matlab

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Summary

MATLAB and GNU Octave numerical computing for matrix operations, data analysis, visualization, and scientific computing. Use when writing MATLAB/Octave scripts for linear algebra, signal processing, image processing, differential equations, optimization, statistics, or creating scientific visualizations. Also use when the user needs help with MATLAB syntax, functions, or wants to convert between MATLAB and Python code. Scripts can be executed with MATLAB or the open-source GNU Octave interpreter.

SKILL.md

MATLAB/Octave Scientific Computing

Routing Boundary

Use this skill only when the user explicitly asks for MATLAB, Octave, Simulink, .m scripts, M-files, or MATLAB-specific tooling. Do not use it for generic NumPy, Python matrix work, Jupyter notebooks, scientific visualization, data analysis, or numerical computing unless MATLAB or Octave is explicit.

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

% 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

% 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');

% 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');

% 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

% 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

% 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]);

% 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');

% 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');

% 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);

% 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{:});

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

matlab

Summary

SKILL.md

MATLAB/Octave Scientific Computing

Routing Boundary

Quick Start

Core Capabilities

1. Matrix Operations

2. Linear Algebra

3. Plotting and Visualization

4. Data Import/Export

5. Control Flow and Functions

6. Statistics and Data Analysis

7. Differential Equations

8. Signal Processing

Common Patterns

Pattern 1: Data Analysis Pipeline

Pattern 2: Numerical Simulation

Pattern 3: Batch Processing

Reference Files

GNU Octave Compatibility

Best Practices

Additional Resources

Related skills