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#![no_std]
extern crate alloc;
use core::{
fmt::{self, Debug},
ops::AddAssign,
};
use num_traits::{cast::FromPrimitive, float::Float, identities::One, identities::Zero};
#[cfg(feature = "serde")]
use serde::{Deserialize, Serialize};
/// A statistics object that continuously calculates min, max, mean, and deviation for tracking time-varying statistics.
/// Utilizes Welford's Online algorithm. More details on the algorithm can be found at:
/// "https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Welford's_online_algorithm"
///
///
/// # Example
///
/// ```
/// use rolling_stats::Stats;
/// use rand_distr::{Distribution, Normal};
/// use rand::SeedableRng;
///
/// type T = f64;
///
/// const MEAN: T = 0.0;
/// const STD_DEV: T = 1.0;
/// const NUM_SAMPLES: usize = 10_000;
/// const SEED: u64 = 42;
///
/// let mut stats: Stats<T> = Stats::new();
/// let mut rng = rand::rngs::StdRng::seed_from_u64(SEED); // Seed the RNG for reproducibility
/// let normal = Normal::<T>::new(MEAN, STD_DEV).unwrap();
///
/// // Generate random data
/// let random_data: Vec<T> = (0..NUM_SAMPLES).map(|_x| normal.sample(&mut rng)).collect();
///
/// // Update the stats one by one
/// random_data.iter().for_each(|v| stats.update(*v));
///
/// // Print the stats
/// println!("{}", stats);
/// // Output: (avg: 0.00, std_dev: 1.00, min: -3.53, max: 4.11, count: 10000)
///
/// ```
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
#[derive(Clone, Debug, Default)]
pub struct Stats<T: Float + Zero + One + AddAssign + FromPrimitive + PartialEq + Debug> {
/// The smallest value seen so far.
pub min: T,
/// The largest value seen so far.
pub max: T,
/// The calculated mean (average) of all the values seen so far.
pub mean: T,
/// The calculated standard deviation of all the values seen so far.
pub std_dev: T,
/// The count of the total values seen.
pub count: usize,
/// The square of the mean value. This is an internal value used in the calculation of the standard deviation.
mean2: T,
}
/// Implementing the Display trait for the Stats struct to present the statistics in a readable format.
impl<T> fmt::Display for Stats<T>
where
T: fmt::Display + Float + Zero + One + AddAssign + FromPrimitive + PartialEq + Debug,
{
/// Formats the output of the statistics.
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
let precision = f.precision().unwrap_or(2);
write!(f, "(avg: {:.precision$}, std_dev: {:.precision$}, min: {:.precision$}, max: {:.precision$}, count: {})", self.mean, self.std_dev, self.min, self.max, self.count, precision=precision)
}
}
impl<T> Stats<T>
where
T: Float + Zero + One + AddAssign + FromPrimitive + PartialEq + Debug,
{
/// Creates a new stats object with all values set to their initial states.
pub fn new() -> Stats<T> {
Stats {
count: 0,
min: T::infinity(),
max: T::neg_infinity(),
mean: T::zero(),
std_dev: T::zero(),
mean2: T::zero(),
}
}
/// Updates the stats object with a new value. The statistics are recalculated using the new value.
pub fn update(&mut self, value: T) {
// Track min and max
if value > self.max {
self.max = value;
}
if value < self.min {
self.min = value;
}
// Increment counter
self.count += 1;
let count = T::from(self.count).unwrap();
// Calculate mean
let delta = value - self.mean;
self.mean += delta / count;
// Mean2 used internally for standard deviation calculation
let delta2 = value - self.mean;
self.mean2 += delta * delta2;
// Calculate standard deviation
if self.count > 1 {
self.std_dev = (self.mean2 / (count - T::one())).sqrt();
}
}
/// Merges another stats object into new one. This is done by combining the statistics of the two objects
/// in accordance with the formula provided at:
/// https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Parallel_algorithm
///
/// This is useful for combining statistics from multiple threads or processes.
///
/// # Example
///
/// ```
/// use rolling_stats::Stats;
/// use rand_distr::{Distribution, Normal};
/// use rand::SeedableRng;
/// use rayon::prelude::*;
///
/// type T = f64;
///
/// const MEAN: T = 0.0;
/// const STD_DEV: T = 1.0;
/// const NUM_SAMPLES: usize = 500_000;
/// const SEED: u64 = 42;
/// const CHUNK_SIZE: usize = 1000;
///
/// let mut stats: Stats<T> = Stats::new();
/// let mut rng = rand::rngs::StdRng::seed_from_u64(SEED); // Seed the RNG for reproducibility
/// let normal = Normal::<T>::new(MEAN, STD_DEV).unwrap();
///
/// // Generate random data
/// let random_data: Vec<T> = (0..NUM_SAMPLES).map(|_x| normal.sample(&mut rng)).collect();
///
/// // Update the stats in parallel. New stats objects are created for each chunk of data.
/// let stats: Vec<Stats<T>> = random_data
/// .par_chunks(CHUNK_SIZE) // Multi-threaded parallelization via Rayon
/// .map(|chunk| {
/// let mut s: Stats<T> = Stats::new();
/// chunk.iter().for_each(|v| s.update(*v));
/// s
/// })
/// .collect();
///
/// // Check if there's more than one stat object
/// assert!(stats.len() > 1);
///
/// // Accumulate the stats using the reduce method. The last stats object is returned.
/// let merged_stats = stats.into_iter().reduce(|acc, s| acc.merge(&s)).unwrap();
///
/// // Print the stats
/// println!("{}", merged_stats);
///
/// // Output: (avg: -0.00, std_dev: 1.00, min: -4.53, max: 4.57, count: 500000)
///```
pub fn merge(&self, other: &Self) -> Self {
let mut merged = Stats::<T>::new();
// If both stats objects are empty, return an empty stats object
if self.count + other.count == 0 {
return merged;
}
// If one of the stats objects is empty, return the other one
if self.count == 0 {
return other.clone();
} else if other.count == 0 {
return self.clone();
}
merged.max = if other.max > self.max {
other.max
} else {
self.max
};
merged.min = if other.min < self.min {
other.min
} else {
self.min
};
merged.count = self.count + other.count;
// Convert to T to avoid overflow
let merged_count = T::from(merged.count).unwrap();
let self_count = T::from(self.count).unwrap();
let other_count = T::from(other.count).unwrap();
let delta = other.mean - self.mean;
merged.mean = (self.mean * self_count + other.mean * other_count) / merged_count;
merged.mean2 =
self.mean2 + other.mean2 + delta * delta * self_count * other_count / merged_count;
merged.std_dev = (merged.mean2 / (merged_count - T::one())).sqrt();
merged
}
}
#[cfg(test)]
mod tests {
use super::*;
use alloc::vec;
use alloc::vec::Vec;
use float_cmp::{ApproxEq, ApproxEqUlps};
use rand::SeedableRng;
use rand_distr::{Distribution, Normal};
use rayon::prelude::*;
type T = f64;
#[test]
fn it_works() {
let mut s: Stats<f32> = Stats::new();
let vals: Vec<f32> = vec![1.0, 2.0, 3.0, 4.0, 5.0];
for v in &vals {
s.update(*v);
}
assert_eq!(s.count, vals.len());
assert_eq!(s.min, 1.0);
assert_eq!(s.max, 5.0);
assert!(s.mean.approx_eq_ulps(&3.0, 2));
assert!(s.std_dev.approx_eq_ulps(&1.5811388, 2));
}
/// Calculate the mean of a vector of values
fn calc_mean(vals: &Vec<T>) -> T {
let sum = vals.iter().fold(T::zero(), |acc, x| acc + *x);
sum / T::from_usize(vals.len()).unwrap()
}
/// Calculate the standard deviation of a vector of values
fn calc_std_dev(vals: &Vec<T>) -> T {
let mean = calc_mean(vals);
let std_dev = (vals
.iter()
.fold(T::zero(), |acc, x| acc + (*x - mean).powi(2))
/ T::from_usize(vals.len() - 1).unwrap())
.sqrt();
std_dev
}
/// Get the maximum value in a vector of values
fn get_max(vals: &Vec<T>) -> T {
let mut max = T::min_value();
for v in vals {
if *v > max {
max = *v;
}
}
max
}
/// Get the minimum value in a vector of values
fn get_min(vals: &Vec<T>) -> T {
let mut min = T::max_value();
for v in vals {
if *v < min {
min = *v;
}
}
min
}
#[test]
fn stats_for_large_random_data() {
// Define some constants
const MEAN: T = 2.0;
const STD_DEV: T = 3.0;
const SEED: u64 = 42;
const NUM_SAMPLES: usize = 10_000;
let mut s: Stats<T> = Stats::new();
let mut rng = rand::rngs::StdRng::seed_from_u64(SEED);
let normal = Normal::<T>::new(MEAN, STD_DEV).unwrap();
// Generate some random data
let random_data: Vec<T> = (0..NUM_SAMPLES).map(|_x| normal.sample(&mut rng)).collect();
// Update the stats
random_data.iter().for_each(|v| s.update(*v));
// Calculate the mean using sum/count method
let mean = calc_mean(&random_data);
// Check the mean value against the stats' mean value
assert!(s.mean.approx_eq(mean, (1.0e-13, 2)));
// Calculate the standard deviation
let std_dev = calc_std_dev(&random_data);
// Check the standard deviation against the stats' standard deviation
assert!(s.std_dev.approx_eq(std_dev, (1.0e-13, 2)));
// Check the count
assert_eq!(s.count, random_data.len());
// Find the max and min values
let max = get_max(&random_data);
let min = get_min(&random_data);
// Check the max and min values
assert_eq!(s.max, max);
assert_eq!(s.min, min);
}
#[test]
fn stats_merge() {
// Define some constants
const MEAN: T = 2.0;
const STD_DEV: T = 3.0;
const SEED: u64 = 42;
const NUM_SAMPLES: usize = 10_000;
let mut s: Stats<T> = Stats::new();
let mut rng = rand::rngs::StdRng::seed_from_u64(SEED);
let normal = Normal::<T>::new(MEAN, STD_DEV).unwrap();
// Generate some random data
let random_data: Vec<T> = (0..NUM_SAMPLES).map(|_x| normal.sample(&mut rng)).collect();
// Update the stats
random_data.iter().for_each(|v| s.update(*v));
// Calculate the stats using the aggregate method instead of the rolling method
let mean = calc_mean(&random_data);
let std_dev = calc_std_dev(&random_data);
let max = get_max(&random_data);
let min = get_min(&random_data);
let chunks_size = 1000;
let stats: Vec<Stats<T>> = random_data
.chunks(chunks_size)
.map(|chunk| {
let mut s: Stats<T> = Stats::new();
chunk.iter().for_each(|v| s.update(*v));
s
})
.collect();
assert_eq!(stats.len(), NUM_SAMPLES / chunks_size);
// Accumulate the stats
let merged_stats = stats.into_iter().reduce(|acc, s| acc.merge(&s)).unwrap();
// Check the stats against the aggregate stats (using sum/count method)
assert!(merged_stats.mean.approx_eq(mean, (1.0e-13, 2)));
assert!(merged_stats.std_dev.approx_eq(std_dev, (1.0e-13, 2)));
assert_eq!(merged_stats.max, max);
assert_eq!(merged_stats.min, min);
assert_eq!(merged_stats.count, NUM_SAMPLES);
// Check the stats against the merged stats object
assert!(merged_stats.mean.approx_eq(s.mean, (1.0e-13, 2)));
assert!(merged_stats.std_dev.approx_eq(s.std_dev, (1.0e-13, 2)));
assert_eq!(merged_stats.max, s.max);
assert_eq!(merged_stats.min, s.min);
assert_eq!(merged_stats.count, s.count);
// Check edge cases
// Check merging with an empty stats object
let empty_stats: Stats<T> = Stats::new();
let merged_stats = s.merge(&empty_stats);
assert_eq!(merged_stats.count, s.count);
// Check merging an empty stats object with a non-empty stats object
let empty_stats: Stats<T> = Stats::new();
let merged_stats = empty_stats.merge(&s);
assert_eq!(merged_stats.count, s.count);
// Check merging two empty stats objects
let empty_stats_1: Stats<T> = Stats::new();
let empty_stats_2: Stats<T> = Stats::new();
let merged_stats = empty_stats_1.merge(&empty_stats_2);
assert_eq!(merged_stats.count, 0);
}
#[test]
fn stats_merge_parallel() {
// Define some constants
const MEAN: T = 2.0;
const STD_DEV: T = 3.0;
const SEED: u64 = 42;
const NUM_SAMPLES: usize = 500_000;
let mut s: Stats<T> = Stats::new();
let mut rng = rand::rngs::StdRng::seed_from_u64(SEED);
let normal = Normal::<T>::new(MEAN, STD_DEV).unwrap();
// Generate some random data
let random_data: Vec<T> = (0..NUM_SAMPLES).map(|_x| normal.sample(&mut rng)).collect();
// Update the stats
random_data.iter().for_each(|v| s.update(*v));
// Calculate the stats using the aggregate method instead of the rolling method
let mean = calc_mean(&random_data);
let std_dev = calc_std_dev(&random_data);
let max = get_max(&random_data);
let min = get_min(&random_data);
let chunks_size = 1000;
let stats: Vec<Stats<T>> = random_data
.par_chunks(chunks_size) // <--- Parallelization by Rayon
.map(|chunk| {
let mut s: Stats<T> = Stats::new();
chunk.iter().for_each(|v| s.update(*v));
s
})
.collect();
// There should be more than one stat
assert!(stats.len() >= NUM_SAMPLES / chunks_size);
// Accumulate the stats
let merged_stats = stats.into_iter().reduce(|acc, s| acc.merge(&s)).unwrap();
// Check the stats against the aggregate stats (using sum/count method)
assert!(merged_stats.mean.approx_eq(mean, (1.0e-13, 2)));
assert!(merged_stats.std_dev.approx_eq(std_dev, (1.0e-13, 2)));
assert_eq!(merged_stats.max, max);
assert_eq!(merged_stats.min, min);
assert_eq!(merged_stats.count, NUM_SAMPLES);
// Check the stats against the merged stats object
assert!(merged_stats.mean.approx_eq(s.mean, (1.0e-13, 2)));
assert!(merged_stats.std_dev.approx_eq(s.std_dev, (1.0e-13, 2)));
assert_eq!(merged_stats.max, s.max);
assert_eq!(merged_stats.min, s.min);
assert_eq!(merged_stats.count, s.count);
}
}