differential-geometry 0.3.1

A library for differential-geometric calculations
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180

use crate::coordinates::{CoordinateSystem, Point};
use crate::tensors::{Covector, InvTwoForm, Matrix, Scalar, TwoForm, Vector};
use crate::typenum::consts::{U0, U1, U2, U4};
use crate::{inner, mul};
use generic_array::arr;
use generic_array::GenericArray;

struct Test2;
impl CoordinateSystem for Test2 {
    type Dimension = U2;
}

struct Test4;
impl CoordinateSystem for Test4 {
    type Dimension = U4;
}

#[test]
fn test_ranks() {
    assert_eq!(Vector::<Test4>::get_rank(), 1);
    assert_eq!(Matrix::<Test4>::get_rank(), 2);
}

#[test]
fn test_num_coords() {
    assert_eq!(Vector::<Test4>::get_num_coords(), 4);
    assert_eq!(Matrix::<Test4>::get_num_coords(), 16);
}

#[test]
fn test_iter_coords() {
    let p1 = Point::new(GenericArray::default());
    let matrix1 = Matrix::<Test2>::zero(p1);
    let p2 = Point::new(GenericArray::default());
    let matrix2 = Matrix::<Test4>::zero(p2);

    let mut i = 0;
    for _ in matrix1.iter_coords() {
        i += 1;
    }
    assert_eq!(i, 4);

    i = 0;
    for _ in matrix2.iter_coords() {
        i += 1;
    }
    assert_eq!(i, 16);
}

#[test]
fn test_add() {
    let p = Point::new(GenericArray::default());
    let vector1 = Vector::<Test2>::new(p, arr![f64; 1.0, 2.0]);
    let vector2 = Vector::<Test2>::new(p, arr![f64; 1.5, 1.6]);

    let result = vector1 + vector2;

    assert_eq!(result[0], 2.5);
    assert_eq!(result[1], 3.6);
}

#[test]
fn test_sub() {
    let p = Point::new(GenericArray::default());
    let vector1 = Vector::<Test2>::new(p, arr![f64; 1.0, 2.0]);
    let vector2 = Vector::<Test2>::new(p, arr![f64; 1.5, 1.75]);

    let result = vector1 - vector2;

    assert_eq!(result[0], -0.5);
    assert_eq!(result[1], 0.25);
}

#[test]
fn test_trace() {
    let p = Point::new(GenericArray::default());
    let matrix = Matrix::<Test2>::new(p, arr![f64; 1.0, 3.0, 0.0, 3.0]);

    let tr = matrix.trace::<U0, U1>();

    assert_eq!(*tr, 4.0);
}

// needed for tests below

use std::ops::Mul;

#[test]
fn test_mul_trait() {
    assert_eq!(<Vector<Test2> as Mul<Vector<Test2>>>::Output::get_rank(), 2);
    assert_eq!(
        <Vector<Test2> as Mul<Vector<Test2>>>::Output::get_num_coords(),
        4
    );
    assert_eq!(<Vector<Test2> as Mul<f64>>::Output::get_rank(), 1);
    assert_eq!(<Vector<Test2> as Mul<f64>>::Output::get_num_coords(), 2);
}

#[test]
fn test_mul_scalar() {
    let p = Point::new(GenericArray::default());
    let vector1 = Vector::<Test2>::new(p, arr![f64; 1.0, 2.0]);
    // this works
    let result: Vector<Test2> = mul!(_, f64; vector1, 5.0);
    // this doesn't
    // let result: Vector<Test2> = vector1 * 5.0;

    assert_eq!(result[0], 5.0);
    assert_eq!(result[1], 10.0);
}

#[test]
fn test_mul_vector() {
    let p = Point::new(GenericArray::default());
    let vector1 = Vector::<Test2>::new(p, arr![f64; 1.0, 2.0]);
    let vector2 = Vector::<Test2>::new(p, arr![f64; 3.0, 4.0]);

    // this works
    let result: InvTwoForm<Test2> = mul!(_, Vector<Test2>; vector1, vector2);
    // this doesn't
    // let result = vector1 * vector2;

    assert_eq!(result[0], 3.0);
    assert_eq!(result[1], 4.0);
    assert_eq!(result[2], 6.0);
    assert_eq!(result[3], 8.0);
}

#[test]
fn test_inner_product() {
    let p = Point::new(GenericArray::default());
    let vector1 = Vector::<Test2>::new(p, arr![f64; 1.0, 2.0]);
    let vector2 = Covector::<Test2>::new(p, arr![f64; 3.0, 4.0]);

    let result: Scalar<Test2> = inner!(_, Covector<Test2>; U0, U1; vector1, vector2);

    assert_eq!(*result, 11.0);
}

#[test]
fn test_complex_inner_product() {
    let p = Point::new(GenericArray::default());
    let form = TwoForm::<Test2>::new(p, arr![f64; 1.0, 0.0, 0.0, 1.0]);
    let vector1 = Vector::<Test2>::new(p, arr![f64; 1.0, 2.0]);
    let vector2 = Vector::<Test2>::new(p, arr![f64; 3.0, 4.0]);

    let temp = inner!(_, Vector<Test2>; U0, U2; form, vector1);
    let result = inner!(_, Vector<Test2>; U0, U1; temp, vector2);

    assert_eq!(*result, 11.0);
}

#[test]
fn test_transpose() {
    let p = Point::new(GenericArray::default());
    let matrix = Matrix::<Test2>::new(p, arr![f64; 1.0, 2.0, 3.0, 4.0]);

    let result = matrix.transpose();

    assert_eq!(result[0], 1.0);
    assert_eq!(result[1], 3.0);
    assert_eq!(result[2], 2.0);
    assert_eq!(result[3], 4.0);
}

#[test]
fn test_inverse() {
    let p = Point::new(GenericArray::default());
    let matrix = Matrix::<Test2>::new(p, arr![f64; 1.0, 2.0, 3.0, 4.0]);

    let result = matrix.inverse().unwrap();

    // unfortunately the inverse matrix calculation isn't perfectly accurate
    let epsilon = 0.0000001;

    assert!((result[0] + 2.0).abs() < epsilon);
    assert!((result[1] - 1.0).abs() < epsilon);
    assert!((result[2] - 1.5).abs() < epsilon);
    assert!((result[3] + 0.5).abs() < epsilon);
}