feat(alma): add Arnaud Legoux Moving Average

Gaussian-weighted moving average with configurable centre (offset in
[0, 1]) and kernel width (sigma > 0). Pre-computes normalised weights
at construction so each update is a single rolling window dot product.

Reference: Arnaud Legoux and Dimitrios Kouzis-Loukas, 2009.

Touchpoints:
- crates/wickra-core: alma.rs + mod.rs + lib.rs re-export
- bindings/python: PyAlma + __init__.py + test_new_indicators +
  test_known_values reference
- bindings/node: AlmaNode + index.d.ts/index.js + indicators.test.js
  factory + reference value
- bindings/wasm: wasm_scalar_indicator! macro
- fuzz: indicator_update target covers ALMA(9, 0.85, 6.0)
- crates/wickra/benches: bench_scalar entry
- README + CHANGELOG: Moving Averages row + Unreleased entry

crates/wickra-core/src/indicators/alma.rs

@@ -0,0 +1,335 @@
+//! Arnaud Legoux Moving Average (ALMA).
+
+use std::collections::VecDeque;
+
+use crate::error::{Error, Result};
+use crate::traits::Indicator;
+
+/// Arnaud Legoux Moving Average — a Gaussian-weighted moving average.
+///
+/// Each output is a weighted sum of the last `period` inputs:
+///
+/// ```text
+/// w[i] = exp(-(i - m)^2 / (2 * s^2))   for i in 0..period
+/// m    = offset * (period - 1)
+/// s    = period / sigma
+/// ALMA = sum(price[i] * w[i]) / sum(w[i])
+/// ```
+///
+/// The Gaussian is centred on the relative index `offset * (period - 1)`, so
+/// `offset = 0.85` puts the peak near the newest sample (responsive), while
+/// `offset = 0.5` centres the peak in the middle of the window (smooth).
+/// `sigma` controls how concentrated the Gaussian is: larger `sigma` ->
+/// narrower kernel, smaller `sigma` -> broader (closer to SMA).
+///
+/// Reference: Arnaud Legoux and Dimitrios Kouzis-Loukas, 2009.
+///
+/// # Defaults
+///
+/// The community-standard parameters are `period = 9`, `offset = 0.85`,
+/// `sigma = 6.0`. The first output lands after exactly `period` inputs.
+///
+/// # Example
+///
+/// ```
+/// use wickra_core::{Alma, Indicator};
+///
+/// let mut alma = Alma::new(9, 0.85, 6.0).unwrap();
+/// let mut last = None;
+/// for i in 0..40 {
+///     last = alma.update(100.0 + f64::from(i));
+/// }
+/// assert!(last.is_some());
+/// ```
+#[derive(Debug, Clone)]
+pub struct Alma {
+    period: usize,
+    offset: f64,
+    sigma: f64,
+    /// Pre-computed, normalised weights (sum to 1). `weights[0]` is the oldest
+    /// sample in the window, `weights[period - 1]` the newest.
+    weights: Vec<f64>,
+    window: VecDeque<f64>,
+    current: Option<f64>,
+}
+
+impl Alma {
+    /// Construct a new ALMA with the given period, offset and sigma.
+    ///
+    /// # Errors
+    ///
+    /// - [`Error::PeriodZero`] if `period == 0`.
+    /// - [`Error::InvalidPeriod`] if `offset` is outside `[0.0, 1.0]` or
+    ///   `sigma <= 0.0` or either of `offset` / `sigma` is non-finite.
+    pub fn new(period: usize, offset: f64, sigma: f64) -> Result<Self> {
+        if period == 0 {
+            return Err(Error::PeriodZero);
+        }
+        if !offset.is_finite() || !(0.0..=1.0).contains(&offset) {
+            return Err(Error::InvalidPeriod {
+                message: "ALMA offset must be a finite value in [0, 1]",
+            });
+        }
+        if !sigma.is_finite() || sigma <= 0.0 {
+            return Err(Error::InvalidPeriod {
+                message: "ALMA sigma must be a finite positive value",
+            });
+        }
+        let m = offset * (period as f64 - 1.0);
+        let s = period as f64 / sigma;
+        let denom = 2.0 * s * s;
+        // The raw Gaussian weights sum to a strictly positive value because
+        // every term is `exp(_) > 0`, so the normalisation below cannot divide
+        // by zero.
+        let mut raw: Vec<f64> = (0..period)
+            .map(|i| (-((i as f64 - m).powi(2)) / denom).exp())
+            .collect();
+        let sum: f64 = raw.iter().sum();
+        for w in &mut raw {
+            *w /= sum;
+        }
+        Ok(Self {
+            period,
+            offset,
+            sigma,
+            weights: raw,
+            window: VecDeque::with_capacity(period),
+            current: None,
+        })
+    }
+
+    /// Construct ALMA with the community-standard parameters
+    /// `(period = 9, offset = 0.85, sigma = 6.0)`.
+    pub fn classic() -> Self {
+        Self::new(9, 0.85, 6.0).expect("classic ALMA parameters are valid")
+    }
+
+    /// Configured period.
+    pub const fn period(&self) -> usize {
+        self.period
+    }
+
+    /// Configured offset.
+    pub const fn offset(&self) -> f64 {
+        self.offset
+    }
+
+    /// Configured sigma.
+    pub const fn sigma(&self) -> f64 {
+        self.sigma
+    }
+}
+
+impl Indicator for Alma {
+    type Input = f64;
+    type Output = f64;
+
+    fn update(&mut self, input: f64) -> Option<f64> {
+        if !input.is_finite() {
+            return self.current;
+        }
+        if self.window.len() == self.period {
+            self.window.pop_front();
+        }
+        self.window.push_back(input);
+        if self.window.len() < self.period {
+            return None;
+        }
+        let mut acc = 0.0;
+        for (w, p) in self.weights.iter().zip(self.window.iter()) {
+            acc += w * p;
+        }
+        self.current = Some(acc);
+        Some(acc)
+    }
+
+    fn reset(&mut self) {
+        self.window.clear();
+        self.current = None;
+    }
+
+    fn warmup_period(&self) -> usize {
+        self.period
+    }
+
+    fn is_ready(&self) -> bool {
+        self.current.is_some()
+    }
+
+    fn name(&self) -> &'static str {
+        "ALMA"
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::traits::BatchExt;
+    use approx::assert_relative_eq;
+
+    #[test]
+    fn rejects_zero_period() {
+        assert!(matches!(Alma::new(0, 0.85, 6.0), Err(Error::PeriodZero)));
+    }
+
+    #[test]
+    fn rejects_invalid_offset() {
+        assert!(matches!(
+            Alma::new(9, -0.1, 6.0),
+            Err(Error::InvalidPeriod { .. })
+        ));
+        assert!(matches!(
+            Alma::new(9, 1.1, 6.0),
+            Err(Error::InvalidPeriod { .. })
+        ));
+        assert!(matches!(
+            Alma::new(9, f64::NAN, 6.0),
+            Err(Error::InvalidPeriod { .. })
+        ));
+    }
+
+    #[test]
+    fn rejects_invalid_sigma() {
+        assert!(matches!(
+            Alma::new(9, 0.85, 0.0),
+            Err(Error::InvalidPeriod { .. })
+        ));
+        assert!(matches!(
+            Alma::new(9, 0.85, -1.0),
+            Err(Error::InvalidPeriod { .. })
+        ));
+        assert!(matches!(
+            Alma::new(9, 0.85, f64::INFINITY),
+            Err(Error::InvalidPeriod { .. })
+        ));
+    }
+
+    #[test]
+    fn accessors_and_metadata() {
+        let alma = Alma::new(9, 0.85, 6.0).unwrap();
+        assert_eq!(alma.period(), 9);
+        assert_eq!(alma.warmup_period(), 9);
+        assert_eq!(alma.name(), "ALMA");
+        assert!((alma.offset() - 0.85).abs() < 1e-12);
+        assert!((alma.sigma() - 6.0).abs() < 1e-12);
+        // Weights are normalised by construction.
+        let sum: f64 = alma.weights.iter().sum();
+        assert_relative_eq!(sum, 1.0, epsilon = 1e-12);
+    }
+
+    #[test]
+    fn classic_factory() {
+        let a = Alma::classic();
+        assert_eq!(a.period(), 9);
+        assert!((a.offset() - 0.85).abs() < 1e-12);
+        assert!((a.sigma() - 6.0).abs() < 1e-12);
+    }
+
+    #[test]
+    fn constant_series_yields_the_constant() {
+        // Normalised weights sum to 1, so any constant is reproduced exactly.
+        let mut alma = Alma::new(9, 0.85, 6.0).unwrap();
+        let out = alma.batch(&[42.0_f64; 40]);
+        for v in out.iter().skip(8).flatten() {
+            assert_relative_eq!(*v, 42.0, epsilon = 1e-12);
+        }
+    }
+
+    #[test]
+    fn warmup_emits_first_value_at_period() {
+        let mut alma = Alma::new(5, 0.85, 6.0).unwrap();
+        for i in 0..4 {
+            assert_eq!(alma.update(f64::from(i)), None);
+        }
+        assert!(alma.update(4.0).is_some());
+    }
+
+    #[test]
+    fn reference_value_period_3() {
+        // ALMA(period=3, offset=0.85, sigma=6) on [10, 20, 30].
+        // m = 0.85 * 2 = 1.7;  s = 3 / 6 = 0.5;  2*s^2 = 0.5.
+        // Independently compute the normalised Gaussian weights and the
+        // expected weighted sum, then check the indicator output matches.
+        // Computing the expectation here (rather than pinning a printed
+        // constant) keeps the test stable across libm `exp` implementations.
+        let mut alma = Alma::new(3, 0.85, 6.0).unwrap();
+        alma.update(10.0);
+        alma.update(20.0);
+        let v = alma.update(30.0).expect("ALMA emits after period");
+
+        let w0 = (-((0.0_f64 - 1.7).powi(2)) / 0.5).exp();
+        let w1 = (-((1.0_f64 - 1.7).powi(2)) / 0.5).exp();
+        let w2 = (-((2.0_f64 - 1.7).powi(2)) / 0.5).exp();
+        let s = w0 + w1 + w2;
+        let expected = (10.0 * w0 + 20.0 * w1 + 30.0 * w2) / s;
+
+        // The weighted sum is heavily skewed toward the newest sample so the
+        // output must sit close to but below the latest input (30).
+        assert!(v > 25.0 && v < 30.0, "ALMA(3) on [10,20,30] = {v}");
+        assert_relative_eq!(v, expected, epsilon = 1e-12);
+    }
+
+    #[test]
+    fn offset_zero_centres_on_oldest_sample() {
+        // With offset = 0 the Gaussian peaks at index 0, so ALMA leans toward
+        // the oldest sample in the window and away from the newest.
+        let mut alma = Alma::new(5, 0.0, 6.0).unwrap();
+        let series: Vec<f64> = (1..=5).map(f64::from).collect();
+        let mut last = None;
+        for p in &series {
+            last = alma.update(*p);
+        }
+        let v = last.unwrap();
+        let mean = series.iter().sum::<f64>() / series.len() as f64;
+        // Oldest sample is 1.0, mean is 3.0; an offset-0 ALMA should sit
+        // strictly below the mean.
+        assert!(v < mean, "{v} should be less than {mean}");
+    }
+
+    #[test]
+    fn offset_one_centres_on_newest_sample() {
+        // Symmetric to the above: offset = 1 leans toward the newest sample.
+        let mut alma = Alma::new(5, 1.0, 6.0).unwrap();
+        let series: Vec<f64> = (1..=5).map(f64::from).collect();
+        let mut last = None;
+        for p in &series {
+            last = alma.update(*p);
+        }
+        let v = last.unwrap();
+        let mean = series.iter().sum::<f64>() / series.len() as f64;
+        assert!(v > mean, "{v} should exceed {mean}");
+    }
+
+    #[test]
+    fn batch_equals_streaming() {
+        let prices: Vec<f64> = (1..=100)
+            .map(|i| (f64::from(i) * 0.2).sin() * 5.0 + f64::from(i) * 0.1)
+            .collect();
+        let mut a = Alma::new(9, 0.85, 6.0).unwrap();
+        let mut b = Alma::new(9, 0.85, 6.0).unwrap();
+        assert_eq!(
+            a.batch(&prices),
+            prices.iter().map(|p| b.update(*p)).collect::<Vec<_>>()
+        );
+    }
+
+    #[test]
+    fn reset_clears_state() {
+        let mut alma = Alma::new(9, 0.85, 6.0).unwrap();
+        alma.batch(&(1..=40).map(f64::from).collect::<Vec<_>>());
+        assert!(alma.is_ready());
+        alma.reset();
+        assert!(!alma.is_ready());
+        assert_eq!(alma.update(1.0), None);
+    }
+
+    #[test]
+    fn ignores_non_finite_input() {
+        let mut alma = Alma::new(5, 0.85, 6.0).unwrap();
+        alma.batch(&(1..=5).map(f64::from).collect::<Vec<_>>());
+        let before = alma.update(6.0).unwrap();
+        // Non-finite inputs leave the window/current untouched.
+        assert_eq!(alma.update(f64::NAN), Some(before));
+        assert_eq!(alma.update(f64::INFINITY), Some(before));
+    }
+}

crates/wickra-core/src/indicators/mod.rs

@@ -7,6 +7,7 @@
 mod accelerator_oscillator;
 mod adl;
 mod adx;
+mod alma;
 mod aroon;
 mod aroon_oscillator;
 mod atr;
@@ -79,6 +80,7 @@ mod zlema;
 pub use accelerator_oscillator::AcceleratorOscillator;
 pub use adl::Adl;
 pub use adx::{Adx, AdxOutput};
+pub use alma::Alma;
 pub use aroon::{Aroon, AroonOutput};
 pub use aroon_oscillator::AroonOscillator;
 pub use atr::Atr;

crates/wickra-core/src/lib.rs

@@ -44,7 +44,7 @@ pub mod indicators;
 
 pub use error::{Error, Result};
 pub use indicators::{
-    AcceleratorOscillator, Adl, Adx, AdxOutput, Aroon, AroonOscillator, AroonOutput, Atr,
+    AcceleratorOscillator, Adl, Adx, AdxOutput, Alma, Aroon, AroonOscillator, AroonOutput, Atr,
     AtrTrailingStop, AwesomeOscillator, BalanceOfPower, BollingerBands, BollingerBandwidth,
     BollingerOutput, Cci, ChaikinMoneyFlow, ChaikinOscillator, ChaikinVolatility, ChandeKrollStop,
     ChandeKrollStopOutput, ChandelierExit, ChandelierExitOutput, ChoppinessIndex, Cmo, Coppock,

crates/wickra/benches/indicators.rs

@@ -19,7 +19,7 @@
 use criterion::{criterion_group, criterion_main, BenchmarkId, Criterion, Throughput};
 use std::hint::black_box;
 use wickra::{
-    Atr, BatchExt, BollingerBands, Candle, Ema, Indicator, MacdIndicator, Obv, Rsi, Sma,
+    Alma, Atr, BatchExt, BollingerBands, Candle, Ema, Indicator, MacdIndicator, Obv, Rsi, Sma,
     Stochastic, Wma,
 };
 use wickra_data::csv::CandleReader;
@@ -139,6 +139,7 @@ fn benches(c: &mut Criterion) {
     bench_scalar(c, "ema", &closes, || Ema::new(14).unwrap());
     bench_scalar(c, "wma", &closes, || Wma::new(14).unwrap());
     bench_scalar(c, "rsi", &closes, || Rsi::new(14).unwrap());
+    bench_scalar(c, "alma", &closes, || Alma::new(9, 0.85, 6.0).unwrap());
     bench_macd(c, &closes);
     bench_bollinger(c, &closes);
     bench_candle_input(c, "atr", &candles, || Atr::new(14).unwrap());