MATLAB

An Introduction to MATLAB (Matrix Laboratory)

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MATLAB Windows

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Command WindowCurrent Directory

Command HistoryWorkspace Window

Command WindowCurrent Directory

Command HistoryWorkspace Window

MATLAB Windows

• Command Window– Heart of MATLAB– Access most commands and functions

• Workspace window– Shows created variables during present session– Variables remain only for present session

• Current Directory Window– Contains options for locating, opening, editing, and saving files

• Command History Window– Keeps a history of commands used and executed in the Command

Window– Does not show results of your commands

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Document Window(Double-click on any Variable in the Workspace window

automatically launches a document window)

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Document Window

Figure WindowWhen Figures are created a new window opens

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Edit Window

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Save and Run

Order of Operation

1. Exponentiation2. Multiplication / division3. Parentheses first4. Addition / subtraction

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5*(3+6) = 45

5*3+6 = 21

White space does not matter!!!

5 * 3+6 = 21

Parentheses

• Use only ( )• { } and [ ] mean something different • MATLAB does not assume operators

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5 * (3+4) not 5(3+4)

5*6/6*5 = 25

5*6/(6*5) = 1

Basic Math Functions

• Built into MATLAB– Addition (+)– Subtraction (-)– Multiplication (*)– Division (/)– Exponentiation (^)

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Saving a MATLAB SessionOnly values of the variables are saved in the workspace Window

(Caution: Do not program in the Command Window.Program in the Editor Window)

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Variables are saved, not the work space

Saving a MATLAB Session(Caution: Use Editor Window to program.)

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Save either by using the file menu or...

Save with a command in the command window

Saving a Program as a M-file

1. Save your work by creating an m-file2. File->New->m-file 3. Type your commands in the edit window that

opens4. Save as XXX.m 5. The file is saved into the current directory6. It runs in the command window

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Comments (%)

• Be sure to comment your code– Add your name– Date– Section #– Assignment #– Descriptions of what you are doing and why

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Comments (%)

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The % sign identifies comments

You need one on each line

Elementary Math Functions

• abs(x) absolute value• sign(x) plus or minus• exp(x) ex

• log(x) natural log• log10(x) log base 10

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Rounding Functions

• round(x)• fix(x)• floor(x)• ceil(x)

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Rounding Functions

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Discrete Mathematics

• factor(x)• gcd(x,y) greatest common

denominator

• lcm(x) lowest common multiple

• rats(x) represent x as a fraction

• factorial(x)• primes(x)• isprime(x)

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Trigonometric Functions

• sin(x) sine• cos(x) cosine• tan(x) tangent• asin(x) inverse sine• sinh(x) hyperbolic sine• asinh(x) inverse hyperbolic

sine• sind(x) sine with degree input• asind(x) inverse sin with

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Data Analysis

• max(x)• min(x)• mean(x)• median(x)• sum(x)• prod(x)• sort(x)

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Data Analysis

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When x is a matrix, the max is found for each column

Data Analysis

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max value

element number where the max value occurs

Data Analysis

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Vector of row numbers

Vector of maximums

Data Analysis

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Determining Matrix Size

• size(x) number of rows and columns• length(x) biggest dimension

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Determining Matrix Size

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Variance and Standard Deviation

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• std(x)

• var(x)

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N

xN

kk

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Random Numbers

• rand(x)– Returns an x by x matrix of random numbers

between 0 and 1

• rand(n,m)– Returns an n by m matrix of random numbers

• These random numbers are evenly distributed

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Random Numbers

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Matrices

• Group of numbers arranged into rows and columns

• Single Value (Scalar)– Matrix with one row and one column

• Vector (One dimensional matrix)– One row or one column

• Matrix (Two dimensional)

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Scalar Calculations

• You can use MATLAB like you’d use a calculator

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>> 9 + 10

Ans=19

Command Prompt

Result

Scalar Calculations

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Variables

• MATLAB allows you to assign a value to a variable• A=3• Should be read as A is assigned a value of 3• Use the variables in subsequent calculations

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Predefined MATLAB Functions

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• Functions consist of– Name– Input argument(s)– Output

Sqrt (x) = resultsSqrt (4) = 2

Functions accept either scalar or matrix input

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X=1:10 is one row matrix 1 to 10

d - Matrix

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Array Operations

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To create a row vector, enclose a list of values in brackets

Array Operations

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You may use either a space or a comma as a “delimiter” in a row vector

Array Operations

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Use a semicolon as a delimiter to create a new row

Array Operations

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Use a semicolon as a delimiter to create a new row

Array Operations

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Hint: It’s easier to keep track of how many values you’ve entered into a matrix, if you enter each row on a separate line. The semicolons are optional

Array Operations

• While a complicated matrix might have to be entered by hand, evenly spaced matrices can be entered much more readily. The command

b= 1:5 or the command

b = [1:5] both return a row matrix

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Array Operations

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The default increment is 1, but if you want to use a different increment put it between the first and final values

Array Operations

• Array multiplication .*• Array division ./• Array exponentiation .^

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In each case the size of the arrays must match

Array OperationsRepetitive Calculations

• assume you have a list of angles in degrees that you would like to convert to radians.

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Array OperationsRepetitive Calculations

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Either the * or the .* operator can be used for this problem, because it is composed of scalars and a single matrix

The value of pi is built into MATLAB as a floating point number, called pi

Array Operations Transpose Operator

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The transpose operator makes it easy to create tables

Array Operations Transpose Operator

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table =[degrees;radians]’ would have given the same result

Array Operations Transpose Operator

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The transpose operator works on both one dimensional and two dimensional arrays

Number Display

• Scientific Notation– Although you can enter any number in

decimal notation, it isn’t always the best way to represent very large or very small numbers

– In MATLAB, values in scientific notation are designated with an e between the decimal number and exponent. (Your calculator probably uses similar notation.)

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Number Display

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It is important to omit blanks between the decimal number and the exponent. For example, MATLAB will interpret

6.022 e23as two values (6.022 and 1023 )

To calculate spacing between elements use linspace and logspace

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Initial value in the array

Final value in the array

number of elements in the array

logspace

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Initial value in the array expressed as a power of 10

Final value in the array expressed as a power of 10

number of elements in the array

e =

10 100 1000

Manipulating MATLAB Matrices

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