API map

Each module below is imported as import Nautilus.<Module> (names). The linked chapter gives each function's signature, input domain, and failure behavior.

Module	Start here
Nautilus.Special	Special functions
Nautilus.Distributions	Distributions and sampling limits
Nautilus.LinAlg	Linear algebra and conjugate gradient
Nautilus.Stats	Descriptive statistics
Nautilus.Testing	Hypothesis testing
Nautilus.Rolling	Rolling and expanding windows
Nautilus.Integrate	Numerical quadrature
Nautilus.Distance	Distance metrics
Nautilus.Ode	ODE solvers
Nautilus.Optim	Scalar optimization
Nautilus.Roots	Root finding
Nautilus.Interpolation	Interpolation
Nautilus.Sde	SDE solvers
Nautilus.CurveFit	Curve fitting
Nautilus.Signal	fftfreq

Smaller modules

These modules are a few formulas each and are documented here in full. All are f32 and check no arguments.

Nautilus.Info

Function	Signature	Returns
entropy	[n](p: &tensor[n, f32]) -> f32	-sum(p_i * ln(p_i)) in nats, skipping p_i <= 0
distribution_cross_entropy	[n](p: &tensor[n, f32], q: &tensor[n, f32]) -> f32	-sum(p_i * ln(q_i)), skipping p_i <= 0
kl_divergence	[n](p: &tensor[n, f32], q: &tensor[n, f32]) -> f32	sum(p_i * ln(p_i / q_i)), skipping p_i <= 0

The inputs are not normalized for you; pass probability vectors whose entries are non-negative and sum to 1. A q_i = 0 where p_i > 0 gives inf.

Nautilus.StateSpace

Scalar Kalman filter steps. Each returns a tuple; read fields with .0, .1, .2.

Function	Signature	Returns
kalman_predict_scalar	(mean, covariance, transition, process_var, control, control_input: f32) -> (f32, f32)	predicted (mean, covariance): transition * mean + control * control_input and transition^2 * covariance + process_var
kalman_update_scalar	(predicted_mean, predicted_covariance, observation, observation_matrix, observation_var: f32) -> (f32, f32, f32)	updated (mean, covariance, gain)
kalman_step_scalar	(mean, covariance, observation, transition, process_var, observation_matrix, observation_var: f32) -> (f32, f32, f32)	predict with no control input, then update
local_level_predict	(mean, covariance, process_var: f32) -> (f32, f32)	predict with transition = 1
local_level_update	(predicted_mean, predicted_covariance, observation, observation_var: f32) -> (f32, f32, f32)	update with observation_matrix = 1
local_level_step	(mean, covariance, observation, process_var, observation_var: f32) -> (f32, f32, f32)	one local-level (random walk plus noise) step

The gain is predicted_covariance * observation_matrix / innovation_covariance. Variances must be non-negative; a zero innovation covariance divides by zero.

Nautilus.TimeSeries

One-step point forecasts. values is the history, oldest first.

Function	Signature	Returns
ts_ewma_next	[n](values: &tensor[n, f32], alpha: f32, initial: f32) -> f32	the final EWMA, s = alpha * x + (1 - alpha) * s from s = initial
ts_ewma_series	[n](values: &tensor[n, f32], alpha: f32, initial: f32) -> tensor[n, f32]	the EWMA after each value
exponential_smoothing_next, exponential_smoothing_series	same arguments, with initial_level	identical to the two EWMA functions
ar1_predict_next	[n](values: &tensor[n, f32], intercept: f32, phi: f32) -> f32	intercept + phi * last
arma11_predict_next	[n](values: &tensor[n, f32], intercept: f32, phi: f32, theta: f32, last_error: f32) -> f32	intercept + phi * last + theta * last_error
arima110_predict_next	[n](values: &tensor[n, f32], drift: f32, phi: f32, theta: f32, last_error: f32) -> f32	last + drift + phi * (last - previous) + theta * last_error

These functions apply given coefficients; they do not estimate phi, theta, or alpha from data. alpha belongs in [0, 1]. On an empty history last is 0, and on a one-value history previous is 0.

Nautilus.Optimize

Function	Signature	Same as
minimize	(f: f32 -> f32, lo, hi, tol: f32, max_iters: i64) -> f32	brent_minimize in Scalar optimization
root	(f: f32 -> f32, lo, hi, tol: f32, max_iters: i64) -> f32	brent in Root finding

Nautilus.Core

version() -> string returns the installed Nautilus version string.