%% MATLAB Session 1 - Basics, vectors, matrices, plotting % 2026 % Goal: Introduction to basic MATLAB operations, % without overlap with OLS/econometrics. clear; % Clears all variables from the workspace close all; % Closes all open figure windows clc; % Clears the Command Window %% 1. Basic calculations and variables 4*5 % Calculates the product of 4 and 5 a = 4*5 % Creates variable a and stores the result of 4*5 b = 2+3 % Creates variable b and stores the result of 2+3 a*b % Calculates the product of variables a and b %% 2. Create vectors myVector = [1 2 3 4 5] % Creates a row vector with elements 1, 2, 3, 4, 5 myVector2 = 1:2:7 % Creates a vector from 1 to 7 with step size 2 myVector3 = 3:-2:-7 % Creates a vector from 3 to -7 with step size -2 myVector4 = linspace(1,100) % Creates 100 equally spaced points from 1 to 100 myVector5 = linspace(1,100,200) % Creates 200 equally spaced points from 1 to 100 %% 3. Refer to and modify vector elements clear myVector % Clears only the variable myVector from the workspace myVector = 10:10:50 % Creates a vector from 10 to 50 with step size 10 myVector(4) % Displays the 4th element of the vector myVector(3:5) % Displays elements from the 3rd to the 5th position myVector(3:end) % Displays elements from the 3rd position to the end myVector(4) = 1000 % Replaces the 4th element of the vector with 1000 myVector(8) = 50 % Adds a value in the 8th position and fills intermediate positions with zeros myVector' % Transposes the row vector into a column vector %% 4. Basic linear algebra with vectors 0.5*myVector + 1 % Multiplies each element of the vector by 0.5 and adds 1 % The following product is not conformable because myVector is 1 x 8. % Therefore, myVector*myVector would be 1 x 8 times 1 x 8, % where the inner dimensions do not agree. try myVector*myVector % Tries to calculate a nonconformable matrix product catch ME disp('Expected error for myVector*myVector:') % Displays a message that the error was expected disp(ME.message) % Displays the MATLAB error message end myVector*myVector' % Inner product: 1 x 8 times 8 x 1, gives a scalar myVector'*myVector % Outer product: 8 x 1 times 1 x 8, gives an 8 x 8 matrix %% 5. Create matrices myMatrix = [1 2 3; 4 5 6] % Creates a 2 x 3 matrix. The semicolon starts a new row myMatrix myMatrix2 = [1:4; 8:11] % Creates a 2 x 4 matrix using sequences myMatrix2 myMatrix3 = zeros(3) % Creates a 3 x 3 square matrix of zeros myMatrix3 myMatrix4 = zeros(3,2) % Creates a 3 x 2 matrix of zeros myMatrix4 myMatrix5 = ones(3,2) % Creates a 3 x 2 matrix of ones myMatrix5 %% 6. Refer to and modify matrix elements myMatrix(2,2) % Displays the element in row 2 and column 2 myMatrix(1,:) % Displays all elements of the 1st row myMatrix(1:2,2:3) % Displays rows 1 to 2 and columns 2 to 3 myMatrix(1:2,2:end) % Displays rows 1 to 2 and columns from the 2nd to the last myMatrix(1,2:3) = [20 30] % Replaces the elements of row 1 in columns 2 and 3 %% 7. Matrix operations clear myMatrix % Clears the variable myMatrix from the workspace myMatrix = [1 2 3; 4 5 6] % Creates the matrix myMatrix again 2*myMatrix + 1 % Multiplies each element of the matrix by 2 and adds 1 myMatrix + myMatrix % Adds the matrix to itself element by element % The following product is not conformable because myMatrix is 2 x 3. % The product myMatrix*myMatrix would be 2 x 3 times 2 x 3, % so the inner dimensions 3 and 2 do not agree. try myMatrix*myMatrix % Tries to calculate a nonconformable matrix product catch ME disp('Expected error for myMatrix*myMatrix:') % Displays a message that the error was expected disp(ME.message) % Displays the MATLAB error message end myMatrix*myMatrix' % Valid product: 2 x 3 times 3 x 2, gives a 2 x 2 matrix % Element-by-element operations. % The dot before the operator means that the operation is applied element by element. myMatrix.*myMatrix % Multiplies each element of the matrix by the corresponding element myMatrix.^2 % Squares each element of the matrix %% 8. Matrix-vector multiplication clear myMatrix myVector % Clears variables myMatrix and myVector myMatrix = [1 2 3; 4 5 6] % Creates a 2 x 3 matrix myVector = 1:3 % Creates a 1 x 3 row vector % The following product is not conformable. % The matrix is 2 x 3 and the vector is 1 x 3. % For matrix multiplication, the vector must be 3 x 1. try myMatrix*myVector % Tries to calculate a nonconformable product catch ME disp('Expected error for myMatrix*myVector:') % Displays a message that the error was expected disp(ME.message) % Displays the MATLAB error message end myMatrix*myVector' % Valid product: 2 x 3 times 3 x 1, gives a 2 x 1 vector %% 9. Random matrices, size, and deleting rows clear myMatrix % Clears the variable myMatrix from the workspace rand(3) % Creates a 3 x 3 random matrix with values from the uniform distribution on (0,1) rand(3,1) % Creates a 3 x 1 random column vector with values from the uniform distribution on (0,1) myMatrix = [1 2 3; 4 5 6] % Creates a 2 x 3 matrix size(myMatrix) % Displays the dimensions of the matrix [nrows,ncolumns] = size(myMatrix) % Stores the number of rows and columns in two variables myMatrix(1,:) = [] % Deletes the 1st row of the matrix %% 10. Rounding functions myVector = [1.2 1.9] % Creates a vector with decimal values round(myVector) % Rounds each element to the nearest integer floor(myVector) % Rounds each element downward ceil(myVector) % Rounds each element upward %% 11. Simple plot clear; % Clears all variables from the workspace close all; % Closes all open figure windows clc; % Clears the Command Window x = 0:0.1:20; % Creates vector x from 0 to 20 with step size 0.1 y = exp(-x/10).*sin(x); % Calculates y = exp(-x/10)*sin(x) element by element figure % Opens a new figure window plot(x,y) % Plots y as a function of x grid on % Adds a grid to the plot xlabel('x') % Adds a label to the horizontal axis ylabel('f(x) = e^{-x/10} sin(x)') % Adds a label to the vertical axis title('A simple plot') % Adds a title to the plot %% 12. Multiple plots with subplot clear; % Clears all variables from the workspace close all; % Closes all open figure windows clc; % Clears the Command Window t = linspace(0,2*pi,100); % Creates 100 equally spaced points from 0 to 2*pi figure % Opens a new figure window subplot(2,2,1) % Divides the figure into a 2 x 2 grid and selects position 1 plot(t,sin(t)) % Plots sin(t) title('sin(t)') % Adds a title to the first plot grid on % Adds a grid to the plot subplot(2,2,2) % Selects position 2 in the 2 x 2 grid plot(t,cos(t)) % Plots cos(t) title('cos(t)') % Adds a title to the second plot grid on % Adds a grid to the plot subplot(2,2,3) % Selects position 3 in the 2 x 2 grid plot(t,sin(2*t)) % Plots sin(2t) title('sin(2t)') % Adds a title to the third plot grid on % Adds a grid to the plot subplot(2,2,4) % Selects position 4 in the 2 x 2 grid plot(t,cos(2*t)) % Plots cos(2t) title('cos(2t)') % Adds a title to the fourth plot grid on % Adds a grid to the plot