Matlab for Scientific Programming A Brief Introduction Mark Levene Follow the links to learn more! Many features will be demonstrated

What can we achieve in 3 hours? Demonstration of why you may consider to use Matlab and for what types of tasks. Tips on getting you started as a Matlab programmer. You will need to practice Malab at home, and/or when doing a project for which Matlab may be suitable.

Matlab Resources There are many!! Matlab tutorials and learning resources Attaway, MATLAB A Practical Introduction to Programming and Problem Solving, Second Edition, Elsevier, 2012 (Introductory). Banches, Text Mining with Matlab, Springer, 2012 (Intermediate). Martinez et al., Exploratory Data Analysis with Matlab, Second Edition, CRC Press, 2011(Advanced). Matlab claims over 1 million users world wide in 2012!! There are many Matlab books.Matlab books Also see Matlab documentation centre.Matlab documentation centre

Why Matlab? Introductory Example Example5_2 from Martinez – load iris 3 classes of Iris to be distinguished by –sepal length, sepal width –petal length, petal width Look at the “data” Briefly discuss the kmeans algorithm for grouping data into k groups (here k=3); demonstrate help in Matlab

What can you do in Matlab? The normal things you can do in any other programming languages, but is interpreted and not strict in its typing to allow quick prototyping. Has many built-in features to handle matrices, maths & stats, data analysis and plotting. Has a wide range of toolboxes such as curve fitting, neural networks, bioinformatics, symbolic maths and finance.toolboxes Although Matlab is proprietary there are many open source toolboxes; see Matlab central.Matlab central

A simple function in Matlab function area = conearea(radius, height) area = pi/3 * radius^2 * height; end conearea(4,6.1)  ans = Matlab has the usual control flow that other languages have – use help when needed !!

Vectorised code Chapter 5 in Attaway for i=1:10 v(i) = i; end %create a vector v = 1:1:10 %start=1, increment=1,end=10 for i=1:10 w(i) = w(i)^2; end %standard loop w=w.^2; %vectorised code Can use any other vector operations! w=log(v); %a vector can be an argument Can query a vector using find: find(w>5); %returns indices satisfying condition

Matrices and Linear Algebra Chapter 12 in Attaway Can also vectorise (try it out yourselves!) m = rand(3,3); %create a random 3x3 matrix Matrix operations work as expected! n = m.*m %Matrix multiplication You will need to revise your linear algebra to make use of these Matlab features.

Example SVD and PCA (Eigenvector decomposition) For example Singular Value Decomposition (SVD) – Look this up for maths details, SVD has applications in many areas including Information Retrieval is easy in Matlab. m = rand(100,10); svd(m); Principal Components Analysis (PCA) is a special case of SVD measuring the directions along which the variance is maximised. load filteredyeastdata; mapcaplot(yeastvalues, genes);

Basic Statistics Chapter 13 in Attaway x= [8 9 3; ; ]; mean(x)  ans = var(x)  ans = std(x)  ans = y = [ ]; mode(y)  ans = 10 median(y)  ans = 9 There is much more in the statistics toolbox

Curve fitting Example7_3 in Martinez Demonstrate cftool with (x,x) and (x,y) Example 9_2 in Martinez Demonstrate histogram Demonstrate cftool with (xk,nuk) normfit = [33,40,42,41,39,32]; linfit = [2,44,49,61,82,95]

Maths Chapter 15 in Attaway Symbolic maths syms x y f = x^2 + y^2 + 2*x*y simplify(f)  ans = (x + y)^2 expand(ans)  f ezplot(x^2+2*x+2) % plot the function

Solving equations solve(2*x^2+x-6)  ans = -2 3/2 syms x a b c solve(a*x^2+b*x+c)  ans = -(b + (b^2 - 4*a*c)^(1/2))/(2*a) -(b - (b^2 - 4*a*c)^(1/2))/(2*a) Can try and solve more complex equations solve(exp(x)-3)  ans = log(3)

Calculus syms x diff(x^3,x)  ans = 3*x^2 %differentiation int(3*x^2)  ans = x^3 %integration Can do much more, including solving differential equations. Do not worry about the Maths as such, as in Matlab we pick up the tools as and when we need them.

Summary Matlab provides and easy-to-use, state-of-the- art environment for scientific computing. There are a wide variety of toolboxes for different applications, many of which are open source. Matlab may not always be the most efficient solution but it is great for quick prototyping. Matlab is not designed for general purpose programming, although it is a complete language.