LAB: 5 POLYNOMIAL EVALUATIONS, ROOTS
OF POLYNOMIAL, ARITHMETIC OPERATIONS
ON POLYNOMIALS.
AIM: To write a program using the concept of polynomials in SCILAB
SOFTWARE REQUIRED: SCILAB
COMMANDS USED:
[Pl fill all the polynomial commands you use for executing the following Questions]
QUESTION 1: Evaluate the value of the polynomial y=s2+4s+2 at s = -2, s = 4.5 and s = 2+4i.
Answer :
Step 1: For polynomials use the command p = poly([2,4,1],"s","coeff")
Step 2: The polynomial s2 + 4s + 2 will be displayed.
Step 3: Find the values of the polynomial for s = -2, 4.5, 2 + 4i by the command horner(p, -2), horner(p,
4.5), horner (p, 2 + 4*%i).
Output:
-->p = poly([2,4,1],"s","coeff")
p =
2 + 4s + s2
-->horner(p, -2)
ans =- 2.
-->horner(p, 4.5)
ans =40.25
-->horner (p, 2 + 4*%i)
ans = - 2. + 32.i
QUESTION 2: Find the roots of the polynomial s2+4s+9=0, s3+3s2+4s+1=0
Answer:
Step 1: To find out the given polynomial use the above command and denote qw for the polynomial
s2 + 4s + 9 = 0 and q for s3 + 3s2 - 4s + 1 = 0. Ex. q = poly([1,-4,3,1],"s","coeff")
Step 2: To find the roots of the given polynomial, use the command roots(qw) and roots (q).
Output:
-->qw = poly([9,4,1],"s","coeff");
-->q = poly([1,-4,3,1],"s","coeff");
-->roots(q)
ans =
- 4.0489173
0.6920215
0.3568959
-->roots(qw)
ans =
- 2. + 2.236068i
- 2. - 2.236068i
QUESTION 3: Find the roots of the Polynomial s4+3s3-15s2-2s+9=0.
Answer:
Step : Enter the polynomial command to find out the given polynomial and denote it by q. Use the
root command (i.e.root(q)) to find out its roots.
Output:
-->q = poly([9,-2,-15,3,1],"s","coeff");
-->roots(q)
ans =
- 5.5745065
2.5836011
- 0.7950666
0.7859721
QUESTION 4: Add and subtract the two polynomials, i) a=(s2+8s+3) and b=(s2+2).
ii) c=(8s3+6s2+5s+10) and d= (s3+2)
Answer:
Step 1: Enter the polynomial command to find out the given polynomials a and b and c and d.
Step 2: To add and substract use the commands addition operator (a + b),(c+d) and substraction
operator (a - b),(c-d).
Result:
(i)
-->a = poly([3,8,1],"s","coeff");
-->b = poly([2,0,1],"s","coeff");
-->a+b
ans =
5 + 8s + 2s2
-->a-b
ans =
1 + 8s
(ii)
-->c = poly([10,5,6,8],"s","coeff");
-->d = poly([2,0,0,1],"s","coeff");
-->c+d
ans =
12 + 5s + 6s2+ 9s3
->c-d
ans =
8 + 5s + 6s2 + 7s3
QUESTION 5: Evaluate the product of two polynomials i) (s3+4s2+5s+1) and (s2+2s+1).
ii) (s+3),(s+6) and (s+2).
Answer:
(i)
Step: Enter the polynomial command to find out the given polynomials a = s3 + 4s2 + 5s + 1 and b
= s2 + 2s + 1 and use the multiplication operator (c*d) for the desired result.
(ii)
Step : Enter the polynomial command to find out the given polynomials. Denote them by p,q and
r.{Ex. p = poly([3,1],"s","coeff")}.
Result:
(i)
-->a = poly([1,5,4,1],"s","coeff");
-->b = poly([1,2,1],"s","coeff");
-->a*b
ans =
1 + 7s + 15s2 + 14s3 + 6s4 + s5
(ii)
-->p = poly([3,1],"s","coeff");
-->q = poly([6,1],"s","coeff");
-->r = poly([2,1],"s","coeff");
-->p*q*r
ans =
36 + 36s + 11s2 + s3
QUESTION 6: Divide the polynomial P by Q where P=s3+4s+10 and Q=s3+3s2+4s+2.
Answer:
Step : Enter the polynomial command to find out the given polynomials P = s3 + 4s + 10 and Q =
s3 + 3s2 + 4s + 2 and use the division operator (P/Q) for the desired result.
Result:
-->q = poly([2,4,3,1],"s","coeff");
-->p = poly([10,4,0,1],"s","coeff");
-->p/q
ans =
10 + 4s + s3
--------------2 + 4s + 3s2 + s3
QUESTION 7: i) Determine the polynomial with roots = -2, 4 and 6.
ii) Determine the polynomial whose roots are (-0.5 +0.866i) and (-0.5 -0.866i).
Answer:
(i)Step : To find the polynomial from its roots, use the command p = poly([-2,4,6],"s","roots")
where -2,4,6 are the roots.
(ii)Step : To find the polynomial from its roots, use the command p = poly([-0.5+ 0.866*%i,-0.5 0.866*%i],"s","roots") where -0.5+ 0.866i and -0.5 - 0.866i are the roots.
Result:
(i)p = 48 + 4s - 8s2 + s3
(ii) p =0.999956 + s + s2
QUESTION
1 2 0
A= 0 2 3
1 2 4
8:
Determine
the
characteristic
equation
of
the
matrix
A.
Answer:
Step 1 : First evaluate the given matrix by the matrix command A = [1 2 0; 0 2 3; 1 2 4]
Step 2 : To find the characteristic equation of the polynomial with eigen value K, use the command
poly charPoly
Step 3 : So the command charPoly = poly(A,"K") gives the characteristic equation of the
polynomial with the Eigen Value K.
Result:
- 8 + 8K - 7K2 + K 3
QUESTION 9: Evaluate the derivative and integral of the polynomial
p(s) =s4+4s3+10s2+20s+15. Assume the constant of integration to be 1.
Answer:
To find the derivative:
Step 1: Enter the polynomial command to find out the given polynomial s4 + 4s3 + 10s2 + 20s +
15 and denote it by q.
Step 2: pd=derivat(q) gives the derivative of the polynomial as pd = 4s3 - 13s2 + 20s + 20.
To find the integration:
QUESTION 10: Find a polynomial of degree 3 to fit the following data:
Answer:
Step : The function reglin fits polynomials of degree 3.
X
2
5
7
9
Y
24
156
384
500
For example, The slope of the line is given by m = c(1) and the y-intercept is given by b = c(2).
The Linear fit is y = mx + b
(matlab): c = polyfit([1 2 3],[2 4 8],1) returns 3.0000 -1.3333 and the equation stands as y = 3x 1.3333
(scilab): [m b] = reglin([1 2 3],[2 4 8],1) returns b = -1.3333333,m = 3.0000
So, for a polynomial of degree 3, the fit is y = x3 + ax2 + bx + c.
The command for the polynomial is [a b c] = reglin([ 2 5 7 9 ],[ 24 156 384 500 ],3).
Result:
c =
34.185858
b =
- 141.98131
a =
70.953271
RESULT: The programs were written in SCILAB using commands related to polynomials and
were executed successfully.
EXPT NO: 6
DATE:1/04/2015
TITLE: IMPLEMENTATION OF INPUT OUTPUT FUNCTIONS
AIM: To study various input output functions using SCILAB.
SOFTWARE REQUIRED: SCILAB
QUESTION 1: Write a program to illustrate the use of keyboard command
PROGRAM :
clc;
clear all;
close all;
a = eye(5);
for j= 1:5,
disp(j);
if j ==3
keyboard;
end;
end;
OUTPUT:
1
2
k>>
>>return
QUESTION 2:
Write a program to illustrate the use of keyboard command to check the intermediate results
and to add new data.
Z
PROGRAM:
a=10;
b=16;
x=a+b;
y=x/2;
keyboard
ans=y-3+9
OUTPUT:
ans =
14
QUESTION 3: Illustrate the use of menu function, to choose a particular size from three
different given sizes i.e., Large, Medium, Small
PROGRAM:
clc;
clear all;
close all;
i=menu('choose a size' ,'large' , 'medium', 'small')
OUTPUT:
QUESTION 4:
Using menu function, Select a candidate of your choice from the given choices, i.e., Kiran,
Roshan, Surinder, John, Alka, Umesh, Abha and Neha
PROGRAM:
choice=menu('select student','Kiran','Roshan','Surinder','John'
,’Alka’,’Umesh’,’Abha’,’Neha’);
disp(choice);
OUTPUT:
QUESTION 5:
Write a program to illustrate the use of pause command.
PROGRAM:
p=[1 2;3 4];
q=[5 6;7 8];
disp('the matrix p is given as:');
disp(p);
disp('program is paused,press any key to display q');
pause
disp('the matrix q is given as :');
disp(q);
z=p+q;
disp('program is paused,press any key to display sum');
pause
disp(z);
OUTPUT:
the matrix p is given as:
1 2
3 4
program is paused,press any key to display q
the matrix q is given as :
5 6
7 8
program is paused,press any key to display sum
6 8
10 12
QUESTION 6:
Illustrate the use of fprintf function to varying display the values of x varying from 0 to 180
with four equal intervals and also display its sine values.
PROGRAM:
x=0:45:180;
y=[x;sin(x)];
disp(y);
fprintf('%6.2f%6.4f\n',y);
OUTPUT:
0.0
0.0000
45.00 0.7071
90.00 1.0000
135.00 0.7071
180.00 0.0000
QUESTION 7:
Suppose x has five uniformly distributed values between 0 and 2. Represent the values of x in
the following formats (fid =0, that is, standard screen Output’s):
(a)
Default format
(b)
Floating point format with width 6 and precision 3 and newline
(c)
Floating point format with zero padding and newline
(d)
Signed values and newline
(e)
Exponential format and newline
(f)
Compact format and newline
PROGRAM:
clc;
clear all;
close all;
x=0:0.4:2;
disp(x);
fprintf('%6.3f\n',x);
fprintf('%0.6.3f\n',x);
fprintf('%16.3f\n',x);
fprintf('%6.3\n',x);
fprintf('%g\n',x);
OUTPUT:
0 0.4000
0.8000
1.2000
1.6000
2.0000
0.000
0.400
0.800
1.200
1.600
2.000
0.000
0.400
0.800
1.200
1.600
2.000
0
0.4
0.8
1.2
1.6
2
QUESTION 8:
Display the following statement as formatted output using format command: ‘The largest 3
digit no. is: 999’:
PROGRAM:
clc;
clear all;
close all;
fprintf('the largest 3 digit number.is%f\n',999);
OUTPUT:
the largest 3 digit number is 999
QUESTION 9:
Illustrate use of fscanf to read a file test.txt having first ten integer numbers in
(a)
(2 X 5) array format
(b)
One column
(c)
(5 X 2) array format
PROGRAM:
clc;
clear all;
close all;
fid=fopen('text.txt','r')
[a,count1]=fscanf(fid,'%f',[2,5]);
fid=fopen('text.txt','r');
[a,count2]=fscanf(fid,'%f');
fid=fopen('text.txt','r');
[a,count3]=fscanf(fid,'%f',[5,2]);
OUTPUT:
a=
1 3 5 7 9
2 4 6
count1 =
10
8 10
a=
1
2
3
4
5
6
7
8
9
10
count2=
10
a=
1
6
2
7
3
8
4
9
5
10
count3 =
10
QUESTION 10:
llustrate the use of fwrite function for writing binary data of different formats to a file named
check.txt.
PROGRAM:
clc;
clear all ;
close all;
a=[2 4 6 ; 3 5 7];
b=105;
c='today is world cup final'
fid=fopen('check.txt','w')
x=fwrite (fid,a,'double')
y=fwrite (fid,b,'short')
z=fwrite (fid,c,'char')
fclose(fid)
OUTPUT:
c=
today is world cup final
fid =
3
x=
6
y=
1
z=
24
ans =
0
QUESTION 11:
PROGRAM:
clc;
clear all ;
close all;
fid1 =fopen('check.txt','r')
[A, count1]=fread(fid1,[2,3],'double')
[B,count2]=fread(fid1,[1],'short')
[c,count3]=fread(fid1,[24],'char')
c=c';
c=setstr(c)
fclose(fid1)
OUTPUT:
fid1 =
3
A=
2
3
4
5
count1 =
6
B=
105
count2 =
1
c=
116
111
100
97
121
32
105
115
32
119
111
114
108
6
7
100
32
99
117
112
32
102
105
110
97
108
count3 =
24
c=
today is world cup final
ans =
0
QUESTION 12:
Write a program to generate first five odd numbers and illustrate the use of fopen, fprintf and
fclose commands related to file input-output
PROGRAM:
clc;
clear all;
close all;
A(1)=1;
for i=1:4
A(i+1)=A(i)+2;
end;
fid=fopen('odd.txt','w');
fprintf(fid,'First five odd numbers\n');
fprintf(fid,'*********************\n');
fprintf(fid,'%3i\n',A);
fclose(fid);
OUTPUT:
First five odd numbers
******************
1
3
5
7
9
RESULT: Thus the various input output functions are studied and program’s were execute.
EXPERIMENT NO: 7
DATE:1/04/2015
TITLE: STUDY OF SCILAB GRAPHICS
AIM: To study useful commands and functions that can be applied to SCILAB graphics using
SCILAB.
SOFTWARE REQUIRED: SCILAB
QUESTION 1: Plot the given curve by equation y = x^2 where x varies 0 to 10.
PROGRAM:
clc;
clear all;
close all;
x=0: 1: 10;
y=x.^2;
plot(x,y)
OUTPUT:
QUESTION 2: plot a graph for the following variables
a = [1 13 6 9 23 12]
b = [1-2i,3+4i, 5+6i, 3+8i, 4+9i, 23+12i]
PROGRAM:
clc;
clear all;
close all;
a=[1 13 6 9 23 12 ]
plot(a)
b= [1-2i,3+4i,5+6i,3+8i,4+9i,23+12i]
plot(b)
OUTPUT:
QUESTION 3: Plot the curve given by equation y = sin(x), as x varies from 0 to 2π .Also label
the x-axis and y-axis and provide a suitable title to the plot.
PROGRAM:
clc;
clear all;
close all;
x=0:pi/100: 2*pi;
y=sin(x);
plot(x,y);
xlabel('x-axis');
ylabel('y-axis');
title('plot of sine wave');
OUTPUT:
QUESTION 4:Plot the curve given by the equation a = 10 e^-t for t = 0 to 5 show the f=grid
lines on the plot.
PROGRAM:
clc;
clear all;
close all;
t=0:0.1:5;
a=10*exp(-t);
plot(t,a);
xlabel('time(t) in sec');
ylabel('output');
title('plot of a=10*exp(-t)');
grid on;
OUTPUT:
QUESTION 5:Plot the function b=4a^2 for 0< a <20 and illustrate the box command.
PROGRAM:
clc;
clear all;
close all;
a=0:0.05:20;
b=4*a.^2;
plot(a,b);
box off;
xlabel('x-axis');
ylabel('y-axis');
title('plot of function b=4*a.^2 ');
OUTPUT:
QUESTION 6: Illustrate the use of gtext command on the plot of the equation y = 3x + 5 for x =
0 to 10.
PROGRAM:
clc;
clear all;
close all;
x=0:0.5:10;
y=3*x+5;
plot(x,y);
gtext('it is a straightline');
grid on
xlabel('x-axis----->time (t)');
ylabel('y-axis----->output (y)');
title('plot of y=3*x+5 ');
OUTPUT:
QUESTION 7: Illustrate the use of axis command with specified limits for plot of function y =
3𝑥 2 + 2𝑥 + 5 for x = -5 to 10.
PROGRAM:
clc;
clear all;
close all;
x=-5:0.1:10;
y=3*x.^2+2*x+5;
plot(x,y);
axis([-5 5 0 20]);
xlabel('x-axis');
ylabel('y-axis');
title('plot of function y=3.x62+2.x+5 ');
grid on
OUTPUT:
QUESTION 8: Illustrate the use of plot command for generating multiple plots
PROGRAM:
clc;
clear all;
close all;
x1=0:0.1:20;
y1=(0.1*x1).*sin(x1);
x2=0:0.1:20;
y2=sin(x2);
x3=0:0.1:20;
y3=cos(x3);
plot(x1,y1,x2,y2,x3,y3);
gtext('curve y1');gtext('curve y2');gtext('curve y3')
title('multiple plot using plot command');
xlabel('x-axis');
ylabel('y-axis');
grid on ;
OUTPUT:
QUESTION 9: Illustrate the use of hold command for generating multiple plots
PROGRAM:
clc;
clear all;
close all;
x=0:0.5:10;
y1=5+4*x;
plot(x,y1);
hold on;
y2=x.^2;
plot(x,y2);
hold off;
gtext(' y1=5+4*x');
gtext('y2=x.^2');
title('multiple plot using hold command');
xlabel('x-axis');
ylabel('y-axis');
OUTPUT:
QUESTION 10: Illustrate the use of line command to generate multiple plots.
PROGRAM:
clc;
clear all;
close all;
x=1:0.1:100;
y1=sqrt(x.^2+1);
y2=5*x+20;
y3=10*x+20;
plot(x,y1);
gtext('y1=sqrt(x.^2+1)');
line(x,y2);
gtext('y2=5*x+20');
line(x,y3);
gtext('y3=10*x+20');
title('multiple polts using line command');
grid on;
OUTPUT:
QUESTION 11: Illustrate the different style options as used in plots.
PROGRAM:
clc;
clear all;
close all;
t=0:0.1:10;
y1=3*t.^2+5*t+6;
y2=t.^3+4;
plot(t,y1,'r',t,y2,'mo');
xlabel('x-axis');
ylabel('y-axis');
title('plot illustrating use of style option');
grid on;
OUTPUT:
QUESTION 12: The table below gives of induced voltage E1 V/s field current If,for a dc
generator operating at N = 1500 rpm, plots the open circuit characteristics for this generator at
1500 rpm, 1200 rpm and 1000 rpm on the same sheet (Note E α N).Use the proper hold and
legend commands.
If
0
0.4
0.1
1.45
2.0
3.0
4.0
5.0
6.0
E1
5
30
70
110
PROGRAM:
clc;
clear all;
close all;
If=[0.0 0.4 1.0 1.45 2.0 3.0 4.0 5.0 6.0];
E1=[5 30 70 110 150 215 240 250 260];
plot(If,E1,'-');
hold on;
E2=(1200/1500)*E1;
plot(If,E2,':');
E3=(1000/1500)*E1;
plot(If,E3,'-.');
legend('1500rpm','1200rpm','1000rpm');
hold off;
title('use of legend command');
xlabel('x-axis');
ylabel('y-axis');
OUTPUT:
150
245
240
250
260
QUESTION 13: Divide the figure window onto four sub-windows and plot the following
functions:
1.
2.
3.
4.
Plot v v/s I, where v = 4*I and I = 1, 2, 3, 4, on the upper left sub-window.
Plot y v/s x, where y = 𝑥 2 and x = 1, 2, 3, 4, on the upper right sub-window.
For t = 0:2 * pi in step t = pi/60, plot sin(t) v/s t on the lower left sub-window.
For t = 0: pi/30:2 * pi, plot cos(t) v/s t on the lower right sub-window.
PROGRAM:
clc;
clear all;
close all;
I=1:4;
v=4*I;
subplot(2,2,1);
plot(I,v);
title('voltage v/s current');
xlabel('I-amps');
ylabel('v-volt');
x=[1 2 3 4];
y=[1 4 9 16];
subplot(2,2,2);
plot(x,y);
title('parabolic plot');
xlabel('x--->');
ylabel('y--->');
t=0:pi/60:2*pi;
subplot(2,2,3);
plot(t,sin(t));
xlabel('t--->');
ylabel('sin(t)');
title('plot of sine function');
subplot(2,2,4);
plot(t,cos(t));
xlabel('t--->');
ylabel('cos(t)');
title('plot of cos function');
OUTPUT:
QUESTION 14: Plot function x = 𝑒 −𝑎 , y = 𝑎2 where 0<=a<=10, using semilogx function.
PROGRAM:
clc;
clear all;
close all;
time=0:0.2:8;
w=190*(1-exp(-0.15*time));
torque=8*exp(-0.15*time);
power=w.*torque;
semilogy(time,power)
grid on
xlabel('Time ''t''[linear scale]');
ylabel('power=w.*torque[logarithmic scale]');
title('Illustrate the use of semilogy command')
OUTPUT:
QUESTION 15: plot power v/s time for 0<t<8 sec, with power on the log scale and time in the
linear scale of a motor whose performance equations are given as follows:
Rotational speed, w = 190(1 - 𝑒 −0.15𝑡 )
Torque, T = 8𝑒 −0.15𝑡
Power = w x T
PROGRAM:
clc;
clear all;
close all;
time=0:0.2:8;
w=190*(1-exp(-0.15*time));
torque=8*exp(-0.15*time);
power=w.*torque;
semilogy(time,power)
grid on
xlabel('Time ''t''[linear scale]');
ylabel('power=w.*torque[logarithmic scale]');
title('Illustrate the use of semilogy command')
OUTPUT:
QUESTION 16: plot magnitude v/s frequency on log-log scale for the transfer function
1
G(s) = 1+0.02𝑠
Where s = jw = j2πf and f is the frequency.
PROGRAM:
clc;
clear all;
close all;%
%program used to illustrate the use of loglog command
%Plot loglog graph beween frequency and magnitude of given function
freq=1:2:1000;
Gs=1./(1+j*2*pi*freq*0.02);
mag=abs(Gs);
loglog(freq,mag);
grid on;
xlabel('Frequency''f''[Logarthemic scale]');
ylabel('Magnitude [Logarthemic scale]');
title('Illustrate the use loglog command');
OUTPUT:
QUESTION 17: Plot the following fuction on a polar plot
𝝅
f(𝜃) = sin 4θ for- - 𝟐 ≤ θ ≤
𝝅
𝟐
where θ is radius
PROGRAM:
clc;
clear all;
close all;
%Program to illustrate the use of polar command
%Plot function f = sin(4*theta) as per the given data
theta = -pi/2:pi/40:pi/2;
f = sin(4.*theta);
polar(theta,f,'r-');
title('Plot of funcion f = sin(4*theta) using polar function');
OUTPUT:
QUESTION 18: The area function is similar to plot function except the area under plot is filled
with colour. The syntax is given as area(x, y).
PROGRAM:
clc;
clear all;
close all;
%Program to plot y = cos(x) as x varies from 0 to 4pi using area function
x=0:0.02:4*pi;
y=cos(x);
area(x,y);
xlabel('x-axis');
ylabel('cos x');
title ('graph to plot y = cos (x) using area function');
OUTPUT:
QUESTION 19: Plot a bar graph for the data given as
x = [0 1 2 3 4 5 6] and y = [10 15 25 20 30 27 19]
PROGRAM:
clc;
clear all;
close all;
%program to show bar function
x=[ 0 1 2 3 4 5 6];
y=[10 15 25 20 30 27 19 ];
bar(x,y, 'c');
xlabel('x-axis');
ylabel('y-axis');
title('graph to show bar function');
OUTPUT:
QUESTION 20: Plot a bar graph to show the comparison of average temperature in City A, B,
and C for the months from September to February. The data is given as
City A
City B
City C
September
31
28
24
October
29
26
22
November
28
25
20
December
27
24
16
January
26
22
17
February
29
25
20
PROGRAM:
clc;
clear all;
close all;
%Program to show average Temparature of city A, B and C for
%months from sept to feb using bar graph
temp=[31,28,24; 29 26 22;28 25 20; 27 24 16; 26 22 17; 29 25 20];
bar(temp,'group');
ylabel('Temparature in Celcius');
xlabel('Months from Sept to Feb');
legend('City A','City B','City C');
title ('temperature of City A, City B and City C for months from September to
February');
OUTPUT:
QUESTION 21: Illustrate the use or barh function of
x = [0 1 2 3 4 5 6] and y = [10 15 25 20 30 27 19]
PROGRAM:
clc;
clear all;
close all;
%program to show 'barh' function
x=[0 1 2 3 4 5 6];
y=[10 15 25 20 30 27 19];
barh(x,y, 'g');
xlabel(x-axis);
ylabel(y-axis);
title('Graph to show barh function');
OUTPUT:
QUESTION 22: Illustrate the use of hist function
PROGRAM:
clc;
clear all;
close all;
%program to illustrate the use of hist function
x=randn(100,1)*pi;
hist(x);
title('Histogram to show 100-random values in 10-bins');
OUTPUT:
QUESTION 23: Illustrate the use of hist function with 15 bins
PROGRAM:
clc;
clear all;
close all;
%program to illustrate the use of hist function with 15 bins
x=randn(200,1);
hist(x,15);
title('Histogram to show 200 random values in 15-bins');
OUTPUT:
QUESTION 24: Illustrate the use of hist function with no. of bins specified in a vector p.
PROGRAM:
clc;
clearall;
closeall;
%program to illustrate the use of hist function with no. of bins specified
%by a vector
x=randn(300,1);
p=-2:0.1:2;
hist(x,p);
title('Histogram to show 300 random values in no. of bins specified by a vector');
OUTPUT:
QUESTION 25 :Illustrate the use of rose function
PROGRAM:
clc;
clearall;
closeall;
%Program to illustrate the use of rose function
x=randn(100,1)*pi; %Generate 100 random data points
%Draw the Histogram with no. of bins in vector p rose(x)
title('Polar histogram to show 100 random values using rose function');
OUTPUT:
QUESTION 26: Illustrate the use of rose function
PROGRAM:
%Program to illustrate the use of rose function
x=randn(500,1)*pi; %Generate 500 random data points
%Specifies the number of bins in a vector v
v=-pi:0.5:pi;
%Draw the histogram with no. of bins in vector
rose (x,v);
title('Polar Histogram using rose function with no. of bins specified by a
vector');
OUTPUT:
QUESTION 27: Illustrate the use of pie function to show the concentration of different
industries in the region as per the following data
NAME OF THE INDUSTRY
NO. OF INDUSTRIAL UNITS
Cement
4
Textile
8
Software
20
Chemical
2
Telecom
7
Banking
10
PROGRAM:
clc;
clearall;
closeall;
%program to draw a pie chart showing concentration of different Industries
%in a region
industry=[4 8 20 2 7 10];
pie(industry);
title('Pie chart showing concentration of different industries');
OUTPUT:
QUESTION 28: Repeat question 27 to show sliced pie chart
PROGRAM:
clc;
clearall;
closeall;
%program to draw a sliced pie chart showing concentrtion of different
%industries in a region
industry =[4 8 20 2 7 10];
show =[0 0 0 1 0 1];
pie(industry, show)
title('Sliced Pie chart showing the concentration of Different industries');
legend('Cement','Textile','Software','Chemical','Telecom','Banking',3);
OUTPUT:
QUESTION 29:
Illustrate the use of pie chart
NAME OF THE INDUSTRY
NO. OF INDUSTRIAL UNITS
Cement
4
Textile
8
Software
20
Chemical
2
Telecom
7
Banking
10
PROGRAM:
clc;
clear all;
close all;
%program to draw a pie chart showing the concentration of different
%industries in a region
industry =[4 8 20 2 7 10];
show =[0 1 0 0 1 0];
label= ({'cement','Textiles','Software','Chemical','Telecom','Banking'});
pie(industry,show,label);
title('Labelled and Sliced Pie chart showing the concentration of Different industries')
OUTPUT:
QUESTION 30:Draw the stairs plot to show the function y=x.*x,where -2<=x<=2
PROGRAM:
clc;
clear all;
close all;
%Program to show stairs plot to show the function y = x.*x
x=-2:0.1:2;
y=x.*x;
stairs(x,y,'r');
grid on;
xlabel(' x-axis');
ylabel('y = x.*x');
title('Stairs plot to show the function y = x.*x');
OUTPUT:
QUESTION 31: Draw the stairs plot for the following data:
X = [0 2 3 4 5 7]
Y = [5 -1 8 4 7 3]
PROGRAM:
clc;
clear all;
close all;
%program to Illustrate the stairs function
x = [0 2 3 4 5 7];
y = [5 -1 8 4 7 3];
stairs(x,y,'*-.');
box off;
title('Graph to Illustrate stairs function');
xlabel('x-axis');
ylabel('y-axis');
OUTPUT:
QUESTION 32: Draw the stem plot for the following data:
X=[0 1 2 3 4 5 6]
Y=[3 -1 6 -4 5 2 3]
PROGRAM:
clc;
clear all;
close all;
%program to Illustrate stem function
x = [0 1 2 3 4 5 6 ];
y = [3 -1 -6 4 5 2 3];
stem(x,y);
title('Graph to Illustrate the stem function');
xlabel('x-label');
ylabel('y-axis');
OUTPUT:
QUESTION 33: Draw the compass plot for the following data:
Z=[1+1i 4-8i 20+7i 6+8i 9+2i 12-4i]
PROGRAM:
clc;
clear all;
close all;
%program to Illustrate the compass function
z= [1+1i 4-8i 20+7i 6+8i 9+2i 12-4i];
compass(z);
title('Graph to Illustrate the compass function');
OUTPUT:
QUESTION 34: Given is x=t2 and y=4t for -4<t<4.Obtain a 3-D plot showing the matrix in (x,y)
space as a factors for time
PROGRAM:
clc;
clearall;
closeall;
%program to illustrate the plot3 funtion
t=-4:0.1:4;
x=t.^2;
y=4*t;
plot3(x,y,t);
gridon;
xlabel('x-axis');
ylabel('y-axis');
zlabel('z-axis');
title('illustrate of plot3 function');
OUTPUT:
QUESTION 35: Draw 3-D bar graph for following data
X=[0 1 2 3 4 5 6]
Y=[5 17 25 21 31 27 19]
PROGRAM:
clc;
clearall;
closeall;
%program to plot 3-D graph using bar3 functtion
x=[ 0 1 2 3 4 5 6];
y=[5 17 25 21 31 27 19 ];
bar3(x,y,'g');
xlabel('x-axis');
ylabel('y-axis');
title('Graph to show bar3 function');
OUTPUT:
QUESTION 36:Draw a 3-D horizontal bar to show the growth of a state as per the following
date:
Year=[1992 1993 1994 1995 1996 1997 1998]
Growth (in % age) = [12 15 10 8 6.5 9 11]
PROGRAM:
clc;
clearall;
closeall;
%program to illustrate use of bar3h function function
year=[1992 1993 1994 1995 1996 1997 1998];
growth=[12 15 10 8 6.5 9 11];
bar3h(year,growth,'c');
title('Yearly growth using bar3h function');
zlabel('Year');
ylabel('Precentage growth');
OUTPUT:
QUESTION 37:Illustrate the use of pie3 function to show different profession people in a group
as per the following data:
Profession
No. Of Persons
Manager
12
Engineer
15
Professor
13
Doctor
11
Architect
6
Designer
10
PROGRAM:
clc;
clearall;
closeall;
%Program to Illustrate use of pie3 function
person =
[{'Manager','Engineer','Professor','Doctor','Architect','Designer'}];
strength=[12 15 13 11 6 10];
explode= [0 0 1 0 0 1];
pie3(strength,explode,person);
title('Person in a group using pie3 function');
OUTPUT:
QUESTION 38: Write a program to illustrate the use of stem3 function to plot the following
function: y = xcos(x); z = exp(x/5)cos(x) + 1 for 0 ≤ x ≤ 6π.
PROGRAM:
clc;
clearall;
closeall;
%Program to Illustrate the stem3 command
x=linspace(0,6*pi,200);
y=x.*cos(x)+1;
z=exp(x/5).*cos(x)+1;
stem3(x,y,z);
title('Graph to Illustrate stem3 function');
xlabel('x-axis');
ylabel('y-axis');
zlabel('z-axis');
OUTPUT:
QUESTION 39: Create meshgrid for the data -1 ≤ x ≤ 1 and -2 ≤ y ≤ 2.
PROGRAM:
clc;
clearall;
closeall;
[x,y]= meshgrid(-1:0.5:1, -2:1:2)
OUTPUT:
QUESTION 40: Create a mesh plot of the function z = 2/(𝑥 2 + 𝑦 2 +1) over the interval -5 ≤ x ≤
5 and -5 ≤ y ≤ 5.
PROGRAM:
clc;
clearall;
closeall;
%Program to Illustrate the mesh function
[x,y]=meshgrid(-5:0.1:5);
;z=2./(x.^2+y.^2+1);
mesh(x,y,z);
gridon;
title('Program to illustrate the mesh function');
xlabel('x-axis');
ylabel('y-axis');
zlabel('z-axis');
OUTPUT:
QUESTION 41: Create a surface plot of the function f(x,y) = 8-𝑥 2 − 9𝑦 2 over the interval -2 ≤ x
≤ 2 and -3 ≤ y ≤ 3.
PROGRAM:
clc;
clearall;
closeall;
%Program to illustrate the surf function
[x,y]= meshgrid (-2:0.1:2, -3:0.5:3);
z = 8-x.^2-9*y.^2;
surf(x,y,z);
gridon;
title('Program to illustrate the surf function');
xlabel('x-axis');
ylabel('y-axis');
zlabel('z-axis');
OUTPUT:
QUESTION 42:Create a contour 3-D plot of the function z = sqrt(y.^2-x.^2) over the interval -3
≤ x ≤ 3 and -3 ≤ y ≤ 3.
PROGRAM:
clc;
clearall;
closeall;
%Program to illustrate the contour3 function
[x,y]=meshgrid(-3:0.5:3, -3:0.5:3);
z=sqrt(y.^2-x.^2);
contour3(x,y,z);
gridon;
title('Program to illustrate the contur3 function');
xlabel('x-axis');
ylabel('y-axis');
zlabel('z-axos');
OUTPUT:
RESULT:
Thus the programs related to SCILAB Graphics are studied and executed.