Tensorial.jl

Tensorial.jl provides statically sized tensor types for Julia. They behave like AbstractArrays, but carry tensor-specific structure such as symmetry.

This manual is organized by what you want to do. If you are new to Tensorial, start with Getting Started; it gives a short executable tour of the main pieces: tensor construction, operations, @einsum, symmetry, automatic differentiation, and direct sums.

Installation

Install Tensorial with Julia's package manager:

pkg> add Tensorial

Choose by task

• Understand tensor spaces, aliases, and symmetry in tensor types: Tensor Types and Spaces.
• Create vectors, matrices, higher-order tensors, and symmetric tensors: Constructing Tensors.
• Write contractions, tensor products, and indexed formulas: Operations.
• Differentiate tensor formulas and get tensor results back: Automatic Differentiation.
• Pack several related unknowns into one block-structured state: Direct Sum.
• Convert tensors at array boundaries with Voigt or Mandel notation: Voigt Form.
• Work with 3D rotations and quaternions: Quaternion.
• Check practical notes for writing Tensorial code: Practical Tips.

Reference pages

• Look up public signatures and docstrings: API Reference.
• Check small-tensor performance against Array and SArray: Benchmarks.