Intro to Matlab

1. Using scalar variables

2. Vectors, matrices, and arithmetic

3. Plotting

4. Solving Systems of Equations

Can be found at: http://www.cs.unc.edu/~kim/matlab.ppt

New Class--for Engineers

• ENGR196.3

• SPECIAL TOPICS: INTRODUCTION TO MATLAB

• Description: Fundamentals of MATLAB programming applied to problems in science and mathematics. Solving systems of equations, basic scripting, functions, vectors, data files, and graphics. (Credit course for grade or CR/NC)

Why use Matlab?

• Drawbacks:

Slow (execution) compared to C or Java

• Advantages:

Handles vector and matrices very nice

Quick plotting and analysis

EXTENSIVE documentation (type ‘help’)

Lots of nice functions: FFT, fuzzy logic, neural nets, numerical integration, OpenGL (!?)

One of the major tools accelerating tech change

A tour of Matlab’s features• Click on Help>Full Product Family Help:

Check out Fuzzy Logic

Genetic Algorithms

Symbolic Math

Scalars

• The First Time You Bring Up MATLAB

• MATLAB as a Calculator for Scalars

• Fetching and Setting Scalar Variables

• MATLAB Built-in Functions, Operators, and Expressions

• Problem Sets for Scalars

3-1 The First Time You Bring Up MATLAB

Basic windows in MATLAB are:• Command - executes single-line commands• Workspace - keeps track of all defined variables• Command History - keeps a running record of all single

line programs you have executed• Current Folder - lists all files that are directly available for

MATLAB use• Array Editor - allows direct editing of MATLAB arrays• Preferences - for setting preferences for the display of

results, fonts used, and many other aspects of how MATLAB looks to you

3-2 MATLAB as a Calculator for Scalars

• A scalar is simply a number…

• In science the term scalar is used as opposed to a vector, i.e. a magnitude having no direction.

• In MATLAB, scalar is used as opposed to arrays, i.e. a single number.

• Since we have not covered arrays (tables of numbers) yet, we will be dealing with scalars in MATLAB.

,4,7

22,5.3

3-3 Fetching and Setting Scalar Variables

• Think of computer variables as named containers.

• We can perform 2 types of operations on variables:

we can set the value held in the container: x = 22we can set the value held in the container: x = 22

we can look at the value held in the container: xwe can look at the value held in the container: x

The Assignment Operator (=)

• The equal sign is the assignment operator in MATLAB.

>> x = 22places number 22 in container x

• How about:>> x = x + 1

• Note the difference between the equal sign in mathematics and the assignment operator in MATLAB!

Useful Constants

• Inf infinity• NaN Not a number (div by zero)• eps machine epsilon• ans most recent unassigned answer• pi 3.14159….• i and j Matlab supports imaginary

numbers!

Using the Command History Window

3-4 MATLAB Built-in Functions, Operators, and Expressions

• MATLAB comes with a large number of built-in functions (e.g.. sin, cos, tan, log10, log, exp)

• A special subclass of often-used MATLAB functions is called operators– Assignment operator (=)– Arithmetic operators (+, -, *, /, ^)– Relational operators (<, <=, = =, ~=, >=, >)– Logical operators (&, |, ~)

Example – Arithmetic Operators

Hint: the function exp(x) gives e raised to a power x

Example – Relational and Logical Operators

Vector Operations

Chapter 5

Vector Operations

• Vector Creation

• Accessing Vector Elements

• Row Vectors and Column Vectors, and the Transpose Operator

• Vector Built-in Functions, Operators, and Expressions

Vectors and Matrices• Can be to command line or from *.m file

scalar: x = 3vector: x = [1 0 0]2D matrix: x = [1 0 0; 0 1 0; 0 0 1]arbitrarily higher dimensions (don’t use much)

• Can also use matrices / vectors as elements:

x = [1 2 3]

y = [ x 4 5 6]

2-D Plotting and Help in MATLAB

Chapter 6

2-D Plotting and Help in MATLAB

• Using Vectors to Plot Numerical Data

• Other 2-D plot types in MATLAB

• Problem Sets for 2-D Plotting

6-2 Using Vectors to Plot Numerical Data• Mostly from observed data - your goal is to

understand the relationship between the variables of a system.

• Determine the independent and dependent variables and plot:

speed = 20:10:70;stopDis = [46,75,128,201,292,385];plot(speed, stopDis, '-ro') % note the ‘-ro’ switch

• Don’t forget to properly label your graphs:title('Stopping Distance versus Vehicle Speed', 'FontSize', 14)xlabel('vehicle speed (mi/hr)', 'FontSize', 12)ylabel('stopping distance (ft)', 'FontSize', 12)grid on

Speed (mi/hr) 20 30 40 50 60 70

Stopping Distance (ft) 46 75 128 201 292 385

Sample Problem – Plotting Numerical Data

3D Plotting• 3D plots – plot an outer product

x = 1:10y = 1:10z = x’ * ymesh(x,y,z)

Single quote ‘ means transpose (can’t cut and paste though…)

Flow Constructs

• IF block

if (<condition>)

<body>

elseif

<body>

end

• WHILE block

while (<condition>)

<body>

end

Conditions same as C, ( ==, >=, <=) except != is ~=

More Flow Constructs

• FOR block

for i = 1:10

<body>

end

• SWITCH statement

switch <expression>

case <condition>,

<statement>

otherwise <condition>,

<statement>

end

Other Language Features

• Matlab language is pretty sophisticated– Functions

Stored in a *.m file of the same name:

function <return variable> = <function name>(<args>)

<function body>

– Structs• point.x = 2; point.y = 3; point.z = 4;

– Even has try and catch (never used them)

Solving Systems of Equations

• Consider a system of simultaneous equations

3x + 4y + 5z = 32

21x + 5y + 2z = 20

x – 2y + 10z = 120

• A solution is a value of x, y, and z that satisfies all 3 equations

• In general, these 3 equations could have

1 solution, many solutions, or NO solutions

Using Matlab to Solve Simultaneous Equations

• Set up the equation in matrix/vector form:

A = [3 4 5; 21 5 2; 1 -2 10] u = [ x y z]’ b = [ 32 20 120]’In other words, A u = b (this is linear algebra)

3 4 5

21 5 2

1 -2 10

x

y

z

*

32

20

120

=

The solution uses matrix inverse

• If you multiply both sides by 1/A you get

u = 1/A * b

• In the case of matrices, order of operation is critical (WRONG: u = b/A )

• SO we have “Left division” u = A \ b

(recommended approach)

• OR use inv( ) function: u = inv(A) * b

The solution>> u = A\b

u =

1.4497 ( value of x)

-6.3249 ( value of y)

10.5901 ( value of z)

• You can plug these values in the original equation test = A * u and see if you get b

Caution with Systems of Eqs

• Sometimes, Matrix A does not have an inverse:

• This means the 3 equations are not really independent and there is no single solution (there may be an infinite # of solns)

• Take determinant det(A) if 0, it’s singular

1 -1 0

1 0 -1

0 1 -1

x

y

z

*

32

10

22

=