CTens

CTens is a modular software framework for tensor algebra and tensor-based computation. It is designed to support scientific computing, machine learning, and data analysis by providing a consistent interface for high-dimensional array operations and a set of optimized backends. CTens emphasizes performance, lazy evaluation, and expressive indexing, enabling users to describe complex tensor contractions and transformations at a high level while the system generates efficient low-level code.

Origins of CTens lie in a collaboration among researchers in physics, mathematics, and computer science who sought a portable tool for symbolic and numeric tensor calculations. Early development focused on enabling automatic differentiation and efficient contraction algorithms. The project released its first stable version in the mid-2010s and has since evolved into a community-driven framework with multiple backends and extensions.

CTens is designed around a backend-agnostic core that exposes tensor operations through a high-level API. It supports dense, sparse, and structured tensors, as well as Einstein summation conventions and arbitrary index notation. The architecture includes a lazy evaluation engine, a just-in-time compiler, and backends that leverage BLAS, cuBLAS, and custom kernels for CPUs, GPUs, and accelerators. It also provides automatic differentiation to facilitate gradient-based optimization.

Common use cases include physical simulations, quantum chemistry, and machine learning research, where large-scale tensor manipulations are central. CTens integrates with numerical libraries and data pipelines, enabling integration with existing workflows without requiring users to rewrite code for different hardware.

CTens is released under an open-source license and is maintained by a distributed community of contributors. The project maintains documentation and tutorials to help new users learn tensor notation, performance tuning, and backend configuration. Related topics include tensor algebra, automatic differentiation, and tensor libraries used in deep learning.