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Lecture 3

# ENG 06 – Lecture 3 notes

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University of California - Davis

Engineering

ENG 6

A H M E D R A W Y

Spring

Description

ENG 06 – Lecture #3; 1/15/2013
Arrays
Very important; “the backbone” of MATLAB
Arrays and Matrices
Matrix: a grid/array of numbers, w/ rows and columns
Refers to number of rows, then number of columns
o Ex. 2x4 array has 2 rows and 4 columns
Arrays: Vectors (1D Matrix)
o Only 1 row or 1 column
o Row vector: enclose a list of elements in square brackets
Ex. x = [1 5 8 9]
Gives a 1 row and 4 columns
o Column vector: tell MATLAB to skip to next row using semicolon
Ex. y = [1;5;8;9]
Gives a 4 row, 1 column array
Matrix
o Z = [1 2 3;4 5 6]
o 2x3 matrix (2 rows by 3 columns)
Transpose (perform operation using apostrophe ‘ )
o Switches rows and columns
st st nd nd
o 1 row becomes 1 column, 2 row becomes 2 column, etc.
o diagonal does not change for square matrices
Ways to Create Arrays
Generating Arrays: Colon
o Use colon to create a vector x:y “from x to y”
Ex. a = 1:1000
o By default, colon uses steps of 1
o Add a number in the middle, x:z:y, to go from x to y with step size z
o Ex. a = 1:0.1:1000 gives a vector containing [1 1.1 1.2…999.8 999.9 1000]
Generating Arrays: Linspace/Logspace
o Linspace operator: spaces points evenly between a start number and end
number
Variable = linspace(start,stop,# of points)
Ex. c = linspace(5,22,200)
o Logspace operator: spaces points logarithmically between a start and end
number
o Both operators determine step size for you
Variable = logspace(start,stop,# of points)
Generating Arrays from Other Arrays
o Other vertices/matrices can be included in brackets when creating an array
o Ex. c = [1 2 3]; a = [c;c]
o Creates matrix with 2 rows and 3 columns, each row is vector c o Concatenation (linking matrices) works as long as dimensions are
compatible
Generating Arrays: Ones, Zeros, Eyes
o ones(n) gives nxn matrix with 1s as entries
o ones(n,m) gives nxm matrix with 1s as entries
o zeros(n) gives nxn matrix with 0s as entries
o zeros(nxm) gives nxm matrix with 0s as entries
o eye(n) gives nxn identity matrix
o eye(nxm) gives nxm matrix with a diagonal of 1s starting in the first row and
ending at the last row; remaining columns have 0s
Generating Arrays: rand
o rand(n) returns n x n matrix with pseudorandom values in the interval (0,1)
o rand(n,m) gives n x m matrix
o to create random matrix with integers between 0 and 10:
>>ceil(10*rand(3,3))
creates a 3x3 matrix with random values that are multiplied by 10
then rounded towards infinity (ceil function)
Using Array Editor to See and Access Values
o Double click on variable that defines your vector/matrix in workspace
o Brings up a spreadsheet with values
o Use wi

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