Generic programming

nalgebra allows several kind of generic programming, either through traits of the simba crate, or by keeping the various type parameters of the Matrix<T, R, C, S> structure and the likes. In the end, this allows for:

Genericity wrt. scalars: the most common kind of abstraction. This allows you to write code that will work on any scalar group like i32 and fields like f32 or f64.
Dimensional genericity: allows you to write code that will work generically for 2D, 3D, and higher dimensions.

Genericity wrt. scalars#

This allows to write code that works with algebraic entities constructed on top of a generic scalar type, e.g., floating-point numbers like f32 or f64 and in some more restrictive cases integers like i32 or u64. This can be achieved by keeping generic the first type parameter T of any structure of nalgebra (including aliases). The mandatory trait bound of T is na::Scalar which imposes some simple non-mathematical properties, i.e., T must copyable, printable (using the {:?} format string), and comparable using the equality operator. Other commonly used trait bounds for T are na::RealField or na::ComplexField from the simba crate. This enables operator overloading and useful mathematical functions for signed integers and floating point numbers respectively. Note that the Scalar trait bound does not have to be specified if Real already is.

use na::{RealField, Scalar, Vector3};

fn print_vector<T: Scalar>(m: &Vector3<T>) {
  println!("{:?}", m)
}

fn print_norm<T: RealField>(v: &Vector3<T>) {
  // NOTE: alternatively, nalgebra already defines `v.norm()`.
  let norm = v.dot(v).sqrt();

  // The Real bound implies that T is Display so we can
  // use "{}" instead of "{:?}" for the format string.
  println!("{}", norm)
}

fn main() {
  let v1 = Vector3::new(1, 2, 3);
  let v2 = Vector3::new(1.0, 2.0, 3.0);

  print_vector(&v1);
  print_norm(&v2);
}

note

This section about dimensional-genericity hasn't been written yet.