josh xiaomin xi phd candidate feb 27, 2013 a tutorial from

Josh Xiaomin XiJosh Xiaomin XiPhD CandidatePhD CandidateFeb 27, 2013Feb 27, 2013

A tutorial fromA tutorial from

INFORMS OSU Josh Xiaomin XiA Matlab Tutorial 2 / INF

OverviewOverview

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


IntroIntro

MATLAB: MATrix and LABoratory

First developed by Dr. Cleve Molder: Fortran based

In 1984, MathWorks was founded: C based


Intro: InstallationIntro: Installation

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


Intro: InstallationIntro: Installation

Select the tool boxes that you need

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


Intro: Matlab Windows LayoutIntro: Matlab Windows Layout

Command Window

Command History

Current Directory Browser

Workspace Browser


OverviewOverview

Introduction




Arithmetic Operation

Variables

Matrix

Plot

Functions: inline and sym


m-file


Basics: Arithmetic Basics: Arithmetic OperationsOperations

＋ 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: VariablesBasics: 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.


Basics: MatrixBasics: 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: PlotBasics: 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

3 3/ sin ,ty e t 0 4[ , ]t

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


Basics: FunctionsBasics: Functions

Use “sym” / “syms” Use “inline”

23 2sin( )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)


OverviewOverview

Introduction




Arithmetic Operation

Variables

Matrix

Plot

Functions


m-file: run large program, build large function

Control flow: if-else, while, for


M FileM 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 FlowControl Flow

If-ElseIf 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

240

2130

1020

010

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


Control FlowControl 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

Result: n ＝ 5 。

Because 5x4x3x2x1=120


Optimization In MatlabOptimization 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


Optimization: linprogOptimization: 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.

josh xiaomin xi phd candidate feb 27, 2013 a tutorial from

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