MATLAB
Graphics
Two-Dimensional Plots
 Syntax is
plot(x, y)
Where
x = vector containing the x-coordinates
y = vector containing the y-coordinates
Ex: Plot the curve y=x2 where x varied from 0 to 10.
Sol:
>>x=0:1:10;
>>y=x.^2;
>>plot(x,y)
Note:
1.
2.
In case figure is already exits, it clears the figure widow and
draw a new plot
Size of vector x & y must be same
Two-Dimensional Plots
Ex: Plot following single variables
%Note
1. a=[1 13 6 9 23 12]
%one real variable
2. b=[1-2i, 3+4i, 5+6i, 3+8i, 4+9i, 23+12i] %one complex variable
Sol:
1.
>>a=[1 13 6 9 23 12]
>>plot(a)
%plot(1:length(a), a)
2.
b=[1-2i, 3+4i, 5+6i, 3+8i, 4+9i, 23+12i]
>>plot(b)
%plot(real(b), imag(b))
Two-D Plots: Labels
Ex: Plot the curve given by equation y=sin(x), as x varies from 0 to 2pi. Also
label the x and y axis and provide a suitable title for the plot.
Sol: Make a .m file for the following code and run it
x=0:pi/100:2*pi;
y=sin(x);
plot(x,y);
xlabel('x-axis');
%naming x-axis
ylabel('y-asix');
%naming y-axis
title('Plot for sine wave');
%naming the plot
Two-D Plots: Grid & Axes Box
Ex: Plot the curve given by equation a=10 e-t as t varies from 0 to 5. Also label
the x and y axis, provide a suitable title for the plot, show the grid lines and
axes box.
Sol: Make a .m file for the following code and run it
t=0:0.1:5;
a=10*exp(-t);
plot(t,a);
box on;
%box on or box off to on & off
xlabel('Time (t) in Sec');
%naming x-axis
ylabel('Output (a)');
%naming y-axis
title('Plot for a=10*exp(-t)');
%naming the plot
grid on;
%grid on or grid off to on & off
Note: Box means figure window is enclosed in the box , see plot outer portion
Two-D Plots: Entering text in plot
 Putting a text at some desired place
Syntax are
text(x-coordinate, y-coordinate, ‘text to be written’)
Or
gtext(‘text to be written’)
%put the cursor on the graph
Ex: Plot the curve given by equation a=10 e-t as t varies from 0 to 5. Also label
the x and y axis, provide a suitable title for the plot, show the grid lines and
axes box and enter a text on the plot.
Sol: Make a .m file for the following code and run it
t=0:0.1:5;
a=10*exp(-t);
plot(t,a);
box on;
%box on or box off to on & off
xlabel('Time (t) in Sec');
%naming x-axis
ylabel('Output (a)');
%naming y-axis
title('Plot for a=10*exp(-t)');
%naming the plot
grid on;
%grid on or grid off to on & off
gtext(‘this is the desired curve’);
Two-D Plots: Axis Control & Aspect Ratio
 Axis Control: Changing the minimum & maximum values of x & y-axis
Syntax is
axis([xmin, xmax, ymin, ymax])
 Axis Aspect Ratio: There are some pre-defined string arguments for the axis
command for setting the axis aspect ratio
axis(‘equal’)
%sets equal scale on both axes
axis(‘square’) %sets default rectangular frame to a square frame
axis(‘normal’) %rests to default values
axis(‘axis”)
%freezes the current axes limits
axis(‘off’)
%turn off all axis line, tick marks & labels
Two-D Plots: Axis Control & Aspect Ratio
Ex: write a .m file and run it.
x=-5:0.1:10;
y=3*x.^2+2.*x+5;
plot(x,y);
axis([-5 5 0 20]); %xmin=-5, xmax=5, ymin=0, ymax=20
xlabel('x-axis');
ylabel('y-axis');
title('Plot of y=3x^2+2x+5');
grid on;
Two-D Plots: Multiple plots
 Multiple plots : Generating multiple plots on same graphic window. Thee
methods:
1. Using plot command
2. Using hold command
3. Using line command
Two-D Plots: Multiple plots conti…
1.
Using ‘plot’ command: Here plot command is modified as
Plot(x1, y1,x2, y2, x3, y3);
It will generate 3 graphs in the same window.
Ex: Make a .m file of following code and run it.
x1=0:0.01:20;
y1=exp(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 of y1');gtext('curve of y2');gtext('curve of y3');
%axis('equal');
xlabel('x-axis');
ylabel('y-axis');
title('multiple plots using plot command');
grid on;
Two-D Plots: Multiple plots conti…
2.
Using ‘hold’ command: Write following command to hold the previous
figure
hold on or hold off
Ex: Make a .m file of following code and run it.
x=0:pi/100:2*pi;
y1=cos(x);
plot(x,y1)
hold on;
y2=sin(x);
plot(x,y2)
hold off;
xlabel('x-axis'); ylabel('y-axis');
title('multiple plots using hold on & hold off command');
grid on;
Note: Run the program without hold on & hold off command & see difference
Two-D Plots: Multiple plots conti…
3.
Using ‘line’ command: ‘line’ command is used along with plot command to
generate multiple plots.
Ex: Make a .m file of following code and run it.
x=0:0.1:100;
y1=sqrt(x.^2+1);
y2=5*x+20;
y3=10*x+3;
plot(x,y1)
gtext('y1=sqrt(x^2+1)');
line(x,y2);
gtext('y2=5x+20');
line(x,y3);
gtext('y3=10x+3');
xlabel('x-axis'); ylabel('y-axis');
title('multiple plots using line command');
grid on;
Two-D Plots: Style option
Style Option: These are optional parameters that can be given to plot
command for better illustration and outlook of plots.
Syntax is
plot(x-value, y-value, ‘style options’)
Where
style options = one to three characters which represents
color (red, green, yellow, blue etc)
line style (solid, dashed, dotted etc)
point marker style ( +, *, o, . etc )
Note: Default option in MATLAB plot is blue solid line.
Two-D Plots: Style option conti…
Ex: Make a .m file of following code and run it.
x1=0:0.01:20;
y1=exp(0.1*x1).*sin(x1);
x2=0:0.1:20;
y2=sin(x2);
x3=0:0.1:20;
y3=cos(x3);
plot(x1,y1,’b:’,x2,y2,’g-’, x3,y3,’ro’); %note this line now
gtext('curve of y1');gtext('curve of y2');gtext('curve of y3');
%axis('equal');
xlabel('x-axis');
ylabel('y-axis');
title('multiple plots using plot command');
grid on;
Two-D Plots: Style option conti…
Colors, line style and marker style of style option
Two-D Plots: legend command
‘legend’ command: This is another optional parameters that can be given to
plot command for better illustration and outlook of plots.
Syntax are
legend(string1, string2, string3,……)
legend(linestyle, string1, linestyle, string2……..)
legend(srting1, string2, string3,……,pos)
Where
pos = position
0 = Automatic ‘best’ placement (least conflict with data)
1 = Upper right hand corner (default)
2 = Upper left hand corner
3 = Lower left hand corner
4 = Lower right hand corner
5 = To the right of the plot
Two-D Plots: legend command conti…
Ex: Following table gives the values of induced voltage E for different filed
current If for a DC generator operating at N = 1500 RPM, plot the open circuit
characteristics for this generator at 1500 RPM, 1200 RPM & 1000 RPM on the
same sheet. Use the proper ‘hold’ and ‘legend’ commands. (Note E α N)
Sol: Make a .m file of following code and run it.
If=[0 0.4 1.0 1.45 2.0 3.0 4.0 5.0 6.0];
%field current
E = [5 30 70 110 150 215 240 250 260];
%induced emf
plot(If, E, 'r-');
%red solid line
hold on;
E2=(1200/1500)*E;
plot(If, E2, 'b:');
%blue doted line
E3=(1000/1500)*E;
plot(If, E3, 'c-.');
%cyan dash dot line
legend('1500 RPM','1200 RPM','1000 RPM',2);
hold off;
Sub-Plots
Sub-plots: A graphic window can be sub divided into many sub-graphs or
subplots using subplot command.
Syntax is
Subplot(I, j, k)
% total sub-plots=i*j, i row, j column
%select the kth area for sub-plot
Ex: Divide the figure window into four sub-windows and plot the following
functions
1. Plot v v/s I, where v=4*I & I =1, 2, 3, 4 on the upper left sub window.
2. Plot y v/s x, where y=x2 & x= 1,2,3,4 on the upper right sub-window.
3. For t=0:2*pi in step t=pi/60, plot sin(t) v/s t on the lower left sub-window .
4. For t=0:pi/30:2*pi, plot cost(t) v/s t on the lower right sub-window.
Sub-Plots conti…
I=[1 2 3 4];
V=4*I;
subplot(2,2,1);
plot(I, V);
xlabel('Current I');ylabel('Voltage V'); title('V-I characteristic');
x=[1 2 3 4];
y=x.^2;
subplot(2,2,2);
plot(x, y);
xlabel('x');ylabel('y'); title('y=x^2');
t=0:pi/60:2*pi;
subplot(2,2,3);
plot(t,sin(t));
xlabel('Angle');ylabel('sin(angle)');title('ploat of sin function');
t=0:pi/30:2*pi;
subplot(2,2,4);
plot(t, cos(t));
xlabel('Angle');ylabel('cos(angle)');title('plot of cos function');
Special 2-D Plots
Specialized 2-D plots: There are many specialized graphics functions in the
MATLAB for 2-D plotting. They are following
1. Logarithmic plot function
I.
semilogx
II. semilongy
III. loglog
2. polar function
3. area function
4. bar function
5. barh funtion
6. hist function
7. rose function
8. pie function
9. stairs function
10. stem function
11. compass function
Special 2-D Plots conti…
1.
Logarithmic plot function
I.
semilogx: The x-axis is drawn on logarithmic scale and y-axis on liner
scale
Ex: plot function x=e-a, y=a2 where 0<=a<=10 using semilogx function.
a=0:1:10;
y=a.^2;
x=exp(-a);
semilogx(x,y);
grid on;
xlabel('x=exp(-a)');ylabel('y=a^2');
title('showing the use of semilogx plot');
Special 2-D Plots conti…
1.
Logarithmic plot function
II. semilogy: The y-axis is drawn on logarithmic scale and x-axis on liner
scale
Ex: Plot power v/s time for 0<t<8 sec, with power on the log scale and time in
the linear scale for a motor whose performance equations are given as
follows
Rotor speed, w=190(1-e-0.15t)
Torque, T=8e-0.15t
Power, P=w*T
time=0:0.2:8
w=190*(1-exp(-0.15*time));
T=8*exp(-0.15*time);
P=w.*T;
semilogy(time,P);
grid on;
xlabel('time');ylabel('torque');
title('showing the use of semilogy plot');
Special 2-D Plots conti…
1.
Logarithmic plot function
III. loglog: Both x & y-axis are drawn on logarithmic scale.
Ex: Plot magnitude v/s frequency on log-log scale for the transfer function G(s)
= 1/(1+0.02s). Where s=jw=j*2pi*f
freq=1:2:1000;
Gs=1./(1+0.02*j*2*pi*freq);
mag=abs(Gs);
loglog(freq,mag);
grid on;
xlabel('frequency on log scale');ylabel('magnitude on log scale');
title('showing the use of loglog plot');
Special 2-D Plots conti…
2.
Polar plot: To draw plot in polar coordinates
Syntax is
polar(theta, r)
Or polar(theta, r, p)
where
theta = angle vector
r = radius or corresponding distance vector
p = optional characteristic string describing color, line style
Ex: Plot the following function f(θ)=sin (θ) for - π/2 ≤ θ≤π/2
theta=-pi/2:pi/100:pi/2;
f=sin(4.*theta);
polar(theta,f,'r-');
title('plot of function f=sin(4*theta) using polar function');
Special 2-D Plots conti…
3.
area plot: similar to plot function except that the area under plot is filled
with color.
Syntax is
area(x,y)
Ex: Plot the following function f(θ)=sin (θ) for - π/2 ≤ θ≤π/2
theta=0:pi/100:4*pi;
f=cos(theta);
area(theta,f);
title('plot of function f=cos(theta) using area function');
Special 2-D Plots conti…
4.
bar plot: It draws vertical bar plot.
Syntax are
bar(y)
%draws vertical bar plot using default values of
x=1:k, where k is no of data values in vector y,
the values of y determines the height of bar.
or bar(x, y) %if y is a matrix of mxn, then it draws m grourps
of n vertical bars
or bar(x, y, ‘style options’)
or bar(x, y, width)
%width specifies width of bars, if width>1 →
overlapped bar, default width = 0.8
Ex:
x=[0 1 2 3 4 5 6];
y=[10 15 25 20 30 27 19];
bar(x, y, 'c') %c means cyan color
Special 2-D Plots conti…
Ex: Plot a bar graph to show the comparison of average temp in city A, B & C for
the months from September to February. The data is given as
Months
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
temp=[31 28 24;29 26 22; 28 25 20; 27 24 16; 26 22 17; 29 25 20];
bar(temp);
legend('City A', 'City B', 'City C');
xlabel('Months from sep to feb');
ylabel('Temp in celsius');
Special 2-D Plots conti…
5.
hist plot: It draws histogram of the given data.
Syntax are
hist(x)
%draws 10-bin(default) histogram of vector x
or bar(x, n)
% draws n-bin histogram of vector x
or bar(x, p)
%draws histogram of vector x using the bins
specified in vector p
Ex:
x=randn(100,1)*pi;
%generate 100 random data points
hist(x);
title('Histogram to show 100 random values in 10-bins');
Ex
x=randn(100,1)*pi;
%generate 100 random data points
hist(x, 5);
%histogram with 5 bins
title('Histogram to show 200 random values in 10-bins');
Note: bins means no of vertical lines.
Special 2-D Plots conti…
6.
‘rose’ plot: It draws angle histogram of the given data.
Syntax are
rose(a)
%draws 20-bin(default) angle histogram of
angle given in vector a
or rose(a, n)
% draws n-bin angle histogram
or rose(a, v)
%draws angle histogram of angle given in
vector a using the bins specified in vector v
Ex:
x=randn(100,1)*pi;
%generate 100 random data points
rose(x);
title('Histogram to show 100 random values in 20-bins');
Ex
x=randn(100,1)*pi;
%generate 100 random data points
rose(x, 5);
%histogram with 5 bins
title('Histogram to show 200 random values in 10-bins');
Special 2-D Plots conti…
7.
‘pie’ plot: It draws pie plot of the given data.
Syntax are
pie(x)
%x is the vector whose pie plot is to be drawn
or pie(x, k)
% k optional vector which specifies slices that
should be pulled out from the pie
or pie(x, k, labels)
%labels is also an optional vector which is use
to label each pie slice with cell array labels
Special 2-D Plots conti…
Ex: Following table show the concentration of different industries in the region,
show it with pie chart.
Name of industry
No of industrial Units
Cement
4
Textile
8
Software
20
Chemical
2
Telecom
7
Banking
10
industry=[4 8 20 2 7 10];
pie(industry);
title('Pie char showing percentage of different industries');
Special 2-D Plots conti…
Repeat above example with sliced pie chart
industry=[4 8 20 2 7 10];
show=[0 0 0 1 0 1];
%show slice of 4th & 6th industiry
pie(industry, show);
title('Pie char showing percentage of different industries');
legend('Cement','Textile','Software','Chemical','Telecom','Banking',3);
Try this also
industry=[4 8 20 2 7 10];
company=[{'Cement','Textile','Software','Chemical','Telecom','Banking‘}];
show=[0 0 0 1 0 1];
%show slice of 4th & 6th industiry
pie(industry, show, industry);
title('Pie char showing different industries');
Special 2-D Plots conti…
8.
‘stairs’ plot: It draws staircase graph of the given data.
Syntax are
stairs(y)
%y is the vector whose staircase plot is to be drawn
or stairs (x, y)
% y optional vector which specifies location
or stairs(x, y, style)
%style is also an optional which is use for line style
Special 2-D Plots conti…
Ex: Draw the stairs plot to show the function y = x.*x, where -2≤x≤2
Sol: make a .m file and run it
x=-2:0.1:2; y=x.*x;
stairs(x,y,'r'); grid on
xlabel('x-axis'); ylabel('y=x.*x');
title('showing the stair plot');
Ex: Draw the stairs plot for the following data
X=[0 2 3 4 5 7] & y= [5 -1 8 4 7 3]
Sol:
X=[0 2 3 4 5 7]; Y= [5 -1 8 4 7 3];
stairs(X,Y,'*-.');
box off;
xlabel('x-axis'); ylabel('y-axis');
title('showing the stair plot');
Special 2-D Plots conti…
9.
‘stem’ plot: It draws staircase graph of the given data.
Syntax are
stem(y)
%y is the vector whose stem plot is to be drawn
or stem (x, y)
% x optional vector which specifies location
or stem(x, y, style)
%style is also an optional which is use for line style
Special 2-D Plots conti…
Ex: Draw the stem plot to show the function y = x.*x, where -2≤x≤2
Sol: make a .m file and run it
x=-2:0.1:2; y=x.*x;
stem(x,y,'r'); grid on
xlabel('x-axis'); ylabel('y=x.*x');
title('showing the stem plot');
Ex: Draw the stem plot for the following data
X=[0 2 3 4 5 7] & Y= [5 -1 8 4 7 3]
Sol:
X=[0 2 3 4 5 7]; Y= [5 -1 8 4 7 3];
stem(X,Y,‘*');
box off;
xlabel('x-axis'); ylabel('y-axis');
title('showing the stem plot');
Special 2-D Plots conti…
10. ‘compass’ plot: complex data can be plotted by using compass function. It
displays angle and magnitude of the complex number on a circular grid.
Syntax are
compass(y)
%draws angle & magnitude of the complex data of vector y
%It is equivalent to compass( real(y), imag(y))
%It draws n arrows from origin, n= now of elements of y
Ex:
Z=[1+1i 4-8i 20+7i 6+8i 9+2i 12-4i];
compass(Z);
xlabel('x-axis'); ylabel('y-axis');
title('showing the compass plot');
3-D Plots
For visualization of data in three dimensions, MATLAB has a number of
functions. These are extension of 2-D functions i.e.
1. plot3
2. bar3
3. bar3h
4. pie3
etc
Note: All style option of 2-D plots are also applicable to 3-D plots
3-D Plots conti…
1.
‘plot3’ function:
Syntax is
plot3(x, y, t, ‘style_option’)
Ex: Given is x=t2 & y = 4t for -4≤t≤4. Obtain a 3-D plot showing the matrix in (x,
y) space as a factors of time .
Sol:
t=-4:0.1:4;
x=t.^2;
y=4*t;
plot3(x,y,t);
grid on;
xlabel('x-axis');
ylabel('y-axis');
zlabel('z-axis-time');
title('Showing 3-D plot');
3-D Plots conti…
2.
‘bar3’ & bar3h function:
bar3 : for horizontal 3-D bar plot
bar3h: for vertical 3-D bar plot
Ex: Draw 3-D bar plots of the following data.
x=[0 1 2 3 4 5 6];
y=[5 17 25 21 31 27 19];
Sol:
x=[0 1 2 3 4 5 6];
y=[5 17 25 21 31 27 19];
bar3(x, y, 'c');
% try this with bar3h(x, y, ’c’)
3-D Plots conti…
2.
‘pie3’ function: Similar as pie in 2-D
Syntax are
pie3(x)
or pie3(x, k)
or pie3(x, k, labels)
Ex: Repeat the example of pie plot with pie3
industry=[4 8 20 2 7 10];
company=[{'Cement','Textile','Software','Chemical','Telecom','Banking'}];
show=[0 0 0 1 0 1];
%show slice of 4th & 6th industiry
pie3(industry, show, company);
title('Pie char showing different industries');
3-D Plots conti…
3.
‘stem3’ function: Similar as stem in 2-D
Syntax are
stem3(x)
or stem3(x, y, z)
or stem3(x, y, ‘filled’)
Ex: Repeat the example of stem plot with stem3
x=-2:0.1:2; y=x.*x;
stem3(x,y,'r'); grid on
xlabel('x-axis'); ylabel('y=x.*x');
title('showing the stem3 plot');
And
X=[0 2 3 4 5 7]; Y= [5 -1 8 4 7 3];
stem(X,Y,‘*');
box off;
xlabel('x-axis'); ylabel('y-axis');
title('showing the stem plot');
3-D Plots conti…
3.
‘stem3’ function: Similar as stem in 2-D
Syntax are
stem3(x)
or stem3(x, y, z)
or stem3(x, y, ‘filled’)
Ex: Repeat the example of stem plot with stem3
x=-2:0.1:2; y=x.*x;
stem3(x,y,'r'); grid on
xlabel('x-axis'); ylabel('y=x.*x');
title('showing the stem3 plot');
And
X=[0 2 3 4 5 7]; Y= [5 -1 8 4 7 3];
stem(X,Y,‘*');
box off;
xlabel('x-axis'); ylabel('y-axis');
title('showing the stem plot');
3-D Plots conti…
4.
‘meshgrid’ function: Meshgrid function transforms the domain specified
by vector x and y into matrix x and y that can be used for evaluation of the
function of two variables in 3-D surface plot. Syntax is
[x, y]=meshgrid(x_begin : x_increment : x_end, y_begin : y_increment : y_end)
After evaluating matrix (arrays) of x & y values, the given function is
evaluated and plotted suing mesh, surf or contour plots.
Ex: Create meshgrid for data -1≤x≤1 and -2≤y≤2
Sol:
[x,y]=meshgrid(-1:0.5:1, -2:1:2)
3-D Plots conti…
5.
‘mesh’ function: It is wireframe plot
Syntax is
mesh(x, y, z);
Or
mesh(s, y, z, linestyle);
Ex: Create mesh plot for the function z=2/(x2+y2+1) over the interval
-5≤x≤5 and -5≤y≤5
Sol:
[x,y]=meshgrid(-5:0.1:5, -5:0.1:5);
z=2./(x.^2+y.^2+1);
mesh(x,y,z);
grid on
xlabel('x-axis');ylabel('y-axis');zlabel('z-axis')
6. ‘surf’ function: it is similar to mesh function with the difference that instead
of wireframe plot it is a surface plot. ( Try above example)
3-D Plots conti…
7.
‘contour’ & ‘contour3’ function: They are used to draw contour in 2-D & 3D respectively.
Syntax are
contour(z);
%gives the contour plot of the specified matrix treating the values
given in the matrix as the heights above the plane.
Or
contour(x, y, z)
%similar to countour(z) with the difference that x & y specifies
(x,y) coordinates of the surface as for surf function.
Ex: Create contour & contour 3-D plots for the function z=sqrt(y2+x2) over the
interval -3≤x≤3and -3≤y≤3
Sol:
[x,y]=meshgrid(-5:0.1:5, -5:0.1:5);
z=sqrt(y.^2-x.^2+1);
contour3(x,y,z);
grid on
xlabel('x-axis');ylabel('y-axis');zlabel('z-axis')