Extending MATLAB

Write your own scripts and/or functions Scripts and functions are plain text files with

extension .m (m-files) To execute commands contained in m-files,

MATLAB needs to know where they are! store in working directory store in any directory, add to MATLAB's path

To check/change working directory pwd, cd, ls, dir menu bar current directory window

To check/modify path path addpath, rmpath, savepath File >> Set Path...

Reminders

Scripts

No input/output Operate on pre-defined workspace variables

and variables defined in script Variables created during script are saved in

workspace (side effects) Kind of like macros, relatively inflexible

→ good for executing repeated long/complicated sequences of commands on same data

How to execute a script

Save list of commands, variable definitions, etc in plain text file 'scriptEx.m'

Make sure 'scriptEx.m' is saved in wd, OR, its directory is added to path

type 'scriptEx' at command prompt (no quotes) Be aware of side effects

Functions

Basically, scripts that take input and create some output

Operate on input variables and variables defined in function

Variables created during function call only exist as long as function is running can be saved to workspace if defined as output

→ good for performing general tasks with optional parameters on different datasets

How to call your function (1)

Write it (we'll get to that), and save as plain text file 'functionEx.m'

Make sure 'functionEx.m' is saved in wd, OR, its directory is added to path

Let's assume your function has 2 input arguments, these could be input data or parameters to pass to function body

Examples ...

How to call your function (2)

Arg1 is data stored as workspace variable, Arg2 is file containing data, or could be a file to create for output

>> functionEx(x, 'filename.txt')

Arg1 is another function, Arg2 is scalar parameter

>> functionEx(@func, 1000) >> functionEx('func', 1000)

Defining your function

First line must contain the following 'function' command name(s) of output, if any name of function, should be same as name of m-file name(s) of input parameters/arguments

function output = userFunc(arg1, arg2)

function [ ] = userFunc(arg1, arg2, arg3)

function [out1, out2] = userFunc(arg1)

What about lines 2,3,4,...?

Function body can contain anything, as long as it's a valid MATLAB statement/command

Any text preceded by a % is not executed →

% this is a comment If function definition on line 1 is followed by

block of commented lines, comments will be printed as help file when user types

>> help userFunc

Programming basics

Loops for loop → perform command(s) for some

predetermined amount of times while loop → perform command(s) as long as some

condition is met If-then statements

if some condition is met → perform command(s) else and elseif

For loop While loop

for index = 1:n

do something

end

for i = 1:5

i

end

while condition

do something

end

j = 1;

while j <= 5

j

j = j+1;

end

For loops

Avoid hogging memory, use vector alternatives in MATLAB

vec = [2:2:10]

for i = 1:length(vec)

vec(i) = vec(i) + 10; end

vec =

12 14 16 18 20

vec = vec + 10

How to loop through a matrix

m = [1:4; 5:8; 9:12]; % create 3x4 matrix, values % 1:12 [rows cols] = size(m); % store # of rows and columns % in variablesfor rowstep = 1:rows % loop through rows for colstep = 1:cols % loop through columns rowstep % print current row colstep % print current column m(rowstep, colstep) % print value at current % position end % close column loopend % close row loop

Turn that script into a function...function [] = read_matrix(m)%% function [] = read_matrix(m)%% HELPFILE for trivial function 'read_matrix.m'%% 'm' is a matrix % elements of 'm' will be read starting with [1,1]% % at each step, indices and their corresponding value% will be printed to the screen % START CODE [rows cols] = size(m); % store # of rows and columns in variables for rowstep = 1:rows % loop through row numbers for colstep = 1:cols % loop through column numbers rowstep % print current row colstep % print current column m(rowstep, colstep) % print value at current position end % close column loopend % close row loop

If statements

if condition

do something

end

--------

if condition

do something

else

do something

end

val = m(3,2) if val < 5 val = 0; elseif val > 5 val = val * 10; else val = val^2;end

File handling

>>help iofun

>>help fileformats

load dlmread, dlmwrite xlsread, xlswrite urlread, urlwrite unzip, untar

More file handling, C style

fopen, fclose fgetl, fscanf, fseek, ftell

fid = fopen('mean.m'); % open file for reading while 1 % start loop, basically will loop % forever unless it is stopped line = fgetl(fid); % get next line in 'fid' if ~ischar(line) % if 'line' is empty break loop break end disp(line) % print the current lineend fclose(fid); % close file

Let's put this all to use...

Example: transition probabilities

Probabilistic sequence of events We have multiple examples of this sequence Given a particular event, how reliably can we

predict the next event (including the end)? Assume sequence is always same number of

events long Represent each event with a number

Ex. Sequence: 1 – 1 – 2 – 3 – 3 – 3 – 1 – 4 – 4 – 4

Basic idea

Represent each sequence as series of integers Collect a bunch of these sequences and put

them in a matrix where each row is one example of the sequence

We'll write code that will take the matrix and two of the events as arguments Code will return a probability: How often one event

follows the other

Some sequences2 3 4 6 71 2 3 4 61 2 3 4 61 2 3 4 61 2 3 4 61 2 3 4 61 2 3 2 31 2 3 4 61 2 3 4 61 2 3 4 61 2 4 6 71 2 3 4 61 2 3 4 62 1 4 6 71 2 3 4 61 2 3 4 61 2 3 4 61 2 3 4 51 2 3 4 62 3 4 6 7

Example: transition probabilities

Givens A matrix 'data' containing events/numbers, each

row is a sequence two events, 'leader' and 'follower'

Tasks Compute how often 'follower' immediately follows

'leader' Compute how often 'leader' ends the sequence, i.e.

is the last number in its row

Strategy

Loop through matrix, looking for 'leader' Check to see if it is at the end of the row

if yes, tally 1 Check to see if the next element is 'follower'

if yes, tally 1 Count total number of times 'leader' occurs Total up the tallies and divide each by the total

occurrences of 'leader'

Implement in a function

function [prob term_prob] = transProbEXAMPLE(filename,leader,follower)%% function [prob term_prob] = transProbEXAMPLE(filename,leader,follower)%% 'filename' is plain text file containing sequences stored in a matrix%% 'leader' and 'follower' are events/numbers of interest% % This function will compute transition probability from 'leader' to % 'follower'% i.e. how often 'leader' is immediately followed by 'follower'%% returns 'prob' - 'leader' -> 'follower' transition probability% 'term_prob' - probability that 'leader' is last element% in its row

read in data and define variables...

data = dlmread(filename); % pass info in 'filename' to variable 'data' % initialize empty counting vectorstrack_trans = []; % for tracking instances when 'leader' is % followed by 'follower' track_terms = []; % for tracking instances when 'leader' % terminates the line [data_row, data_col] = size(data); % save dimensions of 'data' % to use for looping

do the work...% loop over 'data' rowsfor row = 1:data_row % loop over 'data' columns for col = 1:data_col % look for instances of 'leader' if data(row, col) == leader % check if 'leader' terminates line if col == data_col % if yes, add 1 to counting vector track_terms = [track_terms 1]; % see if next element is 'follower' elseif data(row, col + 1) == follower % if yes, add 1 to counting vector track_trans = [track_trans 1]; end end endend

do the work...% loop over 'data' rowsfor row = 1:data_row % loop over 'data' columns for col = 1:data_col % look for instances of 'leader' if data(row, col) == leader % check if 'leader' terminates line if col == data_col % if yes, add 1 to counting vector track_terms = [track_terms 1]; % see if next element is 'follower' elseif data(row, col + 1) == follower % if yes, add 1 to counting vector track_trans = [track_trans 1]; end end endend

do the work...% loop over 'data' rowsfor row = 1:data_row % loop over 'data' columns for col = 1:data_col % look for instances of 'leader' if data(row, col) == leader % check if 'leader' terminates line if col == data_col % if yes, add 1 to counting vector track_terms = [track_terms 1]; % see if next element is 'follower' elseif data(row, col + 1) == follower % if yes, add 1 to counting vector track_trans = [track_trans 1]; end end endend

do the work...% loop over 'data' rowsfor row = 1:data_row % loop over 'data' columns for col = 1:data_col % look for instances of 'leader' if data(row, col) == leader % check if 'leader' terminates line if col == data_col % if yes, add 1 to counting vector track_terms = [track_terms 1]; % see if next element is 'follower' elseif data(row, col + 1) == follower % if yes, add 1 to counting vector track_trans = [track_trans 1]; end end endend

compute outputs...

% count total number of instances of 'leader'total_leader = length(find(data == leader)); % count number of times 'follower' followed 'leader' count_trans = sum(track_trans);

% count number of times 'leader' terminated lineterminations = sum(track_terms); % calculate probability that 'follower' follows 'leader'prob = count_trans/total_leader;

% calculate probability that 'leader' terminates lineterm_prob = terminations/total_leader;

compute outputs...

% count total number of instances of 'leader'total_leader = length(find(data == leader)); % count number of times 'follower' followed 'leader' count_trans = sum(track_trans);

% count number of times 'leader' terminated lineterminations = sum(track_terms); % calculate probability that 'follower' follows 'leader'prob = count_trans/total_leader;

% calculate probability that 'leader' terminates lineterm_prob = terminations/total_leader;

compute outputs...

% count total number of instances of 'leader'total_leader = length(find(data == leader)); % count number of times 'follower' followed 'leader' count_trans = sum(track_trans);

% count number of times 'leader' terminated lineterminations = sum(track_terms); % calculate probability that 'follower' follows 'leader'prob = count_trans/total_leader;

% calculate probability that 'leader' terminates lineterm_prob = terminations/total_leader;

Extra credit

Generalize this function to deal with sequences of variable length

Hint: more of a data representation problem than a coding problem can't have a matrix with rows of different lengths use 'NaN' to fill space, >>help isnan still want to know if 'leader' is last event in sequence

Only need a couple extra lines of code

Extra credit

Could also use C style file handling functions fopen, fgetl, etc to read one line at a time instead of loading whole data file at once into matrix

Then no problems with unmatched row lengths etc, but would need more changes to code