F2: add ZLEMA, T3 and VWMA advanced moving averages
Completes the F2 family (Advanced MAs) end to end: - Rust core: zlema.rs (Zero-Lag EMA over the de-lagged series 2·price − price[lag]), t3.rs (Tillson's six-EMA cascade with the volume-factor polynomial), vwma.rs (volume-weighted rolling mean with a zero-volume fallback to the unweighted mean). Each with a full Indicator impl, runnable doctest and reference-value / warmup / reset / batch==streaming / non-finite tests. - Python: PyZlema / PyT3 / PyVwma PyO3 classes + module registration + .pyi stubs (T3 defaults v=0.7). - Node: ZlemaNode via the scalar macro, explicit T3Node and VwmaNode classes; index.d.ts and index.js updated. - WASM: WasmZlema / WasmT3 via the scalar macro, explicit WasmVwma. - Wiki: Indicator-Zlema.md, Indicator-T3.md, Indicator-Vwma.md plus rows in Indicators-Overview.md and entries in Home.md. cargo fmt + clippy (core/wickra/data/wasm/node) clean; 232 core tests, 25 data tests and 33 doctests green.
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kingchenc
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//! Tillson T3 Moving Average.
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use crate::error::{Error, Result};
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use crate::traits::Indicator;
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use super::Ema;
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/// Tillson's T3 — a six-fold cascaded EMA recombined with a *volume factor* `v`.
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///
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/// T3 is the generalised DEMA applied three times. Tim Tillson's expansion of
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/// that triple application over six chained EMAs (`e1 … e6`, each of the same
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/// `period`) gives the closed form used here:
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///
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/// ```text
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/// c1 = −v³
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/// c2 = 3v² + 3v³
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/// c3 = −6v² − 3v − 3v³
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/// c4 = 1 + 3v + v³ + 3v²
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/// T3 = c1·e6 + c2·e5 + c3·e4 + c4·e3
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/// ```
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///
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/// The volume factor `v ∈ [0, 1]` controls the lag/smoothness trade-off:
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/// `v = 0` collapses T3 to the plain triple-cascaded EMA `e3`, while the
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/// conventional `v = 0.7` adds a hump that sharpens the response to turns.
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/// The coefficients always sum to `1`, so a constant series maps to itself.
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///
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/// The first output lands after `6·period − 5` inputs — the index at which the
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/// sixth cascaded EMA seeds.
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///
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/// # Example
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///
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/// ```
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/// use wickra_core::{Indicator, T3};
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///
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/// let mut indicator = T3::new(5, 0.7).unwrap();
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/// let mut last = None;
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/// for i in 0..120 {
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/// last = indicator.update(100.0 + f64::from(i));
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/// }
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/// assert!(last.is_some());
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/// ```
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#[derive(Debug, Clone)]
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pub struct T3 {
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period: usize,
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v: f64,
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c1: f64,
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c2: f64,
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c3: f64,
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c4: f64,
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e1: Ema,
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e2: Ema,
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e3: Ema,
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e4: Ema,
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e5: Ema,
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e6: Ema,
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current: Option<f64>,
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}
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impl T3 {
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/// Construct a new T3 with the given `period` and volume factor `v`.
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///
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/// # Errors
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///
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/// Returns [`Error::PeriodZero`] if `period == 0`, or
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/// [`Error::InvalidPeriod`] if `v` is non-finite or outside `[0.0, 1.0]`.
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pub fn new(period: usize, v: f64) -> Result<Self> {
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if period == 0 {
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return Err(Error::PeriodZero);
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}
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if !v.is_finite() || !(0.0..=1.0).contains(&v) {
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return Err(Error::InvalidPeriod {
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message: "T3 volume factor must be a finite value in [0.0, 1.0]",
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});
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}
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let v2 = v * v;
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let v3 = v2 * v;
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Ok(Self {
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period,
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v,
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c1: -v3,
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c2: 3.0 * v2 + 3.0 * v3,
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c3: -6.0 * v2 - 3.0 * v - 3.0 * v3,
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c4: 1.0 + 3.0 * v + v3 + 3.0 * v2,
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e1: Ema::new(period)?,
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e2: Ema::new(period)?,
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e3: Ema::new(period)?,
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e4: Ema::new(period)?,
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e5: Ema::new(period)?,
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e6: Ema::new(period)?,
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current: None,
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})
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}
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/// Configured period.
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pub const fn period(&self) -> usize {
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self.period
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}
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/// Configured volume factor `v`.
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pub const fn volume_factor(&self) -> f64 {
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self.v
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}
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/// Current value if available.
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pub const fn value(&self) -> Option<f64> {
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self.current
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}
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}
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impl Indicator for T3 {
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type Input = f64;
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type Output = f64;
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fn update(&mut self, input: f64) -> Option<f64> {
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if !input.is_finite() {
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// Non-finite input is ignored; the cascade is not advanced.
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return self.current;
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}
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let e1 = self.e1.update(input)?;
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let e2 = self.e2.update(e1)?;
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let e3 = self.e3.update(e2)?;
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let e4 = self.e4.update(e3)?;
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let e5 = self.e5.update(e4)?;
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let e6 = self.e6.update(e5)?;
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let out = self.c1 * e6 + self.c2 * e5 + self.c3 * e4 + self.c4 * e3;
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self.current = Some(out);
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Some(out)
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}
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fn reset(&mut self) {
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self.e1.reset();
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self.e2.reset();
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self.e3.reset();
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self.e4.reset();
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self.e5.reset();
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self.e6.reset();
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self.current = None;
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}
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fn warmup_period(&self) -> usize {
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6 * self.period - 5
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}
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fn is_ready(&self) -> bool {
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self.current.is_some()
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}
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fn name(&self) -> &'static str {
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"T3"
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}
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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use crate::traits::BatchExt;
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use approx::assert_relative_eq;
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#[test]
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fn new_rejects_zero_period() {
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assert!(matches!(T3::new(0, 0.7), Err(Error::PeriodZero)));
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}
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#[test]
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fn new_rejects_out_of_range_volume_factor() {
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assert!(matches!(T3::new(5, -0.1), Err(Error::InvalidPeriod { .. })));
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assert!(matches!(T3::new(5, 1.5), Err(Error::InvalidPeriod { .. })));
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assert!(matches!(
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T3::new(5, f64::NAN),
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Err(Error::InvalidPeriod { .. })
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));
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assert!(T3::new(5, 0.0).is_ok());
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assert!(T3::new(5, 1.0).is_ok());
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}
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#[test]
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fn coefficients_sum_to_one() {
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// c1 + c2 + c3 + c4 == 1 for any v, so a constant series is preserved.
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for &v in &[0.0, 0.3, 0.7, 1.0] {
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let t3 = T3::new(5, v).unwrap();
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assert_relative_eq!(t3.c1 + t3.c2 + t3.c3 + t3.c4, 1.0, epsilon = 1e-12);
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}
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}
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#[test]
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fn first_emission_at_warmup_period() {
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let mut t3 = T3::new(4, 0.7).unwrap();
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assert_eq!(t3.warmup_period(), 6 * 4 - 5);
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let out = t3.batch(&(1..=60).map(f64::from).collect::<Vec<_>>());
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for v in out.iter().take(t3.warmup_period() - 1) {
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assert!(v.is_none());
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}
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assert!(out[t3.warmup_period() - 1].is_some());
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}
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#[test]
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fn constant_series_yields_the_constant() {
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let mut t3 = T3::new(6, 0.7).unwrap();
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let out = t3.batch(&[50.0; 80]);
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let last = out.iter().rev().flatten().next().unwrap();
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assert_relative_eq!(*last, 50.0, epsilon = 1e-9);
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}
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#[test]
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fn zero_volume_factor_collapses_to_triple_cascaded_ema() {
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// With v = 0 the coefficients are c1=c2=c3=0, c4=1, so T3 == e3,
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// the third stage of the EMA cascade.
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let prices: Vec<f64> = (1..=80)
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.map(|i| 100.0 + (f64::from(i) * 0.2).sin() * 9.0)
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.collect();
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let mut t3 = T3::new(5, 0.0).unwrap();
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let got = t3.batch(&prices);
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let mut e1 = Ema::new(5).unwrap();
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let mut e2 = Ema::new(5).unwrap();
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let mut e3 = Ema::new(5).unwrap();
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let want: Vec<Option<f64>> = prices
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.iter()
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.map(|p| {
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e1.update(*p)
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.and_then(|a| e2.update(a))
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.and_then(|b| e3.update(b))
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})
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.collect();
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for i in (t3.warmup_period() - 1)..prices.len() {
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assert_relative_eq!(got[i].unwrap(), want[i].unwrap(), epsilon = 1e-9);
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}
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}
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#[test]
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fn ignores_non_finite_input() {
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let mut t3 = T3::new(4, 0.7).unwrap();
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let out = t3.batch(&(1..=60).map(f64::from).collect::<Vec<_>>());
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let last = *out.last().unwrap();
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assert!(last.is_some());
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assert_eq!(t3.update(f64::NAN), last);
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assert_eq!(t3.update(f64::INFINITY), last);
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}
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#[test]
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fn reset_clears_state() {
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let mut t3 = T3::new(4, 0.7).unwrap();
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t3.batch(&(1..=60).map(f64::from).collect::<Vec<_>>());
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assert!(t3.is_ready());
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t3.reset();
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assert!(!t3.is_ready());
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assert_eq!(t3.update(1.0), None);
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}
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#[test]
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fn batch_equals_streaming() {
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let prices: Vec<f64> = (1..=120)
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.map(|i| 100.0 + (f64::from(i) * 0.25).sin() * 7.0)
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.collect();
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let batch = T3::new(7, 0.7).unwrap().batch(&prices);
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let mut b = T3::new(7, 0.7).unwrap();
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let streamed: Vec<_> = prices.iter().map(|p| b.update(*p)).collect();
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assert_eq!(batch, streamed);
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}
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}
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