uncertainty

Unc, or an Uncertainty is a way of representing a numerical value of which the true value is not known. The uncertainty can be expressed using absolute uncertainty (AbUnc::new()) or relative uncertainty (RelUnc::new).

These can look like so:

Absolute: 14.6 ± 0.2 mm

Relative: 14.7 ± 0.01369%

It should be apparent upon inspection that these two measurements are equal to each other, even though they slightly differ in value. This is because there is some overlap between the two measurements when the uncertainty value is considered. This can be determined as follows:

use uncertainty::*;
let one = AbUnc::new(14.6, 0.2);
let two = RelUnc::new(14.7, 0.01369);
assert!(one.overlap(&two));

There are also more arithmetic operations supported; absolute uncertainties can be added and subtracted, and relative uncertainties can be multiplied and divided. Relative uncertainties can also be raised to powers. To convert between the two, you can make use of the Uncertainty trait.

use uncertainty::*;
use approx::assert_abs_diff_eq;

let one = AbUnc::new(14.6, 0.2);
let two = RelUnc::new(14.7, 0.01369);
let three = RelUnc::new(2.0, 0.05);

let eq: AbUnc = one + two.to_ab();
let eq: RelUnc = eq.to_rel() * three;

assert_abs_diff_eq!(eq.val(), 58.6, epsilon = 0.0000001);
assert_abs_diff_eq!(eq.unc(), 0.0636943, epsilon = 0.0000001);

Conversion between the types can also be done via the From trait:

let x: AbUnc = RelUnc::new(2.0, 0.1).into();
assert_abs_diff_eq!(x.unc(), 0.2);

let y = AbUnc::from(2.0);
assert_abs_diff_eq!(y.val(), 2.0);
assert_abs_diff_eq!(y.unc(), 0.0);

Using the From trait to create an Uncertainty value will result in a value with zero uncertainty in it's value. This is the way scalar values should be treated within the system for arithmetic purposes.

It's possible to write a function which takes either an absolute or relative uncertainty using the Uncertainty trait:

fn print<T: Uncertainty>(x: T) {
    let x = x.to_ab();
    println!("The value is: {}, and the uncertainty is: {}!", x.val(), x.unc());
}

print(AbUnc::from(10.0));
print(RelUnc::from(20.0));

However, if you only want to accept specifically Relative or Absolute uncertain values, you can do this by using the AbUnc and RelUnc types:

fn print_ab(x: AbUnc) {
    println!("The value of this absolute uncertainty is: {}", x.val());
}

print_ab(AbUnc::new(14.7, 0.02));

License: MIT