VectorInterface.jl

A small Julia interface for vector-like objects.

VectorInterface.jl proposes a minimal set of methods that any type representing an element of a vector space should support. Code written against this interface can then operate uniformly on Numbers, AbstractArrays, nested arrays, tuples, named tuples, and arbitrary user-defined types — without conflating vector-space operations with the iteration, container, or LinearAlgebra interfaces.

Installation

julia> using Pkg; Pkg.add("VectorInterface")

What's provided

• A scalar-type query: scalartype.
• Construction of zero vectors: zerovector, zerovector!, zerovector!!.
• Scalar multiplication: scale, scale!, scale!!.
• Linear combinations: add, add!, add!!.
• Inner product and norm: inner, and norm is re-exported from LinearAlgebra.
• Singleton helpers One and Zero for hard-coded coefficients in linear combinations.

Each !-suffixed method modifies its first argument in place. Each !!-suffixed method tries to do so but falls back to allocating when in-place updates are not possible (e.g. for immutable types or incompatible scalar types). This convention follows BangBang.jl.

Contents

• Motivation
• • What is a vector?
  • Problems with the current Julia situation
  • Existing approaches in the ecosystem
  • How VectorInterface.jl addresses this
• Interface
• • Scalar type
  • Zero vector
  • Scaling
  • Linear combinations
  • Inner product and norm
  • Hard-coded coefficients: One and Zero
  • Supported types
  • Implementing the interface for a new type
• API reference