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:
# MATLAB (commercial)
matlab -nodisplay -nosplash -r "run('script.m'); exit;"
# GNU Octave (free, open-source)
octave script.m
Install GNU Octave:
# 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:
% 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.
2. Linear Algebra
% 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.
3. Plotting and Visualization
% 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.
4. Data Import/Export
% 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.
5. Control Flow and Functions
% 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.
6. Statistics and Data Analysis
% 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.
7. Differential Equations
% 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.
8. Signal Processing
% 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.
Common Patterns
Pattern 1: Data Analysis Pipeline
% 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
% 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
% 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 - Matrix creation, indexing, manipulation, and operations
- mathematics.md - Linear algebra, calculus, ODEs, optimization, statistics
- graphics-visualization.md - 2D/3D plotting, customization, export
- data-import-export.md - File I/O, tables, data formats
- programming.md - Functions, scripts, control flow, OOP
- python-integration.md - Calling Python from MATLAB and vice versa
- octave-compatibility.md - Differences between MATLAB and GNU Octave
- 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.
Best Practices
-
Vectorize operations - Avoid loops when possible:
% Slow
for i = 1:1000
y(i) = sin(x(i));
end
% Fast
y = sin(x);
-
Preallocate arrays - Avoid growing arrays in loops:
% Slow
for i = 1:1000
y(i) = i^2;
end
% Fast
y = zeros(1, 1000);
for i = 1:1000
y(i) = i^2;
end
-
Use appropriate data types - Tables for mixed data, matrices for numeric:
% Numeric data
M = readmatrix('numbers.csv');
% Mixed data with headers
T = readtable('mixed.csv');
-
Comment and document - Use function help:
function y = myfunction(x)
%MYFUNCTION Brief description
% Y = MYFUNCTION(X) detailed description
%
% Example:
% y = myfunction(5);
y = x.^2;
end
Additional Resources