MATLAB An Introduction to MATLAB (Matrix Laboratory) 1

MATLAB Windows 2

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 3

Document Window (Double-click on any Variable in the Workspace window automatically launches a document window ) 4 Document Window

Figure Window When Figures are created a new window opens 5

Edit Window 6 Save and Run

Order of Operation 1.Exponentiation 2.Multiplication / division 3.Parentheses first 4.Addition / subtraction 7

Parentheses Use only ( ) { } and [ ] mean something different MATLAB does not assume operators 8 5 * (3+4) not 5(3+4)

Basic Math Functions Built into MATLAB – Addition (+) – Subtraction (-) – Multiplication (*) – Division (/) – Exponentiation (^) 9

Saving a MATLAB Session Only values of the variables are saved in the workspace Window ( Caution: Do not program in the Command Window. Program in the Editor Window) 10

Saving a MATLAB Session ( Caution: Use Editor Window to program.) 11

Saving a Program as a M-file 1.Save your work by creating an m-file 2.File->New->m-file 3.Type your commands in the edit window that opens 4.Save as XXX.m 5.The file is saved into the current directory 6.It runs in the command window 12

Comments (%) Be sure to comment your code – Add your name – Date – Section # – Assignment # – Descriptions of what you are doing and why 13

Comments (%) 14

Elementary Math Functions abs(x)absolute value sign(x)plus or minus exp(x)e x log(x) natural log log10(x)log base 10 15

Rounding Functions round(x) fix(x) floor(x) ceil(x) 16

Rounding Functions 17

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) 18

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 degree output 19

Data Analysis max(x) min(x) mean(x) median(x) sum(x) prod(x) sort(x) 20

Data Analysis 21 When x is a matrix, the max is found for each column

Data Analysis 22

Data Analysis 23

Data Analysis 24

Determining Matrix Size size(x)number of rows and columns length(x) biggest dimension 25

Determining Matrix Size 26

Variance and Standard Deviation 27

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 28

Random Numbers 29

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) 30

Scalar Calculations You can use MATLAB like you’d use a calculator 31

Scalar Calculations 32

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 33

Predefined MATLAB Functions 34 Functions consist of – Name – Input argument(s) – Output Sqrt (x) = results Sqrt (4) = 2

Functions accept either scalar or matrix input 35 X=1:10 is one row matrix 1 to 10

d - Matrix 36

Array Operations 37 To create a row vector, enclose a list of values in brackets

Array Operations 38 You may use either a space or a comma as a “delimiter” in a row vector

Array Operations 39 Use a semicolon as a delimiter to create a new row

Array Operations 40 Use a semicolon as a delimiter to create a new row

Array Operations 41 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 42

Array Operations 43 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.^ 44 In each case the size of the arrays must match

Array Operations Repetitive Calculations assume you have a list of angles in degrees that you would like to convert to radians. 45

Array Operations Repetitive Calculations 46

Array Operations Transpose Operator 47

Array Operations Transpose Operator 48

Array Operations Transpose Operator 49

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.) 50

Number Display 51

To calculate spacing between elements use linspace and logspace 52

logspace 53 e =

Manipulating MATLAB Matrices 54

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