Interpolation

The Nautilus.Interpolation module provides three interpolation functions for f32 data. All are pure (no effects) and polymorphic over tensor length.

linear_interp_uniform

Interpolates on a uniformly-spaced grid. The caller provides the y-values as a tensor, the x-range endpoints, and a query point.

import Nautilus.Interpolation (linear_interp_uniform)

// ys: 5 equally-spaced y-values over [0, 4]
// Query at x = 1.5 (between indices 1 and 2)
result = linear_interp_uniform(ys, cast(0.0, f32), cast(4.0, f32), cast(1.5, f32))

Signature: [n](ys: tensor[n, f32], x_min: f32, x_max: f32, x_query: f32) -> f32

Extrapolation is clamped: queries outside [x_min, x_max] return the nearest endpoint value. Internally uses fold over enumerate(to_list(ys)) to locate the bracketing interval.

linear_interp_sorted

Interpolates on a non-uniform but sorted grid. The caller provides both x-knots and y-values as separate tensors.

import Nautilus.Interpolation (linear_interp_sorted)

result = linear_interp_sorted(xs, ys, cast(2.5, f32))

Signature: [n](xs: tensor[n, f32], ys: tensor[n, f32], x_query: f32) -> f32

Extrapolation is flat: queries below the first knot return the first y-value; queries above the last knot return the last y-value. The xs tensor must be sorted in ascending order.

cubic_hermite

Single-interval cubic Hermite spline. The caller supplies two endpoints (x0, y0) and (x1, y1), tangent slopes m0 and m1 at each endpoint, and a query point.

import Nautilus.Interpolation (cubic_hermite)

// Linear data with matching slopes -> reduces to linear interpolation
result = cubic_hermite(
  cast(0.0, f32), cast(1.0, f32),   // x0, x1
  cast(0.0, f32), cast(1.0, f32),   // y0, y1
  cast(1.0, f32), cast(1.0, f32),   // m0, m1
  cast(0.5, f32)                     // x_query
)
// result = 0.5

Signature: (x0: f32, x1: f32, y0: f32, y1: f32, m0: f32, m1: f32, x_query: f32) -> f32

Uses the standard Hermite basis polynomials h00, h10, h01, h11 to ensure C1 continuity. Returns NaN if x0 == x1 (zero-width interval). To build a full piecewise Hermite spline, call this function once per interval.