Crate hyperdual[−][src]
Expand description
Dual Numbers
Fully-featured Dual Number implementation with features for automatic differentiation of multivariate vectorial functions into gradients.
Usage
extern crate hyperdual;
use hyperdual::{Dual, Hyperdual, Float, differentiate};
fn main() {
// find partial derivative at x=4.0
let univariate = differentiate(4.0f64, |x| x.sqrt() + Dual::from_real(1.0));
assert!((univariate - 0.25).abs() < 1e-16, "wrong derivative");
// find the partial derivatives of a multivariate function
let x: Hyperdual<f64, 3> = Hyperdual::from_slice(&[4.0, 1.0, 0.0]);
let y: Hyperdual<f64, 3> = Hyperdual::from_slice(&[5.0, 0.0, 1.0]);
let multivariate = x * x + (x * y).sin() + y.powi(3);
assert!((multivariate[0] - 141.91294525072763).abs() < 1e-13, "f(4, 5) incorrect");
assert!((multivariate[1] - 10.04041030906696).abs() < 1e-13, "df/dx(4, 5) incorrect");
assert!((multivariate[2] - 76.63232824725357).abs() < 1e-13, "df/dy(4, 5) incorrect");
// You may also use the new Const approach (both U* and Const<*> use the const generics)
let x: Hyperdual<f64, 3> = Hyperdual::from_slice(&[4.0, 1.0, 0.0]);
let y: Hyperdual<f64, 3> = Hyperdual::from_slice(&[5.0, 0.0, 1.0]);
let multivariate = x * x + (x * y).sin() + y.powi(3);
assert!((multivariate[0] - 141.91294525072763).abs() < 1e-13, "f(4, 5) incorrect");
assert!((multivariate[1] - 10.04041030906696).abs() < 1e-13, "df/dx(4, 5) incorrect");
assert!((multivariate[2] - 76.63232824725357).abs() < 1e-13, "df/dy(4, 5) incorrect");
}
Previous Work
Modules
Structs
An allocator based on GenericArray
and VecStorage
for statically-sized and dynamically-sized
matrices respectively.
Dim of dynamically-sized algebraic entities.
Dual Number structure
Traits
A matrix allocator of a memory buffer that may contain R::to_usize() * C::to_usize()
elements of type T
.
Trait implemented by any type that can be used as a dimension. This includes type-level
integers and Dynamic
(for dimensions not known at compile-time).
Trait implemented exclusively by type-level integers.
Generic trait for floating point numbers
Trait implemented by Dynamic
.
Trait implemented by Dynamic
and type-level integers different from U1
.
The base trait for numeric types, covering 0
and 1
values,
comparisons, basic numeric operations, and string conversion.
Defines a multiplicative identity element for Self
.
Defines an additive identity element for Self
.
Functions
Evaluates the function using dual numbers to get the partial derivative at the input point
Type Definitions
The owned data storage that can be allocated from S
.