integraal/
parameters.rs

1//! integral parameterization code
2
3use crate::Scalar;
4
5/// Domain description enum
6///
7/// This represents a discretization of the integrated space.
8///
9/// Only 1D domains are currently supported. the type used for values must implement [`Scalar`]; the trait
10/// is automatially implemented for types satisfying its requirements. In the future, adding support for
11/// higher dimension can be considered.
12#[derive(Debug, Clone)]
13pub enum DomainDescriptor<X: Scalar> {
14    /// List of values taken by the variable on which we integrate.
15    Explicit(Vec<X>),
16    /// Description of a uniform discretization over a certain range of values.
17    Uniform {
18        /// First value of the range
19        start: X,
20        /// Step between each value of the range
21        step: X,
22        /// Total number of values
23        n_step: usize,
24    },
25}
26
27/// Function description enum
28///
29/// This holds information about the function's values, as either explicit values or a closure that
30/// can be used to compute those.
31pub enum FunctionDescriptor<X>
32where
33    X: Scalar,
34{
35    /// Direct expression of the function, taking a value of the domain as input & returning the
36    /// image of that value.
37    Closure(Box<dyn Fn(X) -> X>),
38    /// List of values taken by the function. An error will be raised at computation if the length
39    /// of the list isn't consistent with the domain descriptor.
40    Values(Vec<X>),
41}
42
43/// Numerical integration method enum
44///
45/// # Note on computations
46///
47/// For the considered integral to be consistent across compute methods for a given description,
48/// the left-rectangle (resp. right-rectangle) has to ignore the last (resp. first) value given
49/// in the descriptors. This can be visualized in the following example:
50///
51/// ![COMPARISON](https://imrn99.github.io/integraal/compute_methods.svg)
52///
53/// Out of 11 samples, both methods compute the area of 10 polygons. In the case where the domain
54/// is uniform & described using a step, the eleventh sample value is useless (for a left-rectangle
55/// method).
56///
57/// The crate assumes that the first and last samples making up your domain corresponds to the
58/// limits of the integral. Therefore, these values will be ignored when computing the integral
59/// using rectangles.
60#[derive(Debug, Clone, Copy)]
61pub enum ComputeMethod {
62    /// Rectangle method, using the left rule --
63    /// [reference](https://en.wikipedia.org/wiki/Riemann_sum#Left_rule)
64    RectangleLeft,
65    /// Rectangle method, using the right rule --
66    /// [reference](https://en.wikipedia.org/wiki/Riemann_sum#Right_rule)
67    RectangleRight,
68    /// Trapezoid method -- [reference](https://en.wikipedia.org/wiki/Trapezoidal_rule)
69    Trapezoid,
70    /// Simpson's rule(s), the exact rule applied depends on integral definition --
71    /// [reference](https://en.wikipedia.org/wiki/Simpson%27s_rule)
72    Simpson,
73    /// Boole's method -- [reference](https://en.wikipedia.org/wiki/Boole%27s_rule#Composite_Boole's_Rule)
74    #[cfg(feature = "boole")]
75    Boole {
76        /// Force the computation by truncating inputs to fit method requirements
77        force: bool,
78    },
79    /// Romberg's method -- [reference](https://en.wikipedia.org/wiki/Romberg%27s_method#Implementation)
80    #[cfg(feature = "romberg")]
81    Romberg {
82        /// Maximum number of iteration done by the algorithm
83        max_steps: usize,
84    },
85    #[cfg(feature = "montecarlo")]
86    /// Monte-Carlo method -- [reference](https://en.wikipedia.org/wiki/Monte_Carlo_integration)
87    MonteCarlo {
88        /// Number of samples per step computation.
89        n_sample: usize,
90    },
91}
integraal/parameters.rs

integraal/
parameters.rs
