interp

Status: released v0.2.1.

Interpolation, splines and smoothing in pure Go (CGO_ENABLED=0), validated against SciPy and NumPy.

go get github.com/go-approx/interp@v0.2.1

import "github.com/go-approx/interp"

s, _ := interp.NewCubicSpline(x, y, "not-a-knot")   // scipy CubicSpline, MATLAB spline
v := s.At(2.5); d := s.Derivative(1).At(2.5); area := s.Integrate(0, 4)

b, _ := interp.MakeInterpSpline(x, y, 5, nil)       // make_interp_spline
sm, _ := interp.MakeSplrep(x, y, 3, 0.05, nil)      // FITPACK smoothing spline

What is provided

The README has the full table with the MATLAB equivalents.

Verification

The reference tools are SciPy 1.18.1 and NumPy 2.5.4, run as oracles from Go by the tag-gated harness oracle_test.go. The harness generates the inputs and writes the answers to testdata/*.json; the ordinary tests read them and need no Python.

Inputs include the edge cases: 1, 2 and 3 points, duplicate and unsorted x, NaN and Inf in x and y, queries outside the range and exactly on the nodes, nodes clustered over 14 orders of magnitude, offsets of 1e8, spans of 1e-9, values of 1e150 and 1e-290, mismatched lengths, invalid boundary conditions and knots, and n = 1e5 and 1e6. Where SciPy raises, the Go constructor returns an error and the fixture says so.

Octave is not installed on the build host, so MATLAB/Octave semantics are implemented from the MathWorks documentation and checked through the SciPy objects that implement the same maths, not against Octave.

Differences from SciPy

Errors are returned, not raised, and no function panics on input. NewInterp1D rejects NaN in x. numpy.interp is reproduced with math.FMA because NumPy’s C loop is compiled with fused multiply-add on arm64; every other kernel rounds each product before summing. Tensor-product splines are solved one axis at a time. RectBivariateSpline smoothing (s > 0) and the periodic smoothing spline of make_splrep are not provided.

Performance

docs/perf.md has the table: construction and evaluation at 10^3 to 10^6 points, Go against SciPy on one core, interleaved rounds, with the load average of the host.

The README, measured 2026-10-19 (load 3–5) and, for the rows the second performance pass touched, 2026-10-21 (load 5–7), reports interp faster than SciPy on PCHIP, Akima/makima, cubic construction (1.3–4x) and evaluation (2–2.7x), periodic cubic construction, B-spline evaluation (quintic 1.95–2.4x), numpy.interp (1.2–2x), linear interp1d, nearest-neighbour interp1d, make_splrep (2x), the legacy splrep with Splrep (2.8–2.9x), least-squares splines, every RegularGridInterpolator construction and RectBivariateSpline construction (2.1–2.5x) and evaluation (1.6–2.6x). The third performance pass (go-approx/interp#5, measured 2026-10-22 at load 7.4–8) makes RegularGridInterpolator linear evaluation 7–10x and the cubic evaluation of shuffled queries 3.3–9.2x faster than SciPy, with bit-identical results.

The two former gaps are closed in v0.2.1: RegularGridInterpolator linear evaluation (7–10x faster than SciPy) and the cubic evaluation of shuffled queries (3–9x faster). Every measured interp case is now at or below SciPy’s time; the only row at parity is quintic make_interp_spline construction at 10^4 points (0.99x, within noise).

Gaps

Scattered-data interpolation (Delaunay, natural neighbour, RBF) is a later work item. There is no periodic smoothing spline, no parametric splines (make_splprep), no make_smoothing_spline, no MATLAB interp2 cubic kernel, no complex-valued data, no N-dimensional y, and PPoly.roots and BSpline.roots are not provided.

Source: go-approx/interp, BSD-3-Clause.