MATLAB PROGRAMMING

1. Programming
BY
R.IMMANUAL
Certified on MATLAB
Onramp by Math works
Training services(MATLAB
Academy)

2. About this Session
• We will coverthe following
topics
• MATLAB basics
• Arrays: Unlocking potential of
MATLAB

3. Starting and Exiting MATLAB
• We will go over starting a MATLABsession, layoutof MATLAB
window, MATLAB editor,etc.
• Also see video“GettingStarted with MATLAB”on MATLAB site
http://in.mathworks.com/videos/getting-started-with-matlab-68985.html
Open and Explain it…

4. Customizing our window
 Manual
 Using layout
 How create a new editor
 How to set path

5. MATLAB Code: Main Code
Blocks %% Define Parameters and Initial Conditions
param.g =
9.81;
% gravitational
acceleration
% air drag coefficient
param.kappa =
0.006; u0 =
35*cos(pi/4); v0
= 35*sin(pi/4);
%% Setting up and Solving the problem
X0 = [0; 0;
u0; v0];
tSpan = [0
20];
% starting position is the
origin
% starting velocity is given
% simulation time
[tOut, XOut] = ode45(@ballTrajectoryFun,tSpan,X0, [],
param);
%% Displaying the
results figure(1);
plot(XOut(:,1),XOut(:,2
),'bo');
xlabel('x (m)'); ylabel('y (m)');
%% Animating results
exitCode = ballAnimation(tOut,XOut);
Input
block
Computation
Output
block

6. MATLAB Code: Key Parts
%% Define Parameters and Initial
Conditions
param.g = 9.81;
u0 = 35*cos(pi/
Comment
Assignment
(Math)Expression
[tOut, XOut] = ode45(@bal
Calling a function
plot(XOu
Calling a function

7. MATLAB Code
%% Define Parameters and Initial
Conditions
param.g = 9.81;
% gravitational
acceleration
% air drag coefficient
param.kappa = 0.006;
u0 = 35*cos(pi/4);
v0 = 35*sin(pi/4);
%% Setting up and Solving the
problem
X0 = [0; 0;u0; v0];
tSpan = [0 20];
% starting position is the
origin
% starting velocity is given
% simulation time
[tOut, XOut] = ode45(@ballTrajectoryFun,tSpan,X0, [], param);
%% Displaying the results
figure(1);
plot(XOut(:,1),XOut(:,2),'bo');
xlabel('x (m)'); ylabel('y (m)');
%% Animating results
exitCode = ballAnimation(tOut,XOut);

8. Basic Data Types
• Matlab easily works with
arrays
• Scalars, vectors and arrays
• Assigningvariables
• Row vs. column vectors
• Arrays /Matrices
• Suppress“echo”
• Variables arecase-sensitive

9. Basic MathematicalExpressions
Variable Meaning
pi Number /
eps Machine precision
i Imaginary unit
inf Infinity
NaN Not a Number (e.g., 0/0)
ans Last displayedresult
end Last element of array
realmax Largest real number
intmax Largest integer
Scalar Operations Special
Variables
• + - * / ^
• log, exp
• pow, sqrt
• sin, cos, tan
• asin, acos, atan
• rem, round, ceil, floor
When type functions we use ()… pow2(5)

10. Tasks from Entering Commands

11. Task 01
 Try multiplying the numbers 3 and 5 together
with the command 3*5.

12. Task 02
 Try assigning the 3*5 calculation to a variable
named m as shown: m = 3*5.

13. Task 03
 Try entering the command m = m + 1 to see
what happens.

14. Task 04
 Now try creating a variable named y that has
the value m/2.

15. Task 05
 Try entering k = 8-2; with a semicolon at the
end.
 Echo will be supressed

16. Task 06
 Try entering k = 8-2; with a semicolon at the
end.
 Echo will be supressed

17. Task 07
 Try pressing the Up arrow to return to the
command m =3*5 and edit the command to
be m = 3*k.
 Echo will be supressed

18. Tasks on variables
Task 1
 Try clearing all variables by entering the
command clear.

19. Tasks 02
 clean up the command window using the clc
command..

20. Task 03
 Try creating a variable called x with a value
of π/2.

21. Task 04
 Try using the sin function to calculate the sine
of x. Assign the result to a variable named y.

22. Task 06
 Now try using the sqrt function to calculate the
square root of -9. Assign the result to a
variable named z..
 CREATE pi = 9;
 Clear the pi variable

23. Arrays are the most powerful aspect of
MATLAB
•We will learn
•Building arrays
•Colon notations
•Array operations and functions
•Also view “Working with Arrays in
MATLAB” on MATLAB website:
http://in.mathworks.com/videos/working-with-arrays-in-matlab-
69022.html

24. Building Arrays
 Create random matrix (a = rand(6,4))
 Indexing of an array (a(1,2))
 Assign a value to the array elements
(a(1,2)=2;)
 Assign an empty matrix a=[];
 Create an Identity matrix of c =eye(3);
 Combine two matrix C = horzcat(A1,...,AN)
(same rows)

25. Building Arrays
 Manually crate arrays a= [1 2 3 ; 1 2 3]
 Transpose of a matrix a’
 Elemental operation a(2,1) select that element
 Size of a matrix size (a)
 Ones(m,n)
 diag(a)

26. Colon notations
 A=1:5;
 A(1:3,5)

27. Task 01
 Create a variable named x with a value of 4.

28. Task 02
 Create an array named x with two elements in
a single row:
7 and 9.

29. Task 03
 Now create an array named x with two
elements, 7 and 9, in a single column. Try
recalling the previous command and changing
the space between the numbers to a
semicolon (;).

30. Task 04
 Now try creating a 1-by-3 row vector
named x that contains the values 3, 10,
and 5 in that order.

31. Task 05
 Now try creating a 3-by-1 column vector
named x that contains the values 8, 2, and -
4 in that order..

32. Task 06
 Try creating a matrix named x with the values
shown below.
5 6 7
8 9 10

33. Task 07
 Try creating a 1-by-2 row vector named x that
contains sqrt(10) as its first element
and pi^2 (π2) as its second element.

34. Task 08
 Try creating a row vector named x that
contains the values 1, 2, and 3, in that order.

35. Task 09
 Try recreating the row vector named x (still
with values 1, 2, and 3), but this time using
the : operator.

36. Task 10
 Try creating a row vector named x that starts
at 1, ends at 5, and each element is
separated by 0.5.

37. Task 11
 Try creating a row vector named x that starts
at 3 and ends at 13, with each element
separated by 2.

38. Task 12
 Try creating a row vector named x that starts
at 3 and ends at 13, with each element
separated by 2.

39. Task 13
 Try creating a row vector named x that starts
at 1, ends at 10, and contains 5 elements.
x = linspace(0,1,5)
start
End
Number of Components

40. Task 14
 Transpose x from a row vector to a column
vector using the transpose operator.

41. Task 15
 In a single command, create a column vector
named x that starts at 5, ends at 9 and has
elements that are spaced by 2.

42. Task 16
 Try creating a variable named x that is a 5-by-
5 matrix of random numbers.
rand

43. Task 17
 Try using rand to create an array that
contains 5 rows and 1 column. Assign the
result to a variable named x.
rand

44. Task 18
 Now try using the zeros function to create a
matrix of all zeros that has 6 rows
and 3 columns (6-by-3). Assign the result to a
variable named x.
rand

45. Indexing into Arrays
 Task 20
 Create data variable contains 7,4 random
values
 Try creating a variable v that contains the
value in the 6throw and 3rd column of the
variable data.

46. Task 21
 Info: You can use the MATLAB
keyword end as either a row or column index
to reference the last element.
>> x = A(end,2);
 Now try using the end keyword to obtain the
value in the last row and 3rd column of the
variable data. Assign this value to a variable
named v.
rand

47. Basic Mathematical Expressions
“Scalar” Operations Matrix Operations
• + – * / ^
•log, exp • logm, expm
•power, sqrt • mpower, sqrtm
•sin, cos, tan • sum,prod,cumsum,cumprod
•asin, acos, atan • min, max, mean, std
•rem, round, ceil, floor • length, size, eig

48. Task 01
 Try creating a vector vs that is the sum of the
vectors v1and v2.
rand

49. Task 02
 Try creating a variable va that contains the
value vs divided by 2
 Matrix multiplication
 Elemental multiplication
rand

50. Task 03
 Info: Basic statistical functions in MATLAB
can be applied to a vector to produce a single
output. The maximum value of a vector can
be determined using the max function.
>> xMax = max(x)
 Try creating a variable vm containing the
maximum of the va vector.
rand

51. Task 04
 Using the round function, create a variable
named vrwhich contains the rounded average
volumes, va.
rand

52. Task 04
 The .* operator performs elementwise
multiplication and allows you to multiply the
corresponding elements of two equally sized
arrays.
 z = [3 4] .* [10 20]
 z = 30 80
rand

53. Task 05
 Try creating a variable
named dsize containing the size of a matrix.
rand

54. Application Oriented Task
 Solution to system of linear equation

55. Solutions to Systems of Linear Equations
 Example: a system of 3 linear equations with 3 unknowns (x1, x2, x3):
3x1 + 2x2 – x3 = 10
-x1 + 3x2 + 2x3 = 5
x1 – x2 – x3 = -1
Then, the system can be described as:
Ax = b














1
1
1
2
3
1
1
2
3
A











3
2
1
x
x
x
x












1
5
10
b
Let :
Task 01

56. Solutions to Systems of Linear
Equations (con’t…)
 Solution by Matrix Inverse:
Ax = b
A-1Ax = A-1b
x = A-1b
 MATLAB:
>> A = [ 3 2 -1; -1 3 2; 1 -1 -1];
>> b = [ 10; 5; -1];
>> x = inv(A)*b
x =
2.0000
1.0000
2.0000
Answer:
x1 = 2, x2 = 1, x3 = 2
• Solution by Matrix Division:
The solution to the equation
Ax = b
can be computed using left division.
Answer:
x1 = 2, x2 = 1, x3 = 2
 MATLAB:
>> A = [ 3 2 -1; -1 3 2; 1 -1 -1];
>> b = [ 10; 5; -1];
>> x = Ab
x =
2.0000
1.0000
2.0000

57. Task 02
•Consider the following example (Marks earned by students)
Name Math Programmin
g
Thermodyna
mics
Mechanics
Amit 24 44 36 36
Bhavna 52 57 68 76
Chetan 66 53 69 73
Deepak 85 40 86 72
Elizabeth 15 47 25 28
Farah 79 72 82 91

58. HOW to Do This……