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
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
use ndarray::*;
use ndarray_linalg::*;
use petgraph;
use petgraph::prelude::*;
use operators::*;
use error::*;
#[derive(Debug, Clone)]
pub struct Node<A: Scalar> {
value: Option<Value<A>>,
deriv: Option<Value<A>>,
prop: Property,
}
#[derive(Debug, Clone, IntoEnum)]
enum Property {
Variable(Variable),
UnaryOperator(UnaryOperatorAny),
BinaryOperator(BinaryOperatorAny),
}
impl<A: Scalar> Node<A> {
fn new(prop: Property) -> Self {
Self {
value: None,
deriv: None,
prop,
}
}
pub fn is_variable(&self) -> bool {
match self.prop {
Property::Variable(_) => true,
Property::UnaryOperator(_) => false,
Property::BinaryOperator(_) => false,
}
}
}
#[derive(Debug, Clone)]
struct Variable {
name: String,
}
impl Variable {
fn new(name: &str) -> Self {
Variable { name: name.to_string() }
}
}
#[derive(Debug, NewType)]
pub struct Graph<A: Scalar>(petgraph::graph::Graph<Node<A>, ()>);
impl<A: Scalar> Graph<A> {
pub fn new() -> Self {
petgraph::graph::Graph::new().into()
}
pub fn variable(&mut self, name: &str) -> NodeIndex {
let var = Variable::new(name);
self.add_node(Node::new(var.into()))
}
pub fn scalar_variable(&mut self, name: &str, value: A) -> NodeIndex {
let var = self.variable(name);
self.set_value(var, value).unwrap();
var
}
pub fn vector_variable(&mut self, name: &str, value: Array<A, Ix1>) -> NodeIndex {
let var = self.variable(name);
self.set_value(var, value).unwrap();
var
}
pub fn set_value<V: Into<Value<A>>>(&mut self, node: NodeIndex, value: V) -> Result<()> {
if self[node].is_variable() {
self[node].value = Some(value.into());
Ok(())
} else {
Err(NodeTypeError {}.into())
}
}
pub fn add(&mut self, lhs: NodeIndex, rhs: NodeIndex) -> NodeIndex {
let p = self.add_node(Node::new(add().into()));
self.add_edge(lhs, p, ());
self.add_edge(rhs, p, ());
p
}
pub fn neg(&mut self, arg: NodeIndex) -> NodeIndex {
let n = self.add_node(Node::new(neg().into()));
self.add_edge(arg, n, ());
n
}
pub fn sub(&mut self, lhs: NodeIndex, rhs: NodeIndex) -> NodeIndex {
let m_rhs = self.neg(rhs);
self.add(lhs, m_rhs)
}
fn get_arg1(&mut self, op: NodeIndex) -> NodeIndex {
let mut iter = self.neighbors_directed(op, Direction::Incoming);
iter.next().unwrap()
}
fn get_arg2(&mut self, op: NodeIndex) -> (NodeIndex, NodeIndex) {
let mut iter = self.neighbors_directed(op, Direction::Incoming);
let rhs = iter.next().unwrap();
let lhs = iter.next().unwrap();
(lhs, rhs)
}
pub fn get_value(&self, node: NodeIndex) -> Option<&Value<A>> {
self[node].value.as_ref()
}
pub fn get_deriv(&self, node: NodeIndex) -> Option<&Value<A>> {
self[node].deriv.as_ref()
}
pub fn eval_value(&mut self, node: NodeIndex, use_cached: bool) -> Result<()> {
let prop = self[node].prop.clone();
let value_exists = self[node].value.is_some();
match prop {
Property::Variable(ref v) => {
if value_exists {
return Ok(());
}
panic!("Variable '{}' is evaluated before set value", v.name)
}
Property::UnaryOperator(ref op) => {
if use_cached && value_exists {
return Ok(());
}
let arg = self.get_arg1(node);
self.eval_value(arg, use_cached)?;
let res = op.eval_value(self.get_value(arg).unwrap())?;
self[node].value = Some(res);
}
Property::BinaryOperator(ref op) => {
if use_cached && value_exists {
return Ok(());
}
let (lhs, rhs) = self.get_arg2(node);
self.eval_value(rhs, use_cached)?;
self.eval_value(lhs, use_cached)?;
let res = op.eval_value(
self.get_value(lhs).unwrap(),
self.get_value(rhs).unwrap(),
)?;
self[node].value = Some(res);
}
};
Ok(())
}
fn deriv_recur(&mut self, node: NodeIndex, der: Value<A>) -> Result<()> {
self[node].deriv = Some(der);
let prop = self[node].prop.clone();
match prop {
Property::Variable(_) => {}
Property::UnaryOperator(ref op) => {
let arg = self.get_arg1(node);
let der = op.eval_deriv(
self.get_value(arg).unwrap(),
self.get_deriv(node).unwrap(),
)?;
self.deriv_recur(arg, der)?;
}
Property::BinaryOperator(ref op) => {
let (lhs, rhs) = self.get_arg2(node);
let (l_der, r_der) = op.eval_deriv(
self.get_value(lhs).unwrap(),
self.get_value(rhs).unwrap(),
self.get_deriv(node).unwrap(),
)?;
self.deriv_recur(lhs, l_der)?;
self.deriv_recur(rhs, r_der)?;
}
};
Ok(())
}
pub fn eval_deriv(&mut self, node: NodeIndex) -> Result<()> {
self.deriv_recur(node, Value::identity())
}
}