Matlab I An Initial Overview - George Mason Universitymath.gmu.edu/mtc_files/matlab.pdf · Matlab I An Initial Overview Patrick O’Neil Mathematics Testing Center George Mason University

Matlab IAn Initial Overview

Patrick O’Neil

Mathematics Testing CenterGeorge Mason University

April 1, 2016

Patrick O’Neil (GMU) Matlab I April 1, 2016 1 / 26

Introduction

Outline

1 Introduction

2 Data Structures

3 Control Flow

4 Custom Functions

5 Plotting


Introduction

What is Matlab?


Introduction

Variables

Variables can be easily assigned,

x = 3;

y = 4;

Basic arithmetic operations are also simple,

x+y

x*y

x/y

x^y


Introduction

Useful Commands

The following are useful commands,

clc % Clear command window

clear % Clear system memory

ans % Last result

whos % List currently defined data structures

length(x) % Length of vector x

size(A) % Size of array

save filename % save all variables

load filename % load variables

Notice how comments are written.


Data Structures

Outline

1 Introduction

2 Data Structures

3 Control Flow

4 Custom Functions

5 Plotting


Data Structures

Vectors and Matrices

Vectors are defined as follows

x = [1 2 3]; % 1x3 Row-Vector

y = [1;2;3]; % 3x1 Column-Vector

Matrices extend this convention, using the following syntax,

A = [1 2 3 4; 5 6 7 8; 9 10 11 12];


Data Structures

Accessing Elements

Accessing elements uses parentheses. NOTE: Indexing starts at 1.

x = [1 2 3]

A = [1 2 3; 4 5 6; 7 8 9]

x(1) % prints 1

A(2,1) % prints 4

You can also access portions of a vector/matrix,

x(2:10) % Elements 2-10 of x

x(2:end) % Elements 2-end of vector x

x(1:3:end) % Every third element of x until the end

x(:) % All elements of x

A(5,:) % 5th Row of A (row vector)

A(:,5) % 5th Column of A (column vector)

diag(A) % Column vector of diagonal elements of A


Data Structures

Example Mathematical Operations

The following are examples of mathematical operations,

sqrt(5)

exp(12)

log(3)

log10(100)

abs(-5)

sin(2*pi / 3)

Complex values use the imaginary i ,

x = 8 + 2i

y = complex(8,2)

x == y % Returns 1 (i.e. false)


Data Structures

More operations

x*3 % Multiply element-wise by 3

x+2 % Add element-wise by 2

x+y % Element-wise addition

x.*y % Element-wise product

A*y % Matrix-vector product

A*B % Matrix-Matrix product

A^3 % Matrix-exponential

x.^3 % Element-wise exponent

cos(x) % Element-wise cosine

abs(A) % Element-wise absolute value

sqrt(A) % Element-wise square-root


Data Structures

Generating Data

We can create matrices/vectors/arrays using the following

A = eye(3) % Matrix with diag(A) = 1

A = ones(3) % Matrix with all ones

A = zeros(3) % Matrix with all zeros

A = rand(3,3) % Uniformly distributed 3x3 matrix

% Uniformly spaced vector

x = linspace(0, 1, 10)


Data Structures

Special Variables/Constants

ans % Most recent result

i % Imaginary Unit

Inf % Infinity

NaN % Not a Number

pi % Pi

realmax % Maximum floating point value

realmin % Minimum floating point value

eps % Floating point relative accuracy


Data Structures

Solving Equations

You can solve the linear system

Ax = b

using the following

A \ b

You can find the inverse matrix, A−1, using

inv(A)

Eigenvectors: You can easily compute the eigenvectors and eigenvaluesusing the following,

eig(A) % Gives eigenvalues

[V,D] = eig(A) % Eigenvectors and eigenvalues (diag(D))


Control Flow

Outline

1 Introduction

2 Data Structures

3 Control Flow

4 Custom Functions

5 Plotting


Control Flow

If Statements

if ~isvector(x)

error(’Input must be a vector’)

end

The following block checks if x is a vector. If not, it prints an errorstatement. We can extend this further using else and elseif.

if r == c

A(r,c) = 1;

elseif abs(r-c) == 1

A(r,c) = 2;

else

A(r,c) = 0

end


Control Flow

For Loops

To increment over a set of values, use a for loop

x = ones(1,10);

for n = 2:6

x(n) = 2 * x(n-1);

end

You can nest for loops as well

A = zeros(5,100);

for m = 1:5

for n = 1:100

A(m,n) = 1/(m+n-1);

end

end


Control Flow

For Loops: Break

Let’s say that you have this code

x = ones(1,10)

for n = 2:10

x(n) = 2 * x(n-1);

if x(n) > 8

break

end

end

This will modify x until x(n) > 8, and then it will stop.


Control Flow

For Loops: Continue

The continue command also controls the flow of a for loop,

x = ones(1,10)

for n = 2:10

if n == 4

continue

end

x(n) = 2*x(n-1)

end

Instead of stopping processing, continue causes the loop to skip over thecase n = 4.


Control Flow

While Loops

A while loop will run until some condition fails to be met. For example,

n = 10;

f = n;

while n > 1

n = n - 1;

f = f * n;

end

This computes 10!.


Custom Functions

Outline

1 Introduction

2 Data Structures

3 Control Flow

4 Custom Functions

5 Plotting


Custom Functions

Defining Functions

The following syntax is used to define a function

function y = average(x)

if ~isvector(x)


end

y = sum(x) / length(x);

end

If we put this in a file called “average.m” located in our current directory(pwd), then we can call the function as

average( 2:10 ) % Returns 6


Custom Functions

Multi Input/Output functions

The previous function was dependent on a single variable. We can usehigher dimensional inputs as follows,

function [m,s] = stat(x)

if ~isvector(x)


end

n = length(x);

m = sum(x) / n;

s = sqrt( sum( (x-m).^2 / n) );

The return statement is similar to break, but it terminates processing of afunction and returns to the function invoking the current function.


Plotting

Outline

1 Introduction

2 Data Structures

3 Control Flow

4 Custom Functions

5 Plotting


Plotting

2d Plotting

There are many types of plots available in Matlab

bar % Bar chart

barh % Horizontal bar chart

hist % Histogram

loglog % Plot using log-log scales

pie % pie chart

plot % Plot vectors/matrices

polar % Plot in polar coordinates


Plotting

3d Plotting

bar3 % Bar chart

bar3h % Horizontal bar chart

plot3 % Plot lines and points in 3d

quiver3 % Velocity plot

stem3 % Discrete surface data


Plotting

Annotations

You can use the following to annotate you plots

grid % Overlay a grid

legend % Graph legend for lines and patches

title % Title for 2d/3d plots

xlabel % X-axis label

ylabel % Y-axis label

zlabel % Z-axis label


Documents

Matlab I An Initial Overview - George Mason Universitymath.gmu.edu/mtc_files/matlab.pdf · Matlab I An Initial Overview Patrick O’Neil Mathematics Testing Center George Mason University