1. ENE MATHLAB®
Lecture 1

2. MATLAB® overview High-level language for technical computing.
Development environment for managing code, files, and data.
Interactive tools for iterative exploration, design, and problem solving.
Mathematical functions for linear algebra, statistics, signal processing, numerical technique, and etc.
2-D and 3-D graphic functions for visualizing data.
Tools for building custom graphical user interfaces.

3. User interface

4. Entering commands At prompt (>>) type 1+2 and press Enter.
>> 1+2
MATLAB will display the answer as shown below.
ans = 3

5. Variables
MATLAB does not require any type declaration or dimension statements.
If the variable already exists, MATLAB automatically changes its contents and allocates new storage.

6. Numbers The format of numbers can be set using the ‘format’ command.
FORMAT SHORT Scaled fixed point format with 5 digits.
FORMAT LONG Scaled fixed point format with 15 digits for double
and 7 digits for single.
FORMAT SHORT E Floating point format with 5 digits.
FORMAT LONG E Floating point format with 15 digits for double and
7 digits for single.
FORMAT SHORT G Best of fixed or floating point format with 5
digits.
FORMAT LONG G Best of fixed or floating point format with 15
digits for double and 7 digits for single.

7. Format function

8. Format function

9. Operators Addition: + Substraction: - Multiplication: * Division: /
Power: ^

10. Functions
MATLAB have a hugh number of standard mathematical functions.
For a list of the elementary functions, type “help elfun”.
For a list of advanced mathematical functions, type “help specfun” or “help elmat”
Examples of functions:
Abs, sqrt, exp, sin, pi, i, j, inf, and etc.

11. Entering Matrices
There are several different ways to enter matrices into MATLAB:
Enter an explicit list of elements.
Load matrices from external data files.
Generate matrices using built-in functions.
Create matrices with your own functions and save them in files.

12. Entering Matrices These are a few basic conventions:
Separate the elements of a row with blanks or commas.
Use a semicolon (;) to indicate the end of each row.
Surround the entire list of elements with square brackets, [ ].

13. Entering Matrices This is called “Dürer’s matrix”.
The summation along any row, column, or two main diagonals will always be equal.

14. Entering Matrices
For example, try to enter a Dürer’s matrix into MATLAB. At command window, type
>> A = [ ; ; ; ]
MATLAB displays the derised matrix:
A =

15. Sum Let us verify the properties of Dürer’s matrix using MATLAB.
>> sum(A)
ans =

16. Transpose MATLAB has two transpose operators:
The apostrophe operator (A’): a complex conjugate transposition.
The dot-apostrophe operator (A.’): transposing without affecting the sign of complex elements.
>> A'
ans =

17. Diag
>> diag(A) ans =
>>sum(diag(A))
ans = 34

18. Subscripts The element in row I and column j is denoted by A(i,j).
>> A(1,4) + A(2,4) + A(3,4) + A(4,4)
ans = 34

19. Increase the matrix size
By putting ‘;’, the result will not be displayed. The size of the matrix will be automatically increased to accommodate the newcomer.
>> B = A;
>> B(4,5) = 26
B =

20. The Colon Operator
Ex. A row vector contains the integers from 1 to 10:
>> C = 1:10
C =
Ex. To obtain 0 to 4*pi with an increment of pi/4.
>> 0:pi/4:pi
ans =

21. The Colon Operator Ex. The 1st 4 elements of the 3rd column of A.
ans = 2 11 7 14

22. Generating matrices
MATLAB provides four functions to generate basice matrices:
zeros – all zeros.
ones – all ones.
rand – uniformly distributed random elements.
randn – normally distributed random elements.

23. Generating matrices

24. The load function
The load function reads binary files containing matrices generated by earlier MATLAB session, or reads text files containing numeric data.
>> load data1.dat

25. Concatenation
The process of joining smal matrices to make bigger ones.
>> B = [A A+32; A+48 A+16]
B =

26. Deleting rows and columns

27. Arrays

28. Arrays
>> x = [0:9]'; >> table1 = [x x.^2 2.^x] table1 =

29. Arrays

30. Creating a plot
A plot function has different forms depending on the input arguments.
If y is a vector, plot (y) produces a piecewise linear graph of the elements of y versus the index of the element y.
If two vectors are specified, plot(x,y) is used to produce a graph of y versus x.

31. Creating a plot
Example of plotting a vector x, ranging from 0 to 2, versus the sine of those values.
The axes can be labelled using ‘xlabel’ and ‘ylabel’.
The figure is shown on the next page.

32. Creating a plot

33. Plotting multiple data in one graph
A function ‘plot’ can be used to obtain multiple x-y pair arguments with customizable colors to allow discrimination among sets of data.
A legend command is used to identify the individual plots.

34. Plotting multiple data in one graph

35. Specifying line styles and colors
MATLAB allows us to specify line styles, line colors, or even markers using ‘plot’ function.

36. Specifying line styles and colors

37. Specifying line styles and colors

38. Plotting lines and markers
If a marker is specified not a line style, only the marker will be drawn.
The below example plots the data twice using a different number of points for the dotted line and marker plots.

39. Plotting lines and markers

40. Graphing complex data
When the arguments to plot are complex, the imaginary part is ignored except when you pass plot a single complex argument.
For example,
plot(Z) where Z is a complex vector or matrix is equivalent to
plot(real(Z), imag(Z))

41. Graphing complex data

42. Adding plots to an existing graph
A command ‘hold’ allows you to add plots to an existing graph.

43. Adding plots to an existing graph

44. Displaying multiple plots in 1 figure
The ‘subplot’ command enables you to display multiple plots in the same figure.
The figure is partitioned into an m-by-n matrix of small subplots and selects the pth subplot for the current plot.

45. Displaying multiple plots in 1 figure

46. Setting axis limits
MATLAB is automatically setting axis limits to span the range between the maxima and minima.
The ‘axis’ commant allows you to specify your own limit:
For three-dimentional graphs:
To enable automatic limit selection again:

47. Setting axis visibility
The default is set for invisible axis.
To make the axis visible or invisible using:
axis on
axis off

48. Setting grid lines The default is set for no grid line.
To make the grid lines on and off using:
grid on
grid off

49. Adding axis labels and titles
The ‘x-label’, ‘y-label’, and ‘z-label’ commands add x-, y-, and z-axis labels.
The ‘title’ command adds a title at the top of the figure.
The ‘text’ function inserts text anywhere in the figure.

50. Adding axis labels and titles

51. Adding axis labels and titles

52. Saving a figure

53. Graph components

54. Figure tools

55. Figure toolbars

56. Plotting tools

57. Plotting tools

58. Any question??