Matlab Student Copy

Exptno:1 INTRODUCTION TO MATLAB High Performance Numeric Computation and Visualization Software

MATLAB stands for MATRIX LABORATORY. MATLAB is a technical computing environment for high performance numeric computation and visualization. MATLAB integrates numerical analysis, matrix computation, signal processing, and graphics in an easy to use environment, where problems and solutions are expressed just as they are written mathematically without traditional programming. MATLAB also features of application a specific solution that is toolboxes. Areas in which toolboxes are available include signal processing, control systems design, dynamic systems simulation, systems identification, neural networks and others. MATLAB integrates mathematical computing, visualization, and a powerful language to provide a flexible environment for technical computing. MATLAB includes tools for: Data acquisition Data analysis and exploration Visualization and image processing Algorithm prototyping and development Modeling and simulation Programming and application development

A BRIEF LIST OF MATLAB COMMANDS Some Basic Commands (Note command syntax is case-sensitive!) Matlab

loads the program matlab into your workspace.

quit

quits matlab, returning you to the operating system.

exit

same as quit.

who

lists all of the variables in your matlab workspace.

Whos list the variables and describes their matrix size. Clear

deletes all matrices from active workspace.

Save

saves all the matrices defined in the current session into the file, matlab.mat.

Load

loads contents of matlab.mat into current workspace.

Save

filename saves the contents of workspace into filename. Mat

MATLAB COMMANDS 1. PLOT Linear plot Plot (x, y) plots vector y versus vector x. Various line types, plot symbols and colours may be obtained with PLOT(x, y, ‘S’) where S is a character string made from one element from any or all the following 3 tables Line Style

Specifier

solid (default)

-

Dashed

--

Dotted

:

Dash-dot

-.

Marker Type Plus sign Circle Asterisk Point Square Diamond Pentagon Hexagon

Specifier + o * . S d p h

Line

Specifier

Colour Red

r

Green

g

Blue

b

Cyan

c

Magenta

m

Yellow

y

Black

k

White

w

2. STEM discrete sequence or stem plot Stem (x, y) plots the data sequence y at the values specified in x. 3. STAIRS Stair step plot Stairs (x, y) draws a stairs step graph of the elements in vector y at the locations specified in x. 4. BAR- Bar graph Bar (x,y) draws the columns of the M by N matrix. 5. PIE chart Pie (x) draws a pie plot of the data in the vector x. 6. TITLE Graph title Title (‘text’) adds text at the top of the current axis. 7. XLABEL x-axis label xlabel (‘text’) adds text besides the X-axis on the current axis. 8. YLABEL y-axis label ylabel (‘text’) adds text besides the Y-axis on the current axis. 9. AXIS

Control axis scaling and appearance Axis ([xmin xmax ymin ymax]) set scaling for the x and y axes. 10. ZOOM Zoom in and out on a 2-D plot Zoom (factor) zooms the current axis by factor. 11. GRID Grid lines Grid sets the x grid, y grid, and z grid properties of the current axis 12. DISP display array Disp (x) if x is a string, the text is displayed 13. Subplot(x,y,z) It will split the figure window into several rows & columns X - no of rows y – no of columns z – position on the window. 14. Linespace (min, max) It will changes the x-axis scaling from min to max 15. Log space (min, max) It will change the scaling of x-axis,when the x-axis is logarithmic.xmin=10min To xmax=10max.It is used in frequency response. If A=[1 2 3;4 5 6;7 8 0] Then,

Sorting columns and rows follow the syntax: B=sort(A,dim), where dim is the dimension of the matrix with the value 1 for column; 2 for row. Matrix A is the variable specified by the user.

Example: Sorting columns:

Note that without dim being specified, the default value is 1. The default setting is ascending order. The variable name of the sorted matrix can be omitted if no needed. Sorting column in descending order:

Sorting row in descending order

The inverse of matrix A can be obtained with the command:

SPECIAL MATRICES Zeros (n) creates an nxn matrix whose elements are zero. Zeros (m,n) creates a m-row, n-column matrix of zeros. Ones (n) creates a n x n square matrix whose elements are 1's Ones (m, n) creates a m x n matrix whose elements are 1's. Eye (n) creates the nxn identity matrix with 1's on the diagonal. MISCELLANEOUS COMMANDS length(x) returns the number elements in a vector. size(x) returns the size m(rows) and n(columns) of matrix x. rand

returns a random number between 0 and 1.

rand(A) returns a matrix of size A of random numbers. COMMANDS FOR DISPLAY FORMAT format short format long format short e format long e format short g format long g format bank LIST OF PREDEFINED VARIABLES ans , pi, eps, inf, i , j ELEMENTARY MATH FUNCTIONS sqrt(x) , exp(x) , abs(x) , log(x) , factorial(x) , sin(x) , cos(x) ROUNDING FUNCTIONS Round (x) , fix(x) , ceil(x) , floor(x) , rem(x,y) , sign(x)

ALGEBRAIC OPERATIONS IN MATLAB Scalar Calculations. +

addition

-

subtraction

*

multiplication

/

right division (a/b means a ÷ b)

\

left division (a\b means b ÷ a)

Arithmetic operators. + Plus. X + Y adds matrices X and Y. X and Y must have the same dimensions unless one is a scalar (a 1-by-1 matrix). A scalar can be added to anything. - Minus. X - Y subtracts matrix X from Y. X and Y must have the same dimensions unless one is a scalar. A scalar can be subtracted from anything. * Matrix multiplication. X*Y is the matrix product of X and Y. Any scalar (a 1-by-1 matrix) may multiply anything. Otherwise, the number of columns of X must equal the number of rows of Y. .* Array multiplication X.*Y denotes element-by-element multiplication. X and Y must have the same dimensions unless one is a scalar. A scalar can be multiplied into anything. ^ Matrix power. Z = X^y is X to the y power if y is a scalar and X is square. If y is an integer greater than one, the power is computed by repeated multiplication. For other values of y the calculation

involves eigen values and eigenvectors. Z = x^Y is x to the Y power, if Y is a square matrix and x is a scalar, computed using eigen values and eigenvectors. Z = X^Y, where both X and Y are matrices, is an error. .^ Array power. Z = X.^Y denotes element-by-element powers. X and Y must have the same dimensions unless one is a scalar. A scalar can operate into anything. Relational operators. < > Relational operators. The six relational operators are <, <=, >, >=, ==, and ~=. A < B does element by element comparisons between A and B and returns a matrix of the same size with elements set to one where the relation is true and elements set to zero where it is not. A and B must have the same dimensions (or one can be a scalar). & Logical AND. A & B is a matrix whose elements are 1's where both A and B have non-zero elements, and 0's where either has a zero element. A and B must have the same dimensions (or one can be a scalar). | Logical OR. A | B is a matrix whose elements are 1's where either A or B has a non-zero element, and 0's where both have zero elements. A and B must have the same dimensions (or one can be a scalar). ~ Logical complement (NOT). ~A is a matrix whose elements are 1's where A has zero elements, and 0's where A has non-zero elements. xor Exclusive OR. xor(A,B) is 1 where either A or B, but not both, is non-zero.

See XOR. ARRAY PRODUCTS Sometimes it is desired to simply multiply or divide each element of a matrix by the corresponding element of another matrix. These are called 'array operations" in 'matlab'. Array or element-by-element operations are executed when the operator is preceded by a '.' (Period). Thus a.* b

multiplies each element of a by the respective element of b

a ./ b

divides each element of a by the respective element of b

a .\ b

divides each element of b by the respective element of a

a .^ b

raise each element of a by the respective b element

Matlab Basics Tutorial a = [1 2 3 4 5 6 9 8 7] Matlab should return: a= 1 2 3 4 5 6 9 8 7 t = 0:2:20 t= 0 2 4 6 8 10 12 14 16 18 20

b=a+2

b= 3 4 5 6 7 8 11 10 9 Polynomials In Matlab, a polynomial is represented by a vector. To create a polynomial in Matlab, simply enter each coefficient of the polynomial into the vector in descending order. For instance, let's say you have the following polynomial:

To enter this into Matlab, just enter it as a vector in the following manner x = [1 3 -15 -2 9] x= 1 3 -15 -2 9 For example,

would be represented in Matlab as: y = [1 0 0 0 1]

A = [1; 2; 3] A= 1 2 3 B= [10; 20; 30]

B= 10 20 30 A' 123 B' 10 20 30 A+B 11 22 33

A-B -9 -18 -27 A+10 11 12

13 B-5 5 15 25 A*B ??? Error using ==> * , Inner matrix dimensions must agree. A.*B 10 40 90 A'*B 140

A*B' 10 20 30 20 40 60

30 60 90 A*2 2 4 6 A.*2 2 4 6 A\B 10 A.\B 10 10 10

2\A 0.5000 1.0000 1.5000 2.\A

0.5000 1.0000 1.5000

A/B 0 0 0.0333 0 0 0.0667 0 0 0.1000

A. /B 0.1000 0.1000 0.1000

A/2 0.5000 1.0000 1.5000 A. /2 0.5000

1.0000 1.5000

B^A ??? Error using ==> ^ Matrix dimensions must agree. B. ^A 10 400 27000 A^2 ??? Error using ==> ^ Matrix must be square.

A. ^2 1 4 9

2^A

??? Error using ==> ^ Matrix must be square. 2. ^A 2 4 8 Relational Operators dimensions

Relational operators are used to compare matrices of equal

< Less than <= less than or equal > Greater than >= greater than or equal == Equal ~= not equal

A==B 0 0 0 2 + 2 ==4

1 A>B 0 0 0 A
Vector and Matrix Manipulation Commas or spaces are used to separate elements in a row while semicolons, ; , are used to separate rows. For example: Z = [1,2,3; 4 5 6;7,8,9] Z= 123 456 789 Some subscripting tips can be used to generate matrices, extract parts of matrices, and manipulate matrices. The colon, : , is an important character in matrix manipulation. First, the colon can be used to generate a vector. For example,

y=1:5 y= 12345 The colon, : , can also be used to increment in creating a vector. x = 0:5:50 x= 0 5 10 15 20 25 30 35 40 45 50 The colon can also be used to construct larger matrices or extract portions of a matrix. Using Z as defined above. The following command extracts the first two rows and third column of Z. ZZ = Z(1:2,3) ZZ = 3 6

The colon, : , by itself can be used to specify an entire row or column. The following command gives the second column of Z. ZZZ = Z(:,2) ZZZ = 2 5

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