Matlab

1. Matlab It’s good

2. Variables • Doubles (numbers) • String (text) • Cell: a 1x1 size space containing another variable, of any size, inside it • Structure (struct): a variable holding other variables attached to it

3. Variables: size • Variables can be considered a martix. They are always at least 2-dimentional • A variable with a single number has a size of 1x1 • While a variable such as: • Is 2 x 4 (rows x columns)

4. Accessing variable elements • Variable elements can be accessed (or defined) by the variable name, followed by indices in brackets. • Indices are (row, column) • A(1,1) is 5, A(2,1) is 7, A(2,3) = 55 • A(2,3) is row 2, third value. • In a double variable, each number has a separate index A =

5. Defining Variables • Variables are defined by an = sign • E.g. A = 5.3 makes a 1x1 double with a value of 5.3 • Now if we say A(1,2) = 6, we will have a 1x2 variable, [5.3 6] • Try it!

6. Defining variables • Several values can be entered aty once using square brackets [] • A = [1 2 5 6 7] gives a 1x5. A(1,5) is 7. • You can also, in simple variables like this, just say A(5) • A semi colon adds lines • A = [1 3 5 7; 2 4 6 8] • Must have the same number of elements per line

7. Padding with zeros • Matlab will expand the size of variables as needed. In a double, zeros are padded as needed. • A = 1 • A(6) = 2 • A is now 1 0 0 0 0 2

8. Colon operator • In matlab, a colon has two meanings: • By itself, it means ‘all’ • With numbers on each side it means ‘from x to y’ • E.g. 2:6 = 2 3 4 5 6 • You can use colons inside variable indexs when calling them • E.g. A = [2 4 6 8 10 12 14 16] • B = A(3:5); B is now [6 8 10]

9. Colon wackiness • A(1:5) = 10; Ai is now [10 10 10 10 10] • A = 1:5; A is now [1 2 3 4 5] • A = 2:2:10; the middle number becomes an incrimentor • A is now 2 4 6 8 10

10. Exercise 1: defining double variables • Make a double “A” with values 5, 10, 15, 20, 25, 30 • Change the third value to 100 • Make a variable “B” which is equal to the first 3 values in A • Make a variable “C” which has the same value as the last value of A (by calling A, not cheating!) Pause here to contemplate the nature of existance

11. Exercise 1b: a matrix, using colons • Clear • (this clears all variables from the matlab workspace) • A = [1 5 7 9; 11 33 55 77; 100 200 300 400] • Set Change the 4th value on the first row (the 9) to 3 • Set B equal to the first row of A • Set C equal to the first 3 numbers in the last row of A • Set D as the first COLUMN of A

12. Error: In an assignment A(I) = B, the number of elements in B and I must be the same. • Matlab tries to fit values into the exact space you define. If you tell it to fit 4 things in a space of 3 or 5 items, it throws an error: “In an assignment A(I) = B, the number of elements in B and I must be the same.” • For example, A(3:5) = [1 2] • you are saying “in these 3 spaces, fit 2 things” • If you give a single value for multiple spaces, Matlab sets them all to that values • E.g. A(1:4) = 10, A is [10 10 10 10].

13. Multiple Dimensions • Matlab variables are always treated as if they were AT LEAST 2D, but can in fact have as much dimensionality as you wish. • A third dimension can be thought of a cube. • So: • A(:,:,1) = [1 2 3; 7 8 9] • A(:,:,2) = [11 12 13; 21 22 25] • Now we have a 3D variable of size 2x3x2 • Extra variables can be added (e.g. fMRI data is typically 4D): a cube, in a ‘room’

14. Basic Matlab Math • Matlab treats double variables as matrices, and will often default to doing matrix math, if you provide it two matrices • If you give a matrix an a mathmatical operand that is a single number, it applies that to all elements of a matrix • E.g. A = [1 2 3 4] • B = A+2; B is now [3 4 5 6] <<Do some examples together>>

15. Calling matlab functions • Matlab has thousands of useful functions you can call. A function call looks like this: • Output = functionname(inputs, moreinput, etc) • Output is any variable name into which the functions return value is assigned • Multiple input values are separated by commas

16. HELP! • All built-in matlab functions have a help. Type the word help and the function name • Try “help sum” • Lets try calling sum • A = [1 2 3 4]; • B =sum(A) >> B is now 10 (1+2+3+4)

17. Sum part 2 • Sum has an option to put in a second input variable. By default, sum outputs data for each row of the input • A = [1 2 3; 4 5 6] • Sum(a) gives [6 15] • This is because by default it calls as sum(A,1), working on the sum based off the first dimension • BUT sum(A,2) gives [5 7 9] (1+4, 2+5, 3+6)

18. Sum of sums, of more sums? Want sum? • Since sum only works on one dimension, we can ‘nest it’ go get a total sum: • B = sum(sum(A)) NOTE: brackets MUST be balanced!!!! • B is now 21. • Matlab evaluates functions inside-out. The ‘deepest’ thing gets evaluated first. • <<stop here and marvel at the wonders of nesting>> • Other basic math functions: mean, min, max, median

19. Strings • Matlab treats strngs as an array of charaters • Strings are defined by encasing in single quotes • A = ‘happy’ • Now has a 1x6 variable • A(2) is ‘a’

20. String variables: size matters.a lot. • One of the biggest issues with string variables is the issue of size during variable assignments. • Matlab pads strings with whitespace • When making lists, spaces at the end of names can be an issue (e.g. a list of file names to call) << examples of using string here>>

21. Strings are NOT numbers • A = ‘1’ is a string, not a number • A+1 is 50. Because when you do math on a string, it uses asci reference to the string. • There are useful fucntions for this • num2str • str2num • Examples!

22. Concatenating strings • When we assigned double variables, we used square brackets. • This can be thought of as concatenating a series of numbers • We can also concatinate strings (or other variables) using [] • E.g. direc = ‘/data/cool/fMRI/’ • file = ‘nicebrain.nii’ • fullfile = [direc file]

23. Cell: take a variable, and fit it into a space of 1x1 • Cells are a type of ‘container’ variable to hold other variables. • They can be especially useful for strings which can vary in length. • Cells are defined by { } • A{1} = [1 2 3 4] gives a 1x1 sized cell. A(1) is a cell with a value {1 2 3 4} • A cell can be ‘extracted’ using curly braces • B = A{1} gives a 1x4 double variable [1 2 3 4]

24. Error:Cell contents assignment to a non-cell array object. • If you tried the above code you got this • This is because A is probably defined in your workspace as a string or double. • You can only put a cell inside a cell variable • Do some cell practice here

25. Saving variables • Matlab always has a working directory, shown up top • You can save data with the save command • “Save mydata” will create a file names mydata.mat in the current directoy, with all variables from the workspace • Load mydata will load this variable IF YOU ARE IN THAT DIRECTORY • You can also specify a path • Load c:/scientceisfun/mydata.mat • Or as a function call with a string • Load(‘c:/scientceisfun/mydata.mat’) • Specific variables can also be saved (see help save)

26. Scripts and functions • Matlab has a great editor which allows you to make scripts and functions • Scripts just act as if you had copy/pasted the data into the main matlab windows • Functions create a new workspace, and only have access to variables you send to it. • Functions do not modify variables in your main workspace, except the output variable!

27. Script example • Type edit myscript • His will open the editor with a file called myscript.m, which isn’t saved • Type some commands in there and save • Now if you type myscript in the matlab prompt, it will run those commands

28. Functions • Functions are defined by having the word function on the first line, and the function call e.g. edit myfunc Function out = myfunc(in) Out = in* 10; • Functions do not require an end statement or anything. They run line by line until the end • A ‘return’ commend exists the function

29. Commenting scripts/functions • Any content starting with a % is treated as a comment and not run • A comment can be a while line, or after a command • E.g. A = B %set A to B because SCIENCE • Comments at the top of a function, immediately before the function line, will become the help for that function.

30. Basic complex syntax • Most important things in matlab are completed via only the following steps: • Define and cotnrol variables (covered, more or less) • Calling functions (covered) • If statements • For/while loops

31. If statements • In Matlab, if statements make code conditional • The code following the if will only execute when the if condition is true • For a mathmatical equals, use “==“, or “isequal” (which also works on strings) • The if code applied until it hits an end statement

32. If example If A == 1 B=A; A = 2; end ------------------------------------- If A> 1 A = 1; end -------------------------------------- If A >=2 A = 1 end sSome allowable pp[erands: ==, >, <, <= (less or equal), >=, ~= (not equal)

33. Else • An if statements can also have else. In this case, when the ‘if’ is untrue, an ‘else’ will be run e.g. if A == 1 B=A; A = 2; else B =1; end

34. elseif • Elseif runs a new if, ONLY when the first if is not true • Can be chained • Lower elseif only ever run if no above command is run • Once any if/elseif is true, onlt that sub-block of code is run, and then it skips to the end startment

35. elseif example If a < 10 b = 1 elseif a > 100 b = 3 else %only runs if a is between 11 and 99 b = 2 end *there is no limit on the number of elseifs, though an else has to be the last condition. **In a chain of elseif’s it is possible none get run. If there is an if and else, at least one is going to run

36. For loops • Probably the most important code in matlab • Iterates a variable, usually a double for idx = 1:10 %is use idx by convention, any name is OK %code goes here end If can also call a variable Or a specified series of numbers, e.g. For ii = [1 2 5 6 8 10] • Like if, the loop terminates with an ‘end’ statement. A ‘break’ can also kill a loop

37. Loops in loops • For loops and if statement can be nested count =1; for idx = 1:20 a(idx) = sum(b(idx,:)); if a(idx) > 100 for jdx = 1:5 c(idx,jdx) = a(idx) + jdx; end elseif a(idx) > 1000 break end %end of if d(idx) = a(idx); count = count+1; End %end for idx

38. While loops • While works are in other programming formats, only running while/if the condition is true • When it hits the end, it returns to the while and checks the condition n=1; a=1; while n < 10 a = a+b(n); %lets assume “b” was defined above somewhere if a < 10 n = n+1; end %end if end %will now check is n is still less than 10

39. Try and switch • ‘try’ will try to run the code. If the code fails, instead of crashing matlab will go the end • Switch allows testing multiple conditions switch method case {'linear','bilinear'} disp('Method is linear') case 'cubic' disp('Method is cubic') end

40. Structure variable • Structures are variables encasing other variables by name. • Like pointers • Attached “sub-variable” defined by a “.” e.g. A.dat = [1 2 3] Creates a struct variable A, with sub variable “dat” which is a 1x3 double. • Structures are useful to save lots of data into a single variable, keeping thing organized • Can be nested • E.g. • a.dat.name = ‘funfun’ • a.dat.num = [1 2 3 4]

41. Appendix of useful functions find disp length size