MATLAB

1
MATLAB

• COMM2M
• Harry R. Erwin, PhD
• University of Sunderland

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Resources

• Higham and Higham, 2000, MATLAB Guide, SIAM.
• http//www.utexas.edu/math/Matlab/Manual/faq.html
  source of the history presented here.

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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.

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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.

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LAPACK

• A high performance matrix processing library,
  commonly used in computational science.
• A descendent of LINPACK
• Currently integrated with MATLAB.

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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.

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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.

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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.

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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.

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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.

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Character Set

• ASCII Character Set
• The following are used as operators
• ! ( ) , / lt lt gt gt _at_ ..
  \ gtgt
• . . ./ .\ .

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Comments

• A line beginning with

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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

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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

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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 !

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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

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Matrices and Arrays

• A(i,j,k) accesses that entry in the matrix A
• More next week

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Operators 1

• ! System command
• Conjugate transpose, string delimiter
• Quote
• ( ) Used in matrix subscripting
• , Separates commands
• Continuation
• / Right division
• Colon
• Terminates a command without output

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Operators 2

• lt Less than
• lt Less than or equal
• Logical equal
• gt Greater than
• gt Greater than or equal
• _at_ Function handle
• .. Matrix building
• Empty matrix
• Comment
• Logical and

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Operators 3

• \ Left division
• Power
• Logical or
• gtgt Prompt
• Logical not
• Logical not equal
• Multiplication
• Addition
• - Subtraction

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Array Operators

• . Transpose
• . Array multiplication
• ./ Array right division
• .\ Array left division
• . Array exponentiation
• inv(A) Inverse

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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.

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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

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Functions

• MATLAB has thousands of functions, and you can
  add your own using m-files.

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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

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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)

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Storage Allocation

• Automatic, as necessary, and with garbage
  collection (notorious for memory leaks).
• Array dimensions are expanded automatically as
  needed to make assignments sensible.

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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
  root-locus, pole-placement, and LQR optimal
  control are also included.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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Spline Toolbox

• This is a toolbox for working with splines and
  is typically used for curve fitting, solution of
  function equations, and functional approximation.

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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.

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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.

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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).

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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.

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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).

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Hi-SpecToolbox

• 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

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Tutorial Exercises

• Work through the brief tutorial if you have the
  text.