High-level programming language Translate mathematical formulas into programs. Matrices and vectors area treated as high-level objects. Data structures such as lists and in-memory tables. Iterative loops, IF-THEN/ELSE logic, etc. More than 300 built-in functions. Define new functions and subroutines. In the iml action: Functions can execute in parallel on multiple threads. Matrix computations Read from a data table into a matrix. Multithreaded matrix operations: addition, multiplication, raise to power, etc. Solve linear systems. Matrix decompositions: Cholesky, eigenvalues, SVD, etc. Send matrices to functions. In the iml action: additional multithreaded matrix computations. Numerical analysis Linear algebra. Root-finding algorithms. Integrals and derivatives. Differential equations (DEs). Interpolation. In the iml action: Find multiple roots, solve multiple DEs, in parallel. Differential equation solver with a simple UI lets more people use algorithms without being an expert. Optimization Linear programming. Mixed-integer linear programming. Simulation Simulate from dozens of built-in distributions. Univariate: Normal, lognormal, exponential, etc. Multivariate: Normal, multinomial, Wishart, etc. Time series models: ARIMA and multivariate variations. Program custom simulations. Regression models. Spatial models. In the iml action: Generate independent samples in multiple threads. Statistics & data analysis Means and standard deviations. Correlation and covariance matrices. Tabulate categorical data. Implement hypothesis tests. Multivariate data analysis. In the iml action: bootstrap methods and permutation tests in parallel.
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