Environment

• Interactive — type matrix expressions and see results
• Development — full development environment for developing programs and commands
• Automatically compiled code

General features and matrix operators

• Support for real and complex values
• Joining by rows or columns
• Addition, subtraction, multiplication, scalar division
• Elementwise arithmetic
• Transposition and reshaping
• Kronecker and Hadamard products
• Inner and outer products

Optimizer

• Code the function, function and gradient, or function, gradient, and Hessian
• Newton–Raphson, BFGS, DFP, BHHH, and Nelder–Mead techniques
• Debugger
• Covariance matrix based on Hessian, outer product of gradients, or robust/sandwich

Mathematical and matrix functions

• LAPACK numerical analysis routines
• Symmetric, nonsymmetric, and generalized inverses
• Cholesky, LU, QR, and SVD solvers
• Transcendental and trigonometric functions
• Gamma and factorial functions
• Density and distribution functions
• Polynomial evaluation, arithmetic, and calculus
• Hilbert, Toeplitz, and Vandermonde matrices
• Random-number generation
• Fast Fourier analysis
• Cubic splines
• Means, sums, minimums, and maximums of matrices

Decompositions

• Eigenvalues and eigenvectors
• Cholesky
• LU and LUD
• QR
• Singular value
• Permutation matrices

Data accumulation

• Cross products
• Cross products of deviations from means
• Weighted and GLS-type cross products
• Support for quad-precision cross products

Stata interface

• Convert Stata datasets to matrices and vice versa
• Virtual matrix views onto dataset
• Access and set estimation-class and other macros
• Manipulate dataset value labels

Other features

• String scalars and matrices
• File I/O, including buffered I/O
• C-like syntax
• Fast execution