Introduction to MATLAB

Transcription

1 Introduction to MATLAB An introductory guide to using MATLAB. By following this labsheet you should be able to quickly pick up the basics of the language for use in the following lab sessions. MATLAB and a variety of toolboxes are installed on university networked machines. For use off campus you will need to register an account with your university on the Mathworks website and the COSIT group to obtain a license. For more information check the MATLAB API at The toolboxes installed as part of the campus license can be found with the command ver Contents MATLAB GUI Writing code Getting Help and Documentation Path Scope Workspace clean up Variable Initialisation Basic Operators Matrix Handling Cells Indexing Structures Printing to command window Conditionals State Checks For loops External Functions Plotting 3D Scatter Plot Load / Save k means clustering GMM Marked Tasks: MATLAB GUI The main MATLAB window shows a number of key areas. These can be arranged to your preference in the "Layout" selection of the "Environment" tab in the IDE. A: Current Folder The current working directory. B: Variables Viewer for exploring matrices and data structures in the workspace. C: Editor Built in IDE for script and function development. D: Workspace Current variables available in memory. E: Command Window Prompt interface for code prototyping. F: Command History Previously entered code for easy access. Writing code When writing MATLAB code there is the ability to quickly prototype code within the Command Window, or to write program scripts or functions in the the Editor. Scripts execute as if typed directly into the command window, and share the base workspace variables. Functions have their own individual workspace, and only have scope to this workspace. A script or function is called by entering its filename without the '.m' extension. Comments are preceeded by the percentage symbol '%', use these to document your code for future reference! All work for this module should be called from a script. If you wish to implement certain elements as functions this is fine, however they should then be called via the main script.

2 Getting Help and Documentation If information is required about a certain function then it is often possible to search the documentation or the help function by calling 'doc' and 'help' on the function of interest. help plus + Plus. X + Y adds matrices X and Y. X and Y must have the same dimensions unless one is a scalar (a 1-by-1 matrix). A scalar can be added to anything. C = PLUS(A,B) is called for the syntax 'A + B' when A or B is an object. Reference page in Doc Center doc plus Other functions named plus calendarduration/plus gf/plus laurmat/plus codistributed/plus gpuarray/plus laurpoly/plus cvdata/plus icsignal/plus sym/plus datetime/plus InputOutputModel/plus timeseries/plus duration/plus Path Scope MATLAB can only see files that are on its defined path. Any new directories that you wish to work with must be added to the current session's path by right clicking on the directory and selecting "Add to Path" and then choosing "Selected folders and subfolders". Workspace clean up When working in MATLAB it can be useful to tidy up the environment. clc % Clear command window. clear % Clear current workspace variables. clear X % Clear variable X from current workspace. close % Close current figure. close all % Close all open figures. Variable Initialisation The basis of MATLAB usage is in the handling of vectors and matrices. The common syntax is to enclose a matrix using square brackets. Initialise 1*1 double A with a value of 1 Initialise 1*3 vector B of the values 4, 5 and 6, incrementing in steps of +1. A comma separates columns. Initialise a vector C containing values from 0 to 100 in steps of 10 A = 1 B = [4,5,6] C = 0:10:100 A = 1 B = C = Initialise 3*3 matrix D. A semicolon separates rows Intialise 5*4*2 matrix of zeros E D = [1,2,3;4,5,6;7,8,9] E = zeros(5,4,2)

3 D = E(:,:,1) = E(:,:,2) = Initialise 3*3 matrix of magic numbers F, ones G, NaNs H and infs I F = magic(3) G = ones(3) H = nan(3) I = inf(3) F = G = H = NaN NaN NaN NaN NaN NaN NaN NaN NaN I = Inf Inf Inf Inf Inf Inf Inf Inf Inf Basic Operators Plus + and Minus [1,2,3] + 2 [1,2,3] - [3,2,1] %[1,2,3] + [1,2] % Will not work

4 Elementwise Multiplication.* and Division./ 1.* 2 % Equal to the scalar multiplication 1 * 2 [1,2].* 2 [1,2].* [3,2] %[1,2,3].* [1,2] % Will not work [15,8,3]./ [5,4,3] Matrix Multiplication * 1 * 2 [1,2] * 2 % Equal to the scalar multiplication [1,2].* 2 %[1,2] * [3,2] % Will not work [1,2] * [3;2] % Same as 1*3+2*2 [1;2] * [3,2] % Same as 1*3,1*2;2*3,2* Raise to power ^ and elementwise power.^ 5^2 [5,6].^ [2,3]

5 Matrix Handling Transpose (reflect along diagonal/swap row and column indices) with apostrophe/single quote J = magic(4) J' J = Reshape F from 3*3 matrix to a 8*2 vector. Note the columnwise operation! J reshape(j,8,2) J = Cells Cells allow us to hold data of varying types and sizes. Each cell element then stores its own contents which can be accessed directly. Initialise 3*3 cell matrix K = cell(3) K = [] [] [] [] [] [] [] [] [] Cells are accessed using brace notation. K{1,1} = [1,2,3,4]; K{1,2} = 'Cells are fun!'; % Single quotes surround a string K{3,3} = cell(1,10); K K = [1x4 double] 'Cells are fun!' [] [] [] [] [] [] {1x10 cell}

6 We can index contents within a cell in the normal fashion. K{1,1}(1,4) = 9001; % This accesses the fourth element within the first cell and changes it to 9001 K{1,1} Indexing If we want to access a given element in a vector/matrix/array we utilise indexing. Note that MATLAB index starts from 1! F F = Subscript indexing: Index into ith row and jth column F(i,j) F(1,3) % Row 1, column 3 6 Range index with colon operator: F(1,:) % Row 1, all columns F(1:2,2:end) % Rows 1 and 2, columns 2 to the last Linear indexing Index into ith element F(i). Note columnwise. F(7) % 7th columnwise element 6 Logical indexing Index using a logical array/matrix corresponding to the matrix we are indexing index = F < 5 % Logical indices of A lower than 15 F(index) = 0 % Set these elements to 0 index =

7 F = Structures Structure arrays in MATLAB hold data within fields that can vary in size and types. L(1).fieldname1 = 5; L(1).fieldname2 = 'Here'; L(1).fieldname3 = [1,2,3;4,5,6]; L(2).fieldname1 = 1337; L(2).fieldname2 = 'There'; L(2).fieldname3 = [3,4,1;5,7,2;3,4,5]; L L = 1x2 struct array with fields: fieldname1 fieldname2 fieldname3 Data stored with a given field is accessed via dot notation. L(1).fieldname2 Here Printing to command window Ommiting semicolon prints variable to the command window. Nice for tracing through a program, hideous when you have large matrices. Try ones(1000,1000) to see why. F F = Surpress this output with semicolon. F; % This won't be printed fprintf fprintf('csm77 is fun!'); CSM77 is fun! fprintf can handle string specifiers and variables from the workspace linenum = [1,2, ]; fprintf('line %d\nline %d\nline %.2f',lineNum); Line 1 Line 2 Line 3.14

8 Conditionals Blocks in MATLAB start with the keyword and end with the 'end' keyword. Indentation is not required but is encouraged in good practice. Read up on the NOT (~), AND (&), and OR () logical operators. Note AND and OR have short circuit logical operators in (&& and ). condition = 9; if condition >= 10 fprintf('here.\n'); elseif condition >= 0 fprintf('there.\n'); else fprintf('everywhere.\n'); end There. State Checks is*(x) detects the state of an entity X in the workspace. This is useful to determine the property of a variable before performing some function on it M = [nan,5,inf,10] M = NaN 5 Inf 10 isnan(m) isinf(m) isempty(m) For loops Loops in MATLAB create an index variable and iterate through a vector in sequential order n = 5; t = 0; for i = 1 : n t = t + 1; end t t = 5 While loops check a condition before exectuting the statement inside while t > 0 t = t - 1; end t t = 0

9 External Functions The below code shows MATLAB function notation. These are saved into their own.m file and located on the path for use in other functions and scripts. function [output] = addone(input) output = input + 1; end These can then be called by their function name. n = 1; n = addone(n) n = 2 Plotting figure; % Open new figure x1 = 0:pi/10:4*pi; % Create a vector of linearly spaced datapoints for x y1 = sin(x1); % plot(x1,y1); % Plot our first wave xlabel('x'); % Label our axes ylabel('y'); title('plot of Waves'); hold on; % Hold the current figure so that we can plot without clearing y2 = cos(x1); plot(x1,y2,':r') %plot our cos wave wih a dotted red line 3D Scatter Plot figure; z = 0:(4*pi)/250:4*pi; x = 2*cos(z); y = 2*sin(z); scatter3(x,y,z) % plot our data in the new figure xlabel('x') ylabel('y') zlabel('z')

10 Load / Save Saving a selection of workspace variables requires the filename and the variables to save into the.mat file. Ommitting the second argument saves all current workspace variables. save('csm77_savefile'); % Loading data from a.mat file is just as easy. Provide the filename to % load the whole file, or specific variables to save memory. clear; % Clear the workspace so that we can see it is reloaded. load('csm77_savefile'); k means clustering The following section implements k means algorithm on some built in dataset. Our basic pipeline is as follows: Load the data Visualise the feature space Select features for clustering Call the kmeans function on the data Check the clustering performance by plotting label assignments Make sure to use doc or help to check the usage of different functions. 1 Load data and visualise feature space clear; clc; close all; % workspace cleanup load('kmeansdata','x') % load the variable X from the built-in kmeansdata dataset. There are 560 observations and 4 recorded features. featurelabels = {'D1';'D2';'D3';'D4'}; % give some informative labels to the features truthlabels = []; % we don't have any ground truth color = []; % we don't need different colors markersymbol = []; % we don't need different symbols markersize = [];% we don't need different marker sizes drawlegend = 1; diagstyle = 'stairs'; % what to plot on the diagonal figure gplotmatrix(x,x,truthlabels,color,markersymbol,markersize,drawlegend,diagstyle,featurelabels,featurelabels)% visualise feat relations title('feature space scatter matrix for X') 2 Set up kmeans parameters and perform clustering %Perform k-means on X. We can cheat here because we know there are 4 %clusters, however run this multiple times to see that k-means only reaches %a local minima. Try altering the number of clusters (k) to see the %effect. feats = [1,2,3,4]; % select features to cluster data = X(:,feats); k = 4; % number of clusters maximumiter = 100; % maximum number of kmeans iterations to run starttype = 'sample'; % the centroid position seed. Try: 'cluster', 'plus' and 'uniform' nrep = 1; % number of times to perform kmeans, returns the clustering with lowest sum of distances 3 Perform k means clustering [idx,c] = kmeans(data,k,'start',starttype,'maxiter',maximumiter,'replicates',nrep); %perform kmeans

11 4 Plot k means clustering results figure; gscatter(data(:,1),data(:,2),idx) % scatter plot X against Y with group labels in idx hold on plot(c(:,1),c(:,2),'kx','markersize',15,'linewidth',3) % highlight centroids title 'K-Means Clustering' xlabel('d2') ylabel('d1') GMM The following section implements the fitting of a Gaussian Mixture model to the same data as above. We follow a similar pipeline as before: Load the data Visualise the feature space Select features for clustering Call the GMM fitting function on the data Check the clustering performance by plotting label assignments Plot the 99% confidence coverage 1 Load data and visualise feature space clear; clc; close all; % workspace cleanup load('kmeansdata','x') % load the variable X from the built-in kmeansdata dataset. There are 560 observations and 4 recorded features. featurelabels = {'D1';'D2';'D3';'D4'}; % give some informative labels to the features truthlabels = []; % we don't have any ground truth color = []; % we don't need different colors markersymbol = []; % we don't need different symbols markersize = [];% we don't need different marker sizes drawlegend = 1; diagstyle = 'stairs'; % what to plot on the diagonal figure gplotmatrix(x,x,truthlabels,color,markersymbol,markersize,drawlegend,diagstyle,featurelabels,featurelabels)% visualise feat relations title('feature space scatter matrix for X')

12 2 Select data for clustering feats = [1,2,3,4]; % select features to cluster data = X(:,feats); 3 Set up GMM parameters Try altering these parameters, and try further ones outlined in doc fitgmdist k = 4; % number of clusters starttype = 'randsample'; % the centroid position seed. Try: 'cluster', 'plus' and 'uniform' nrep = 1; % number of times to perform kmeans, returns the clustering with lowest sum of distances 4 Fit GMM to data and cluster original observations GMM = fitgmdist(data,k,'start',starttype,'replicates',nrep); % fits GMM predictedy = cluster(gmm,data); % cluster the observations in X using the model GMM 5 Plot clustering and the model confidence coverage plotcolors = parula(k); % make some colors threshold = sqrt(chi2inv(0.99,k)); % Determine confidence threshold figure hold on for ik = 1:k % for every cluster % create grid that covers the input space d = 300; x1 = linspace(min(data(:,1)),max(data(:,1)),d); x2 = linspace(min(data(:,2)),max(data(:,2)),d); x3 = GMM.mu(ik,3); x4 = GMM.mu(ik,4); [x1grid,x2grid,x3grid,x4grid] = ndgrid(x1,x2,x3,x4); X0 = [x1grid(:) x2grid(:) x3grid(:) x4grid(:)]; % Calculate Mahalanobis distance of points to the GMM mus mahaldist = mahal(gmm,x0); % Select points that fall under threshold idx = mahaldist(:,ik)<=threshold; %find coverage for 99% for Gaussian m % Plot the Gaussian coverage plot(x0(idx,1),x0(idx,2),'.','color',plotcolors(ik,:),'markersize',5); alpha(.5) end % Plot data points points gscatter(data(:,1),data(:,2),predictedy); % plot predicted clustering plot(gmm.mu(:,1),gmm.mu(:,2),'kx','linewidth',2,'markersize',10) % plot GMM mus title 'GMM Clustering' xlabel('d1') ylabel('d2')

13 Marked Tasks: Part 1: MATLAB The first task is to follow through this labsheet and the lecture slides on the MATLAB syntax. Write a script that performs the above code. Take your time to go through each point and understand the basics of the syntax. It is important that you are able to inspect MATLAB code that we give out in the coming lab sessions. Once you have finished, we will come and check your script, before signing you off. Part 2: K means and GMMs Perform clustering on the built in Fisher iris dataset. The choice of parameters are up to you. We will check your scripts in the lab and sign you off. Please provide both a kmeans AND GMM clustering, these can be in separate scripts for ease of reading. Follow the pipeline from above: Load the data Visualise the feature space Select features for clustering Call the kmeans function on the data Check the clustering performance by plotting label assignments Consider the following: 1. How many observations are there in the dataset? 2. How many features are there? 3. What is the true number of clusters? 4. What impact will altering a kmeans parameter have on performance? Hints: The Fisher iris dataset can be loaded by calling load fisheriris The Fisher iris dataset contains two variables: meas and species meas contains the data observations, species is a cell array of the data labels You can find further information regarding the dataset online. Even though we are using data driven clustering methods, we do have ground truth labels for each point. This can be useful in evaluating how our clustering has performed. The gscatter plotting function can take labels from species as an argument, i.e. gscatter(x(:,1),x(:,2),y) check doc gscatter. Published with MATLAB R2016a