace.
4-21
4
Programming
Functions
Functions are M-files that can accept input arguments and return output
arguments. The names of the M-file and of the function should be the same.
Functions operate on variables within their own workspace, separate from the
workspace you access at the MATLAB command prompt.
A good example is provided by rank. The M-file rank.m is available in the
directory
toolbox/matlab/matfun
You can see the file with
type rank
Here is the file:
function r = rank(A,tol)
%
RANK Matrix rank.
%
RANK(A) provides an estimate of the number of linearly
4-22
Scripts and Functions
%
%
%
%
independent rows or columns of a matrix A.
RANK(A,tol) is the number of singular values of A
that are larger than tol.
RANK(A) uses the default tol = max(size(A)) * norm(A) * eps.
s = svd(A);
if nargin==1
tol = max(size(A)') * max(s) * eps;
end
r = sum(s > tol);
The first line of a function M-file starts with the keyword function. It gives
the function name and order of arguments. In this case, there are up to two
input arguments and one output argument.
The next several lines, up to the first blank or executable line, are comment
lines that provide the help text. These lines are printed when you type
help rank
The first line of the help text is the H1 line, which MATLAB displays when
you use the lookfor command or request help on a directory.
The rest of the file is the executable MATLAB code defining the function. The
variable s introduced in the body of the function, as well as the variables on
the first line, r, A and tol, are all local to the function; they are separate from
any variables in the MATLAB workspace.
This example illustrates one aspect of MATLAB functions that is not
ordinarily found in other programming languages—a variable number of
arguments. The rank function can be used in several different ways:
rank(A)
r = rank(A)
r = rank(A,1.e-6)
Many M-files work this way. If no output argument is supplied, the result is
stored in ans. If the second input argument is not supplied, the function
computes a default value. Within the body of the function, two quantities
named nargin and nargout are available that tell you the number of input
4-23
4
Programming
and output arguments involved in each particular use of the function. The
rank function uses nargin, but does not need to use nargout.
Types of Functions
MATLAB offers several different types of functions to use in your
programming.
Anonymous Functions
An anonymous function is a simple form of MATLAB function that does not
require an M-file. It consists of a single MATLAB expression and any number
of input and output arguments. You can define an anonymous function right
at the MATLAB command line, or within an M-file function or script. This
gives you a quick means of creating simple functions without having to create
M-files each time.
The syntax for creating an anonymous function from an expression is
f = @(arglist)expression
The statement below creates an anonymous function that finds the square of
a number. When you call this function, MATLAB assigns the value you pass
in to variable x, and then uses x in the equation x.^2:
sqr = @(x) x.^2;
To execute the sqr function defined above, type
a = sqr(5)
a =
25
Primary and Subfunctions
All functions that are not anonymous must be defined within an M-file. Each
M-file has a required primary function that appears first in the file, and any
number of subfunctions that follow the primary. Primary functions have a
wider scope than subfunctions. That is, primary functions can be invoked from
outside of their M-file (from the MATLAB command line or from functions in
4-24
Scripts and Functions
other M-files) while subfunctions cannot. Subfunctions are visible only to the
primary function and other subfunctions within their own M-file.
The rank function shown in the section on “Functions” on page 4-22 is an
example of a primary function.
Private Functions
A private function is a type of primary M-file function. Its unique
characteristic is that it is visible only to a limited group of other functions.
This type of function can be useful if you want to limit access to a function, or
when you choose not to expose the implementation of a function.
Private functions reside in subdirectories with the special name private.
They are visible only to functions in the parent directory. For example,
assume the directory newmath is on the MATLAB search path. A subdirectory
of newmath called private can contain functions that only the functions in
newmath can call.
Because private functions are invisible outside the parent directory, they can
use the same names as functions in other directories. This is useful if you
want to create your own version of a particular function while retaining the
original in another directory. Because MATLAB looks for private functions
before standard M-file functions, it will find a private function named test.m
before a nonprivate M-file named test.m.
Nested Functions
You can define functions within the body of any MATLAB M-file function.
These are said to be nested within the outer function. A nested function
contains any or all of the components of any other M-file function. In this
example, function B is nested in function A:
function x = A(p1, p2)
...
B(p2)
function y = B(p3)
...
end
...
end
4-25
4
Programming
Like other functions, a nested function has its own workspace where variables
used by the function are stored. But it also has access to the workspaces
of all functions in which it is nested. So, for example, a variable that has
a value assigned to it by the primary function can be read or overwritten
by a function nested at any level within the primary. Similarly, a variable
that is assigned in a nested function can be read or overwritten by any of the
functions containing that function.
Function Overloading
Overloaded functions act the same way as overloaded functions in most
computer languages. Overloaded functions are useful when you need to create
a function that responds to different types of inputs accordingly. For instance,
you might want one of your functions to accept both double-precision and
integer input, but to handle each type somewhat differently. You can make
this difference invisible to the user by creating two separate functions having
the same name, and designating one to handle double types and one to
handle integers. When you call the function, MATLAB chooses which M-file
to dispatch to based on the type of the input arguments.
Global Variables
If you want more than one function to share a single copy of a variable, simply
declare the variable as global in all the functions. Do the same thing at
the command line if you want the base workspace to access the variable.
The global declaration must occur before the variable is actually used in a
function. Although it is not required, using capital letters for the names of
global variables helps distinguish them from other variables. For example,
create an M-file called falling.m:
function h = falling(t)
global GRAVITY
h = 1/2*GRAVITY*t.^2;
Then interactively enter the statements
global GRAVITY
GRAVITY = 32;
y = falling((0:.1:5)');
4-26
Scripts and Functions
The two global statements make the value assigned to GRAVITY at the
command prompt available inside the function. You can then modify GRAVITY
interactively and obtain new solutions without editing any files.
Passing String Arguments to Functions
You can write MATLAB functions that accept string arguments without the
parentheses and quotes. That is, MATLAB interprets
foo a b c
as
foo('a','b','c')
However, when you use the unquoted form, MATLAB cannot return output
arguments. For example,
legend apples oranges
creates a legend on a plot using the strings apples and oranges as labels. If
you want the legend command to return its output arguments, then you
must use the quoted form:
[legh,objh] = legend('apples','oranges');
In addition, you must use the quoted form if any of the arguments is not
a string.
Caution While the unquoted syntax is convenient, in some cases it can be
used incorrectly without causing MATLAB to generate an error.
Constructing String Arguments in Code
The quoted form enables you to construct string arguments within the
code. The following example processes multiple data files, August1.dat,
August2.dat, and so on. It uses the function int2str, which converts an
integer to a character, to build the filename:
for d = 1:31
4-27
4
Programming
s = ['August' int2str(d) '.dat'];
load(s)
% Code to process the contents of the d-th file
end
The eval Function
The eval function works with text variables to implement a powerful text
macro facility. The expression or statement
eval(s)
uses the MATLAB interpreter to evaluate the expression or execute the
statement contained in the text string s.
The example of the previous section could also be done with the following
code, although this would be somewhat less efficient because it involves the
full interpreter, not just a function call:
for d = 1:31
s = ['load August' int2str(d) '.dat'];
eval(s)
% Process the contents of the d-th file
end
Function Handles
You can create a handle to any MATLAB function and then use that handle
as a means of referencing the function. A function handle is typically passed
in an argument list to other functions, which can then execute, or evaluate,
the function using the handle.
Construct a function handle in MATLAB using the at sign, @, before the
function name. The following example creates a function handle for the sin
function and assigns it to the variable fhandle:
fhandle = @sin;
You can call a function by means of its handle in the same way that you would
call the function using its name. The syntax is
fhandle(arg1, arg2, ...);
4-28
Scripts and Functions
The function plot_fhandle, shown below, receives a function handle and
data, generates y-axis data using the function handle, and plots it:
function x = plot_fhandle(fhandle, data)
plot(data, fhandle(data))
When you call plot_fhandle with a handle to the sin function and the
argument shown below, the resulting evaluation produces a sine wave plot:
plot_fhandle(@sin, -pi:0.01:pi)
Function Functions
A class of functions called “function functions” works with nonlinear functions
of a scalar variable. That is, one function works on another function. The
function functions include
• Zero finding
• Optimization
• Quadrature
• Ordinary differential equations
MATLAB represents the nonlinear function by a function M-file. For example,
here is a simplified version of the function humps from the matlab/demos
directory:
function y = humps(x)
y = 1./((x-.3).^2 + .01) + 1./((x-.9).^2 + .04) - 6;
Evaluate this function at a set of points in the interval 0 ≤ x ≤ 1 with
x = 0:.002:1;
y = humps(x);
Then plot the function with
plot(x,y)
4-29
4
Programming
The graph shows that the function has a local minimum near x = 0.6. The
function fminsearch finds the minimizer, the value of x where the function
takes on this minimum. The first argument to fminsearch is a function
handle to the function being minimized and the second argument is a rough
guess at the location of the minimum:
p = fminsearch(@humps,.5)
p =
0.6370
To evaluate the function at the minimizer,
humps(p)
ans =
11.2528
Numerical analysts use the terms quadrature and integration to distinguish
between numerical approximation of definite integrals and numerical
integration of ordinary differential equations. MATLAB quadrature routines
are quad and quadl. The statement
4-30
Scripts and Functions
Q = quadl(@humps,0,1)
computes the area under the curve in the graph and produces
Q =
29.8583
Finally, the graph shows that the function is never zero on this interval. So,
if you search for a zero with
z = fzero(@humps,.5)
you will find one outside the interval
z =
-0.1316
Vectorization
One way to make your MATLAB programs run faster is to vectorize the
algorithms you use in constructing the programs. Where other programming
languages might use for loops or DO loops, MATLAB can use vector or matrix
operations. A simple example involves creating a table of logarithms:
x = .01;
for k = 1:1001
y(k) = log10(x);
x = x + .01;
end
A vectorized version of the same code is
x = .01:.01:10;
y = log10(x);
For more complicated code, vectorization options are not always so obvious.
For More Information See “Improving Performance and Memory Usage”
in the MATLAB Programming documentation for other techniques that you
can use.
4-31
4
Programming
Preallocation
If you cannot vectorize a piece of code, you can make your for loops go faster
by preallocating any vectors or arrays in which output results are stored. For
example, this code uses the function zeros to preallocate the vector created in
the for loop. This makes the for loop execute significantly faster:
r = zeros(32,1);
for n = 1:32
r(n) = rank(magic(n));
end
Without the preallocation in the previous example, the MATLAB interpreter
enlarges the r vector by one element each time through the loop. Vector
preallocation eliminates this step and results in faster execution.
4-32
5
Data Analysis
Introduction (p. 5-2)
Components of a data analysis
Preprocessing Data (p. 5-3)
Preparing data for analysis
Summarizing Data (p. 5-10)
Computing basic statistics
Visualizing Data (p. 5-14)
Looking for patterns and trends
Modeling Data (p. 5-19)
Descriptions and predictions
5
Data Analysis
Introduction
Every data analysis has some standard components:
• Preprocessing — Consider outliers and missing values, and smooth data
to identify possible models.
• Summarizing — Compute basic statistics to describe the overall location,
scale, and shape of the data.
• Visualizing — Plot data to identify patterns and trends.
• Modeling — Give data trends fuller descriptions, suitable for predicting
new values.
Data analysis moves among these components with two basic goals in mind:
1 Describe the patterns in the data with simple models that lead to accurate
predictions.
2 Understand the relationships among variables that lead to the model.
This section of the Getting Started guide explains how to use MATLAB to
carry out a basic data analysis.
5-2
Preprocessing Data
Preprocessing Data
In this section...
“Overview” on page 5-3
“Loading the Data” on page 5-3
“Missing Data” on page 5-4
“Outliers” on page 5-4
“Smoothing and Filtering” on page 5-6
Overview
Begin a data analysis by loading data into suitable MATLAB container
variables and sorting out the “good” data from the “bad.” This is a preliminary
step that assures meaningful conclusions in subsequent parts of the analysis.
Note This section begins a data analysis that is continued in “Summarizing
Data” on page 5-10, “Visualizing Data” on page 5-14, and “Modeling Data”
on page 5-19.
Loading the Data
Begin by loading the data in count.dat:
load count.dat
The 24-by-3 array count contains hourly traffic counts (the rows) at three
intersections (the columns) for a single day.
See “MATLAB for Data Analysis” and “Importing and Exporting Data” in the
MATLAB Data Analysis documentation for more information on storing data
in MATLAB variables for analysis.
5-3
5
Data Analysis
Missing Data
In MATLAB, NaN (Not a Number) values represent missing data. NaN values
allow variables with missing data to maintain their structure—in this case,
24-by-1 vectors with consistent indexing across all three intersections.
Check the data at the third intersection for NaN values using the MATLAB
isnan function:
c3 = count(:,3); % Data at intersection 3
c3NaNCount = sum(isnan(c3))
c3NaNCount =
0
isnan returns a logical vector the same size as c3, with entries indicating the
presence (1) or absence (0) of NaN values for each of the 24 elements in the
data. In this case, the logical values sum to 0, so there are no NaN values
in the data.
NaN values are introduced into the data in the section on “Outliers” on page
5-4.
See “Removing and Interpolating Missing Values” in the MATLAB Data
Analysis documentation for more information on handling missing data in
MATLAB.
Outliers
Outliers are data values that are dramatically different from patterns in
the rest of the data. They may be due to measurement error, or they may
represent significant features in the data. Identifying outliers, and deciding
what to do with them, depends on an understanding of the data and its source.
One common method for identifying outliers is to look for values more than
a certain number of standard deviations σ from the mean μ. The following
code plots a histogram of the data at the third intersection together with
lines at μ and μ + nσ, for n = 1, 2:
bin_counts = hist(c3); % Histogram bin counts
N = max(bin_counts); % Maximum bin count
mu3 = mean(c3); % Data mean
5-4
Preprocessing Data
sigma3 = std(c3); % Data standard deviation
hist(c3) % Plot histogram
hold on
plot([mu3 mu3],[0 N],'r','LineWidth',2) % Mean
X = repmat(mu3+(1:2)*sigma3,2,1);
Y = repmat([0;N],1,2);
plot(X,Y,'g','LineWidth',2) % Standard deviations
legend('Data','Mean','Stds')
hold off
The plot shows that some of the data are more than two standard deviations
above the mean. If you identify these data as errors (not features), replace
them with NaN values as follows:
outliers = (c3 - mu3) > 2*sigma3;
c3m = c3; % Copy c3 to c3m
5-5
5
Data Analysis
c3m(outliers) = NaN; % Add NaN values
See “Removing Outliers” in the MATLAB Data Analysis documentation for
more information on handling outliers in MATLAB.
Smoothing and Filtering
A time-series plot of the data at the third intersection (with the outlier
removed in “Outliers” on page 5-4) looks like this:
plot(c3m,'o-')
hold on
The NaN value at hour 20 appears as a gap in the plot. This handling of NaN
values is typical of MATLAB plotting functions.
5-6
Preprocessing Data
Noisy data shows random variations about expected values. You may want
to smooth the data to reveal its main features before building a model. Two
basic assumptions underlie smoothing:
• The relationship between the predictor (time) and the response (traffic
volume) is smooth.
• The smoothing algorithm results in values that are better estimates of
expected values because the noise has been reduced.
Apply a simple moving average smoother to the data using the MATLAB
convn function:
span = 3; % Size of the averaging window
window = ones(span,1)/span;
smoothed_c3m = convn(c3m,window,'same');
h = plot(smoothed_c3m,'ro-');
legend('Data','Smoothed Data')
5-7
5
Data Analysis
The extent of the smoothing is controlled with the variable span. The
averaging calculation returns NaN values whenever the smoothing window
includes the NaN value in the data, thus increasing the size of the gap in the
smoothed data.
The MATLAB filter function is also used for smoothing data:
smoothed2_c3m = filter(window,1,c3m);
delete(h)
plot(smoothed2_c3m,'ro-');
5-8
Preprocessing Data
The smoothed data are shifted from the previous plot. convn with the 'same'
parameter returns the central part of the convolution, the same length as the
data. filter returns the initial part of the convolution, the same length as
the data. Otherwise, the algorithms are identical.
Smoothing estimates the center of the distribution of response values at each
value of the predictor. It invalidates a basic assumption of many fitting
algorithms, namely, that the errors at each value of the predictor are normally
distributed. Accordingly, smoothed data should not be used to fit a model. Use
smoothed data to identify a model.
See “Filtering Data” in the MATLAB Data Analysis documentation for more
information on smoothing and filtering.
5-9
5
Data Analysis
Summarizing Data
In this section...
“Overview” on page 5-10
“Measures of Location” on page 5-10
“Measures of Scale” on page 5-11
“Shape of a Distribution” on page 5-11
Overview
MATLAB includes many functions for summarizing the overall location, scale,
and shape of a data sample.
One of the advantages of working in MATLAB is that functions operate on
entire arrays of data, not just on single scalar values. The functions are said
to be vectorized. Vectorization allows for both efficient problem formulation,
using array-based data, and efficient computation, using vectorized statistical
functions.
Note This section continues the data analysis from “Preprocessing Data”
on page 5-3.
Measures of Location
Summarize the location of a data sample by finding a “typical” value. Common
measures of location or “central tendency” are computed by the MATLAB
functions mean, median, and mode:
5-10
x1 = mean(count)
x1 =
32.0000
46.5417
65.5833
x2 = median(count)
x2 =
23.5000
36.0000
39.0000
Summarizing Data
x3 = mode(count)
x3 =
11
9
9
Like all of the statistical functions in MATLAB, the functions above
summarize data across observations (rows) while preserving variables
(columns). The functions compute the location of the data at each of the three
intersections in a single call.
Measures of Scale
There are many ways to measure the scale or “dispersion” of a data sample.
The MATLAB functions max, min, std, and var compute some common
measures:
dx1 = max(count)-min(count)
dx1 =
107
136
250
dx2 = std(count)
dx2 =
25.3703
41.4057
68.0281
dx3 = var(count)
dx3 =
1.0e+003 *
0.6437
1.7144
4.6278
Like all of the statistical functions in MATLAB, the functions above
summarize data across observations (rows) while preserving variables
(columns). The functions compute the scale of the data at each of the three
intersections in a single call.
Shape of a Distribution
The shape of a distribution is harder to summarize than its location or
scale. The MATLAB hist function plots a histogram that provides a visual
summary:
figure
hist(count)
5-11
5
Data Analysis
legend('Intersection 1',...
'Intersection 2',...
'Intersection 3')
Parametric models give analytic summaries of distribution shapes.
Exponential distributions, with parameter mu given by the data mean, are a
good choice for the traffic data:
c1 = count(:,1); % Data at intersection 1
[bin_counts,bin_locations] = hist(c1);
bin_width = bin_locations(2) - bin_locations(1);
hist_area = (bin_width)*(sum(bin_counts));
figure
hist(c1)
hold on
5-12
Summarizing Data
mu1 = mean(c1);
exp_pdf = @(t)(1/mu1)*exp(-t/mu1); % Integrates
% to 1
t = 0:150;
y = exp_pdf(t);
plot(t,(hist_area)*y,'r','LineWidth',2)
legend('Distribution','Exponential Fit')
Methods for fitting general parametric models to data distributions are
beyond the scope of this Getting Started guide. Functions for computing
maximum likelihood estimates of distribution parameters are available in
Statistics Toolbox.
See “Descriptive Statistics” in the MATLAB Data Analysis documentation for
more information on summarizing data samples.
5-13
5
Data Analysis
Visualizing Data
In this section...
“Overview” on page 5-14
“2-D Scatter Plots” on page 5-14
“3-D Scatter Plots” on page 5-16
“Scatter Plot Arrays” on page 5-18
Overview
MATLAB provides many plots for visualizing data patterns and trends.
Histograms and time-series plots of the traffic data are described in the
sections on “Preprocessing Data” on page 5-3 and “Summarizing Data”
on page 5-10. Scatter plots, described in this section, help to visualize
relationships among the traffic data at different intersections.
Note This section continues the data analysis from “Summarizing Data”
on page 5-10.
2-D Scatter Plots
A 2-D scatter plot, created with the MATLAB scatter function, shows the
relationship between the traffic volume at the first two intersections:
c1 = count(:,1); % Data at intersection 1
c2 = count(:,2); % Data at intersection 2
figure
scatter(c1,c2,'filled')
xlabel('Intersection 1')
ylabel('Intersection 2')
5-14
Visualizing Data
The strength of the linear relationship between the two variables (how tightly
the data lies along a least-squares line through the scatter) is measured by
the covariance, computed by the MATLAB cov function:
C12 = cov([c1 c2])
C12 =
1.0e+003 *
0.6437
0.9802
0.9802
1.7144
The results are displayed in a symmetric square matrix, with the covariance
of the i th and j th variables in the (i, j)th position. The i th diagonal element
is the variance of the i th variable.
Covariances have the disadvantage of depending on the units used to measure
the individual variables. They are often divided by the standard deviations
5-15
5
Data Analysis
of the variables to normalize values between +1 and –1. The results are
correlation coefficients, computed by the MATLAB corrcoef function:
R12 = corrcoef([c1 c2])
R12 =
1.0000
0.9331
0.9331
1.0000
r12 = R12(1,2) % Correlation coefficient
r12 =
0.9331
r12sq = r12^2 % Coefficient of determination
r12sq =
0.8707
Because it is normalized, the value of the correlation coefficient is readily
comparable to values for other pairs of intersections. Its square, the coefficient
of determination, is the variance about the least-squares line divided by the
variance about the mean. That is, it is the proportion of variation in the
response (in this case, the traffic volume at intersection 2) that is eliminated
or non-causally “explained” by a least-squares line through the scatter.
3-D Scatter Plots
A 3-D scatter plot, created with the MATLAB scatter3 function, shows the
relationship between the traffic volume at all three intersections:
figure
scatter3(c1,c2,c3,'filled')
xlabel('Intersection 1')
ylabel('Intersection 2')
zlabel('Intersection 3')
5-16
Visualizing Data
The strength of the linear relationship among the variables in the 3-D scatter
is measured by computing eigenvalues of the covariance matrix with the
MATLAB eig function:
vars = eig(cov([c1 c2 c3]))
vars =
1.0e+003 *
0.0442
0.1118
6.8300
explained = max(vars)/sum(vars)
explained =
0.9777
The eigenvalues are the variances along the principal components of the data.
The variable explained measures the proportion of variation “explained” by
5-17
5
Data Analysis
the first principal component, along the axis of the data. Unlike the coefficient
of determination for 2-D scatters, this measure does distinguish predictor
and response variables.
Scatter Plot Arrays
Use the MATLAB plotmatrix function to make comparisons of the
relationships between multiple pairs of intersections:
figure
plotmatrix(count)
The plot in the (i, j)th position of the array is a scatter with the i th variable
on the vertical axis and the j th variable on the horizontal axis. The plot in
the i th diagonal position is a histogram of the i th variable.
See “Plotting Data” in the MATLAB Data Analysis documentation for more
information on statistical visualization.
5-18
Modeling Data
Modeling Data
In this section...
“Overview” on page 5-19
“Polynomial Regression” on page 5-19
“General Linear Regression” on page 5-20
Overview
Parametric models translate an understanding of data relationships into
analytic tools with predictive power. Polynomial and sinusoidal models are
simple choices for the up and down trends in the traffic data.
Note This section continues the data analysis from “Visualizing Data” on
page 5-14.
Polynomial Regression
Use the MATLAB polyfit function to estimate coefficients of polynomial
models, then use the MATLAB polyval function to evaluate the model at
arbitrary values of the predictor.
The following code fits the traffic data at the third intersection with a
polynomial model of degree six:
c3 = count(:,3); % Data at intersection 3
tdata = (1:24)';
p_coeffs = polyfit(tdata,c3,6);
figure
plot(c3,'o-')
hold on
tfit = (1:0.01:24)';
yfit = polyval(p_coeffs,tfit);
plot(tfit,yfit,'r-','LineWidth',2)
legend('Data','Polynomial Fit','Location','NW')
5-19
5
Data Analysis
The model has the advantage of being simple while following the up-and-down
trend. The accuracy of its predictive power, however, is questionable,
especially at the ends of the data.
General Linear Regression
Assuming that the data are periodic with a 12-hour period and a peak around
hour 7, it is reasonable to fit a sinusoidal model of the form:
y = a + b cos((2π / 12)(t − 7))
The coefficients a and b appear linearly. Use the MATLAB mldivide
(backslash) operator to fit general linear models:
c3 = count(:,3); % Data at intersection 3
tdata = (1:24)';
5-20
Modeling Data
X = [ones(size(tdata)) cos((2*pi/12)*(tdata-7))];
s_coeffs = X\c3;
figure
plot(c3,'o-')
hold on
tfit = (1:0.01:24)';
yfit = [ones(size(tfit)) cos((2*pi/12)*(tfit-7))]*s_coeffs;
plot(tfit,yfit,'r-','LineWidth',2)
legend('Data','Sinusoidal Fit','Location','NW')
Use the MATLAB lscov function to compute statistics on the fit, such as
estimated standard errors of the coefficients and the mean squared error:
[s_coeffs,stdx,mse] = lscov(X,c3)
s_coeffs =
65.5833
5-21
5
Data Analysis
73.2819
stdx =
8.9185
12.6127
mse =
1.9090e+003
Check the assumption of a 12-hour period in the data with a periodogram,
computed using the MATLAB fft function:
Fs = 1; % Sample frequency (per hour)
n = length(c3); % Window length
Y = fft(c3); % DFT of data
f = (0:n-1)*(Fs/n); % Frequency range
P = Y.*conj(Y)/n; % Power of the DFT
figure
plot(f,P)
xlabel('Frequency')
ylabel('Power')
predicted_f = 1/12
predicted_f =
0.0833
5-22
Modeling Data
The peak near 0.0833 supports the assumption, although it occurs at a
slightly higher frequency. The model can be adjusted accordingly.
See “Linear Regression Analysis” and “Fourier Analysis” in the MATLAB
Data Analysis documentation for more information on data modeling.
5-23
5
5-24
Data Analysis
6
Creating Graphical User
Interfaces
What Is GUIDE? (p. 6-2)
Introduces GUIDE, the MATLAB
graphical user interface design
environment
Laying Out a GUI (p. 6-3)
Briefly describes the GUIDE Layout
Editor
Programming a GUI (p. 6-6)
Introduces callbacks to define
behavior of the GUI components.
6
Creating Graphical User Interfaces
What Is GUIDE?
GUIDE, the MATLAB graphical user interface development environment,
provides a set of tools for creating graphical user interfaces (GUIs). These
tools greatly simplify the process of designing and building GUIs. You can
use the GUIDE tools to
• Lay out the GUI.
Using the GUIDE Layout Editor, you can lay out a GUI easily by clicking
and dragging GUI components—such as panels, buttons, text fields, sliders,
menus, and so on—into the layout area. GUIDE stores the GUI layout
in a FIG-file.
• Program the GUI.
GUIDE automatically generates an M-file that controls how the GUI
operates. The M-file initializes the GUI and contains a framework for the
most commonly used callbacks for each component—the commands that
execute when a user clicks a GUI component. Using the M-file editor, you
can add code to the callbacks to perform the functions you want.
Note You can also create GUIs programmatically. For information on how to
get started, see “Creating a Simple GUI Programmatically” in the MATLAB
Creating Graphical User interfaces documentation.
6-2
Laying Out a GUI
Laying Out a GUI
In this section...
“Starting GUIDE” on page 6-3
“The Layout Editor” on page 6-4
Starting GUIDE
Start GUIDE by typing guide at the MATLAB command prompt. This
displays the GUIDE Quick Start dialog box, as shown in the following figure.
From the GUIDE Quick Start dialog box, you can
• Create a new GUI from one of the GUIDE templates—prebuilt GUIs that
you can modify for your own purposes.
• Open an existing GUI.
6-3
6
Creating Graphical User Interfaces
The Layout Editor
When you open a GUI in GUIDE, it is displayed in the Layout Editor, which is
the control panel for all of the GUIDE tools. The following figure shows the
Layout Editor with a blank GUI template.
Component
palette
Layout Area
You can lay out your GUI by dragging components, such as panels, push
buttons, pop-up menus, or axes, from the component palette, at the left side
of the Layout Editor, into the layout area. For example, if you drag a push
button into the layout area, it appears as in the following figure.
6-4
Laying Out a GUI
You can also use the Layout Editor (along with the Toolbar Editor and Icon
Editor) to create menus and toolbars, create and modify tool icons, and set
basic properties of the GUI components.
To get started using the Layout Editor and setting property values, see
“Creating a Simple GUI with GUIDE” in the MATLAB Creating Graphical
User Interfaces documentation. “Examples of GUIDE GUIs” in the same
documentation illustrates the variety of GUIs that you can create with
GUIDE.
6-5
6
Creating Graphical User Interfaces
Programming a GUI
After laying out the GUI and setting component properties, the next step is to
program the GUI. You program the GUI by coding one or more callbacks for
each of its components. Callbacks are functions that execute in response to
some action by the user. A typical action is clicking a push button.
A GUI’s callbacks are found in an M-file that GUIDE generates automatically.
GUIDE adds templates for the most commonly used callbacks to this M-file,
but you may want to add others. Use the M-file Editor to edit this file.
The following figure shows the Callback template for a push button.
To learn more about programming a GUI, see “Creating a Simple GUI with
GUIDE” in the MATLAB Creating GUIs documentation.
6-6
7
Desktop Tools and
Development Environment
If you have an active Internet connection, you can watch the Working in
The Development Environment video demo for an overview of the major
functionality.
Desktop Overview (p. 7-2)
Access tools, arrange the desktop,
and set preferences.
Command Window and Command
History (p. 7-6)
Run functions and enter variables.
Help (p. 7-8)
Find and view documentation and
demos.
Current Directory Browser and
Search Path (p. 7-14)
Manage and use M-files with
MATLAB.
Workspace Browser and Array
Editor (p. 7-17)
Work with variables in MATLAB.
Editor/Debugger (p. 7-20)
Create and debug M-files (MATLAB
programs).
M-Lint Code Check and Profiler
Reports (p. 7-23)
Improve and tune your M-files.
Other Development Environment
Features (p. 7-28)
Interface with source control
systems, and publish M-file results.
7
Desktop Tools and Development Environment
Desktop Overview
In this section...
“Introduction to the Desktop” on page 7-2
“Arranging the Desktop” on page 7-4
“Start Button” on page 7-4
Introduction to the Desktop
Use desktop tools to manage your work in MATLAB. You can also use
MATLAB functions to perform the equivalent of most of the features found
in the desktop tools.
The following illustration shows the default configuration of the MATLAB
desktop. You can modify the setup to meet your needs.
7-2
Desktop Overview
Menus change,
depending on the
tool you are using.
Enter MATLAB
statements at the
prompt.
View or change the
current directory.
Move or resize the
Command Window.
7-3
7
Desktop Tools and Development Environment
For More Information For an overview of the desktop tools, watch the
video tutorials, accessible by typing demo matlab desktop (requires an
Internet connection). For complete details, see the MATLAB Desktop Tools
and Development Environment documentation.
Arranging the Desktop
These are some common ways to customize the desktop:
• Show or hide desktop tools via the Desktop menu.
• Resize any tool by dragging one of its edges.
• Move a tool outside of the desktop by clicking the undock button
tool’s title bar.
in the
• Reposition a tool within the desktop by dragging its title bar to the new
location. Tools can occupy the same position, as shown for the Current
Directory and Workspace browser in the preceding illustration, in which
case, you access a tool via its name in the title bar.
• Maximize or minimize (temporarily hide) a tool within the desktop via
the Desktop menu.
• Change fonts and other options by using File > Preferences.
Start Button
The MATLAB Start button provides easy access to tools, demos, shortcuts,
and documentation. Click the Start button to see the options.
7-4
Desktop Overview
For More Information See “Desktop” in the MATLAB Desktop Tools and
Development Environment documentation.
7-5
7
Desktop Tools and Development Environment
Command Window and Command History
In this section...
“Command Window” on page 7-6
“Command History” on page 7-7
Command Window
Use the Command Window to enter variables and to run functions and M-file
scripts.
Run functions and
enter variables at
the MATLAB prompt.
MATLAB displays
the results.
Press the up arrow key to recall a statement you previously typed. Edit the
statement as needed and then press Enter to run it. For more information
about entering statements in the Command Window, see “Controlling
Command Window Input and Output” on page 2-30.
7-6
Command Window and Command History
For More Information See “Running Functions — Command Window and
History” in the MATLAB Desktop Tools and Development Environment
documentation for complete details.
Command History
Statements you enter in the Command Window are logged in the Command
History. From the Command History, you can view and search for previously
run statements, as well as copy and execute selected statements. You can also
create an M-file from selected statements.
Timestamp
marks the start
of each session.
Select one or
more entries
and right-click
to copy, evaluate,
or create an M-file
from the selection.
To save the input and output from a MATLAB session to a file, use the diary
function.
For More Information See “Command History Window” in the MATLAB
Desktop Tools and Development Environment documentation, and the
reference page for the diary function.
7-7
7
Desktop Tools and Development Environment
Help
In this section...
“Help Browser” on page 7-8
“Other Forms of Help” on page 7-11
“Typographical Conventions” on page 7-12
Help Browser
Use the Help browser to search for and view documentation and demos for all
your MathWorks products. The Help browser is an HTML viewer integrated
into the MATLAB desktop.
To open the Help browser, click the Help button
in the desktop toolbar.
The Help browser consists of two panes, the Help Navigator, which you use
to find information, and the display pane, where you view the information.
7-8
Help
Tabs in the Help Navigator pane provide
different ways to find information.
Click the Close box
to hide the pane.
Drag the separator bar to
adjust the width of the panes.
View documentation
in the display pane.
7-9
7
Desktop Tools and Development Environment
These are the key features:
• Search for field — Look for specific words in the documentation and
demos. You can
-
Specify an exact phrase by enclosing words in double quotation marks,
such as "word1 word2"
Use a wildcard symbol (*) in place of letters, such as wo*d1
Include Boolean operators between words, such as word1 NOT word2
• Contents tab — View the titles and tables of contents of the documentation.
By default, the contents synchronizes to the displayed page. If you get to
a page from a search or by following a link, click the Contents tab if you
want to see the context within the overall documentation for the page you
are viewing.
• Index tab — Find specific index entries (selected keywords) in the
documentation.
• Search Results tab — Displays results from Search for, separating the
results in Documentation from the results in Demos.
• Demos tab — View and run demonstrations for your MathWorks products.
Demos include code that you can use as a basis for creating your own
M-files.
While viewing the documentation, you can
• Browse to other pages — Use the arrows at the tops and bottoms of the
pages to move through the document, or use the back and forward buttons
in the toolbar to go to previously viewed pages.
• Bookmark pages — Use the Favorites menu.
• Print a page — Click the print button in the toolbar.
• Find a term in the page — Click the find icon
in the toolbar.
• Copy or evaluate a selection — Select text, such as code from an example,
then right-click and use a context menu item to copy the selection or
evaluate (run) it.
7-10
Help
Other Forms of Help
In addition to the Help browser, you can use help functions. To get help for
a specific function, use the doc function. For example, doc format displays
documentation for the format function in the Help browser.
To see a briefer form of the documentation for a function, type help followed
by the function name. The resulting help text appears in the Command
Window. It shows function names in all capital letters to distinguish them
from the surrounding text. When you use the function names, type them
in lowercase or they will not run. Some functions actually consist of both
uppercase and lowercase letters, and the help text clearly indicates that. For
those functions, match the case used in the help function.
7-11
7
Desktop Tools and Development Environment
Other means for getting help include contacting Technical Support
(www.mathworks.com/support) and participating in the Usenet newsgroup
for MATLAB users, comp.soft-sys.matlab.
Typographical Conventions
These conventions are used in the Help browser and PDF documentation.
Item
Convention
Example
Buttons and keys
Boldface
Press the Enter key.
Example code
Monospace font
To assign the value 5 to
A, enter
A = 5
Function names,
syntax, filenames,
directory/folder names,
user input, items in
drop-down lists
Monospace font
The cos function finds
the cosine of each array
element.
Literal strings (in
syntax descriptions in
reference chapters)
Monospace bold font
f =
freqspace(n,'whole')
Mathematical
expressions
Italics for variables
Standard text font for
functions, operators,
and constants
This vector represents
the polynomial p = x2 +
2x + 3.
MATLAB output
Monospace font
MATLAB responds with
A =
5
Menu titles and items
7-12
Boldface
Select File > Save.
Help
Item
Convention
Example
New terms and for
emphasis
Italics
In MATLAB, a matrix is
a rectangular array of
numbers.
Omitted input
arguments
(...) ellipsis denotes
all of the input/output
arguments from
preceding syntaxes
[c, ia, ib] =
union(...)
String variables (from
a finite list)
Monospace italics
format('type')
For More Information See “Help for Using MATLAB” in the MATLAB
Desktop Tools and Development Environment documentation, and the
reference pages for the doc and help functions.
7-13
7
Desktop Tools and Development Environment
Current Directory Browser and Search Path
In this section...
“Running Files” on page 7-14
“Current Directory” on page 7-14
“Search Path” on page 7-15
Running Files
MATLAB file operations use the current directory and the search path as
reference points. Any file you want to run must either be in the current
directory or on the search path.
Current Directory
A quick way to view or change the current directory is by using the current
directory field in the desktop toolbar, shown here.
To search for, view, open, and make changes to MATLAB related directories
and files, use the MATLAB Current Directory browser. Alternatively, you can
use the functions dir, cd, and delete. Use “Directory Reports in Current
Directory Browser” to help you tune and manage M-files.
7-14
Current Directory Browser and Search Path
Change the directory here.
This field only appears here when
the Current Directory browser is
undocked from the desktop.
Search for files
and content
within text files.
Access directory
reports.
Double-click a file
to open it in an
appropriate tool.
For More Information See “File Management Operations” in the MATLAB
Desktop Tools and Development Environment documentation, and the
reference pages for the dir, cd, and delete functions.
Search Path
MATLAB uses a search path to find M-files and other MATLAB related files,
which are organized in directories on your file system. Any file you want to
run in MATLAB must reside in the current directory or in a directory that is
on the search path. When you create M-files and related files for MATLAB,
add the directories in which they are located to the MATLAB search path. By
default, the files supplied with MATLAB and other MathWorks products are
included in the search path.
7-15
7
Desktop Tools and Development Environment
To see which directories are on the search path or to change the search
path, select File > Set Path and use the resulting Set Path dialog box.
Alternatively, you can use the path function to view the search path, addpath
to add directories to the path, and rmpath to remove directories from the path.
For More Information See “Search Path” in the MATLAB Desktop Tools
and Development Environment documentation, and the reference pages for
the path, addpath, and rmpath functions.
7-16
Workspace Browser and Array Editor
Workspace Browser and Array Editor
In this section...
“Workspace Browser” on page 7-17
“Array Editor” on page 7-18
Workspace Browser
The MATLAB workspace consists of the set of variables (named arrays) built
up during a MATLAB session and stored in memory. You add variables to the
workspace by using functions, running M-files, and loading saved workspaces.
To view the workspace and information about each variable, use the
Workspace browser, or use the functions who and whos.
To delete variables from the workspace, select the variables and select
Edit > Delete. Alternatively, use the clear function.
The workspace is not maintained after you end the MATLAB session. To save
the workspace to a file that can be read during a later MATLAB session,
select File > Save, or use the save function. This saves the workspace to a
binary file called a MAT-file, which has a .mat extension. You can use options
7-17
7
Desktop Tools and Development Environment
to save to different formats. To read in a MAT-file, select File > Import
Data, or use the load function.
For More Information See “MATLAB Workspace” in the MATLAB Desktop
Tools and Development Environment documentation, and the reference pages
for the who, clear, save, and load functions.
Array Editor
Double-click a variable in the Workspace browser, or use openvar
variablename, to see it in the Array Editor. Use the Array Editor to view and
edit a visual representation of variables in the workspace.
View and change values
of array elements.
Use the document bar to view other variables
you have open in the Array Editor.
7-18
Arrange the display of
array documents.
Workspace Browser and Array Editor
For More Information See “Viewing and Editing Workspace Variables
with the Array Editor” in the MATLAB Desktop Tools and Development
Environment documentation, and the reference page for the openvar function.
7-19
7
Desktop Tools and Development Environment
Editor/Debugger
Use the Editor/Debugger to create and debug M-files, which are programs you
write to run MATLAB functions. The Editor/Debugger provides a graphical
user interface for text editing, as well as for M-file debugging. To create or
edit an M-file use File > New or File > Open, or use the edit function.
7-20
Editor/Debugger
Set breakpoints
where you want
execution to pause
so you can examine
the variables.
Comment selected lines
and specify the indenting style
using the Text menu.
Hold the cursor over a variable
and its current value appears
(known as a data tip).
Arrange the display of documents
in the Editor/Debugger.
Find and replace text.
M-lint automatic
code analyzer.
Use the document bar to access other
documents open in the Editor/Debugger.
You can use any text editor to create M-files, such as Emacs. Use preferences
(accessible from the desktop File menu) to specify that editor as the default.
7-21
7
Desktop Tools and Development Environment
If you use another editor, you can still use the MATLAB Editor/Debugger for
debugging, or you can use debugging functions, such as dbstop, which sets a
breakpoint.
If you just need to view the contents of an M-file, you can display the contents
in the Command Window using the type function.
Use the M-Lint automatic code analyzer to help you identify problems and
potential improvements in your code. For details, see “M-Lint Code Check
and Profiler Reports” on page 7-23.
You can evaluate your code in sections, called cells, and can publish your code,
including results, to popular output formats like HTML. For more information,
see “Using Cells for Rapid Code Iteration and Publishing Results” in the
MATLAB Desktop Tools and Development Environment documentation.
For More Information See “Editing and Debugging M-Files” in the
MATLAB Desktop Tools and Development Environment documentation, and
the function reference pages for edit, type, and debug.
7-22
M-Lint Code Check and Profiler Reports
M-Lint Code Check and Profiler Reports
In this section...
“M-Lint Code Check Report” on page 7-23
“Profiler” on page 7-26
M-Lint Code Check Report
The M-Lint Code Check Report displays potential errors and problems, as
well as opportunities for improvement in your M-files. The term lint is used
by similar tools in other programming languages such as C.
Access the M-Lint Code Check Report and other directory reports from the
Current Directory browser. You run a report for all files in the current
directory.
Directory reports
7-23
7
Desktop Tools and Development Environment
In MATLAB, the M-Lint Code Check Report displays a message for each line
of an M-file it determines might be improved. For example, a common M-Lint
message is that a variable is defined but never used in the M-file.
7-24
M-Lint Code Check and Profiler Reports
The report displays a line number and message for
each potential problem or improvement opportunity.
Click a line number to open the M-file
in the Editor/Debugger at that line.
7-25
7
Desktop Tools and Development Environment
Alternatively, you can use automatic M-Lint code checking to view M-Lint
messages while you work on a file in the Editor/Debugger. You can also use
the mlint function to get results for a single M-file.
For More Information See “Tuning and Managing M-Files” and “M-Lint
Code Analyzer” in the MATLAB Desktop Tools and Development Environment
documentation, and the reference page for the mlint function.
Profiler
MATLAB includes the Profiler to help you improve the performance of
your M-files. Run a MATLAB statement or an M-file in the Profiler and it
produces a report of where the time is being spent. Access the Profiler from
the Desktop menu, or use the profile function.
7-26
M-Lint Code Check and Profiler Reports
For More Information See “Tuning and Managing M-Files” in the MATLAB
Desktop Tools and Development Environment documentation, and the
reference page for the profile function.
7-27
7
Desktop Tools and Development Environment
Other Development Environment Features
Additional development environment features include
• Source Control — Access your source control system from within MATLAB.
• Publishing Results — Use the Editor/Debugger’s cell features to publish
M-files and results to popular output formats including HTML and
Microsoft Word. You can also use MATLAB Notebook to access MATLAB
functions from within Microsoft Word.
For More Information See “Source Control Interface” and “Publishing
Results” in the MATLAB Desktop Tools and Development Environment
documentation.
7-28
8
External Interfaces
Use MATLAB External Interfaces to connect MATLAB to programs, devices
and data. Application developers use external interfaces to integrate
MATLAB functionality with their applications. External interfaces also
facilitate data collection, such as from peripheral devices like an oscilloscope
or a remote network server.
Programming Interfaces (p. 8-2)
Write C and Fortran programs to
integrate with MATLAB. Use Java
classes and objects or functions in
dynamic link libraries (DLLs) in
MATLAB. Learn techniques for
importing data to and exporting data
from the MATLAB environment.
Component Object Model Interface
(p. 8-4)
Use COM on the Microsoft
Windows platform to integrate
application-specific components from
different vendors into MATLAB.
Web Services (p. 8-5)
Build MATLAB applications using
Simple Object Access Protocol
(SOAP) or Web Services Description
Language (WSDL) Web service
technologies.
Serial Port Interface (p. 8-6)
Communicate directly with
peripheral devices.
8
External Interfaces
Programming Interfaces
In this section...
“Call MATLAB from C and Fortran Programs” on page 8-2
“Call C and Fortran Programs from MATLAB” on page 8-2
“Call Java from MATLAB” on page 8-3
“Call Functions in Shared Libraries” on page 8-3
“Import and Export Data” on page 8-3
Call MATLAB from C and Fortran Programs
Use the MATLAB engine library to call MATLAB from C and Fortran
programs. When you call MATLAB from your own programs, MATLAB acts
as a computation engine. For example, you can:
• Use MATLAB as a programmable mathematical subroutine library.
• Build an application with a front end (GUI) programmed in C and a back
end (analysis) programmed in MATLAB.
Call C and Fortran Programs from MATLAB
Use MEX-files to call your own C or Fortran subroutines from MATLAB as if
they were built-in functions. For example, you can:
• Call preexisting C and Fortran programs from MATLAB without having
to rewrite them as M-files.
• Code bottleneck computations that do not run fast enough in MATLAB in
C or Fortran for efficiency.
The mxArray access library creates and manipulates MATLAB arrays. The
mex library performs operations in the MATLAB environment.
8-2
Programming Interfaces
Call Java from MATLAB
MATLAB includes a Java Virtual Machine (JVM). This allows you to use the
Java interpreter with MATLAB commands and to create and access Java
objects. For example, you can:
• Access Java API class packages that support I/O and networking.
• Access third-party Java classes.
• Construct Java objects in MATLAB.
• Call Java methods, using either Java or MATLAB syntax.
• Pass data between MATLAB variables and Java objects.
Call Functions in Shared Libraries
Use the MATLAB interface to generic DLLs to interact with functions in a
dynamic link library (.dll) on Windows, a shared object file (.so) on UNIX
and Linux, or a dynamic shared library (.dylib) on Intel-based Macintosh
platforms.
MATLAB supports any shared library written in C, or in any language that
can provide a C interface.
Import and Export Data
MAT-files and the MAT-file access library provide a convenient mechanism
for moving MATLAB binary data between platforms, and for importing and
exporting data to stand-alone MATLAB applications.
8-3
8
External Interfaces
Component Object Model Interface
With Component Object Model (COM) tools and technologies, you can
integrate application-specific components from different vendors into your
own applications. With COM, MATLAB can include ActiveX controls or OLE
server processes, or you can configure MATLAB as a computational server
controlled by your client application programs.
For example, you can:
• Include ActiveX components, like a calendar, in your MATLAB program.
• Access existing applications that expose objects via Automation, like
Microsoft Excel.
• Access MATLAB as an Automation server from an application written
in Visual Basic or C.
COM support in MATLAB is only available on the Microsoft Windows
platform.
8-4
Web Services
Web Services
Web services are XML-based technologies for making remote procedure calls
over a network. They enable communication between applications running
on disparate operating systems and development platforms. Web service
technologies available in MATLAB are:
• Simple Object Access Protocol (SOAP)
• Web Services Description Language (WSDL)
8-5
8
External Interfaces
Serial Port Interface
The MATLAB serial port interface provides direct access to peripheral devices
that you connect to your computer’s serial port, such as modems, printers, and
scientific instruments. For example, you can:
• Configure serial port communications.
• Use serial port control pins.
• Write and read data.
• Use events and callbacks.
• Record information to disk.
8-6
Index
: operator 2-8
B
2-D scatter
getting
3-D scatter
getting
bit map 3-70
break function 4-7
built-in functions
defined 2-13
Index
plots
started 5-14
plots
started 5-16
A
C
algorithms
vectorizing 4-31
annotating plots 3-17
ans function 2-5
application program interface (API) 1-4
Array Editor 7-18
array operators 2-24
arrays
and matrices 2-24
cell 4-11
character 4-13
columnwise organization 2-26
creating in M-files 2-17
deleting rows and columns 2-19
elements 2-12
generating with functions and operators 2-16
listing contents 2-11
loading from external data files 2-17
multidimensional 4-9
notation for elements 2-12
preallocating 4-32
structure 4-16
variable names 2-11
arrow keys for editing commands 2-32
aspect ratio of axes 3-58
axes
managing 3-58
visibility 3-59
axis
labels 3-59
titles 3-59
axis function 3-58
callbacks 6-6
case function 4-4
catch function 4-7
cell arrays 4-11
char function 4-15
character arrays 4-13
characteristic polynomial 2-23
coefficient of determination 5-16
colon operator 2-8
colormap 3-65
colors
lines for plotting 3-51
Command History 7-7
command line
editing 2-32
Command Window 7-6
complex numbers
plotting 3-53
concatenation
defined 2-18
of strings 4-14
constants
special 2-13
continue function 4-6
continuing statements on multiple lines 2-32
control keys for editing commands 2-32
correlation coefficient 5-16
covariance 5-15
current directory 7-14
Current Directory browser 7-14
Index-1
Index
D
data analysis
getting started 5-1
data source
for graphs 3-32
debugging M-files 7-20
deleting array elements 2-19
demos
running from the Start button 7-4
desktop for MATLAB 1-7
desktop tools 7-1
determinant of matrix 2-21
diag function 2-5
distribution modeling
getting started 5-11
documentation 7-8
E
editing command lines 2-32
Editor/Debugger 7-20
eigenvalue 2-22
eigenvector 2-22
elements of arrays 2-12
entering matrices 2-4
eval function 4-28
executing MATLAB 1-7
exiting MATLAB 1-8
exporting graphs 3-46
expressions
evaluating 4-28
examples 2-14
using in MATLAB 2-11
F
figure function 3-55
figure tools 3-6
figure windows 3-55
with multiple plots 3-56
Index-2
figures
adding and removing graphs 3-4
filtering data
getting started 5-6
find function 2-28
finding object handles 3-81
fliplr function 2-7
floating-point numbers 2-12
flow control 4-2
for loop 4-5
format
of output display 2-30
format function 2-30
function functions 4-29
function handles
defined 4-28
using 4-30
function keyword 4-23
function M-files 4-20
naming 4-22
function of two variables 3-63
functions
built-in, defined 2-13
defined 4-22
how to find 2-13
running 7-6
variable number of arguments 4-23
G
global variables 4-26
graphical user interface
creating 6-1
laying out 6-3
programming 6-6
graphics
files 3-72
Handle Graphics 3-74
objects 3-75
printing 3-71
Index
grids 3-59
GUIDE 6-1
H
Handle Graphics 3-74
defined 1-4
finding handles 3-81
Help browser 7-8
help functions 7-11
hold function 3-54
I
if function 4-2
images 3-69
imaginary numbers 2-12
K
keys for editing in Command Window 2-32
L
legend
adding to plot 3-50
legend function 3-50
library
mathematical function 1-3
lighting 3-66
limits
axes 3-58
line continuation 2-32
line styles of plots 3-51
linear regression
getting started 5-20
load function 2-17
loading arrays 2-17
local variables 4-23
log of functions used 7-7
logical vectors 2-27
M
M-files
and toolboxes 1-3
creating 4-20
editing 7-20
for creating arrays 2-17
function 4-20
script 4-20
magic function 2-9
magic square 2-5
markers 3-52
MAT-file 3-69
mathematical function library 1-3
mathematical functions
listing advanced 2-13
listing elementary 2-13
listing matrix 2-13
MATLAB
application program interface 1-4
desktop 1-7
executing 1-7
exiting 1-8
history 1-2
language 1-3
mathematical function library 1-3
overview 1-2
quitting 1-8
running 1-7
shutting down 1-8
starting 1-7
user newsgroup 7-11
matrices 2-20
creating 2-16
entering 2-4
matrix 2-2
antidiagonal 2-7
determinant 2-21
main diagonal 2-6
multiplication 2-21
singular 2-21
Index-3
Index
swapping columns 2-10
symmetric 2-20
transpose 2-5
measures of location
getting started 5-10
measures of scale
getting started 5-11
mesh plot 3-63
Microsoft Word and access to MATLAB 7-28
missing data
getting started 5-4
modeling data
getting started 5-19
multidimensional arrays 4-9
multiple data sets
plotting 3-50
multiple plots per figure 3-56
multivariate data
organizing 2-26
N
newsgroup for MATLAB users 7-11
Notebook 7-28
numbers 2-12
floating-point 2-12
O
object properties 3-77
objects
finding handles 3-81
graphics 3-75
online help
viewing 7-8
operators 2-12
colon 2-8
outliers
getting started 5-4
output
Index-4
controlling format 2-30
suppressing 2-31
overlaying plots 3-54
P
path 7-15
periodogram 5-22
plot edit mode
description 3-17
plot function 3-49
plots
editing 3-17
plotting
adding legend 3-50
adding plots 3-54
basic 3-49
complex data 3-53
complex numbers 3-53
contours 3-54
editing 3-17
functions 3-49
line colors 3-51
line styles 3-51
lines and markers 3-52
mesh and surface 3-63
multiple data sets 3-50
multiple plots 3-56
overview 3-2
tools 3-9
polynomial regression
getting started 5-19
PostScript 3-72
preallocation 4-32
preprocessing data
getting started 5-3
presentation graphics 3-37
principal components 5-17
print function 3-71
print preview
Index
using 3-42
printing
example 3-42
graphics 3-71
Profiler 7-26
Property Editor
interface 3-22
Property Inspector 3-19
using 3-19
Q
quitting MATLAB 1-8
R
return function 4-8
revision control systems
interfacing to MATLAB 7-28
running functions 7-6
running MATLAB 1-7
S
scalar expansion 2-27
scatter plot arrays
getting started 5-18
scientific notation 2-12
script M-files 4-20
scripts 4-21
search path 7-15
semicolon to suppress output 2-31
shutting down MATLAB 1-8
singular matrix 2-21
smoothing data
getting started 5-6
source control systems
interfacing to MATLAB 7-28
special constants
infinity 2-14
not-a-number 2-14
specialized graphs 3-55
Start button 7-4
starting MATLAB 1-7
statements
continuing on multiple lines 2-32
executing 4-28
strings
concatenating 4-14
structures 4-16
subplot function 3-56
subscripting
with logical vectors 2-27
subscripts 2-7
sum function 2-5
summarizing data
getting started 5-10
suppressing output 2-31
surface plot 3-63
switch function 4-4
symmetric matrix 2-20
T
text
entering in MATLAB 4-13
TIFF 3-72
title
figure 3-59
toolboxes 1-3
tools in the desktop 7-1
transpose function 2-5
try function 4-7
V
variables 2-11
global 4-26
local 4-23
vectorization 4-31
vectors 2-2
Index-5
Index
logical 2-27
preallocating 4-32
version control systems
interfacing to MATLAB 7-28
visibility of axes 3-59
visualizing data
getting started 5-14
W
while loop 4-5
Index-6
windows for plotting 3-55
windows in MATLAB 1-7
wireframe
surface 3-63
Word and access to MATLAB 7-28
word processing access to MATLAB 7-28
workspace 7-17
Workspace browser 7-17
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