Matlab revision #1

Denis Schluppeck

2022-11-21

Start Matlab

Everything should work

  • on local machine or
  • on https://matlab.mathworks.com

Quick revision of key ideas

  • variables, assignment, equal sign =
  • arrays (vectors, matrices, rows, columns)
  • indexing: 3 ways (index, logical, linear)
  • problem solving! . Breaking big problems into smaller ones and function…

In 2nd session

  • for loop (repeating things)
  • true(), false() and if statement (doing things only in certain conditions)
  • text, strings, …
  • cell arrays (using more than numbers)
  • any requests?

Some terminology

  • Variables: a named placeholder for something
  • Matlab commands or functions do stuff to inputs and return an outputs
  • operators: really also just functions, but a convenient shortcut for very common jobs + - * / etc.

Doing some maths

add, subtract, multiply, divide numbers like this:

>> 1 + 1 - 1    % + and -

>> 10 .* 5      % use .* and ./ to multiply and divide

>> 2 .^ 0

>> 2 .^ 8       % use .^ to raise to power

.* versus * (/ versus ./)

  • note that the operators for multiply and divide are .* and ./ (more on the extra “dot” later)
  • use parenthesess ( ) to make order of operations explicit:
>> (10 + 1) .* 9
>>  10 + 1  .* 9   % not the same, WHY?

Simple maths

  • 3/2

  • value of pi (\(\pi\)). What do you think this could be called in Matlab?

  • two times pi (\(\pi\))

  • 2 to the power of 8

  • 4 to the power of 3

  • 64 to the power of one third

  • to store the results (and work on them), you can put data in a variable

Variables

>> a = 10   % stores the number 10 in a variable called "a"
>> b = 2+2  % stores the result of 2+2 in "b"
  • you can now use the variables (or place holders)::
>> a .* 2.3 % uses "a"
>> c = a + b    % stores result of a+b in "c"

Vectors and Matrices

  • Matlab is very good with dealing with vectors and matrices
  • Vectors: lists of numbers:
>> x = [1, 2, 3]  % a ROW vector
>> y = [4; 5; 6]  % a COLUMN vector
  • Matrices: tables of numbers::
>> u = [ 1, 2, 3 ;
         4, 5, 6  ]  % a 2 by 3 matrix

Creating Matrices

  • fill a matrix with numbers::
>> ones(2,5)   % 2-by-5 matrix full of 1
>> zeros(3,3)  % 3-by-3 matrix full of 0
>> rand (100)  % a 100-by-100 matrix of uniform random numbers
  • many other useful commands::
>> randn(5) % gaussian random numbers (5-by-5 matrix)
>> nan(10)  % not-a-number ... useful in some cases

Indexing

To illustrate, let’s make a special example matrix (it’s special: all rows and columns add to the same value)

M = magic(5)


Can we check the sums?

sum(M, 1) % sum ACROSS dimension 1

sum(M, 2) % sum ACROSS dimension 2

Indexing by row, column

Use parentheses after variable name. To e.g. get the 2nd row, 4th column:

>> M(2,4)

ans =

    14

Remember: you can use the : to get everything along a dimension.

A useful metaphor

Think of a high-lighter pen colouring in the row and column. Where colours overlap: selected

Logical indexing

Find where the array fulfills certain rules. (true, false)

(M > 5) % where are the values > 5
idx = (M > 5) % store them in idx

M(idx) % use them

A useful metaphor

Think of a high-lighter pen colouring in the entries that meet the criteria: selected

Linear indexing

Pretend your array is one big long list (go down rows first, then columns, …).

For M (which was 5 by 5), that means 25 entries.

M(23) % one but last entry
M(:)  % all entries in one big long list

A useful metaphor

Think of your array as a snake or maybe an unravelling knitwear sweater

Functions

  • what’s the idea
  • why are they useful?
  • an example of one
  • doc('function') to find out much more

That’s all folks!