matlab

# MATLAB/Octave Scientific Computing MATLAB is a numerical computing environment optimized for matrix operations and scientific computing. GNU Octave is a free, open-source alternative with high MATLAB compatibility. ## Quick Start **Running MATLAB scripts:** ```bash # MATLAB (commercial) matlab -nodisplay -nosplash -r "run('script.m'); exit;" # GNU Octave (free, open-source) octave script.m ``` **Install GNU Octave:** ```bash # macOS brew install octave # Ubuntu/Debian sudo apt install octave # Windows - download from https://octave.org/download ``` ## Core Capabilities ### 1. Matrix Operations MATLAB operates fundamentally on matrices and arrays: ```matlab % Create matrices A = [1 2 3; 4 5 6; 7 8 9]; % 3x3 matrix v = 1:10; % Row vector 1 to 10 v = linspace(0, 1, 100); % 100 points from 0 to 1 % Special matrices I = eye(3); % Identity matrix Z = zeros(3, 4); % 3x4 zero matrix O = ones(2, 3); % 2x3 ones matrix R = rand(3, 3); % Random uniform N = randn(3, 3); % Random normal % Matrix operations B = A'; % Transpose C = A * B; % Matrix multiplication D = A .* B; % Element-wise multiplication E = A \ b; % Solve linear system Ax = b F = inv(A); % Matrix inverse ``` For complete matrix operations, see [references/matrices-arrays.md](references/matrices-arrays.md). ### 2. Linear Algebra ```matlab % Eigenvalues and eigenvectors [V, D] = eig(A); % V: eigenvectors, D: diagonal eigenvalues % Singular value decomposition [U, S, V] = svd(A); % Matrix decompositions [L, U] = lu(A); % LU decomposition [Q, R] = qr(A); % QR decomposition R = chol(A); % Cholesky (symmetric positive definite) % Solve linear systems x = A \ b; % Preferred method x = linsolve(A, b); % With options x = inv(A) * b; % Less efficient ``` For comprehensive linear algebra, see [references/mathematics.md](references/mathematics.md). ### 3. Plotting and Visualization ```matlab % 2D Plots x = 0:0.1:2*pi; y = sin(x); plot(x, y, 'b-', 'LineWidth', 2); xlabel('x'); ylabel('sin(x)'); title('Sine Wave'); grid on; % Multiple plots hold on; plot(x, cos(x), 'r--'); legend('sin', 'cos'); hold off; % 3D Surface [X, Y] = meshgrid(-2:0.1:2, -2:0.1:2); Z = X.^2 + Y.^2; surf(X, Y, Z); colorbar; % Save figures saveas(gcf, 'plot.png'); print('-dpdf', 'plot.pdf'); ``` For complete visualization guide, see [references/graphics-visualization.md](references/graphics-visualization.md). ### 4. Data Import/Export ```matlab % Read tabular data T = readtable('data.csv'); M = readmatrix('data.csv'); % Write data writetable(T, 'output.csv'); writematrix(M, 'output.csv'); % MAT files (MATLAB native) save('data.mat', 'A', 'B', 'C'); % Save variables load('data.mat'); % Load all S = load('data.mat', 'A'); % Load specific % Images img = imread('image.png'); imwrite(img, 'output.jpg'); ``` For complete I/O guide, see [references/data-import-export.md](references/data-import-export.md). ### 5. Control Flow and Functions ```matlab % Conditionals if x > 0 disp('positive'); elseif x < 0 disp('negative'); else disp('zero'); end % Loops for i = 1:10 disp(i); end while x > 0 x = x - 1; end % Functions (in separate .m file or same file) function y = myfunction(x, n) y = x.^n; end % Anonymous functions f = @(x) x.^2 + 2*x + 1; result = f(5); % 36 ``` For complete programming guide, see [references/programming.md](references/programming.md). ### 6. Statistics and Data Analysis ```matlab % Descriptive statistics m = mean(data); s = std(data); v = var(data); med = median(data); [minVal, minIdx] = min(data); [maxVal, maxIdx] = max(data); % Correlation R = corrcoef(X, Y); C = cov(X, Y); % Linear regression p = polyfit(x, y, 1); % Linear fit y_fit = polyval(p, x); % Moving statistics y_smooth = movmean(y, 5); % 5-point moving average ``` For statistics reference, see [references/mathematics.md](references/mathematics.md). ### 7. Differential Equations ```matlab % ODE solving % dy/dt = -2y, y(0) = 1 f = @(t, y) -2*y; [t, y] = ode45(f, [0 5], 1); plot(t, y); % Higher-order: y'' + 2y' + y = 0 % Convert to system: y1' = y2, y2' = -2*y2 - y1 f = @(t, y) [y(2); -2*y(2) - y(1)]; [t, y] = ode45(f, [0 10], [1; 0]); ``` For ODE solvers guide, see [references/mathematics.md](references/mathematics.md). ### 8. Signal Processing ```matlab % FFT Y = fft(signal); f = (0:length(Y)-1) * fs / length(Y); plot(f, abs(Y)); % Filtering b = fir1(50, 0.3); % FIR filter design y_filtered = filter(b, 1, signal); % Convolution y = conv(x, h, 'same'); ``` For signal processing, see [references/mathematics.md](references/mathematics.md). ## Common Patterns ### Pattern 1: Data Analysis Pipeline ```matlab % Load data data = readtable('experiment.csv'); % Clean data data = rmmissing(data); % Remove missing values % Analyze grouped = groupsummary(data, 'Category', 'mean', 'Value'); % Visualize figure; bar(grouped.Category, grouped.mean_Value); xlabel('Category'); ylabel('Mean Value'); title('Results by Category'); % Save writetable(grouped, 'results.csv'); saveas(gcf, 'results.png'); ``` ### Pattern 2: Numerical Simulation ```matlab % Parameters L = 1; N = 100; T = 10; dt = 0.01; x = linspace(0, L, N); dx = x(2) - x(1); % Initial condition u = sin(pi * x); % Time stepping (heat equation) for t = 0:dt:T u_new = u; for i = 2:N-1 u_new(i) = u(i) + dt/(dx^2) * (u(i+1) - 2*u(i) + u(i-1)); end u = u_new; end plot(x, u); ``` ### Pattern 3: Batch Processing ```matlab % Process multiple files files = dir('data/*.csv'); results = cell(length(files), 1); for i = 1:length(files) data = readtable(fullfile(files(i).folder, files(i).name)); results{i} = analyze(data); % Custom analysis function end % Combine results all_results = vertcat(results{:}); ``` ## Reference Files - **[matrices-arrays.md](references/matrices-arrays.md)** - Matrix creation, indexing, manipulation, and operations - **[mathematics.md](references/mathematics.md)** - Linear algebra, calculus, ODEs, optimization, statistics - **[graphics-visualization.md](references/graphics-visualization.md)** - 2D/3D plotting, customization, export - **[data-import-export.md](references/data-import-export.md)** - File I/O, tables, data formats - **[programming.md](references/programming.md)** - Functions, scripts, control flow, OOP - **[python-integration.md](references/python-integration.md)** - Calling Python from MATLAB and vice versa - **[octave-compatibility.md](references/octave-compatibility.md)** - Differences between MATLAB and GNU Octave - **[executing-scripts.md](references/executing-scripts.md)** - Executing generated scripts and for testing ## GNU Octave Compatibility GNU Octave is highly compatible with MATLAB. Most scripts work without modification. Key differences: - Use `#` or `%` for comments (MATLAB only `%`) - Octave allows `++`, `--`, `+=` operators - Some toolbox functions unavailable in Octave - Use `pkg load` for Octave packages For complete compatibility guide, see [references/octave-compatibility.md](references/octave-compatibility.md). ## Best Practices 1. **Vectorize operations** - Avoid loops when possible: ```matlab % Slow for i = 1:1000 y(i) = sin(x(i)); end % Fast y = sin(x); ``` 2. **Preallocate arrays** - Avoid growing arrays in loops: ```matlab % Slow for i = 1:1000 y(i) = i^2; end % Fast y = zeros(1, 1000); for i = 1:1000 y(i) = i^2; end ``` 3. **Use appropriate data types** - Tables for mixed data, matrices for numeric: ```matlab % Numeric data M = readmatrix('numbers.csv'); % Mixed data with headers T = readtable('mixed.csv'); ``` 4. **Comment and document** - Use function help: ```matlab function y = myfunction(x) %MYFUNCTION Brief description % Y = MYFUNCTION(X) detailed description % % Example: % y = myfunction(5); y = x.^2; end ``` ## Additional Resources - MATLAB Documentation: https://www.mathworks.com/help/matlab/ - GNU Octave Manual: https://docs.octave.org/latest/ - MATLAB Onramp (free course): https://www.mathworks.com/learn/tutorials/matlab-onramp.html - File Exchange: https://www.mathworks.com/matlabcentral/fileexchange/