E5 Matlab Intro

Erik Cheever - Fall 2009

Simple math
Variables - not equivalent to mathematical notation
Matrices and vectors
Creating a range of numbers, and plotting
Patch graphics

Simple math

addition

3+5

ans = 8

multiplication

3*5

ans = 15

sin() - note the argument is in radians

sin(pi/4)

ans = 0.7071

sind() - takes argument in degrees

sind(45)

ans = 0.7071

sqrt

sqrt(3)

ans = 1.7321

power

3^5

ans = 243

3^0.5

ans = 1.7321

3^1/2

ans = 1.5000

natural log (ln)

log(10)

ans = 2.3026

log base 10

log10(10)

ans = 1

pi

ans = 3.1416

show more digits

format long
pi

ans = 3.141592653589793

show fewer digits

format short
pi

ans = 3.1416

scientific notation

256*256*256*256

ans = 4.2950e+009

Variables - not equivalent to mathematical notation

variables go on left side. Read equals sign as "gets": x gets 3

x=3

x = 3

display value of variable

x = 3

note that you can't switch order.

3=x gives an error

Whatever is on left gets a new value

y=4

y = 4

x=y  %This changes the value of x
     %y=x would have changed value of y

x =  4

anything following a "%" sign is a comment

if you put a semicolon ";" at the end of a line, the result doesn't display.

x=5;

The above result wasn't displayed. But we can check the value of x

x =  5

Matrices and vectors

Row vector

a=[1 3 5 -1]

a =     1     3     5    -1

Column vector

b=[2; 4; 1; 0]

Get 3rd element of each

a(3)

ans = 5

b(3)

ans = 1

Try to add

a+b

Error using ==> plus.
Matrix dimensions must agree.

define another row vector

c=[1 0 3 1]

c =  1     0     3     1

now we can add

a+c

ans = 2     3     8     0

Define a 2x2 (2 rows x 2 colums) matrix.

A=[3 5; 6 -1]

A =
     3     5
     6    -1

Access individual elements

A(2,1)  % 2nd row, 1st column

ans = 6

Retrieve a whole column....

A(:,1)   % 1st column

ans = 
     3
     6

or a row...

A(2,:)   % 2nd row

ans = 6    -1

Another matrix

B=[3 5; 5 2]

B =
     3     5
     5     2

Add matrices

A+B

ans = 
     6    10
    11     1

Multiplication

A*B

ans = 
    34    25
    13    28

Transpose (switch rows and columns)\

A
A'

Find inverse

inv(A)

ans = 
    0.0303    0.1515
    0.1818   -0.0909

check inverse

ans*A

ans = 
    1.0000    0.0000
         0    1.0000

can also define identity matrix

I=eye(2)

I =
     1     0
     0     1

check

A*I

ans = 
     3     5
     6    -1

Creating a range of numbers, and plotting

range of numbers

x=linspace(0,3*pi,12)  %x is linearly spaced with 12 elements

x =
  Columns 1 through 9

         0    0.8568    1.7136    2.5704    3.4272    4.2840    5.1408    5.9976    6.8544

  Columns 10 through 12

    7.7112    8.5680    9.4248

calculate sin()

y=sin(x)

y =
  Columns 1 through 9

         0    0.7557    0.9898    0.5406   -0.2817   -0.9096   -0.9096   -0.2817    0.5406

  Columns 10 through 12

    0.9898    0.7557    0.0000

plot

plot(x,y)

Label the plot

title('Sin(x) vs x');
xlabel('x values');
ylabel('sin(x)');

use more points

x=linspace(0,3*pi,1000);
y=sin(x);
plot(x,y,'r-.','LineWidth',2);

a circle (radius = 2)

theta=linspace(0,6*pi,1000);
x=2*cos(theta);  y=2*sin(theta);
plot(x,y,'r','LineWidth',2);

a spiral (radius=theta)

x=theta.*cos(theta);  y=theta.*sin(theta);
plot(x,y,'r','LineWidth',2);

a 3-D spiral with axes labeled

plot3(x,y,theta,'r','LineWidth',2);
xlabel('x');  ylabel('y');  zlabel('theta');
title('3d Spiral');

Patch graphics

Define a "patch"

clf;  %clear the figure
x=[0 1 1 0];
y=[0 0 1 1];
myPatch=patch(x,y,[1 0 0]);  %(x, y, color)

Set axes

axis([-5 5 -5 5]);  %[xmin xmax ymin ymax]
grid

move the patch

set(myPatch,'Xdata',x+2);

change the color

set(myPatch,'FaceColor',[0 0 1]);

a 3d patch

x=[0 0; 1 1; 1 1];
y=[0 0; 1 -1; 0 0];
z=[0 0; 1 0.5; 0 0];
tcolor(1,1,1:3) = [1 0 0];
tcolor(1,2,1:3) = [0 1 0];
my3dPatch=patch(x,y,z,tcolor)