Transcript Matlab - University of Sunderland

MATLAB
COMM2M
Harry R. Erwin, PhD
University of Sunderland
Resources
• Higham and Higham, 2000, MATLAB
Guide, SIAM.
• http://www.utexas.edu/math/Matlab/Manual
/faq.html—source of the history presented
here.
MATLAB Introduction (FAQ)
• MATLAB was originally developed to be a
"matrix laboratory," written to provide easy
access to matrix software developed by the
LINPACK and EISPACK projects.
• Since then, the software has evolved into an
interactive system and programming
language for general scientific and technical
computation and visualization.
SIMULINK (FAQ)
• SIMULINK is an interactive system for the nonlinear
simulation of dynamic systems.
• A graphical, mouse-driven program that allows systems
to be modeled by drawing a block diagram on the
screen.
• It can handle linear, nonlinear, continuous-time,
discrete-time, multivariable, and multirate systems.
• SIMULINK runs on workstations using X-Windows.
• SIMULINK is fully integrated with MATLAB, and,
together with MATLAB and the Control System
Toolbox, forms a complete control system design and
analysis environment.
LAPACK
• A high performance matrix processing
library, commonly used in computational
science.
• A descendent of LINPACK
• Currently integrated with MATLAB.
MATLAB History (FAQ)
• In the mid-1970s, Cleve Moler and several
colleagues developed the FORTRAN subroutine
libraries called LINPACK and EISPACK under a
grant from the National Science Foundation.
• LINPACK was a collection of FORTRAN
subroutines for solving linear equations, while
EISPACK contained subroutines for solving
eigenvalue problems.
• Together, LINPACK and EISPACK represented
state of the art software for matrix computation.
Second Phase (FAQ)
• In the late 1970s, Moler, who was then chairman
of the computer science department at the
University of New Mexico, wanted to be able to
teach students in his linear algebra courses using
the LINPACK and EISPACK software.
• However, he didn't want them to have to program
in FORTRAN, because this wasn't the purpose of
the course.
• So, as a "hobby" on his own time, he started to
write a program that would provide simple
interactive access to LINPACK and EISPACK.
Emergence of MATLAB (FAQ)
• Moler named his program MATLAB, for MATrix
LABoratory.
• Over the next several years, when he would visit
another university to give a talk, or as a visiting
professor, he would end up by leaving a copy of
his MATLAB on the university machines.
• Within a year or two, MATLAB started to catch
on by word of mouth within the applied math
community as a "cult" phenomena.
Professional MATLAB
Development (FAQ)
• In early 1983, John Little was exposed to MATLAB
because of a visit Cleve made to Stanford.
• Little, an engineer, recognized the potential
application of MATLAB to engineering applications.
• So in 1983, Little teamed up with Moler and Steve
Bangert to develop a second generation, professional
version of MATLAB written in C and integrated with
graphics.
• The MathWorks, Inc. was founded in 1984 to market
and continue development of MATLAB.
Basic Features of MATLAB
(FAQ)
• MATLAB commands are expressed in a form very
similar to that used in mathematics and engineering.
– For instance, b = A x, where A, b, and x are matrices, is
written b = A * x .
– To solve for x in terms of A and b, write x = A\b
• There is no need to program matrix operations
explicitly like multiplication or inversion.
• Solving problems in MATLAB is much quicker than
programming in a high-level language such as C or
FORTRAN.
Character Set
• ASCII Character Set
• The following are used as operators:
– ! ‘ “ ( : ) , … / : ; < <= == > >= @ [..] [] % & \
^ | >> ~ ~=
– .’ .* ./ .\ .^
Comments
• A line beginning with %
Variable Names
•
•
•
•
•
•
•
•
Case sensitive
Up to 31 characters long
Begin with a letter
Followed by letters, digits, underscores
Variables are created when they are assigned.
pi, i, and j are predefined.
To list variables use who or whos (detailed)
clear or clear var clears out the workspace
Commands
•
•
•
•
•
•
•
•
Type exit or quit to quit MATLAB
Type foo to run foo.m
Terminate a command with ; to suppress output
A continuation line is shown with …
clc clears the command window
help foo displays the help for foo()
lookfor will search for a string in the help
^C to abort a command
More Commands
• To save the current workspace to
filename.mat: save filename
• To load: load filename
• To capture output: diary filename and
diary off or diary on
• To display a variable: disp var
• To interact with the operating system: !
Data Types
• Originally just complex matrices
• Now include
–
–
–
–
–
–
–
double
sparse (2-D only)
char
cell
struct
storage (specialized)
function handle
• The fundamental types are multi-dimensional arrays
Matrices and Arrays
• A(i,j,k) accesses that entry in the matrix A
• More next week
Operators 1
•
•
•
•
•
•
•
•
•
! System command
‘ Conjugate transpose, string delimiter
“ Quote
( : ) Used in matrix subscripting
, Separates commands
… Continuation
/ Right division
: Colon
; Terminates a command without output
Operators 2
•
•
•
•
•
•
•
•
•
•
< Less than
<= Less than or equal
== Logical equal
> Greater than
>= Greater than or equal
@ Function handle
[..] Matrix building
[] Empty matrix
% Comment
& Logical and
Operators 3
•
•
•
•
•
•
•
•
•
\ Left division
^ Power
| Logical or
>> Prompt
~ Logical not
~= Logical not equal
* Multiplication
+ Addition
- Subtraction
Array Operators
•
•
•
•
•
•
.’ Transpose
.* Array multiplication
./ Array right division
.\ Array left division
.^ Array exponentiation
inv(A) Inverse
IEEE Arithmetic
• All arithmetic is in accordance with the
double precision IEEE standard.
• 64 bits per number
• All computations are in floating point.
• You can get NaNs if the computations are
undefined.
Statements
• Multiple statements can appear on the same
line, separated by semicolons or commas.
• If a statement is terminated by a semicolon,
output is suppressed; otherwise it is printed.
• Output can be formatted with the format
command
Functions
• MATLAB has thousands of functions, and
you can add your own using m-files.
Function Argument Lists
• Input arguments are to the right of the function
name, within parentheses
• Output arguments are to the left of the function
name, within square brackets
– X = [3 4];
– norm(X)
ans = 5
– norm(X,1)
ans = 7
– [m,n] = size(A)
m=5
n=3
M-Files
• Sample file
%MARKS
Exmark = [12 0 5 28 87 3 56];
Exsort = sort(Exmark)
Exmean = mean(Exmark)
Exmed = median(Exmark)
Exstd = std(Exmark)
Storage Allocation
• Automatic, as necessary, and with garbage
collection (notorious for memory leaks).
• Array dimensions are expanded
automatically as needed to make
assignments sensible.
Control System Toolbox
• This is a toolbox for control system design
and analysis. It supports transfer function
and state-space forms (continuous/discrete
time, frequency domain), as well as
functions for step, impulse, and arbitrary
input responses. Functions for Bode,
Nyquist, Nichols plots, design with rootlocus, pole-placement, and LQR optimal
control are also included.
Image Processing Toolbox
• The Image Processing Toolbox builds on
MATLAB's numeric, signal processing, and
visualization capabilities to provide a
comprehensive system for image processing
and algorithm development.
• Heavily used here.
MMLE3 Identification Toolbox
• The MMLE3 Identification Toolbox is a
specialized toolbox for use with MATLAB
and the Control System Toolbox for the
estimation of continuous-time state-space
models from observed input-output data.
Model Predictive Control
Toolbox
• The Model Predictive Control Toolbox is
especially useful for applications involving
constraints on the manipulated and/or
controlled variables. For unconstrained
problems, model predictive control is
closely related to linear quadratic optimal
control, but includes modeling and tuning
options that simplify the design procedure.
Mu-Analysis and Synthesis
Toolbox
• The Mu-Analysis and Synthesis Toolbox
contains specialized tools for the analysis
and design of robust, linear control systems,
extending MATLAB to provide additional
application-specific capabilities.
Nonlinear Control Design
• This toolbox provides a Graphical User
Interface to assist in time-domain-based
control design. With this toolbox, you can
tune parameters within a nonlinear
SIMULINK model to meet time-domain
performance requirements. You can view
the progress of an optimization while it is
running. Optimization routines have been
taken from the Optimization Toolbox.
Neural Network Toolbox
• This is a toolbox for designing and
simulating neural networks and supports
implementation of the perceptron learning
rule, the Widrow-Hoff rule, and several
variations of the backpropagation rule.
Transfer functions included are hard limit,
linear, logistic, and hypertangent sigmoid.
• This will be the toolbox you use most here.
Optimization Toolbox
• This is a toolbox for linear and nonlinear
optimization. It supports unconstrained and
constrained minimization, minimax,
nonlinear least squares, multi-objective,
semi-infinite optimization, linear
programming, quadratic programming, and
the solution of nonlinear equations.
Robust Control Toolbox
• This is a toolbox for robust control system
design and supports LQG/loop transfer
recovery, H2, H0, and mu- control
synthesis, singular value frequency
response, and model reduction.
Signal Processing Toolbox
• This is a toolbox for digital signal processing
(time series analysis). It includes functions for the
design and analysis of digital filters, like
Butterworth, Elliptic, and Parks-McClellan, and
for FFT analysis (power spectrum estimation). It
also includes some two-dimensional signal
processing capabilities.
• Very popular in the acoustics field.
Spline Toolbox
• This is a toolbox for working with splines
and is typically used for curve fitting,
solution of function equations, and
functional approximation.
Statistics Toolbox
• The Statistics Toolbox builds on the
computational and graphics capabilities of
MATLAB to provide: 1) statistical data
analysis, modeling, and Monte Carlo
simulation 2) building blocks for creating
your own special-purpose statistical tools,
and 3) GUI tools for exploring fundamental
concepts in statistics and probability.
Symbolic Math Toolbox
• The Symbolic Math Toolbox contains
functions for symbolic algebra, exact linear
algebra, variable precision arithmetic,
equation solving, and special mathematical
functions. Its underlying computational
engine is the kernel of Maple. The Extended
Symbolic Math Toolbox augments the
functionality to include Maple
programming features and specialized
libraries.
System Identification Toolbox
• This is a toolbox for parametric modeling.
Identified models are in transfer function
form (either z transform or Laplace
transform) and state-space form (e.g.,
ARMA models or Box-Jenkins models).
Chemometrics Toolbox
• This toolbox contains a library of functions
that allows you to analyze data based on
chemometrics methods including multiple
linear regression, classical least squares,
inverse least squares, Q-matrix, factor based
methods, principle component regression,
and partial least squares in latent variables.
There are also useful functions for plotting
data.
Frequency Domain System
Identification Toolbox
• This toolbox contains tools for accurate
modeling of linear systems with or without
delay. The models are transfer functions in
s-domain or in z-domain. The procedures
include excitation signal design, data
preprocessing, parameter estimation,
graphical presentation of results, and model
validation (tests, uncertainty bounds,
modelling errors).
Hi-Spec™Toolbox
• The Hi-Spec [tm ] Toolbox, a Partner Series
Toolbox, was created by Jerry Mendel, C.L. (Max)
Nikias, and Ananthram Swami. The Hi-Spec
Toolbox is a collection of MATLAB routines
whose primary features are functions for:
– Higher-order spectrum estimation either by
conventional or parametric approaches
– Magnitude and phase retrieval
– Adaptive linear prediction
– Harmonic retrieval and quadratic phase coupling
– Time-delay estimation and array signal processing
Tutorial Exercises
• Work through the brief tutorial if you have
the text.