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
ArrayStorage and VecStorage for statically-sized and dynamically-sized
matrices respectively.Dim of dynamically-sized algebraic entities.
Dual Number structure
Constants
The constant dimension
0
.
The constant dimension 1.
The constant dimension
2
.
The constant dimension
3
.
The constant dimension
4
.
The constant dimension
5
.
The constant dimension
6
.
The constant dimension
7
.
The constant dimension
8
.
The constant dimension
9
.
The constant dimension
10
.
The constant dimension
11
.
The constant dimension
12
.
The constant dimension
13
.
The constant dimension
14
.
The constant dimension
15
.
The constant dimension
16
.
The constant dimension
17
.
The constant dimension
18
.
The constant dimension
19
.
The constant dimension
20
.
The constant dimension
21
.
The constant dimension
22
.
The constant dimension
23
.
The constant dimension
24
.
The constant dimension
25
.
The constant dimension
26
.
The constant dimension
27
.
The constant dimension
28
.
The constant dimension
29
.
The constant dimension
30
.
The constant dimension
31
.
The constant dimension
32
.
The constant dimension
33
.
The constant dimension
34
.
The constant dimension
35
.
The constant dimension
36
.
The constant dimension
37
.
The constant dimension
38
.
The constant dimension
39
.
The constant dimension
40
.
The constant dimension
41
.
The constant dimension
42
.
The constant dimension
43
.
The constant dimension
44
.
The constant dimension
45
.
The constant dimension
46
.
The constant dimension
47
.
The constant dimension
48
.
The constant dimension
49
.
The constant dimension
50
.
The constant dimension
51
.
The constant dimension
52
.
The constant dimension
53
.
The constant dimension
54
.
The constant dimension
55
.
The constant dimension
56
.
The constant dimension
57
.
The constant dimension
58
.
The constant dimension
59
.
The constant dimension
60
.
The constant dimension
61
.
The constant dimension
62
.
The constant dimension
63
.
The constant dimension
64
.
The constant dimension
65
.
The constant dimension
66
.
The constant dimension
67
.
The constant dimension
68
.
The constant dimension
69
.
The constant dimension
70
.
The constant dimension
71
.
The constant dimension
72
.
The constant dimension
73
.
The constant dimension
74
.
The constant dimension
75
.
The constant dimension
76
.
The constant dimension
77
.
The constant dimension
78
.
The constant dimension
79
.
The constant dimension
80
.
The constant dimension
81
.
The constant dimension
82
.
The constant dimension
83
.
The constant dimension
84
.
The constant dimension
85
.
The constant dimension
86
.
The constant dimension
87
.
The constant dimension
88
.
The constant dimension
89
.
The constant dimension
90
.
The constant dimension
91
.
The constant dimension
92
.
The constant dimension
93
.
The constant dimension
94
.
The constant dimension
95
.
The constant dimension
96
.
The constant dimension
97
.
The constant dimension
98
.
The constant dimension
99
.
The constant dimension
100
.
The constant dimension
101
.
The constant dimension
102
.
The constant dimension
103
.
The constant dimension
104
.
The constant dimension
105
.
The constant dimension
106
.
The constant dimension
107
.
The constant dimension
108
.
The constant dimension
109
.
The constant dimension
110
.
The constant dimension
111
.
The constant dimension
112
.
The constant dimension
113
.
The constant dimension
114
.
The constant dimension
115
.
The constant dimension
116
.
The constant dimension
117
.
The constant dimension
118
.
The constant dimension
119
.
The constant dimension
120
.
The constant dimension
121
.
The constant dimension
122
.
The constant dimension
123
.
The constant dimension
124
.
The constant dimension
125
.
The constant dimension
126
.
The constant dimension
127
.
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
Dyn (for dimensions not known at compile-time).Trait implemented exclusively by type-level integers.
Generic trait for floating point numbers
Trait implemented by
Dyn.Trait implemented by
Dyn 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
DynamicDeprecated
The owned data storage that can be allocated from
S.