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//! Linear Regression Slope.
use std::collections::VecDeque;
use crate::error::{Error, Result};
use crate::traits::Indicator;
/// Linear Regression Slope — the slope of a rolling least-squares fit.
///
/// Over the last `period` inputs, indexed `x = 0, 1, …, period − 1`, it fits
/// the line `y = a + b·x` by ordinary least squares and reports the slope:
///
/// ```text
/// b = (n·Σxy − Σx·Σy) / (n·Σxx − (Σx)²)
/// ```
///
/// This is TA-Lib's `LINEARREG_SLOPE`: a momentum-like reading of how steeply
/// price is trending over the window — positive while it rises, negative
/// while it falls, near zero when it is flat — without the band-pass quirks
/// of a difference-based oscillator.
///
/// Each `update` is O(1): the same incremental OLS state as
/// [`LinearRegression`](crate::LinearRegression) is maintained — `Σx` and
/// `Σxx` are precomputed once from `period`, while `Σy` and `Σxy` are slid
/// forward in closed form on every push.
///
/// # Example
///
/// ```
/// use wickra_core::{Indicator, LinRegSlope};
///
/// let mut indicator = LinRegSlope::new(14).unwrap();
/// let mut last = None;
/// for i in 0..80 {
/// last = indicator.update(f64::from(i));
/// }
/// assert!(last.is_some());
/// ```
#[derive(Debug, Clone)]
pub struct LinRegSlope {
period: usize,
window: VecDeque<f64>,
/// Closed form of `Σx` over `x = 0, 1, …, period − 1` — constant in `period`.
sum_x: f64,
/// Closed form of `n · Σxx − (Σx)²` — constant in `period`.
denom: f64,
/// Running sum of the values currently in the window.
sum_y: f64,
/// Running `Σ(x · y)` where `x` is the position within the trailing window.
sum_xy: f64,
}
impl LinRegSlope {
/// Construct a new rolling linear-regression slope over `period` inputs.
///
/// # Errors
/// Returns [`Error::InvalidPeriod`] if `period < 2` — a regression line is
/// undefined for fewer than two points.
pub fn new(period: usize) -> Result<Self> {
if period < 2 {
return Err(Error::InvalidPeriod {
message: "linear regression slope needs period >= 2",
});
}
let n = period as f64;
// Closed forms for x = 0, 1, …, period − 1.
let sum_x = n * (n - 1.0) / 2.0;
let sum_xx = (n - 1.0) * n * (2.0 * n - 1.0) / 6.0;
Ok(Self {
period,
window: VecDeque::with_capacity(period),
sum_x,
denom: n * sum_xx - sum_x * sum_x,
sum_y: 0.0,
sum_xy: 0.0,
})
}
/// Configured period.
pub const fn period(&self) -> usize {
self.period
}
}
impl Indicator for LinRegSlope {
type Input = f64;
type Output = f64;
fn update(&mut self, value: f64) -> Option<f64> {
if self.window.len() == self.period {
// Sliding-window identity: when the window slides one step forward
// the indices `x` for every kept entry shift down by 1, so
// new_sum_xy = old_sum_xy − old_sum_y + y0
// (`y0` is the popped front value).
let y0 = self.window.pop_front().expect("non-empty");
self.sum_xy = self.sum_xy - self.sum_y + y0;
self.sum_y -= y0;
}
let k = self.window.len() as f64;
self.window.push_back(value);
self.sum_y += value;
self.sum_xy += k * value;
if self.window.len() < self.period {
return None;
}
let n = self.period as f64;
Some((n * self.sum_xy - self.sum_x * self.sum_y) / self.denom)
}
fn reset(&mut self) {
self.window.clear();
self.sum_y = 0.0;
self.sum_xy = 0.0;
}
fn warmup_period(&self) -> usize {
self.period
}
fn is_ready(&self) -> bool {
self.window.len() == self.period
}
fn name(&self) -> &'static str {
"LinRegSlope"
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::traits::BatchExt;
use approx::assert_relative_eq;
#[test]
fn reference_values() {
// period 3 over [1, 2, 9]: fit y = 0 + 4x, so the slope is 4.
let mut ls = LinRegSlope::new(3).unwrap();
let out = ls.batch(&[1.0, 2.0, 9.0]);
assert!(out[0].is_none());
assert!(out[1].is_none());
assert_relative_eq!(out[2].unwrap(), 4.0, epsilon = 1e-9);
}
#[test]
fn perfect_line_returns_its_step() {
// A series rising by a fixed step has exactly that slope.
let prices: Vec<f64> = (0..40).map(|i| 2.5 * f64::from(i) + 7.0).collect();
let mut ls = LinRegSlope::new(10).unwrap();
for v in ls.batch(&prices).into_iter().flatten() {
assert_relative_eq!(v, 2.5, epsilon = 1e-6);
}
}
#[test]
fn constant_series_has_zero_slope() {
let mut ls = LinRegSlope::new(8).unwrap();
for v in ls.batch(&[42.0; 20]).into_iter().flatten() {
assert_relative_eq!(v, 0.0, epsilon = 1e-9);
}
}
#[test]
fn falling_series_has_negative_slope() {
let prices: Vec<f64> = (0..30).map(|i| 100.0 - f64::from(i)).collect();
let mut ls = LinRegSlope::new(10).unwrap();
for v in ls.batch(&prices).into_iter().flatten() {
assert!(v < 0.0, "a falling series must have a negative slope");
}
}
#[test]
fn first_value_on_period_th_input() {
let mut ls = LinRegSlope::new(5).unwrap();
let out = ls.batch(&[1.0, 3.0, 2.0, 5.0, 4.0, 6.0]);
for (i, v) in out.iter().enumerate().take(4) {
assert!(v.is_none(), "index {i} must be None during warmup");
}
assert!(out[4].is_some(), "first value lands at index period - 1");
assert_eq!(ls.warmup_period(), 5);
}
#[test]
fn rejects_period_below_two() {
assert!(LinRegSlope::new(0).is_err());
assert!(LinRegSlope::new(1).is_err());
assert!(LinRegSlope::new(2).is_ok());
}
/// Cover the const accessor `period` (80-82) and the Indicator-impl
/// `name` body (125-127). `warmup_period` is exercised elsewhere.
#[test]
fn accessors_and_metadata() {
let ls = LinRegSlope::new(14).unwrap();
assert_eq!(ls.period(), 14);
assert_eq!(ls.name(), "LinRegSlope");
}
#[test]
fn reset_clears_state() {
let mut ls = LinRegSlope::new(5).unwrap();
ls.batch(&[1.0, 2.0, 3.0, 4.0, 5.0]);
assert!(ls.is_ready());
ls.reset();
assert!(!ls.is_ready());
assert_eq!(ls.update(1.0), None);
}
#[test]
fn batch_equals_streaming() {
let prices: Vec<f64> = (0..60)
.map(|i| 50.0 + (f64::from(i) * 0.3).sin() * 10.0)
.collect();
let mut a = LinRegSlope::new(14).unwrap();
let mut b = LinRegSlope::new(14).unwrap();
assert_eq!(
a.batch(&prices),
prices.iter().map(|x| b.update(*x)).collect::<Vec<_>>()
);
}
/// Incremental OLS equivalence for the slope: the O(1) implementation must
/// agree bar-by-bar with a fresh-from-scratch O(n) refit, on a noisy ramp
/// (sliding-phase dominated) and a step function (large pop/push deltas).
#[test]
fn incremental_matches_naive_slope_bar_by_bar() {
fn naive_slope(window: &[f64]) -> f64 {
let n = window.len() as f64;
let mut sum_y = 0.0;
let mut sum_xy = 0.0;
let mut sum_x = 0.0;
let mut sum_xx = 0.0;
for (i, &y) in window.iter().enumerate() {
let x = i as f64;
sum_y += y;
sum_xy += x * y;
sum_x += x;
sum_xx += x * x;
}
(n * sum_xy - sum_x * sum_y) / (n * sum_xx - sum_x * sum_x)
}
fn check(prices: &[f64], period: usize) {
let mut ls = LinRegSlope::new(period).unwrap();
for (t, p) in prices.iter().enumerate() {
let streaming = ls.update(*p);
if t + 1 >= period {
let lo = t + 1 - period;
let expected = naive_slope(&prices[lo..=t]);
let got = streaming.expect("warmed up");
assert!(
(got - expected).abs() < 1e-9,
"slope diverges at t={t}, period={period}: got={got}, expected={expected}",
);
}
}
}
let noisy_ramp: Vec<f64> = (0..120)
.map(|i| 100.0 + f64::from(i) * 0.5 + (f64::from(i) * 0.7).sin() * 3.0)
.collect();
check(&noisy_ramp, 5);
check(&noisy_ramp, 14);
let mut step = vec![1.0; 30];
step.extend(std::iter::repeat_n(100.0, 30));
check(&step, 7);
}
}