calculi/
derive.rs

1use super::utils::*;
2use super::component::Component;
3use super::operators::Operator::*;
4
5fn chain_rule(left: Component, right: &Component) -> Component {
6  create_binary(Multiply, left, derive_component(right))
7}
8
9pub fn derive_component(expr: &Component) -> Component {
10  match expr {
11    Component::Number(_) => Component::Number(0.0),
12    Component::Variable(_) => Component::Number(1.0),
13
14    Component::Function { operator, values } => match operator {
15      Add => create_binary(
16        Add,
17        derive_component(&values[0]),
18        derive_component(&values[1]),
19      ),
20
21      Subtract => create_binary(
22        Subtract,
23        derive_component(&values[0]),
24        derive_component(&values[1]),
25      ),
26
27      Multiply => create_binary(
28        Add,
29        chain_rule(values[0].clone(), &values[1]),
30        chain_rule(values[1].clone(), &values[0]),
31      ),
32
33      Exponent | Pow => {
34        // x^n
35        if let Component::Number(f) = &values[1] {
36          chain_rule(
37            create_binary(
38              Multiply,
39              Component::Number(*f),
40              create_binary(Exponent, values[0].clone(), Component::Number(f - 1.0)),
41            ),
42            &values[0],
43          )
44        // n^x
45        } else if let Component::Number(f) = &values[0] {
46          create_binary(
47            Multiply,
48            create_unary(Ln, Component::Number(*f)),
49            chain_rule(expr.clone(), &expr),
50          )
51        } else {
52          // x^x
53          create_binary(
54            Multiply,
55            expr.clone(),
56            create_binary(
57              Add,
58              create_binary(
59                Multiply,
60                derive_component(&values[1]),
61                create_unary(Ln, values[0].clone()),
62              ),
63              create_binary(
64                Multiply,
65                values[1].clone(),
66                create_binary(Divide, derive_component(&values[0]), values[0].clone()),
67              ),
68            ),
69          )
70        }
71      }
72
73      Log => chain_rule(
74        create_binary(
75          Divide,
76          derive_component(&values[0]),
77          create_binary(
78            Multiply,
79            create_unary(Ln, values[1].clone()),
80            values[0].clone(),
81          ),
82        ),
83        &values[0],
84      ),
85
86      Ln => chain_rule(
87        create_binary(Divide, derive_component(&values[0]), values[0].clone()),
88        &values[0],
89      ),
90
91      Sin => chain_rule(create_unary(Cos, values[0].clone()), &values[0]),
92
93      Cos => chain_rule(
94        create_binary(
95          Multiply,
96          Component::Number(-1.0),
97          create_unary(Sin, values[0].clone()),
98        ),
99        &values[0],
100      ),
101
102      Tan => chain_rule(
103        create_binary(
104          Pow,
105          create_unary(Sec, values[0].clone()),
106          Component::Number(2.0),
107        ),
108        &values[0],
109      ),
110
111      Sec => chain_rule(
112        create_binary(
113          Multiply,
114          create_unary(Sec, values[0].clone()),
115          create_unary(Tan, values[0].clone()),
116        ),
117        &values[0],
118      ),
119
120      Csc => chain_rule(
121        create_binary(
122          Multiply,
123          Component::Number(-1.0),
124          create_binary(
125            Multiply,
126            create_unary(Csc, values[0].clone()),
127            create_unary(Cot, values[0].clone()),
128          ),
129        ),
130        &values[0],
131      ),
132
133      Cot => chain_rule(
134        create_binary(
135          Multiply,
136          Component::Number(-1.0),
137          create_binary(
138            Pow,
139            create_unary(Csc, values[0].clone()),
140            Component::Number(2.0),
141          ),
142        ),
143        &values[0],
144      ),
145
146      _ => Component::End,
147    },
148    _ => Component::End,
149  }
150}
calculi/derive.rs

calculi/
derive.rs
