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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# VWMA
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> Volume-Weighted Moving Average — a rolling mean of closes where each bar
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> is weighted by its own traded volume.
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## Quick reference
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| Field | Value |
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|-------|-------|
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| Family | Trend |
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| Sub-category | Volume-weighted averages |
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| Input type | `Candle` (uses `close` and `volume`) |
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| Output type | `f64` |
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| Output range | unbounded; tracks the input price scale |
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| Default parameters | `period` is required (no default in either binding) |
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| Warmup period | `period` |
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| Interpretation | Trend line that leans toward high-conviction (high-volume) bars. |
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## Formula
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```
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VWMA_t = Σ(close_i · volume_i) / Σ(volume_i) over the last `period` bars
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```
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A heavy bar pulls the average toward its close; a thin bar barely moves
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it. Both the numerator (`Σ price·volume`) and denominator (`Σ volume`)
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are maintained as O(1) rolling sums, so `update` is O(1) regardless of
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`period`.
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If **every** bar in the window has zero volume the weighted mean is
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undefined (`0 / 0`). VWMA then falls back to the plain unweighted mean of
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the `period` closes, so the output is always finite and defined.
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## Parameters
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| Name | Type | Default | Valid range | Description |
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|----------|---------|---------|-------------|-------------|
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| `period` | `usize` | none | `>= 1` | Rolling window length in bars. `period = 0` errors with `Error::PeriodZero`. |
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There is no Python `#[pyo3(signature = …)]` default for `VWMA`, so
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`wickra.VWMA(period)` requires the period explicitly.
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## Inputs / Outputs
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From `crates/wickra-core/src/indicators/vwma.rs`:
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```rust
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impl Indicator for Vwma {
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type Input = Candle;
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type Output = f64;
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// update(&mut self, input: Candle) -> Option<f64>
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}
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```
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`VWMA` is a **candle-input** indicator: it reads `close` and `volume` from
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each `Candle`. In Python the streaming `update` accepts a 6-tuple or a
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dict; the batch helper takes `close` and `volume` numpy arrays. Node and
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WASM expose `update(close, volume)` and `batch(close, volume)`.
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## Warmup
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`Vwma::new(period).warmup_period() == period`. The first `period − 1`
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candles fill the rolling window; the `period`-th `update()` produces the
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first weighted mean.
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## Edge cases
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- **Constant closes.** Closes all equal to `c` give `VWMA = c` regardless
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of the volumes (`Σ c·v / Σ v = c`), and the zero-volume fallback also
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yields `c` (`constant_series_yields_the_constant` pins this).
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- **Zero-volume window.** If every bar in the window has `volume = 0`,
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VWMA returns the unweighted mean of the `period` closes
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(`zero_volume_window_falls_back_to_unweighted_mean` pins this).
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- **Candle validation.** `Candle::new` already rejects NaN/infinite fields
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and negative volume, so `update` never sees an invalid bar — there is no
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separate non-finite guard.
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- **Reset.** `vwma.reset()` clears the window and all three rolling sums.
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## Examples
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### Rust
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```rust
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use wickra::{Candle, Indicator, Vwma};
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fn main() -> Result<(), Box<dyn std::error::Error>> {
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let mut vwma = Vwma::new(2)?;
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// (close, volume): (10, 1) then (20, 3).
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let a = Candle::new(10.0, 10.0, 10.0, 10.0, 1.0, 0)?;
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let b = Candle::new(20.0, 20.0, 20.0, 20.0, 3.0, 1)?;
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println!("{:?}", vwma.update(a));
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println!("{:?}", vwma.update(b));
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Ok(())
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}
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```
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Output:
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```
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None
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Some(17.5)
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```
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The window holds two bars: `(10·1 + 20·3) / (1 + 3) = 70 / 4 = 17.5`. The
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heavier bar at `20` dominates, so the result sits well above the simple
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mean of `15`. This matches the `reference_value` test in
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`crates/wickra-core/src/indicators/vwma.rs`.
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### Python
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```python
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import numpy as np
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import wickra as ta
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vwma = ta.VWMA(2)
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close = np.array([10.0, 20.0, 30.0])
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volume = np.array([1.0, 3.0, 1.0])
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print(vwma.batch(close, volume))
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print("warmup_period =", vwma.warmup_period())
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```
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Output:
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```
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[ nan 17.5 22.5]
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warmup_period = 2
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```
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### Node
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```javascript
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const ta = require('wickra');
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const vwma = new ta.VWMA(2);
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console.log(vwma.batch([10, 20, 30], [1, 3, 1]));
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console.log('warmupPeriod:', vwma.warmupPeriod());
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```
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Output:
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```
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[ NaN, 17.5, 22.5 ]
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warmupPeriod: 2
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```
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## Interpretation
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`Vwma` is a trend line that respects participation. Compared with an
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equal-weighted `Sma` of the same period, it reacts faster to moves backed
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by heavy volume and lags moves on thin volume. The classic read is the
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`Vwma`-vs-`Sma` relationship: `Vwma` above `Sma` means recent strength was
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volume-backed (more trustworthy); `Vwma` below `Sma` means the up-moves
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came on light volume. It is a session-independent cousin of
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[`Vwap`](../volume/Indicator-Vwap.md) — VWAP weights by volume since the
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start of the stream, VWMA over a fixed rolling window.
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## Common pitfalls
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- **Feeding it scalar prices.** `VWMA` needs volume; it takes a `Candle`,
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not an `f64`. Use `Sma`/`Wma` for a pure price series.
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- **Assuming a zero-volume window is an error.** It is not — VWMA falls
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back to the unweighted mean. If that fallback matters to you, screen the
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window's total volume yourself.
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## References
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The volume-weighted moving average is a standard volume-weighted rolling
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mean; the rolling-sum formulation here matches the common pandas
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implementation `(close*volume).rolling(n).sum() / volume.rolling(n).sum()`,
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with an explicit zero-volume fallback added for robustness.
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## See also
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- [Indicator-Sma.md](Indicator-Sma.md) — the equal-weighted counterpart.
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- [Indicator-Vwap.md](../volume/Indicator-Vwap.md) — volume-weighted price
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since the start of the stream.
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- [Indicators-Overview.md](../../Indicators-Overview.md) — the full taxonomy.
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