Crate hyperdual

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, U3};

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, U3> = Hyperdual::from_slice(&[4.0, 1.0, 0.0]);
    let y: Hyperdual<f64, U3> = 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

• https://github.com/novacrazy/dual_num
• https://github.com/FreeFull/dual_numbers
• https://github.com/ibab/rust-ad
• https://github.com/tesch1/cxxduals

Modules

linalg

Structs

DefaultAllocator	An allocator based on GenericArray and VecStorage for statically-sized and dynamically-sized matrices respectively.
Dynamic	Dim of dynamically-sized algebraic entities.
Hyperdual	Dual Number structure
U0	A type level dimension.
U1	A type level dimension with a value of 1.
U2	A type level dimension.
U3	A type level dimension.
U4	A type level dimension.
U5	A type level dimension.
U6	A type level dimension.
U7	A type level dimension.
U8	A type level dimension.
U9	A type level dimension.
U10	A type level dimension.
U11	A type level dimension.
U12	A type level dimension.
U13	A type level dimension.
U14	A type level dimension.
U15	A type level dimension.
U16	A type level dimension.
U17	A type level dimension.
U18	A type level dimension.
U19	A type level dimension.
U20	A type level dimension.
U21	A type level dimension.
U22	A type level dimension.
U23	A type level dimension.
U24	A type level dimension.
U25	A type level dimension.
U26	A type level dimension.
U27	A type level dimension.
U28	A type level dimension.
U29	A type level dimension.
U30	A type level dimension.
U31	A type level dimension.
U32	A type level dimension.
U33	A type level dimension.
U34	A type level dimension.
U35	A type level dimension.
U36	A type level dimension.
U37	A type level dimension.
U38	A type level dimension.
U39	A type level dimension.
U40	A type level dimension.
U41	A type level dimension.
U42	A type level dimension.
U43	A type level dimension.
U44	A type level dimension.
U45	A type level dimension.
U46	A type level dimension.
U47	A type level dimension.
U48	A type level dimension.
U49	A type level dimension.
U50	A type level dimension.
U51	A type level dimension.
U52	A type level dimension.
U53	A type level dimension.
U54	A type level dimension.
U55	A type level dimension.
U56	A type level dimension.
U57	A type level dimension.
U58	A type level dimension.
U59	A type level dimension.
U60	A type level dimension.
U61	A type level dimension.
U62	A type level dimension.
U63	A type level dimension.
U64	A type level dimension.
U65	A type level dimension.
U66	A type level dimension.
U67	A type level dimension.
U68	A type level dimension.
U69	A type level dimension.
U70	A type level dimension.
U71	A type level dimension.
U72	A type level dimension.
U73	A type level dimension.
U74	A type level dimension.
U75	A type level dimension.
U76	A type level dimension.
U77	A type level dimension.
U78	A type level dimension.
U79	A type level dimension.
U80	A type level dimension.
U81	A type level dimension.
U82	A type level dimension.
U83	A type level dimension.
U84	A type level dimension.
U85	A type level dimension.
U86	A type level dimension.
U87	A type level dimension.
U88	A type level dimension.
U89	A type level dimension.
U90	A type level dimension.
U91	A type level dimension.
U92	A type level dimension.
U93	A type level dimension.
U94	A type level dimension.
U95	A type level dimension.
U96	A type level dimension.
U97	A type level dimension.
U98	A type level dimension.
U99	A type level dimension.
U100	A type level dimension.
U101	A type level dimension.
U102	A type level dimension.
U103	A type level dimension.
U104	A type level dimension.
U105	A type level dimension.
U106	A type level dimension.
U107	A type level dimension.
U108	A type level dimension.
U109	A type level dimension.
U110	A type level dimension.
U111	A type level dimension.
U112	A type level dimension.
U113	A type level dimension.
U114	A type level dimension.
U115	A type level dimension.
U116	A type level dimension.
U117	A type level dimension.
U118	A type level dimension.
U119	A type level dimension.
U120	A type level dimension.
U121	A type level dimension.
U122	A type level dimension.
U123	A type level dimension.
U124	A type level dimension.
U125	A type level dimension.
U126	A type level dimension.
U127	A type level dimension.

Traits

Allocator	A matrix allocator of a memory buffer that may contain R::to_usize() * C::to_usize() elements of type N.
Dim	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).
DimAdd
DimDiv
DimMax
DimMin
DimMul
DimName	Trait implemented exclusively by type-level integers.
DimNameAdd
DimNameDiv
DimNameMax
DimNameMin
DimNameMul
DimNameSub
DimSub
Float	Generic trait for floating point numbers
FloatConst
IsDynamic	Trait implemented by Dynamic.
IsNotStaticOne	Trait implemented by Dynamic and type-level integers different from U1.
NamedDim
Num	The base trait for numeric types, covering 0 and 1 values, comparisons, basic numeric operations, and string conversion.
One	Defines a multiplicative identity element for Self.
Zero	Defines an additive identity element for Self.

Functions

differentiate	Evaluates the function using dual numbers to get the partial derivative at the input point
extract_jacobian_and_result
hyperspace_from_vector
vector_from_hyperspace

Type Definitions

DimDiff
DimMaximum
DimMinimum
DimNameDiff
DimNameMaximum
DimNameMinimum
DimNameProd
DimNameQuot
DimNameSum
DimProd
DimQuot
DimSum
Dual
DualN
Owned	The owned data storage that can be allocated from S.