Pre-work Arrays and Matrices in MATLAB week 3

Digital Fundamentals Arrays and Matrices in MATLAB

Lecture Overview

• Introduction to arrays and matrices in MATLAB.

• Tools for manipulating data in these variables.

• Explanation of indexing and its applications in data manipulation.

Numeric Arrays in MATLAB

• Arrays and matrices are essential data types in MATLAB.

• Creating Numeric Row Array:

  speed = [0, 1, 2.6, 3.11, 7];  % Horizontal array

• Creating Numeric Column Array:

  speed = [0; 1; 2.6; 3.11; 7];  % Vertical array

/

• Monotonically Increasing Arrays:

  • Created using the syntax:
    matlab x = start:increment:end;

  • Example: Create a time array between 0 – 10 seconds, stepping at 0.1 seconds:
    matlab time = 0:0.1:10;

  • linspace() also generates a similar array:
    matlab time = linspace(0,10,101);

  • 0 is the start, 10 is the end, and 101 is the number of equally spaced elements.

Plotting Arrays in MATLAB

• Arrays facilitate plotting mathematical functions using the created time array:

  t = 0:0.1:10;  % Time array
  x = sin(2*pi*t);  % 1Hz sinusoid

• Useful Plotting Functions:

  • figure(): Generates a new figure window.

  • plot(x,y): Plots y against x.

  • Define axis limits with axis([xmin xmax ymin ymax]).

  • Use xlabel() and ylabel() to label axes.

  • grid on: Turns on grid lines in the graph.

Matrices in MATLAB

• Arrays are 1-D, while matrices can be multi-dimensional (2-D or 3-D).

• Creating a 3x3 Matrix:

  mat_3x3 = [1, 2, 3; 2, 4, 6; 3, 6, 9];

• Semicolons mark the start of a new row.

Initializing Arrays and Matrices

• Using zeros():

  • Create arrays and matrices filled with zeros:
    matlab x = zeros(1,n); % 1 x n array y = zeros(m,n); % m x n matrix

• Using ones():

  • Create arrays and matrices filled with ones:
    matlab x = ones(1,n); % 1 x n array y = ones(m,n); % m x n matrix

Cell Arrays in MATLAB

• Used to store mixed data types (text and numbers).

• Created using curly braces:

  x = {1, 2; 3, 4; 5, 6};  % Cell array
  y = {'Item number', 'Price'; 1, 23.95; 2, 47.55; 3, 6.73};

• Conversion Functions:

  • cell2mat(): Converts cell to a numeric matrix (if contents are homogeneous).

  • cell2table(): Converts a cell array to a table (supports mixed data types).

Matrix Operations

• Basic Operators:

  • Element-wise operations: * or .*, / or ./, ^ or .^.

  • Matrix-specific operators: Left division , and transpose .'.

• Matrix Multiplication:

  

  • Element-wise:
    matlab z = x.*y; % Element-wise multiplication

  • Matrix multiplication:
    matlab z = x*y'; % Matrix multiplication (dot product)

• The dot product formula:

  𝑥.𝑦 = 𝑥𝑦𝑇 = 1×2 + 2×4 + 3×6 + 4×8 = 60

Mixed opperations, matrix left division

Matrix Division and Powers

• Two ways for division and powers:

  • **Powers **: Element-wise (.^) and matrix (^) powers.

  • Left Division: Use to solve systems of equations:
    matlab A = [-20 10; 9 120]; b = [330; 225]; x = A\b; % Solutions

Indexing Arrays and Matrices

• Indexing facilitates access to specific elements in arrays/matrices:

  • Example of retrieving and modifying:
    matlab x = myArray(5); % Access 5th element myArray(6) = 10; % Change value of 6th element

• Access by Row and Column:

  • 2-D matrix indexing uses two numbers: Row and Column
    matlab x = myMatrix(4,3); % Access element at row 4, column 3

Indexing Techniques

• Use the colon operator for entire rows or columns:

  • All rows in a given column: x = myMatrix(:,2);

  • All columns in a specific row: x = myMatrix(2,:);

• Access a range of elements:

  x = myMatrix(1:3, 2:4);  % Rows 1-3 and columns 2-4

• Multi-dimensional Indexing:

  • Access elements in 3D matrices using three indices (row, column, layer):

   x = MyMatrix(3, 2, 1);  % Access 3rd row, 2nd column, 1st layer

• Applications in Images:

  • Layers correspond to color channels (R, G, B).

Practical Examples of Indexing

• Example 1: From a CSV file with time vs voltage data:

  capture = readmatrix('scope3.csv');
  t = capture(:, 1);  % Time
  V = capture(:, 2);  % Voltage
  figure(1), plot(t, V), xlabel('Time, sec'), ylabel('Voltage');

• Example 2: Manipulating audio arrays:

  y(10000:20000)=zeros(10001, 1);  % Delete audio segment
  soundsc(y, fs);  % Play sound

• Example 3: Manipulating image colors:

  X(:,:,1) = X(:,:,1) + 100;  % Increase red intensity

Conclusion

• Lecture covered arrays and matrices in MATLAB, their creation, operators, and indexing.

• Important concepts for modifying and storing data efficiently in MATLAB.