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
use crate::{VSPD, SpdElement};
pub struct InterpolatorSprague<T>
where
T: SpdElement,
{
x: Vec<T>,
y: Vec<T>,
}
pub trait SpragueCoefficients {
type Item: SpdElement;
fn coeff_c0() -> [Self::Item; 6];
fn coeff_c1() -> [Self::Item; 6];
fn coeff_c2() -> [Self::Item; 6];
fn coeff_c3() -> [Self::Item; 6];
fn coeff_a(r: &Vec<Self::Item>, i: usize) -> [Self::Item; 6];
}
impl SpragueCoefficients for f32 {
type Item = f32;
fn coeff_c0() -> [f32; 6] {
[884.0, -1960.0, 3033.0, -2648.0, 1080.0, -180.0]
}
fn coeff_c1() -> [f32; 6] {
[508.0, -540.0, 488.0, -367.0, 144.0, -24.0]
}
fn coeff_c2() -> [f32; 6] {
[-24.0, 144.0, -367.0, 488.0, -540.0, 508.0]
}
fn coeff_c3() -> [f32; 6] {
[-180.0, 1080.0, -2648.0, 3033.0, -1960.0, 884.0]
}
fn coeff_a(r: &Vec<f32>, i: usize) -> [f32; 6] {
let a0p = r[i];
let a1p = (2.0 * r[i - 2] - 16.0 * r[i - 1] + 16.0 * r[i + 1] - 2.0 * r[i + 2]) / 24.0;
let a2p = (-r[i - 2] + 16.0 * r[i - 1] - 30.0 * r[i] + 16.0 * r[i + 1] - r[i + 2]) / 24.0;
let a3p = (-9.0 * r[i - 2] + 39.0 * r[i - 1] - 70.0 * r[i] + 66.0 * r[i + 1]
- 33.0 * r[i + 2]
+ 7.0 * r[i + 3])
/ 24.0;
let a4p = (13.0 * r[i - 2] - 64.0 * r[i - 1] + 126.0 * r[i] - 124.0 * r[i + 1]
+ 61.0 * r[i + 2]
- 12.0 * r[i + 3])
/ 24.0;
let a5p = (-5.0 * r[i - 2] + 25.0 * r[i - 1] - 50.0 * r[i] + 50.0 * r[i + 1]
- 25.0 * r[i + 2]
+ 5.0 * r[i + 3])
/ 24.0;
[a0p, a1p, a2p, a3p, a4p, a5p]
}
}
impl SpragueCoefficients for f64 {
type Item = f64;
fn coeff_c0() -> [f64; 6] {
[884.0, -1960.0, 3033.0, -2648.0, 1080.0, -180.0]
}
fn coeff_c1() -> [f64; 6] {
[508.0, -540.0, 488.0, -367.0, 144.0, -24.0]
}
fn coeff_c2() -> [f64; 6] {
[-24.0, 144.0, -367.0, 488.0, -540.0, 508.0]
}
fn coeff_c3() -> [f64; 6] {
[-180.0, 1080.0, -2648.0, 3033.0, -1960.0, 884.0]
}
fn coeff_a(r: &Vec<f64>, i: usize) -> [f64; 6] {
let a0p = r[i];
let a1p = (2.0 * r[i - 2] - 16.0 * r[i - 1] + 16.0 * r[i + 1] - 2.0 * r[i + 2]) / 24.0;
let a2p = (-r[i - 2] + 16.0 * r[i - 1] - 30.0 * r[i] + 16.0 * r[i + 1] - r[i + 2]) / 24.0;
let a3p = (-9.0 * r[i - 2] + 39.0 * r[i - 1] - 70.0 * r[i] + 66.0 * r[i + 1]
- 33.0 * r[i + 2]
+ 7.0 * r[i + 3])
/ 24.0;
let a4p = (13.0 * r[i - 2] - 64.0 * r[i - 1] + 126.0 * r[i] - 124.0 * r[i + 1]
+ 61.0 * r[i + 2]
- 12.0 * r[i + 3])
/ 24.0;
let a5p = (-5.0 * r[i - 2] + 25.0 * r[i - 1] - 50.0 * r[i] + 50.0 * r[i + 1]
- 25.0 * r[i + 2]
+ 5.0 * r[i + 3])
/ 24.0;
[a0p, a1p, a2p, a3p, a4p, a5p]
}
}
impl<T> InterpolatorSprague<T>
where
T: SpdElement + SpragueCoefficients<Item = T>,
{
pub fn new(vspd: &VSPD) -> InterpolatorSprague<f64> {
let first = vspd.samples.first().unwrap().nm;
let last = vspd.samples.last().unwrap().nm;
let interval = vspd.samples[1].nm - first;
let x1 = first - interval * 2.0;
let x2 = first - interval;
let x3 = last + interval;
let x4 = last + interval * 2.0;
let mut x = Vec::with_capacity(vspd.len() + 4);
x.push(x1);
x.push(x2);
x.extend(vspd.iter().map(|s| s.nm));
x.push(x3);
x.push(x4);
let mut y = Vec::with_capacity(vspd.len() + 4);
let y1 = f64::coeff_c0()
.iter()
.zip(vspd.iter())
.map(|(c, s)| *c * s.v)
.sum::<f64>();
let y2 = f64::coeff_c1()
.iter()
.zip(vspd.iter())
.map(|(c, s)| *c * s.v)
.sum::<f64>();
let y3 = f64::coeff_c2()
.iter()
.rev()
.zip(vspd.iter().rev())
.map(|(c, s)| *c * s.v)
.sum::<f64>();
let y4 = f64::coeff_c3()
.iter()
.rev()
.zip(vspd.iter().rev())
.map(|(c, s)| *c * s.v)
.sum::<f64>();
y.push(y1 / 209.0);
y.push(y2 / 209.0);
y.extend(vspd.iter().map(|s| s.v));
y.push(y3 / 209.0);
y.push(y4 / 209.0);
InterpolatorSprague { x, y }
}
pub fn evaluate(&self, x: T) -> T {
let i = (self.x.iter().position(|t| x < *t).unwrap() - 1)
.max(2)
.min(self.x.len() - 4);
let dx = (x - self.x[i]) / (self.x[i + 1] - self.x[i]);
let a = T::coeff_a(&self.y, i);
a[0] + a[1] * dx
+ a[2] * dx.powi(2)
+ a[3] * dx.powi(3)
+ a[4] * dx.powi(4)
+ a[5] * dx.powi(5)
}
}
pub struct ExtrapolatorConstant<'a> {
spd: &'a VSPD,
}
impl<'a> ExtrapolatorConstant<'a> {
pub fn new(spd: &'a VSPD) -> ExtrapolatorConstant<'a> {
ExtrapolatorConstant { spd }
}
pub fn evaluate(&self, x: f64) -> f64 {
if x < self.spd.samples.first().unwrap().nm {
self.spd.samples.first().unwrap().v
} else {
self.spd.samples.last().unwrap().v
}
}
}
pub struct InterpolatorLinear<'a> {
spd: &'a VSPD,
}
impl<'a> InterpolatorLinear<'a> {
pub fn new(spd: &'a VSPD) -> InterpolatorLinear<'a> {
InterpolatorLinear { spd }
}
pub fn evaluate(&self, x: f64) -> f64 {
if x <= self.spd.first().nm {
self.spd.first().v
} else if x >= self.spd.last().nm {
self.spd.last().v
} else {
let i = self.spd.iter().position(|s| x < s.nm).unwrap() - 1;
let d = (x - self.spd.samples()[i].nm) / (self.spd.samples()[i+1].nm - self.spd.samples()[i].nm);
(1.0 - d) * self.spd.samples()[i].v + d * self.spd.samples()[i+1].v
}
}
}