part 1 - introduction to matlab

7/31/2019 Part 1 - Introduction to Matlab

1/21

C.B. Pham 1

1. Introduction to Matlab

Matlab: Matrix Laboratory Numerical Computationswith matrices

Every number can be

represented as matrix

Why Matlab?

User Friendly (GUI)

Easy to work with

Powerful tools for complex mathematics.


2/21


3/21

C.B. Pham 3

Help in Matlab

>> help Shows help document for a give function

Eg. help sqrt

>> lookfor

Searches all the help documents for a given keyword

Eg. lookfor sqrt

>> demo


4/21

C.B. Pham 4

2. Matrix operationsAddition>> c = a + b

Substraction>> c = a - b

Multiplication

>> c = a*b % matrix multiplication>> c = a.*b % element wise multiplication

Division (left, right)

>> c = a/b % a * b-1

>> c = a./b % element wise division>> c = a\b % a-1 * b

>> c = a.\b % element wise division


5/21

C.B. Pham 5

Real>> x = 5x =

5

Complex>> x = 5 + 10*ix =

5.0000 + 10.0000i

Variable: constant, vector, matrix

Row vector>> x = [1, 2, 3] % [1 2 3]x =

1 2 3

Column vector>> x = [1; 2; 3]x =

123Matrix

>> x = [1 2 3; 4 5 6]x =

1 2 3

4 5 6Note: Variable Names are case sensitive


6/21

C.B. Pham 6

>> [0 : 0.2 : 1] % 0 to 1 in increments of 0.2ans =

0.0 0.2 0.4 0.6 0.8 1.0

Vectors

>> linspace(0, 1, 6) % 6 points from 0 to 1 on a linear sclans =

0.0 0.2 0.4 0.6 0.8 1.0

>> logspace(0, 1, 6) % 6 points from 100 to 101 on a log scl

ans =

1.0000 1.5849 2.5119 3.9811 6.3096 10.0000


7/21

C.B. Pham 7

Matrix

>> ones(2, 3) % generates an all one 2 x 3 matrixans =

1 1 1

1 1 1

>> zeros(2, 3) % generates an all zero 2 x 3 matrix

ans =

0 0 0

0 0 0 >> [1 2 3; 4 5 6]ans =

1 2 34 5 6


8/21


9/21

C.B. Pham 9

Accessing matrix elements

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

1 2 3 45 6 7 89 10 11 12

>> x = M(2, 3) % element at row 2 & column 3 of M

x =

7>> y = M(2, :) % select the 2nd row M

y =

5 6 7 8>> z = M(2:3, 2:3) % select sub-matrix of Mz =

6 7

10 11


10/21

C.B. Pham 10

Concatenating, Appending,

>> A = [ 1 2 3 ] ;>> B = [ 4 5 6 ] ;

>> R = [ A B ]

R =

1 2 3 4 5 6

>> S = [ A; B ]

S =

1 2 3

4 5 6

>> S(3, 3) = 7

S =

1 2 3

4 5 60 0 7

Note: if you store a value in an element outside of the

matrix, the size increases to accommodate the newcomer.


11/21

C.B. Pham 11

Complex number operations

>> abs(x) % Absolute value

ans =

5

>> x = 3 + 4*i;

>> angle(x) % Phase angle (in radians)

ans =

0.9273

>> conj(x) % Complex conjugate

ans =

3.0000 4.0000i

>> imag(x) % Complex imaginary part

ans =

4

>> real(x) % Complex real part

ans =

3


12/21

C.B. Pham 12

Some Useful Functions

Some useful math functions:sin(x), cos(x), tan(x), atan(x), exp(x), log(x), log10(x),

sqrt(x), >> t = [0 : 0.1 : 10] ;>> x = sin(2 * pi * t) ;

Some useful matrix and vector functions:

>> length(x)ans =

101

>> size(x)ans =

1 101


13/21

C.B. Pham 13

>> M = [ 1 2; 5 6 ]

M =

1 2

5 6>> sum(M)ans =

6 8

>> sum(ans) % equivalent to sum(sum(M))

ans =

14

>> M % equivalent to transpose(M)

ans =

1 5

2 6

>> diag(M) % diagonal elements

ans =

1

6

More Operators and Functions


14/21

C.B. Pham 14

Find the roots of the polynomial

>> f = [ 1 2 3 4 ] ; % create f = x3 + 2x2 + 3x + 4

>> roots(f)

ans =

-1.6506

-0.1747 + 1.5469i-0.1747 - 1.5469i

Partial Fraction Expansion

>> [R, P, K] = residue([ 5 3 ] , [ 1 3 0 -4 ])R = P = K =

-0.8889 -2.0000 [ ]

2.3333 -2.0000

0.8889 1.0000

43

35

23

xx

x

1

98

)2(

37

2

98

2

xxx

More Operators and Functions


15/21

C.B. Pham 15

3. Plots in Matlab


16/21

C.B. Pham 16

The plot function has different forms, depending on the input arguments.

Continuous time plots - plot

>> x = [ 0 : 0.1 : 2*pi ] ;

>> y = sin(x) ;

>> plot(y) >> plot(x, y)


17/21

C.B. Pham 17

Stem function is very similar to plot. It is used to plot discrete time sequences.

Discrete time plots - stem

>> x = [ 0 : 0.5 : 10 ] ;

>> y = x.^2 ;

>> stem(x, y)

>> grid on

>> xlabel(Time, t)

>> ylabel(Speed, s)

>> title(Graph s = t^2)


18/21

C.B. Pham 18

Multiple Data Sets in One Graph

Approach 1

>> plot(t, x, t, y, t, z)

>> t = [ 0 : 0.001 : 2*pi ] ;

>> x = sin(t);

>> y = sin(t - 0.5);

>> z = sin(t - 1);

>> grid on

>> legend(sin(t), sin(t 0.5), sin(t - 1))

Approach 2

>> plot(t, x, t, y, t, z)

>> plot(t, x, b)

>> hold on

>> plot(t, y, g)

>> plot(t, z, r)

>> hold off


19/21

C.B. Pham 19

Plot with two different y-axes

>> t = [ 0 : 0.001 : 2*pi ] ;

>> p = sin(2*t);

>> v = 2*cos(2*t);

>> plot(t, p)>> plot(t, v)

>> plotyy(t, p, t, v)


20/21

C.B. Pham 20

4. Function in Matlab Syntax

function [out1, out2, ] = function_name (in1, in2, )

..

.. % commands

..

Description:

function [out1, out2, ...] = function_name (in1, in2, ...) defines function

function_name that accepts inputs in1, in2, etc. and returns outputs out1,

out2, etc.

Note:

When you create a function in a Matlab .m file and you want to call it from

the workspace, make sure the name of the .m file is the same as the name

of the function itself (good programming practice).


21/21

C.B. Pham 21

function a = dien_tich(l1, l2, d)

if (d == 1) % rectangle

a = l1 * l2 ;

elseif (d == 2) % triangle

a = l1 * l2 / 2 ;

else %others

a = -1 ;

end

Example: make function of area

a

b

A = a.b

a

hA = a.h / 2

File saved as dien_tich.m >> dien_tich(2, 3, 1)

ans =

6

>> dien_tich(2, 3, 2)

ans =

3

>> dien_tich(2, 3, 3)

ans =

-1

part 1 - introduction to matlab

Documents