| Fundamentals | Core matrix manipulation, elementary math, data types, string formatting, and language execution |
| Elementary Matrices and Array Manipulation (elmat) | Elementary matrix constructors, shape modification, indexing, concatenation, and specialized test matrices |
| Elementary Math Functions (elfun) | Trigonometric, hyperbolic, exponential, logarithmic, complex, and rounding operations |
| Operators and Elementary Operations (ops) | Arithmetic (+, -, *, /), relational (==, <, >), logical (&, |, ~, xor), bitwise (bitand, bitshift), and transpose operations |
| Matrix Functions and Numerical Linear Algebra (matfun) | Linear equation solvers, matrix factorizations (LU, QR, SVD, Cholesky), condition numbers, and matrix exponentials |
| Data Analysis and Fourier Transforms (datafun) | Reductions, basic summary statistics, cumulative operations, numerical differences, 1D/2D/N-D Fourier transforms, and accumarray |
| Specialized Mathematical Functions (specfun) | Bessel functions, Airy functions, Gamma, Beta, Error functions, and Number Theory primitives |
| Polynomials and Interpolation (polyfun) | Polynomial curve fitting, roots, derivatives, integration, 1D/2D/3D interpolation, and piecewise cubic splines |
| Character Strings and Text (strfun) | Text composition, formatted string output (sprintf), search, regular expressions, and type conversions |
| Data Types and Structures (datatypes) | Numeric type casting, struct arrays, cell arrays, map/dictionary containers, and type introspection (isa, isnumeric) |
| Time and Dates (timefun) | System clock, benchmarking timers (tic/toc), date calculations, and execution pauses |
| Language Syntax, Diagnostics and Help (lang) | Keywords, variable naming rules, error/warning handling, exception structures, and interactive discovery (help, what) |
| File I/O and Workspace Persistence (iofun) | Formatted file streams, textscan/csvread parsing, and workspace save/load persistence |
| Toolboxes | Domain-specific mathematical and engineering toolboxes matching MATLAB standards |
| Signal Processing Toolbox (signal) | Digital filter design (IIR/FIR), filter implementation (filtfilt/sosfilt), spectral analysis (FFT/pwelch/spectrogram), windows, and waveforms |
| Statistics and Machine Learning Toolbox (stats) | Descriptive statistics, 20+ probability distributions, hypothesis testing (t-test, ANOVA), regression models, PCA, and clustering |
| Image Processing Toolbox (image) | Color space conversions, morphological operations, 2D spatial filtering, geometric transformations, and quality metrics (SSIM, PSNR) |
| Control System Toolbox (control) | Linear time-invariant (LTI) system representation (tf, ss, zpk), frequency response (Bode, Nyquist), time response (step, impulse), and stability |
| Optimization Toolbox (optim) | Unconstrained and bound-constrained nonlinear optimization, root finding (fzero, fsolve), and nonlinear curve fitting |
| Wavelet Toolbox (wavelet) | 1D/2D Discrete Wavelet Transform (DWT), Stationary Wavelet Transform (SWT), filter banks, wavelet denoising, and continuous wavelets |
| Communications Toolbox (comm) | Digital modulation schemes (PSK, QAM, APSK, FSK, OFDM), channel models (AWGN, fading), error correction coding, and source coding |
| Audio Toolbox (audio) | Acoustic feature extraction (pitch, spectral flux, roll-off), audio representations (MFCC, Mel-spectrogram), and equalization DSP |
| Differential Equations (ode) | Explicit and implicit Runge-Kutta numerical ODE solvers (ode45, ode23, ode113, ode15s, ode23s) and event handling |
| 2D & 3D Scientific Graphics (graphics) | Interactive figure management, line plots (plot), surface visualization (surf, mesh), scatter charts, histograms, and colormaps |