Crate nexus_stats 

Fixed-memory, zero-allocation streaming statistics for real-time systems.

65+ algorithms, all O(1) per update (or O(d) for d-dimensional filters), fixed memory. Core types are no_std compatible; types marked (std) require the std feature, (alloc) require alloc, and (std|libm) require either std or libm.

Usage

Import from the category module you need:

use nexus_stats::smoothing::EmaF64;
use nexus_stats::detection::CusumF64;
use nexus_stats::statistics::WelfordF64;
use nexus_stats::{DataError, ConfigError, Direction};

With the full feature (or individual subcrate features), advanced types are available through the same module paths:

// Requires `smoothing` feature
use nexus_stats::smoothing::KamaF64;
// Requires `regression` feature
use nexus_stats::regression::LinearRegressionF64;
// Requires `detection` feature
use nexus_stats::signal::AutocorrelationF64;

Data Quality & Error Policy

nexus-stats distinguishes two failure categories:

Data errors — NaN or Inf values reaching a streaming update. These indicate upstream data quality problems (broken feeds, failed computations, missing values). All update methods that accept float inputs return Result<_, DataError>. The library rejects the input and leaves internal state unchanged. The caller declares the policy:

• .unwrap() to crash on bad data (testing, strict systems)
• Log and continue (monitoring, degraded-mode operation)
• Increment a counter and trigger a circuit breaker (production)

Programmer errors — wrong dimensions, out-of-range indices, type misuse. These are bugs in the calling code. The library panics via assert!. Fix the code.

Internal State Invariant

Given only finite (non-NaN, non-Inf) inputs, all internal accumulators remain finite for typical workloads. Extreme value ranges (>1e150) or very long-running instances (billions of updates) can cause internal accumulator overflow through summation. For long-running systems: call reset() periodically, use exponentially-weighted variants (EW*) which naturally bound growth, or use .max_covariance() on RLS filters to auto-reset when the covariance matrix diverges.

Categories

Core (always available)

Module	Contents
smoothing	EMA, AsymEma, Slew
detection	CUSUM
statistics	Welford, Moments, EwmaVar, Covariance, HarmonicMean, Percentile
monitoring	Drawdown, Windowed Min/Max, CoDel, Liveness, EventRate, Jitter, ErrorRate, Saturation
control	DeadBand, Hysteresis, Debounce, LevelCrossing, Diff

Advanced (feature-gated, re-exported from subcrates)

Feature	Module	Contents
smoothing	smoothing	+ Holt, KAMA, Spring, Kalman1d, WindowedMedian
detection	detection	+ MOSUM, Shiryaev-Roberts, AdaptiveThreshold, RobustZ, TrendAlert, MultiGate
detection	signal	Autocorrelation, CrossCorrelation, Entropy, TransferEntropy
detection	estimation	+ SPRT
regression	regression	Linear, Polynomial, EW variants, Transformed, LogisticRegression
regression	learning	LMS, NLMS, RLS, OnlineKMeans, GD, AdaGrad, Adam
regression	estimation	+ Kalman 2d/3d, BetaBinomial, GammaPoisson
control	control	+ PeakDetector, BoolWindow
control	frequency	TopK, FlexProportion, DecayAccum
full	all	Everything above

Features

Feature	Default	Enables
std	yes	Instant-based windowed/CoDel/liveness/event-rate types, sqrt/exp intrinsics
alloc	with std	MOSUM, KAMA, WindowedMedian, BoolWindow, adaptive filters, optimizers
libm	no	Pure Rust sqrt/exp fallback for no_std (enables Shiryaev-Roberts, etc.)
smoothing	no	Advanced smoothing types (Holt, KAMA, Spring, Kalman1d, WindowedMedian)
detection	no	Advanced detection + signal analysis (implies smoothing)
regression	no	Regression, learning, estimation types
control	no	Advanced control + frequency types
full	no	All subcrates

Modules

control

Control, thresholding, and differencing.

detection

Change detection and anomaly detection.

estimation

State estimation, Bayesian inference, and hypothesis testing.

frequency

Frequency counting and scoring.

learning

Adaptive filters, online learning, and optimization.

monitoring

Monitoring and health tracking. Monitoring and health tracking. System monitoring and operational health.

regression

Regression and classification.

signal

Signal analysis and information theory.

smoothing

Smoothing and filtering primitives.

statistics

Core streaming statistics. Core streaming statistics. Core streaming statistics.

Macros

feature_vector

Generates a named feature vector struct where every field is f64.

Enums

Condition

System condition state.

ConfigError

Configuration error from building a stats primitive.

DataError

Error returned when a streaming update receives invalid data.

Direction

Directional change or anomaly direction.