Module calculus

Vector differential calculus over temporal trajectories.

Provides first and second order finite differences, drift quantification, and basic stochastic process characterization for embedding trajectories.

Conventions

• Timestamps are in microseconds.
• Velocity units: vector displacement per microsecond.
• All functions operate on pre-sorted (timestamp, &[f32]) slices.

Structs

DriftReport

Drift report identifying the most changed dimensions.

Constants

MIN_POINTS_ACCELERATION 🔒

Minimum number of points for acceleration computation.

MIN_POINTS_STOCHASTIC 🔒

Minimum number of points for stochastic characterization.

MIN_POINTS_VELOCITY 🔒

Minimum number of points for velocity computation.

Functions

acceleration

Compute acceleration (second-order finite difference) at a target timestamp.

adf_statistic

Augmented Dickey-Fuller (ADF) test statistic for stationarity.

drift_magnitude_cosine

Compute cosine drift (1 - cosine_similarity) between two snapshots.

drift_magnitude_l2

Compute L2 drift magnitude between two snapshots.

drift_report

Generate a drift report between two snapshots.

find_closest_index 🔒

Find index of the closest point to a target timestamp.

hurst_exponent

Hurst exponent estimation via rescaled range (R/S) analysis.

linear_regression_slope 🔒

Simple linear regression slope.

realized_volatility

Realized volatility over a trajectory (standard deviation of returns).

rescaled_range 🔒

Rescaled range statistic for a given window size.

velocity

Compute velocity (first-order finite difference) at a target timestamp.