MATLAB Crash Course for 2012
PIMS-MPrime-CDM Summer School
Table of Contents
Course Objectives ...............................................................................................................
Housekeeping Commands ....................................................................................................
Scalars, Vectors and Matrices ...............................................................................................
Plotting .............................................................................................................................
Defining Functions .............................................................................................................
Solving ODE .....................................................................................................................
Acknowledgements .............................................................................................................
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Course Objectives
At the end of the course, students should master basic MATLAB syntax and language needed to numerically solve a determinsitic mathematical model of an infectious disease.
Housekeeping Commands
Good practice to begin a new script this way unless you want to keep variables for some reason.
clear;
clc;
clear + *varname*;
Scalars, Vectors and Matrices
Define some scalars
a=10;
b=5;
c=0.5;
Operations on scalars
d=c*a+a/b;
Define some vectors
W=[1 4 2 -1 3 8 6 0 0 1 14];
X=0:1:a;
Y=0:0.5:b;
Z=linspace(a,b,11);
X1=ones(1,11);
X0=zeros(1,11);
Operations on vectors
Xt=X';
X2=b*X1-X;
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MATLAB Crash Course for 2012
PIMS-MPrime-CDM Summer School
XY=X.*Y;
Define some matrices
A=diag(Z);
B=[W;X;Y];
C=zeros(11,11);
C(d,:)=X;
Xid=eye(10);
Xuni=rand(3,4);
Xnorm=randn(3,4);
Bblock=[ones(3) zeros(3,2);zeros(2,3) 4*eye(2)];
Operations with Matrices
D=A+C;
Ax=A*Xt;
AD=A*D;
AD2=A.*D;
Selecting elements of vectors and matrices:
Using indicies
x2=X2(2);
A23=A(2,3);
Vectorised approach for selecting elements of vectors and matrices
X2indexed=X2(1:2:11);
XYindexed=XY(1:2:11);
Aindexed1=A(:,1:2:11);
Using a vector of 1 and 0
indicator=(X2>=0);
X2selected=X2(indicator);
XYselected=XY(indicator);
Aselected1=A(:,indicator);
Aselected2=A(indicator,:);
Aselected3=A(indicator,indicator);
Plotting
Basic Plotting
figure;
plot(X,Ax);
xlabel('X');
ylabel('Ax');
title('Ax vs X')
print('-depsc','AX')
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MATLAB Crash Course for 2012
PIMS-MPrime-CDM Summer School
Multiple plots on a single figure
figure;
plot(X,Ax);
hold all
plot(X, 2+Ax,'LineWidth',2)
xlabel('X');
ylabel('Ax');
title('Multiple plots on a single figure')
legend('AX','2+Ax','Location','NorthWest')
print('-depsc','AXm')
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MATLAB Crash Course for 2012
PIMS-MPrime-CDM Summer School
Loops and Figures
f1=figure();
f2=figure();
for i=1:11
if X2(i)>0
figure(f1);
plot(X,i*Ax);
hold on;
else
figure(f2);
plot(X,-i*Ax);
hold all;
end
end
figure(f1);
print('-depsc','iAXplus')
figure(f2);
print('-depsc','iAXminus')
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MATLAB Crash Course for 2012
PIMS-MPrime-CDM Summer School
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MATLAB Crash Course for 2012
PIMS-MPrime-CDM Summer School
Defining Functions
The function
is defined in the file contact1.m.
c1=contact1(2,2,2);
c2=contact1(1,2,4);
c3=contact1(16,3,2.75);
The fuction in contact1.m is also written so that it can accept a vector for any of the parameters. This
allows matlab to perform multiple computations efficiently and can shorten complicated code.
C1=contact1(X,2,2);
C2=contact1(2,X2,2);
If more than one vector is used, they must be the same length. The function will be calculated componentwise.
C3=contact1(X,X2,2);
Another way to define simple functions
F=@(p) p.^2.+1;
f2=F(2);
F2=F(X);
Calling figure this way just starts a new figure
figure;
plot(F2,X,'r--')
print('-depsc','Fx')
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MATLAB Crash Course for 2012
PIMS-MPrime-CDM Summer School
Solving ODE
Defining the vector field:
The SIR model
Sdot=Lambda-lambda*S*I-dS*S;
Idot=lambda*S*I-gamma*I-dI*I;
Rdot=gamma*I-dR*R;
is defined in the file SIRModel.m as follows:
function f=SIRModel(t,y,par)
%This function takes parameters
%t in R
%y in R3
%par a vector of 6 parameters.
if length(par)<6 disp('Error:Not enough parameters') f=0; D=0; else
%Relabel values of parameters
Lambda = par(1); lambda = par(2); gamma = par(3); dS = par(4); dI = par(5); dR = par(6);
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MATLAB Crash Course for 2012
PIMS-MPrime-CDM Summer School
%Relabel values of y
S=y(1); I=y(2); R=y(3);
%Calculate N
N=S+I+R;
%Calculate RHS of differential equation
Sdot=Lambda-lambda*S*I-dS*S;
Idot=lambda*S*I-gamma*I-dI*I;
Rdot=gamma*I-dR*R;
f=[Sdot Idot Rdot]';
end
Solving the ODE: If SIRModel.m and Solver.m are in the same directory, running Solver.m should give
the following output.
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MATLAB Crash Course for 2012
PIMS-MPrime-CDM Summer School
Acknowledgements
This tuorial is based on a one-class crash course given by R. de Boer in a Mathematical Epidemiology
class. All the m-files used in this tutorial are de Boer's while S. Akinwumi used Matlab's publish function
to organise the tutorial with minor addition.
Complete matlab documentation can be found at http://www.mathworks.com/help/techdoc/.
Published with MATLAB® 7.13
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