QuanTAlib/lib/trends_FIR/trima/Trima.md

TRIMA: Triangular Moving Average

The weighted blanket of moving averages. It doesn't care where the price is going right now; it cares where the price feels most comfortable.

Property	Value
Category	Trend (FIR MA)
Inputs	Source (close)
Parameters	period
Outputs	Single series (Trima)
Output range	Tracks input
Warmup	p1 + p2 - 1 bars
PineScript	trima.pine
Signature	trima_signature

• The Triangular Moving Average (TRIMA) places the majority of its weight on the middle of the data window, tapering off linearly towards the ends.
• Similar: WMA, SMA | Complementary: Volume analysis | Trading note: Triangular MA; double-smoothed SMA with triangle-shaped weights peaking at center.
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

The Triangular Moving Average (TRIMA) places the majority of its weight on the middle of the data window, tapering off linearly towards the ends. This creates a triangular weight distribution (hence the name). It is mathematically equivalent to a double-smoothed SMA.

Historical Context

TRIMA has been a staple in cycle analysis. By double-smoothing the data, it effectively removes high-frequency noise, making it ideal for identifying dominant market cycles. However, this smoothness comes at the cost of significant lag.

Architecture & Physics

TRIMA is implemented as a cascade of two Simple Moving Averages.

TRIMA = SMA(SMA(Price, P_1), P_2)

Where P_1 and P_2 are roughly half the total period.

The Weight Distribution

An SMA has a rectangular weight distribution (all weights equal). A WMA has a linear distribution (heaviest at the end). TRIMA has a triangular distribution (heaviest in the center).

Mathematical Foundation

1. Period Splitting

P_1 = \lfloor \frac{N}{2} \rfloor + 1 P_2 = \lceil \frac{N+1}{2} \rceil

2. The Cascade

TRIMA = SMA(SMA(Price, P_1), P_2)

Performance Profile

Operation Count (Streaming Mode, Scalar)

TRIMA chains two SMA instances. Each SMA is O(1) with ~17 cycles (see SMA.md).

Component	Operations	Cost (cycles)
SMA(P₁)	2 ADD/SUB, 1 DIV	~17
SMA(P₂)	2 ADD/SUB, 1 DIV	~17
Total	4 ADD/SUB, 2 DIV	~34 cycles

Hot path breakdown:

• First SMA smooths the raw price → ~17 cycles
• Second SMA smooths the first SMA's output → ~17 cycles
• No additional combining math required

Batch Mode (SIMD)

Each SMA component benefits from SIMD prefix-sum optimization:

Component	Scalar (512 bars)	SIMD (AVX2)	Speedup
SMA(P₁) prefix sum	~8.5K cycles	~1K cycles	~8×
SMA(P₂) prefix sum	~8.5K cycles	~1K cycles	~8×
Total	~17K	~2K	~8×

Quality Metrics

Metric	Score	Notes
Accuracy	10/10	Matches TA-Lib exactly
Timeliness	2/10	Significant lag; double smoothing delays signals
Overshoot	10/10	Never overshoots input data range (FIR property)
Smoothness	9/10	Very smooth; triangular weighting suppresses noise

Validation

Library	Status	Notes
TA-Lib	✅	Matches TA_TRIMA exactly.
Skender	✅	Matches composite SMA(SMA) logic.
Tulip	✅	Matches trima exactly.
Ooples	N/A	Not implemented.