matlab tutorial slides

Josh Xiaomin Xi PhD Candidate Feb 27, 2013 A tutorial from...  MATLAB: MATrix and LABoratory  First developed by Dr.. INFORMS OSU Josh Xiaomin XiIntro: Installation  Go to: http://oci

Josh Xiaomin

Xi

PhD Candidate

Feb 27, 2013

A tutorial from

INFORMS OSU Josh Xiaomin Xi

Overview

 Introduction

 Installation (Toolboxes)

 Layout of Matlab Windows

 Basics of Matlab language

 Arithmetic Operations

 Variables

 Matrix

 Plot

 Functions: inline and sym

 Programming in Matlab

 m-file

 Optimization in Matlab

 MATLAB: MATrix and LABoratory

 First developed by Dr Cleve Molder: Fortran based

 In 1984, MathWorks was founded: C based

INFORMS OSU Josh Xiaomin Xi

Intro: Installation

 Go to: http://ocio.osu.edu/software/directory/slwin/

Intro: Installation

 Select the tool boxes that you need

 e.g Matlab, curve fitting, optimization, statistics, symbolic math, etc

INFORMS OSU Josh Xiaomin Xi

Intro: Matlab Windows

Layout

 Command Window

 Command History

 Current Directory Browser

 Workspace Browser

 Introduction

 Installation (Toolboxes)

 Layout of Matlab Windows

 Basics of Matlab language

 Arithmetic Operation

 Variables

 Matrix

 Plot

 Functions: inline and sym

 Programming in Matlab

 m-file

INFORMS OSU Josh Xiaomin Xi

Basics: Arithmetic

Operations

＋ plus

－ minus

* multiply / right divide

\ left divide

^ exponential

2+3=5 2-3= -1 2*3=6 2/3=0.6667 2\3=1.5000 2^3=8

Basics: Variables

 How to define a variable name

 Numbers and letter, but first component must be a letter

 Case sensitive

 No space, punctuations (except underline)

 Special variables

 ans

 NaN, nan

 Inf, -Inf

 pi

 i, j

 realmax, realmin

 However, you can redefine these variables, and use “clear”

to clear redefinition.

INFORMS OSU Josh Xiaomin Xi

Basics: Matrix

 How to define a matrix/vector

 A = [1 2 3 4; 4 5 6 7] ~~ [1:4; 4:7] (!!! Comma, colon, semicolon bracket)

 Special matrix

 zeros(m,n)

 ones(m,n)

 diag(vec)

 Matrix operation

 Basic arithmetic operation (!!! Period & dimensions)

 Inverse (inv) and transpose (apostrophe)

 Read/change matrix component (!!! parenthesis)

 Stacking and breaking

 Size(), length(), eig()

Basics: Plot

 An example of attenuation oscillation curve:

t=0:pi/50:4*pi;

y=exp(-t/3).*sin(3*t);

plot(t,y,'-r')

grid

/ sin ,

t

y e = − t t ∈ [ , 0 4 π ]

 Use “help” to find more info of plot, e.g linespec, legend, title, xlabel

loglog log plot, taking log on both x & y

semilogx log plot, taking log only on x

semilogy log plot, taking log only on y

mesh 3-d plot

bar bar chart

Subplot one figure with sub figures

 Other

INFORMS OSU Josh Xiaomin Xi

Basics: Functions

 Use “sym” / “syms”

 Use “inline”

2

3 sin( 2 )

f = x − y

syms x y;

f=3*sin(2*x^2-y)

Df=diff(f) Df2=diff(f,2) subs(f,x,4)

fin=inline(char(f)) fin(1,1)

f=inline(‘3*sin(2*x^2-y)’)

f=inline(‘3*sin(2*x^2-y)’,’x’,’y’)

f(1,1)

 Introduction

 Installation (Toolboxes)

 Layout of Matlab Windows

 Basics of Matlab language

 Arithmetic Operation

 Variables

 Matrix

 Plot

 Functions

 Programming in Matlab

 m-file: run large program, build large function

 Control flow: if-else, while, for

INFORMS OSU Josh Xiaomin Xi

M File

 Replace command window when running large code

 Easy management

 Can be reused in future

 Define functions / sub-sections

 Better structure

 Good for complicated programming/logic

Control Flow

 If-Else If condition

expression(s) 1;

else expression(s) 2;

end

If condition1 expression(s) 1;

else if condition2 expression(s) 2;

else expression(s) 3;

end













≥

<

<

≤

<

≤

=

2 40

2 1

30

1 0

20

0 10

t t t

t F

If t >= 2

F = 40;

else if t > 1

F = 30;

else if t > 0

F = 20;

else

F = 10;

end

INFORMS OSU Josh Xiaomin Xi

Control Flow

 For / while

for i=1:5;

for j=1:3 x(i , j)= i * j;

end end

x =

1 2 3

2 4 6

3 6 9

4 8 12

5 10 15

n=1;

while prod ( 1 : n ) < 100;

n=n+1;

end

n

Because 5x4x3x2x1=120

Optimization In Matlab

 Common optimization functions

 linprog: linear programming

 Quadprog: quadratic programming

 fmincon: constrained non-linear minimization

 fminsearch, fminunc: unconstrained nonlinear minimization

 fsolve: non-linear system of equations solve

 lsqlin: linear least square with linear constraints

INFORMS OSU Josh Xiaomin Xi

Optimization: linprog

 linprog: linear programming

http://www.mathworks.com/help/optim/ug/linprog.html

Min f(x) = –5x1 –4x2 –6x3 s.t x1 – x2 + x3 ≤ 20

3x1 + 2x2 + 4x3 ≤ 42 3x1 + 2x2 ≤ 30

0 ≤ x1, 0 ≤ x2, 0 ≤ x3