Multiple Functions On Same Graph:

In matlab we can draw multiple functions on the same graph by considering some basic colors.

Colors                        code

White                           w

Blue                              b

Cyan                             c

Black                            k

Green                           g

Magenta                       m

Yellow                          y

Red                                r

Let us consider a script for two polynomials.

g(x)= 4x⁴+3x³+2x²+2x+9

h(x)=4x³+9x+2

x=[-15:0.01:15];

g=4*x.^4 + 3* x.^3 + 2 * x.^2 + 2 * x + 9

h=4 * x.^3 + 9 * x + 2;

Plot(x, g, ‘k’, x, h, ‘r’)

When you run the file you will output as shown in below.

AXIS SETTING:

In order to provide minimum and maximum values for x and y axis by considering the axis command. With axis command allow us to set axis scale.

Syntax will be:

axis ([xmin  xmax  ymin  ymax])

FOR GENERATING SUBPLOT:

Subplot in matlab is used to divide the current figure and allow us to plot multiple figures in the m rows and n column.

Syntax for matlab

Subplot (m, n, p)

Let us consider a example for plotting

In order to plot the income in the top half of the figure and outgo in the bottom half of the figure,

      income = [3.2 4.1 5.0 5.6];

outgo = [2.5 4.0 3.35 4.9];

subplot(2,1,1); plot(income)

subplot(2,1,2); plot(outgo)

Below figure shows four subplot regions

The following combinations produce asymmetrical arrangements of subplots.

 subplot(2,2,[1 3])

subplot(2,2,2)

subplot(2,2,4)

IMPORTING DATA:

Where in Matlab importing data is defined as obtaining data from an external file. By using the importing data function we obtain data of different formats with various functions. There are four import functions in Matlab that are described as follows.

C= importdata (format): data from the file named as format is loaded in to the array C.

C=importdata (‘-pastespecial’): loading of records from the system clipboard in place of the document.

C= importdata (___, delimiterIn, headerlinesIn): In this function data is loaded from ASCll file, or clipboard, while the numerical reading starts from line headerlinesIn+1.

C= importdata (___, delimiterIn): In order to separate the column ASCII file or clipboard data we can use delimiterIn.

EXPORT DATA:

In matlab export data means write data in to the file. In matlab there various export data functions, Rectangular, delimited ASCII data file from an array. Diary (or log) document of keystrokes and the ensuing textual content output. Besides from the above there are another way to export a numeric array as a delimited ASCll data file:

With the help of save function we can specify the -ASCII qualifier using the dlmwrite function.

PLOTTING:

In order to plot a graph we use a graph function, to take the following steps:

To draw a graph we should outline the X values from the desired variety for which the graph is plotted.

Let us define the function by considering z=f(x)

Now let’s call plot command, as plot(x,y)

Let us plot simple function y=x for the value in the range of 0 to 200 with an increment in the value of 10.

X= [0:10:200];

z=x;

Plot(x, y)

ADDING TITLE, LABELS AND GRID LINES ON THE GRAPH:

In order to adjust the value in the graph we consider title labels and grid lines. The x label and y label instructions generate labels alongside x-axis and y-axis. The name command permits you to position a name at the graph. The grid on command permits you to position the grid traces at the graph.

Concatenating Matrices:

If you concatenate two matrices it creates a large matrix. Pair of square braces [] is a concatenate operator.

Matlab as two types of concatenate as follows:

Horizontal concatenation:

When you concatenate two matrix which are separated by using commas, they are called horizontal concatenation.

Vertical concatenation:

When you concatenate two matrix which are separated by using semicolon, they are called vertical concatenation.

Let us consider an example of this two concatenation:

a = [10 12 15; 14 8 6; 17 8 9]

b = [12 11 45; 8 1 -9; 18 2 11]

 c = [a, b]

d = [a; b]

Output will be obtained as

a= 10 12 15

     14 8 16

     17 8 9

b = 12 31 45

      8 0 -9

      45 2 11

 c = 10 12 15 12 11 45

       14 8   16   8   1 -9

       17 8   9   18 2 11

d=10 12 23

     14 8 6

     27 8 9

   12 31 45

   8 0 -9

   45 2 11

Matrix multiplication:

Where in matrix multiplication, the elements of rows in the first matrix is multiplied with the columns in the second matrix.

In matlab matrix multiplication is represented by ‘*’.

In matrix multiplication column in A matrix is equal to rows in B matrix.

Let us consider an example

a = [2 3 4; 1 2 3; 1 3 5]

b = [2 3 -1; 2 1 3; 5 0 -2;]

prod = a * b

Output will be

prod = 30 9 -1

           21 5 -1

           33 6 -2

Determinant of matrix:

Determinant of matrix is determined by using det function in matlab, and it represented of a matrix A is det(A). Let us consider an example.

a = [ 1 2 6; 2 3 4; 1 4 5]

 det(a)

output will be

ans =17

Inverse of Matrix:

The inverse of a matrix in matlab of A is represented by A−1 such which holds the following relationship:

AA⁻¹ = A⁻¹ A = 1

If the determinant of matrix is zero then the inverse will not exist and the matrix is singular.

Inverse of matrix is determined by inv function in matlab and it represented by inv(A)

STRING:

The string is really a vector whose additives are the numeric codes for the characters. Matlab has exclusive kind of textual content string.

Character array: best when considering individual letters of text, text is stored in two-dimensional array. The rule of all rows should have same number of column.

Cell array: best when considering word.

Let us create an uncomplicated string that may include a unique quote.

msg = ‘You”re right!’

            msg =

You’re right!

create the string, name, the usage of strategies of concatenation.

name = [‘Thomas’ ‘ R. ‘ ‘Lee’]

name = strcat(‘Thomas’,’ R.’,’ Lee’)

Create a vertical array of strings.

C = strvcat (‘Hello’,’Yes’,’No’,’Goodbye’)

C =

Hello 

Yes   

No    

Goodbye

Create a cell array of strings.

S = {‘Hello’ ‘Yes’ ‘No’ ‘Goodbye’}

S =

    ‘Hello’    ‘Yes’    ‘No’    ‘Goodbye’

Deleting row or column in matrix:

An empty braces [] will define the entire row and column of a matrix is deleted. Let us consider an example deleting 2^nd row of the:

 a = [3 4 5 6 7; 2 3 4 5 6; 1 2 3 4 5;  4 5 6 7 8];

a ( 2 , : ) = []

if we want to delete the 3^rd  column of the given example

a = [2 3 4 5 6; 1 2 3 4 5; 3 4 5 6 7; 4 5 6 7 8];

a(: , 3)=[]

Matrix Operation:

Now let us discuss some commonly used matrix operations are:

Addition and subtraction of matrix:

While performing matrix addition and subtraction when both the operand of matrices must have same number of rows and columns.

Let us consider an example

a = [2 1 3; 4 5 6; 7 8 9];

b = [4 5 6; 1 2 3; 7 8 9];

c = a + b

a = [3 2 4; 4 5 6; 7 8 9];

b = [2 1 3; 3 2 1; 4 5 6];

d = a – b

If we run script file we get:

c= 6 6 9

     5 7 9

     14 16 18

d= 1 1 1

     1 3 5

      3 3 3

Division of (right, left) matrix:

If we want to perform the division of two matrices left (\) or right (/) division operation, when both the operand of matrices must have same number of rows and columns.

Now let us consider an example:

a = [1 2 3; 4 2 6; 7 5 2];

 b = [3 5 6; 2 3 8; 5 7 2];

 c = a / b

d = a \ b

If we run the above example we get output as:

c = -0.7916   0.1666   0.2083

      1.0833   4.3333   0.9166

       2.9583 4.6666   3.8333

 d =

-3.27778   -1.05556   -4.86111

 -0.11111   0.11111   -0.27778

 3.05556      1.27778   4.30556

Transpose of matrix:

The transpose operation will be defined as switching of the rows and columns in a matrix. And it will be represented as a single quote (‘).

Let us consider example:

a = [11 12 13; 14 8 6; 27 8 9]

b = a’

It displayed has:

a = 11 12 13

      14 8   6

      27 8   9

b = 11 14 27

       12 8   8 

       13 6   9

Array:

All the variables in matlab are arrays. A scalar is an array with one element, where as a array with one row and one column is called vector. An array with multiple rows and columns is called matrix.

Simply an array of order M x N with a set of number is arranged in a rectangular block of M horizontal rows and N vertical columns.

Creating one dimension array:

 One dimension array defined as numbers are listed in one row and one column, simply known as vector. Then the i^th element of a vector k= [k₁ k₂ k₃ k₄ … k_n]

  Row vector:

    In order to create a row vector provide the space or comma between the elements inside the brackets;

dates = [1     4    10    17    25]

             Or

dates = [1, 4 ,10,17,25]      

Column Vector: In order to create a row vector provide the semicolon between the elements inside the brackets;

Value= [127; 130; 136; 145; 158; 178; 211]

In colon notation, the first number defines the starting values, whereas the second number defines spacing and last number defines ending value.

Value= 2:2:10

Creating a two-dimensional array:

In these the number of rows are equal two number of columns, A matrix is created with the aid of using assigning the elements of the matrix to a variable. This is carried out with the aid of using typing the elements, row with the aid of using row,  within inside the square brackets [ ].

First kind the left bracket [, then type the first row separating the elements with spaces or commas. In order type, the text in the next row types a semicolon or press Enter. Type the right bracket] on the stop of the final row.