Plotting Graphs in Matlab
Michael Bar, San Francisco State University
Table of Contents
clear %Clearing memory
close all
Example 1: Plotting the graph of quadratic function
One way to plot a 2-dimensional graph of a function is by creating grid of points, and using the plot function.
x = linspace(-10,10,50)'; %50 evenly spaced points in [-10, 10] interval
y = x.^2; %The .^ is element-wise square, i.e. each element is squared
plot(x,y,'LineWidth',2)
title('y = x^2')
xlabel('x')
ylabel('y', "Rotation", 0)
xline(0, 'r--', 'LineWidth',2) %Plots the y-coordinate
grid on
grid minor
Another way to draw the same function is by using the fplot function from the symbolic toolbox.
syms x %Declaring symbolic variable
f(x) = x^2; %Declaring symbolic function
fplot(f(x), [-10,10], 'LineWidth',2)
title('y = x^2', 'FontSize',14) %Notice how we changed the font size
xlabel('x')
ylabel('y', "Rotation", 0)
xline(0, 'r--', 'LineWidth',2) %Plots the y-coordinate
grid on
grid minor
Example 2: Plotting several graphs on one diagram
Using grid and plot function.
Q = linspace(0,10,50)'; %50 evenly spaced points in [0, 10] interval
ATC = 3*Q + 7 + 12./Q; %The ./ is element-wise division
AVC = 3*Q + 7;
MC = 6*Q + 7;
plot(Q,ATC,Q,AVC,'.',Q,MC,'--','LineWidth',2)
set(gca,'FontSize',12); %Notice how we changed the font size of axces
title('ATC,AVC,MC', 'FontSize',14)
xlabel('Q')
ylabel('Costs')
legend('ATC','AVC','MC', 'Location', 'best')
grid on
grid minor
We can achieve the same by using the using the fplot function from the symbolic toolbox.
syms Q %Declaring symbolic variable
clear ATC AVC MC %Clearing previously defined objects
TC(Q) = 3*Q^2 + 7*Q + 12; %Declaring symbolic function (Total Cost)
VC(Q) = 3*Q^2 + 7*Q; %Declaring symbolic function (Variable Cost)
ATC(Q) = TC(Q)/Q; %Declaring symbolic function (Average Total Cost)
AVC(Q) = VC(Q)/Q; %Declaring symbolic function (Average Variable Cost)
MC = diff(TC(Q),Q); %Declaring symbolic function (Marginal Cost)
fplot(ATC,[0.2,10], 'LineWidth',2)
hold on %Adding more plots
fplot(AVC,[0,10], '.','LineWidth',2)
fplot(MC, [0,10], '--','LineWidth',2)
set(gca,'FontSize',12); %Notice how we changed the font size of axces
title('ATC,AVC,MC', 'FontSize',14)
xlabel('Q')
ylabel('Costs')
legend('ATC','AVC','MC', 'Location', 'best')
grid on
grid minor
hold off %Turning off the addition of more plots
Example 3: Plotting 3-dimentional graphs
As with 2-dimensional graphs, one way to go is to plot grid points.
x1 = linspace(0,10,51)'; %100 equally spaced points in [0,10] interval
x2 = linspace(0,20,101)'; %100 equally spaced points in [0,20] interval
[X1,X2] = meshgrid(x1,x2);
y = 10*X1 - X1.^2 + 20*X2 - X2.^2;
surf(X1,X2,y)
title('f(x_1,x_2) = 10x_1 - x_1^2 + 20x_2 - x_2^2')
xlabel('x1')
ylabel('x2')
zlabel('f(x_1,x_2)')
% Tangent plane at x1 = 4, x2 = 11
hold on
plot3(4,11,123,'.r','MarkerSize',25) %Point of tangency
z = 137 + 2*X1 - 2*X2; %Tangent plane
surf(X1,X2,z, 'EdgeColor','none','FaceAlpha',0.5);
hold off
Alternatively, we can use the fsurf function from the symbolic toolbox.
syms x1 x2 %Declaring symbolic variables
f(x1,x2) = 10*x1 - x1^2 + 20*x2 - x2^2; %Declaring symbolic function
% rotate3d on %Use this command if you want to rotate the figure
fsurf(f(x1,x2),[0 10 0 20] )
title('f(x_1,x_2) = 10x_1 - x_1^2 + 20x_2 - x_2^2')
xlabel('x1')
ylabel('x2')
zlabel('f(x_1,x_2)')
% Tangent plane at x1 = 4, x2 = 11
hold on
plot3(4,11,123,'.r','MarkerSize',25) %Point of tangency
d(x1,x2) = 137 + 2*x1 - 2*x2; %Tangent plane
fsurf(d(x1,x2), [0 10 0 20],'EdgeColor','none','FaceAlpha',0.5);
hold off
Example 4: Shaded areas under the graph
We show how to shade the areas under the normal pdf.
x = linspace(-5,5,1001)';
mu = 0; sigma = 1;
y = npdf(x,mu,sigma);
plot(x,y,'k','LineWidth',2);
hold on
shade = x>=2;
h = area(x(shade),y(shade));
h(1).FaceColor = [3 206 229] ./ 255;
shade = x<=-2;
h = area(x(shade),y(shade));
h(1).FaceColor = [3 206 229] ./ 255;
title(['Normal pdf: ','\mu = ',num2str(mu),', \sigma = ',num2str(sigma)],...
'FontSize',12)
xlabel('x')
ylabel('Density, f(x)')
hold off
Example 5: Plotting graph a piecewise function
Plot the graph of:
syms x %Creating symbolic variable
f(x) = piecewise(0<=x<1, x, 1<=x<=2, 3-x); %Defining symbolic piecewize function
fplot(f,[0,2],'LineWidth',2) %Plotting the symbolic function
xlabel('x')
ylabel('y','Rotation',0)
title('Graph of Piecewise Function')
hold on
tol = 1e-10; %Tolerance for jump discontinuities
plot(1,f(1-tol),'ko', 'MarkerSize',5) %Adding circle at (1,1)
plot(1,f(1),'k.', 'MarkerSize',15) %Adding dot at (1,f(1))
grid on
grid minor
hold off
% Saving the figure
print('fig1','-depsc2') %Saving in eps format
% Settings for full-page pdf figure for LaTex
set(gcf,'Units','Inches')
fig = gcf;
fig.PaperUnits = 'inches';
width = fig.Position(3); height = fig.Position(4);
fig.PaperPosition = [0 0 width height];
fig.PaperSize = [width height];
print('-dpdf','fig1')
