Math Vector

A lazily-evaluated linear algebra library for Rust.

Usage

Provides Wrapper types (ex. VectorExpr & MatrixExpr) which represent expressions. These expressions are built up from wrapped concrete collections or numerical values used in methods on the expression (ex. a.add(b)). They can then be evaluated into contrete collections / values by using certain methods (ex. collect() & eval()). Many standard operations with overloads are overloaded (ex. +, -, *, /, %) (notes 1-3) as well as their assign counterpoints when possible (ex. +=, -=, *=, /=, %=) (note 4).

note 1: vec1 * vec2 is not a valid operation, see dot or comp_mul operations
note 2: scalar * vec should be valid but due to orphan rules cannot implemented, vec * scalar is implemented though and for commutative scalar multiplication is identitical, if not see mul_r. (also applies to / and %). Additionally, there is the Scalar type defined which does implement this so Scalar(scalar) * vec is valid.
note 3: scalar / vec (& scaler % vec) (really div_r and rem_r, see note 2) as far as I'm aware these aren't really a thing but is defined such that (scalar / vec)[idx] == scalar / vec[idx].
note 4: By the nature of assign ops, the type of mutated value cannot change so I can't pull the same lazily-evaluation shenanigans so sadly these are readily-evaluated & can only be done on concrete vectors

Miscelaneous

This library is large but not all encompassing it is currently missing:

• eigenvector and eigenvalue calculation
• fast matrix multiplication
• matrix inverse calculation (explicitly, it is still possible, see rref_test for an example)
• matrix diagonalization
• considerations regarding complex vectors (ex: no provided inner product for complex vectors)
• and probably more that I don't realize

Additionally, it will likely never contain more abstract things like:

• Vectorspaces & subspaces (or any other mathematical set regarding linear algebra)
• using functions as vectors / infinite dimensional vectors (can't be meaningfully evaluated)

Although I would love to do so, not all operations are implemented lazily, specifically:

• rref
• det
• all the assign operations

if you are wondering what more there is to do, check todo.txt