Function trix

TRIX (Jack Hutson) — the 1-bar rate of change of a triple-smoothed EMA, in percent, with its own EMA as a signal line:

T          = EMA(EMA(EMA(column, period), period), period)
${prefix}       = 100 × (T[i] − T[i−1]) / T[i−1]
${prefix}Signal = EMA(${prefix}, signalPeriod)
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Appends two columns. Triple smoothing strips the cycles shorter than period almost entirely, so what is left is a slow, nearly noise-free momentum oscillator that crosses zero when the smoothed trend turns.

The line is named ${prefix}, not ${prefix}Line — a deliberate departure from macd's macdLine / macdSignal shape, because "the TRIX" is the line and trixLine reads as a stutter. The signal keeps the family suffix.

Definition — TA-Lib's, exactly

100 · (T[i]/T[i−1] − 1), a percent rate of change, which is what TA-Lib's TRIX computes and what the generator asserts against it (see below). Some write-ups say a log rate of change instead (100 · ln(T[i]/T[i−1])); the two agree to about 0.5% of the reading at a 1% bar-over-bar move and diverge from there, so the choice is real, and this is TA-Lib's.

period is the span of each EMA, not of the chain. trix({ period: 15 }) is three 15-bar EMAs, not a 5-bar one applied three times — the universal convention, restated because "period" on a triple-smoothed study is ambiguous on its face.

This is not TEMA. The K2 menu's tema is Patrick Mulloy's 3·EMA − 3·EMA² + EMA³ — a de-lagged average built from the same three chained EMAs. TRIX wants the chain itself, EMA³, so it composes three movingAverageValues(…, 'ema') passes rather than reaching for tema. (Reusing tema here would be silently wrong, not slightly wrong: the combination changes the phase, and its rate of change is a different indicator.)

The EMA seed, and what the oracle asserts

The EMAs are pond's — first-sample seed, α = 2/(period+1) — as everywhere else in the package, so trix cannot disagree with ema() inside the package (the macd precedent; TA-Lib seeds each EMA on the SMA of its first n values instead). The generator therefore checks the two questions separately: it rebuilds the same formula on TA-Lib's SMA seed and requires bit-level agreement with talib.TRIX (so a wrong coefficient, a dropped stage or a log-vs-percent slip fails at 1e-9), then bounds pond's seed transient over the last 20 shared bars. Measured on the oracle input: the SMA-seeded replication matches talib.TRIX to 2.2e-14 at both period 15 and period 5, with identical null masks; pond's seed transient is 8.75% of scale at the first shared bar and 0.85% over the last 20 at period 15 (11.01% → 0.0000% at period 5). That is a looser tail than the MA family's because TRIX's own scale is a percent rate of change (0.45 here) rather than a price, and at period 15 only 37 bars are shared at all — the generator carries the measured separation from the wrong smoothing rates (8.5% and 9.8%).

The signal line has no vendor reference — TA-Lib's TRIX returns the line alone. signalPeriod defaults to 9, which is ChartIQ's default (and MACD's), and the signal is a pandas replication in the oracle.

Warm-up: per column

Each EMA stage steps over the previous stage's warm-up rather than poisoning its seed with it, so on gap-free input T first lands on bar 3·period − 3 and the rate of change one bar later, at 3·period − 2 — TA-Lib's TRIX lookback (3·(period−1) + 1) exactly, which the generator asserts as a null mask, not just a magnitude. The signal starts signalPeriod − 1 bars after the line. Each column is emitted where it is defined rather than both waiting for the slower.

Edges

• Scale-invariant. A rate of change of a linear filter of the price is a ratio, so multiplying every bar by any positive constant leaves both columns unchanged — pinned as a property test. (Contrast macd, which is linear in price.)
• A zero previous value of the smoothed line → undefined. Percent change off zero has no answer, and x/0 would be an infinity that withColumn rejects outright. Unreachable on real prices — T is a convex combination of positive prices — but reachable when column is another study's output that crosses zero (a MACD histogram, say), which is a supported thing to run this over.
• A leading gap shifts the start; an interior gap blanks the bar and the bar after it (the rate of change reads a predecessor) and the EMAs then carry on — the ema family's skip rule, three stages deep.