What is MATLAB?

• It stands for MATrix LABoratory

• It is developed by The Mathworks, Inc (http://www.mathworks.com)

• It is an interactive, integrated, environment

– for numerical computations

– for symbolic computations

– for scientific visualizations

• It is a high-level programming language

Characteristics of MATLAB

• Programming language based (principally) on matrices .

– Slow (compared with fortran or C) because it is an interpreted language ,i.e . not pre-compiled. Avoid for loops; instead use vector form whenever possible .

– Automatic memory management, i.e., you don't have to declare arrays in advance .

– Intuitive, easy to use .

– Shorter program development time than traditional programming languages such as Fortran and C .

– Can be converted into C code via MATLAB compiler for better efficiency .

• Many application-specific toolboxes available .

Start menu Matlab MATLAB

“>>” – שורת הפקוד ה

>> date

Getting Help

>> help date

>> helpwin date

helpwin gives you the same information as help, but in a different window.

Getting Help

>> doc date

>> lookfor date % search for keywords that best describe the function

>> Ctrl+C % stop Matlab from running

>> clc % clear screen

Special characters

• >> % default command prompt

• % % comment - MATLAB simply ignores anything to the

right of this sign (till the end of the line).

>> % my comment

• ; % semicolon at the end of the line will prevent MATLAB

from echoing the information you type on the screen.

>> a=20

>> B=20;

Creating Variables

• Matlab as a calculator:

• >>2+5

• >>7*10+8

• >>5^2

• ‘ans’ - "answer", used in MATLAB as the default variable.

Defining Your Own Variables

• When Matlab comes across a new variable name it

automatically creates it.

• Begins with a LETTER, e.g., A2z.

• Can be a mix of letters, digits, and underscores (e.g.,

vector_A, but not vector-A)

• Not longer than 31 characters.

• No spaces

• Different mixes of capital and small letters = different

variables.

For example: "A_VaRIAbLe", "a_variable", "A_VARIABLE",

and "A_variablE

• >> String='this is a string'

Listing & Clearing Variables

>> whos

>> clear %clear variables from memory

>> a=10

>> b = 20

>> the_average = (a + b ) / 2

Creating vectors

Column separator:

space/coma (,)

Creating sequences:

From : jump: till

Row separator:

Semicolon (;)

Creating Matrices

• Matrices must be rectangular.

•Creating random matrices:

2-by-4 random matrix

(2 rows and 4 columns).

Creating Matrices

• You can combine existing vectors as matrix elements:

• You can combine existing matrices as matrix elements:

Indexing Into a Matrix

>> mat_from_mat(8)

>> mat_from_mat(4,2)=0

>> mat_from_mat

• The row number is first, followed by the column number.

Linear Algebra Operations

Matrix Multiplication

• Inner dimensions must be equal

• Dimension of resulting matrix = outermost

dimensions of multiplied matrices

• Resulting elements = dot product of the rows of

the 1st matrix with the columns of the 2nd matrix

Type the following:

>>a=[2 3]

>>b=[3 2]

>>a*b

>>a.*b

>>a.*b'

>>a*b'

Vector Multiplication

Example: Solving Equations

• Solve this set of simultaneous equations

Array Operations

Boolean Operators & Indexing

String Arrays

• Created using single quote delimiter (')

• Each character is a separate matrix element (16 bits of

memory per character)

• Indexing same as for numeric arrays

String Array Concatenation

Working with String Arrays

Line Plots in Two Dimensions

• Plot (x,y)

• makes a two-dimensional line plot for each point in X and its

corresponding point in Y: (X(1),Y(1)), (X(2),Y(2)), (X(3),Y(3)), etc.,

and then connect all these points together with line.

• Example:

• >> x=1:1:5;

• >>y=[2 7 0 -8 6];

• >> plot (x,y);

• >> xlabel ('label for x-axis')

• >> ylabel ('label for y-axis')

• >> title ('title')

• Check the following:

• x_points = [-10 : .05 : 10];

• plot(x_points, exp(x_points));

• grid on

• hold on

• plot(x_points, exp(.95 .* x_points), 'm');

• plot(x_points, exp(.85 .* x_points), 'g');

• plot(x_points, exp(.75 .* x_points), 'p');

• xlabel('x-axis'); ylabel('y-axis');

• title('Comparing Exponential Functions');

• legend ('1', '2', '3', '4')

Multiple Plots

-10 -5 0 5 100

0.5

1

1.5

2

2.5x 10

4

x-axisy-

axis

Comparing Exponential Functions

1

2

3

4

Subplots

• multiple plots in the same window, each with their own

axes.

• Subplot (M,N,P)

• M – rows

• N - columns

• P – number of subplot

in the figure

Subplot (2,2,1)

More about figures

• Figure % Open a new figure without closing old figures

• Figure (i) % Open the i-th figure

• Close all % close all open figures

• axis ([xmin xmax ymin ymax]) % sets scaling for the x-

and y-axes on the current plot.

Special Graph Annotations (TeX)

Plot Editor Toolbar

Exercise

• x = (1, 1.05, 1.1, 1.15… 5)

• Y=sin(x)

• Z=log(x)

• Put your name in the title

• Hint: check the doc “linespec”.

Create the following:

1 1.5 2 2.5 3 3.5 4 4.5 5-1

-0.5

0

0.5

1

1.5

2Merav's graph

x

ysin(x)

log(x)

Solution

• >>x=1:0.05:5;

• >>y=sin(x);

• >>z=log(x);

• >> hold on

• >> plot (x,y,'-.r*')

• >> plot (x,z,'-.go')

• >> hold off

• >> title ('Merav''s graph');

• >> xlabel ('x')

• >> ylabel ('y')

• >> legend ('sin(x)', 'log(x)');

More exercise

• Make a 3 three-dimensional graph of (x,y,z) – use Matlab

help.

• Make two separate 2-D graphs, with separate axis, in the

same window: y vs. x, and z vs. x.

1

2

3

4

5

-1

-0.5

0

0.5

10

0.5

1

1.5

2

x

3D graph

y

z

1 2 3 4 5-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1sin(x)

x

y=

sin

(x)

1 2 3 4 50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

x

log(x)

z

Solution

• 3-D graph:

• >> plot3(x,y,z)

• >> grid

• >> xlabel ('x')

• >> ylabel('y')

• >> zlabel('z')

• >> title ('3D graph')

• Subplots

>> subplot (1,2,1);

>> plot(x,y);

>> title ('sin(x)');

>> xlabel('x');

>> ylabel('y=sin(x)');

>> grid;

>> subplot (1,2,2);

>> plot(x,z);

>> xlabel('x');

>> title ('log(x)');

>> grid;

>> ylabel ('z');

Surface Mesh plots

1) Generate a grid of points in the xy-plane using the

meshgrid command.

2) Evaluate the three-dimensional function at these points.

3) Create the surface plot with the mesh command.

Meshgrid - returns all possible combinations of (x,y) points,

where x is taken from X and y is taken from Y, in the form of two

matrices.

you will see in the generated surface mesh plot a bunch of

rectangles, of width and length equal to the regular spacing values

for X and Y, and the height of the corners of the rectangles will be

equal to the value of the function at the rectangles' corner points)

1. >> x_points = [-10 : 1 : 10];

>> y_points = [-10 : 4 : 10];

>> [X, Y] = meshgrid(x_points,y_points);

2. >> Z = X.^2 + Y.^2;

3. >> mesh(X,Y,Z);

>> xlabel('x-axis');

>> ylabel('y-axis');

>> zlabel('z-axis');

-10-8

-6-4

-20

24

68

10

-10

-5

0

5

10

0

20

40

60

80

100

120

140

160

180

200

x-axis

X: -9

Y: -10

Z: 181

y-axis

z-a

xis