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use std::fmt;
/// Holds basic statistics of a dataset
pub struct Statistics {
/// Minimum value
pub min: f64,
/// Maximum value
pub max: f64,
/// Arithmetic mean
pub mean: f64,
/// (sample) Standard deviation (applying Bessel's correction)
pub std_dev: f64,
}
impl Statistics {
/// Calculates basic statistics of a dataset
///
/// # Examples
///
/// ```
/// use russell_stat::Statistics;
///
/// let res = Statistics::new(&[2, 4, 4, 4, 5, 5, 7, 9]);
/// assert_eq!(res.min, 2.0);
/// assert_eq!(res.max, 9.0);
/// assert_eq!(res.mean, 5.0);
/// assert_eq!(res.std_dev, f64::sqrt(32.0/7.0));
///
/// let res = Statistics::new(&[1.0, 1.0, 1.0]);
/// assert_eq!(
/// format!("{}", res),
/// "min = 1\n\
/// max = 1\n\
/// mean = 1\n\
/// std_dev = 0\n"
/// );
/// ```
pub fn new<T>(x: &[T]) -> Self
where
T: Into<f64> + Copy,
{
// handle small slices
if x.len() == 0 {
return Statistics {
min: 0.0,
max: 0.0,
mean: 0.0,
std_dev: 0.0,
};
}
if x.len() == 1 {
return Statistics {
min: x[0].into(),
max: x[0].into(),
mean: x[0].into(),
std_dev: 0.0,
};
}
// average
let sum = x.iter().fold(0.0, |acc, &curr| acc + curr.into());
let n = x.len() as f64;
let mean = sum / n;
// limits and auxiliary data
let mut min = f64::INFINITY;
let mut max = f64::NEG_INFINITY;
let mut corrector = 0.0;
let mut variance = 0.0;
for &val in x {
let x = val.into();
if x < min {
min = x;
}
if x > max {
max = x;
}
let diff = x - mean; // diff ← xi - bar(x)
corrector += diff; // corrector ← Σ diff
variance += diff * diff; // variance ← Σ diff²
}
// (sample) standard deviation (applying Bessel's correction)
variance = (variance - corrector * corrector / n) / (n - 1.0);
let std_dev = variance.sqrt();
// results
Statistics {
min,
max,
mean,
std_dev,
}
}
}
impl fmt::Display for Statistics {
/// Prints statistics
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
match f.precision() {
Some(digits) => write!(
f,
"min = {:.4$}\nmax = {:.4$}\nmean = {:.4$}\nstd_dev = {:.4$}\n",
self.min, self.max, self.mean, self.std_dev, digits
)
.unwrap(),
None => write!(
f,
"min = {}\nmax = {}\nmean = {}\nstd_dev = {}\n",
self.min, self.max, self.mean, self.std_dev
)
.unwrap(),
}
Ok(())
}
}
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
#[cfg(test)]
mod tests {
use super::Statistics;
use russell_lab::approx_eq;
#[test]
fn statistics_handle_small_slices() {
let x: [i32; 0] = [];
let res = Statistics::new(&x);
assert_eq!(res.min, 0.0);
assert_eq!(res.max, 0.0);
assert_eq!(res.mean, 0.0);
assert_eq!(res.std_dev, 0.0);
let x = [1.23];
let res = Statistics::new(&x);
assert_eq!(res.min, 1.23);
assert_eq!(res.max, 1.23);
assert_eq!(res.mean, 1.23);
assert_eq!(res.std_dev, 0.0);
}
#[test]
fn statistics_works() {
let x = [100, 100, 102, 98, 77, 99, 70, 105, 98];
let res = Statistics::new(&x);
assert_eq!(res.min, 70.0);
assert_eq!(res.max, 105.0);
assert_eq!(res.mean, 849.0 / 9.0);
approx_eq(res.std_dev, 12.134661099511597, 1e-17);
let x = [9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4];
let res = Statistics::new(&x);
assert_eq!(res.min, 2.0);
assert_eq!(res.max, 12.0);
assert_eq!(res.mean, 7.0);
approx_eq(res.std_dev, f64::sqrt(178.0 / 19.0), 1e-17);
}
#[test]
fn display_works() {
let x = [9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4];
let res = Statistics::new(&x);
assert_eq!(
format!("{:.3}", res),
"min = 2.000\n\
max = 12.000\n\
mean = 7.000\n\
std_dev = 3.061\n"
);
let x = [1, 1, 1];
let res = Statistics::new(&x);
assert_eq!(
format!("{}", res),
"min = 1\n\
max = 1\n\
mean = 1\n\
std_dev = 0\n"
);
}
}