# Crate num_dual

Expand description

Generalized, recursive, scalar and vector (hyper) dual numbers for the automatic and exact calculation of (partial) derivatives.

### Example

This example defines a generic function that can be called using any (hyper) dual number and automatically calculates derivatives.

``````use num_dual::*;

fn f<D: DualNum<f64>>(x: D, y: D) -> D {
x.powi(3) * y.powi(2)
}

fn main() {
let (x, y) = (5.0, 4.0);

// Calculate a simple derivative
let x_dual = Dual64::from(x).derive();
let y_dual = Dual64::from(y);
println!("{}", f(x_dual, y_dual));                      // 2000 + ε

let xy_dual_vec = StaticVec::new_vec([x, y]).map(DualVec64::<2>::from).derive();
println!("{}", f(xy_dual_vec, xy_dual_vec).eps);  // [1200, 1000]

// Calculate a Hessian
let xy_dual2 = StaticVec::new_vec([x, y]).map(Dual2Vec64::<2>::from).derive();
println!("{}", f(xy_dual2, xy_dual2).v2);         // [[480, 600], [600, 250]]

// for x=cos(t) and y=sin(t) calculate the third derivative w.r.t. t
let t = Dual3_64::from(1.0).derive();
println!("{}", f(t.cos(), t.sin()).v3);                 // 7.358639755305733
}``````

## Structs

A second order dual number for the calculation of Hessians.

A scalar third order dual number for the calculation of third derivatives.

A dual number for the calculations of gradients or Jacobians.

A hyper dual number for the calculation of second partial derivatives.

A statically allocated MxN matrix. The struct is used in the vector (hyper) dual numbers and provides utilities for the calculation of Jacobians.

## Traits

Implementation of bessel functions for double precision (hyper) dual numbers.

A generalized (hyper) dual number.

The underlying data type of individual derivatives. Usually f32 or f64.