mathru 0.16.2

Fundamental algorithms for scientific computing in Rust
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

use crate::algebra::abstr::Real;
use crate::analysis::integral::newton_cotes::ClosedFixedIntervalIterator;

#[cfg(feature = "serde")]
use serde::{Deserialize, Serialize};

/// Closed Newton-Cotes
///
/// <https://en.wikipedia.org/wiki/Newton-Cotes_formulas>
///
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
#[derive(Clone, Debug)]
pub struct NewtonCotes<T>
where
    T: Real,
{
    weight: Vec<T>,
}

impl<T> NewtonCotes<T>
where
    T: Real,
{
    /// # Arguments
    ///
    /// n:
    /// 1 => Trapezoidal rule
    /// 2 => Simpson's rule
    /// 3 => Simpson's 3/8 rule
    /// 4 => Boole0s rule
    /// 5 =>
    ///
    /// # Panics
    ///
    /// Panics if n < 1 || n > 5
    ///
    /// # Examples
    /// ```
    ///
    /// use mathru::{assert_relative_eq,
    ///     analysis::integral::newton_cotes::NewtonCotes
    /// };
    ///
    /// let nc = NewtonCotes::new(1);
    /// let f = | x | {x};
    ///
    /// let integral = nc.integrate(f, 2.0, 4.0, 4);
    ///
    /// assert_relative_eq!(integral, 6.0)
    /// ```
    pub fn new(n: u8) -> NewtonCotes<T> {
        if !(1..=5).contains(&n) {
            panic!("'n' is out of bounds");
        }
        let weight = match n {
            1 => vec![T::from_f32(0.5), T::from_f32(0.5)],
            2 => vec![
                T::from_f64(1.0 / 6.0),
                T::from_f64(2.0 / 3.0),
                T::from_f64(1.0 / 6.0),
            ],
            3 => vec![
                T::from_f64(1.0 / 8.0),
                T::from_f64(3.0 / 8.0),
                T::from_f64(3.0 / 8.0),
                T::from_f64(1.0 / 8.0),
            ],
            4 => vec![
                T::from_f64(7.0 / 90.0),
                T::from_f64(16.0 / 45.0),
                T::from_f64(2.0 / 15.0),
                T::from_f64(16.0 / 45.0),
                T::from_f64(7.0 / 90.0),
            ],
            5 => vec![
                T::from_f64(19.0 / 288.0),
                T::from_f64(25.0 / 96.0),
                T::from_f64(25.0 / 144.0),
                T::from_f64(25.0 / 144.0),
                T::from_f64(25.0 / 96.0),
                T::from_f64(19.0 / 288.0),
            ],
            _ => panic!(""),
        };
        NewtonCotes { weight }
    }

    ///
    /// ```math
    /// \int_{a}^{b}f(x)\,dx
    /// ```
    ///
    /// # Arguments
    /// * 'a'
    /// * 'b'
    ///   num_subintervals: \[a,b\] into smaller subintervals,
    /// #
    pub fn integrate<F>(&self, f: F, a: T, b: T, num_subintervals: u32) -> T
    where
        F: Fn(T) -> T,
    {
        let mut sub_interval: ClosedFixedIntervalIterator<T> =
            ClosedFixedIntervalIterator::new(a, b, num_subintervals);

        let mut lower_bound: T = sub_interval.next().unwrap();
        let num_intervals = self.weight.len() as u32 - 1;
        let mut sum = T::zero();
        sub_interval.for_each(|x_i: T| {
            let interval: ClosedFixedIntervalIterator<T> =
                ClosedFixedIntervalIterator::new(lower_bound, x_i, num_intervals);
            let h = x_i - lower_bound;
            let sum_i = interval
                .zip(self.weight.iter())
                .map(|(x, w)| *w * f(x))
                // .sum()
                .fold(T::zero(), |a, b| a + b)
                * h;

            sum += sum_i;

            lower_bound = x_i;
        });

        sum
    }
}