MatLab Basic Tutorial On Plotting

Plotting in MATLAB
Plotting in MATLAB
By
MOHD RAFIQ
Department of Mathematics
University of Delhi
Delhi
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Plotting in MATLAB
Outline
1 “Plot” Command
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Mohd Rafiq, Department of Mathematics, University of Delhi

Plotting in MATLAB
Outline
2 LineSpec(Line Speciﬁcation)
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Plotting in MATLAB
Outline
3 Some Important Additional Commands in Plot
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Plotting in MATLAB
Outline
4 “fplot” Command
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Plotting in MATLAB
Outline
5 Two variable function( or 3D) plot
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Plotting in MATLAB
Outline
5 Two variable function( or 3D) plot
6 Plotting complex numbers
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Plotting in MATLAB
Plot
Basic Command for Plotting
Two-dimensional line and symbol plots are created with the
plot command. In its simplest form plot takes two arguments:
plot(xdata, ydata)
where xdata and ydata are vectors containing the data.
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Plot
Basic Command for Plotting
Two-dimensional line and symbol plots are created with the
plot command. In its simplest form plot takes two arguments:
plot(xdata, ydata)
where xdata and ydata are vectors containing the data.
Note that xdata and ydata must be the same length and
both must be the same type, i.e., both must be either
row or column vectors.
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Plotting in MATLAB
Plot
Plot Commands
plot
2-D line plot
syntax
plot(X,Y)
plot(X,Y,LineSpec)
plot(X1,Y1,...,Xn,Yn)
plot(X1,Y1,LineSpec1,...,Xn,Yn,LineSpecn)
plot(Y)
plot(Y,LineSpec)
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Plotting in MATLAB
Plot
plot(X,Y) creates a 2-D line plot of the data in Y versus the
corresponding values in X.
plot(X,Y,LineSpec) sets the line style, marker symbol, and color.
plot(X1,Y1,...,Xn,Yn) plots multiple X, Y pairs using the same axes
for all lines.
plot(X1,Y1,LineSpec1,...,Xn,Yn,LineSpecn) sets the line style,
marker type, and color for each line
plot(Y) creates a 2-D line plot of the data in Y versus the index of
each value.
If Y is a vector, then the x-axis scale ranges from 1 to
length(Y).
If Y is a matrix, then the plot function plots the columns of Y
versus their row number. The x-axis scale ranges from 1 to
the number of rows in Y.
If Y is complex, then the plot function plots the imaginary
part of Y versus the real part of Y, such that plot(Y) is
equivalent to plot(real(Y),imag(Y)).
plot(Y,LineSpec) sets the line style, marker symbol, and color. 5 / 83

Plotting in MATLAB
Plot
Example 1
Plot the function y = sin(x) over the interval [−2π, 2π]
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Plotting in MATLAB
Plot
Example 1
Plot the function y = sin(x) over the interval [−2π, 2π]
x=-2*pi:pi/100:2*pi;
or
x=linspace(-2*pi,2*pi)
y=sin(x);
plot(x,y)
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Plotting in MATLAB
Plot
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Plotting in MATLAB
Plot
Example 2
Plot the functions y1 = sin(x) and y2 = cos(x) over the
interval [−2π, 2π]
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Plotting in MATLAB
Plot
Example 2
Plot the functions y1 = sin(x) and y2 = cos(x) over the
interval [−2π, 2π]
x=linspace(-2*pi,2*pi);
y1=sin(x);
y2=cos(x);
plot(x,y1,x,y2)
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Plotting in MATLAB
Plot
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Plotting in MATLAB
Plot
Point to Remember
If you are plotting a graph by using any of the operations:
Power (or Exponent)
Multiplications
Division
Then always put a “.”(dot) before these operations.
i.e., type x.^2, x.*y, x./y and 1./x instead of typing
x^2, x*y, x/y and 1/x respectively.
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Plot
Parametric Plot
Example 3
Plot the parametric curves x = tcos(t) and y = tsin(t)
over[0, 2π].
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Plotting in MATLAB
Plot
Parametric Plot
Example 3
Plot the parametric curves x = tcos(t) and y = tsin(t)
over[0, 2π].
t=linspace(0,2*pi);
x=t.*sin(t);
y=t.*cos(t);
plot(x,y)
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Plotting in MATLAB
Plot
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Plot
Saving Plots into High Quality Images
You can save plot of any function into high quality image in
ﬁgure window as follows:
File → ExportSetup → Properties → Rendering → Resolution
Choose the highest resolution and click on Export. Finally
save the ﬁle in JPG format.
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Plotting in MATLAB
Plot
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Plotting in MATLAB
Plot
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Plotting in MATLAB
LineSpec(Line Speciﬁcation)
LineSpec (Line Speciﬁcation)
The color, point marker, and line style can be changed on a
plot by adding a third parameter (in single quotes) to the plot
command.
Syntax:
plot(x, y, LineSpec )
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Plotting in MATLAB
LineSpec Table
Color Point Marker Line Style
y yellow . point – solid
m magenta o circle : dotted
c cyan x x-mark –. dashdot
r red + plus – – dashed
g green * star
b blue s square
w white d diamond
k black ∨ triangle(down)
∧ triangle(up)
< triangle(left)
> triangle(right)
p pentagram
h hexagon
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Plotting in MATLAB
Example 4
Plot the function y = x3
− 1 with blue dashed lines.
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Plotting in MATLAB
Example 4
− 1 with blue dashed lines.
x = linspace(-10,10);
y=x.^3-1;
plot(x,y,’b--’)
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Some Important Additional Commands in Plot
Combining Two Plots
We can combine two plots by the command
hold on;
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Plotting in MATLAB
Combining Two Plots
We can combine two plots by the command
hold on;
If we apply this to Example 2, then we need to write
x=linspace(-2*pi,2*pi);
y1=sin(x);
y2=cos(x);
plot(x,y1)
hold on;
plot(x,y2)
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Plotting in MATLAB
Displaying the x-axis and y-axis intersecting at
Origin
Note that, by default, the x-axis is at the bottom of the graph
and the y-axis is on the left side. So, if you want to display the
x-axis and y-axis lines so that they cross at the origin point
(0, 0), we add the following command;
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Plotting in MATLAB
Displaying the x-axis and y-axis intersecting at
Origin
Note that, by default, the x-axis is at the bottom of the graph
and the y-axis is on the left side. So, if you want to display the
x-axis and y-axis lines so that they cross at the origin point
(0, 0), we add the following command;
ax=gca;
ax.XAxisLocation=’origin’;
ax.YAxisLocation=’origin’;
Note:
ax=gca; returns the current axes for the current ﬁgure
that can be used to access and modify properties of the
axes.
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Plotting in MATLAB
Example 5
Plot the function y = xSin(x) over the interval [-10,10] and
also show the x-axis and y-axis intersecting at origin.
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Example 5
also show the x-axis and y-axis intersecting at origin.
x=linspace(-10,10);
y=x.*sin(x);
plot(x,y)
ax=gca;
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Removing Outline
If you don’t want to show the axes outline, then you can use
the command.
ax.Box=’oﬀ’;
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Example 6
Plot the function y = xSin(x) over the interval [-10,10]
without axis outline.
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Plotting in MATLAB
Example 6
Plot the function y = xSin(x) over the interval [-10,10]
without axis outline.
x=linspace(-10,10);
y=x.*sin(x);
plot(x,y)
ax=gca;
ax.Box=’off’;
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Plotting in MATLAB
Changing the Location of the Tick Marks
We use the following commands for changing the location of
the tick marks on x-axis and y-axis.
ax.XTick=[a1, a2, . . . , am];
ax.YTick=[b1, b2, . . . , bn];
Note: We can replace comma by space in each command.
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Plotting in MATLAB
Example 7
over the interval [0,10] and display
tick marks along the x-axis at the values 0, 5, and 10.
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Plotting in MATLAB
Example 7
tick marks along the x-axis at the values 0, 5, and 10.
x = linspace(0,10);
y = x.^2;
plot(x,y)
ax=gca;
ax.XTick=[0,5,10];
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Plotting in MATLAB
we can also change the location of tick marks on y-axis as
x = linspace(0,10);
y = x.^2;
plot(x,y)
ax=gca;
ax.XTick=[0,5,10];
ax.YTick=[0,20,40,60,80,100];
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Plotting in MATLAB
Labeling the Tick Marks
We can label the tick marks on x-axis and y-axis by the
commands
ax.XTickLabel={’Label1’ , ’Label2’, . . . , ’Labelm’};
ax.YTickLabel={’Label1’ , ’Label2’, . . . , ’Labeln’};
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Plotting in MATLAB
Example 8
tick marks along the x-axis at the values 0, 5, and 10.Then
specify a label for each tick mark.
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Plotting in MATLAB
Example 8
tick marks along the x-axis at the values 0, 5, and 10.Then
specify a label for each tick mark.
x = linspace(0,10);
y = x.^2;
plot(x,y)
ax=gca;
ax.XTick=[0,5,10];
ax.XTickLabel={’x=0’,’x=5’,’x=10’};
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Plotting in MATLAB
Upgraded Commands
MATLAB’s latest version (either 2017a or 2017b) has some
new commands and four of them are as follows:
xticks([a1, a2, . . . , am]);
yticks([b1, b2, . . . , bn]);
xticklabels({’Label1’ , ’Label2’, . . . , ’Labelm’});
yticklabels({’Label1’ , ’Label2’, . . . , ’Labeln’});
These commands are upgraded form of previous four
commands.
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Plotting in MATLAB
New Figure Window
If you want to show your plot in a new ﬁgure window, then you
can use the command ﬁgure just before the command plot.
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Plotting in MATLAB
New Figure Window
If you want to show your plot in a new figure window, then you
can use the command figure just before the command plot.
figure
plot(x,y)
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Title
You can give a ”title” to your plot by using the command
title(‘title of plot )
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Example 9
Plot the function y = xSin(x) over the interval [-10,10] with
the title “Graph of y=xSin(x)”.
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Plotting in MATLAB
Example 9
Plot the function y = xSin(x) over the interval [-10,10] with
the title “Graph of y=xSin(x)”.
x=linspace(-10,10);
y=x.*sin(x);
plot(x,y)
title(’Graph of y=xSin(x)’)
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Plotting in MATLAB
Labeling the Axis
You can labels x-axis and y-axis with the following command:
xlabel(‘x − label string )
ylabel(‘y − label string )
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Example 10
also label the axis.
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Plotting in MATLAB
Example 10
also label the axis.
x=linspace(-10,10);
y=x.*sin(x);
plot(x,y)
xlabel(’x’)
ylabel(’y=xSin(x)’)
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Plotting in MATLAB
Legend
A legend can be added to the plot to identify various curves,
with command:
legend(‘string1 , ‘string2 ..., ‘stringN )
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Plotting in MATLAB
Example 11
Plot the function xSin(x), Cos(x) and Sin(x) over the interval
[-10,10] and add a legend to for each.
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Plotting in MATLAB
Example 11
Plot the function xSin(x), Cos(x) and Sin(x) over the interval
[-10,10] and add a legend to for each.
x=linspace(-10,10);
y1=x.*sin(x);
y2=cos(x);
y3=sin(x);
plot(x,y1,x,y2,x,y3)
legend(‘xSin(x)’,’Cos(x)’,’Sin(x)’)
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Setting the Limit for Axis
The axis command sets the limits for the current axes of the
plot shown, so only the part of the axis that is desirable is
displayed
axis([xmin, xmax, ymin, ymax])
ax.XLim = [xmin, xmax];
ax.YLim = [ymin, ymax];
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Plotting in MATLAB
Example 12
Plot the function y = e5t
− 1 by the simple command.
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Plotting in MATLAB
Example 12
Plot the function y = e5t
− 1 by the simple command.
t=0:0.01:5;
y=exp(5*t)-1;
plot(t,y)
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To get a better idea of the initial behavior of the
function, let’s resize the axes. Enter the following
command into the MATLAB command window :
t=0:0.01:5;
y=exp(5*t)-1;
plot(t,y)
axis([0, 1, 0, 50])
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Plotting in MATLAB
Note that in Example 11, some part of the curve is not
visible because it is covered by the legend. So to
overcome this problem, we can also use axis command.
x=linspace(-10,10);
y1=x.*sin(x);
y2=cos(x);
y3=sin(x);
figure
plot(x,y1,x,y2,x,y3)
legend(’xSin(x)’,’Cosx)’,’Sin(x)’)
ax=gca;
ax.YLim=[-6 12];
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Plotting in MATLAB
Upgraded commands
If you are using MATLAB’s latest version (either 2017a or
2017b) then you can replace the commands ax.XTick and
ax.YTick by the following two commands:
xlim([xmin, xmax]);
ylim([ymin, ymax]);
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Plotting in MATLAB
fplot command:
fplot command
Use the fplot command to plot either built-in or user defined
functions between specified limits.
fplot(function, interval)
Syntax with Description:
1 fplot(f) plots input f over the default interval [−5 5] for x.
2 fplot(f, x-interval) plots over the specified interval.
Specify the interval as a two-element vector of the form
[xmin xmax].
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Plotting in MATLAB
fplot command:
Example 13
Plot the function xSin(x) over the interval [-20,20].
syms x;
fplot(@(x)sin(x)./x,[-20,20]) fplot(sin(x)/x,[-20,20])
or or
f=@(x)sin(x)./x; syms x;
fplot(f,[-20,20]) f(x)=sin(x)/x;
fplot(f,[-20,20])
All commands will give you the same result.
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Plotting in MATLAB
fplot command:
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fplot command:
Example 14
Plot the piecewise function
f (x) =
ex
, if − 3 < x < 0
cos x, if 0 < x < 3
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Plotting in MATLAB
fplot command:
Example 14
Plot the piecewise function
f (x) =
ex
, if − 3 < x < 0
cos x, if 0 < x < 3
syms x;
fplot(exp(x),[-3 0],’b’)
hold on
fplot(cos(x),[0 3],’b’)
axis([-3.5,3.5,-1.1,1.1])
ax=gca;
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Plotting in MATLAB
fplot command:
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fplot command:
Parametric Plot
fplot command is also used to plot 2-D parametric curve.
fplot(xt, yt, interval)
Syntax with Description:
1 fplot(xt,yt) plots xt = x(t) and yt = y(t) over the
default interval of t, which is [–5 5].
2 fplot(xt,yt,t-interval) plots over the speciﬁed interval.
Specify the interval as a two-element vector of the form
[tmin tmax].
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fplot command:
Example 15
Plot the parametric curve x = cos(t) and y = sin(t).
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fplot command:
Example 15
Plot the parametric curve x = cos(t) and y = sin(t).
syms t;
fplot(cos(t),sin(t))
axis([-2 2 -2 2])
ax=gca;
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Plotting in MATLAB
Two variable function( or 3D) plot
Two variable function plot process
We can plot a function of two variable z = f (x, y) over the
(x, y) region [a, b] × [c, d] as follows:
Steps:
Find grid of (x, y) points as follows
x=a:h1:b;
y=c:h2:d;
[X,Y]=meshgrid(x,y);
Here we have taken grid points step size h1 in the x-direction
and h2 in the y-direction.
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Plotting in MATLAB
Apply the function to the grid to get Z-values, where
Z = f (X, Y );
Plot the resulting mesh by the following functions
mesh(X,Y,Z), surf(X,Y,Z)
mesh(X,Y,Z) Generates an open mesh plot of the surface
deﬁned by matrix Z.
surf(X,Y,Z) Generates a shaded mesh plot of the surface
deﬁned by matrix Z.
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Plotting in MATLAB
Example 16
Use the meshgrid function to generate matrices x and y.
Create a third matrix, z, and plot its mesh and surf over the
(x, y) region [−2, 2] × [−2, 3], where
z = xe−x2−y2
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Plotting in MATLAB
Example 16
Create a third matrix, z, and plot its mesh and surf over the
(x, y) region [−2, 2] × [−2, 3], where
z = xe−x2−y2
x=-2:0.1:2;
y=-2:0.1:3;
Z=X.*exp(-X.^2-Y.^2);
figure
mesh(X,Y,Z)
figure
surf(X,Y,Z)
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Figure: mesh(X,Y,Z)
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Figure: surf(X,Y,Z)
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Contour Plot
Syntax:
contour(x, y, z)
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Plotting in MATLAB
Contour Plot
Syntax:
contour(x, y, z)
Example 17
Create a third matrix z, and plot its contour over the (x, y)
region [−2, 2] × [−2, 3], where
z = xe−x2−y2
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Contour Plot
Syntax:
contour(x, y, z)
Example 17
Create a third matrix z, and plot its contour over the (x, y)
region [−2, 2] × [−2, 3], where
z = xe−x2−y2
x=-2:0.1:2;
y=-2:0.1:3;
Z=X.*exp(-X.^2-Y.^2);
contour(X,Y,Z)
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Figure: contour(X,Y,Z)
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Parametric Plot
Example 18
Plot the following:
x = Sin(t), y = Cos(t), z = t where t ∈ [−10, 10]
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Parametric Plot
Example 18
Plot the following:
x = Sin(t), y = Cos(t), z = t where t ∈ [−10, 10]
t=-10:0.1:10;
[T T]=meshgrid(t,t); % or T=meshgrid(t);
x=sin(T);
y=cos(T);
z=T;
mesh(x,y,z)
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Example 19
The unit sphere centered at the point (0, 0, 1) is given by the
spherical equation
ρ = 2 cos(φ), x = ρ sin(φ) cos(θ), y = ρ sin(φ) sin(θ)
z = ρ cos(φ), where θ ∈ [0, 2π] and φ ∈ [0, π/2]
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Plotting in MATLAB
Example 19
The unit sphere centered at the point (0, 0, 1) is given by the
spherical equation
ρ = 2 cos(φ), x = ρ sin(φ) cos(θ), y = ρ sin(φ) sin(θ)
z = ρ cos(φ), where θ ∈ [0, 2π] and φ ∈ [0, π/2]
t=0:0.1:2*pi;
p=0:0.1:pi/2;
[T P]=meshgrid(t,p);
R=2*cos(P);
X=R.*sin(P).*cos(T);
Y=R.*sin(P).*sin(T);
Z=R.*cos(P);
mesh(X,Y,Z)
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Plotting in MATLAB
f-commands
Just like fplot command in 2D plotting, we have fmesh, fsurf
and fcontour commands in 3D plotting.
Note:
fmesh(f), fsurf(f) and fcontour(f) plot the function
z = f (x, y) over the default interval [-5 5].
Suppose FP denote the fmesh, fsurf and fcontour then
FP(f , xyinterval)
plots over the speciﬁed interval. To use the same interval for
both x and y, specify xyinterval as a two-element vector of the
form [min max]. To use diﬀerent intervals, specify a
four-element vector of the form [xmin xmax ymin ymax].
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If we apply these commands to Example 16 and 17,then we
will get same plots.
syms x y;
f(x,y)=x.*exp(-x.^2-y.^2);
figure
fmesh(f,[-2 2 -2 3])
figure
fsurf(f,[-2 2 -2 3])
figure
fcontour(f,[-2 2 -2 3])
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Plotting in MATLAB
Plotting complex numbers
If the input to the plot command is a vector of complex
numbers, the real parts are used as the x-coordinates and the
imaginary parts as the y-coordinates.
i.e., if z is complex, then plot(z) is equivalent to
plot(real(z), imag(z)).
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If the input to the plot command is a vector of complex
numbers, the real parts are used as the x-coordinates and the
imaginary parts as the y-coordinates.
i.e., if z is complex, then plot(z) is equivalent to
plot(real(z), imag(z)).
Example 20
Deﬁne the complex number z = 3 + 2i and plot it as a point
on the complex plane.
z=complex(3,2); z=complex(3,2);
plot(real(z),imag(z),’*’) plot(z,’o’)
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Figure: plot(real(z),imag(z),’*’) Figure: plot(z,’o’)Mohd Rafiq, Department of Mathematics, University of Delhi

Plotting in MATLAB
Point to remember:
specify a character (’*’, ’+’, ’x’, ’o’, ’.’, etc) to be plotted
at the point.
Example 21
Deﬁne the complex numbers 3 + 2i, −2 + i, −2 − i, 1 − 2i and
plot them all on the complex plane.
z=[3+2i,-2+1i,-2-1i,1-2i];
plot(z,’*’)
axis([-4 4 -4 4])
ax=gca;
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If we don’t deﬁne marker point, then by default MATLAB joins
each point (complex number) in the plot by a line segment.
z=[3+2i,-2+1i,-2-1i,1-2i];
plot(z)
axis([-4 4 -4 4])
ax=gca;
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Example 22
Plot the curve z = teit
for t ∈ [0, 4π].
t=0:0.01:4*pi;
z=t.*exp(i*t); % or z=t.*exp(complex(0,t));
plot(z)
axis([-13 13 -13 13])
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Plotting in MATLAB
Thank You...
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MatLab Basic Tutorial On Plotting

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