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convinterp

High-order convolution interpolation on uniform grids in any number of dimensions, with derivatives and integrals, for Python. The core is written in Rust; the kernels are exact polynomials.

convinterp is a port of the Julia package ConvolutionInterpolations.jl, by the same author, and is tested against it.

Documentation: convinterp.org, with a user guide and accuracy and speed comparisons with SciPy.

Status: alpha. Interpolation, derivatives and integrals on uniform grids work in any dimension. Scattered data are coming.

Installation

pip install convinterp

Example

import numpy as np
from convinterp import convolution_interpolation

# 1D: data on a uniform grid
x = np.linspace(0.0, 2 * np.pi, 50)                     # 50 uniformly spaced knots
itp = convolution_interpolation(x, np.sin(x))           # the interpolant of sin(x)
print(itp(1.0))                                         # ≈ sin(1) = 0.841471

# derivatives: one order for the whole interpolant
d_itp = convolution_interpolation(x, np.sin(x), derivative=1)
print(d_itp(1.0))                                       # ≈ cos(1) = 0.540302

# integrals: a negative order, zero at the first knot x[0] = 0
i_itp = convolution_interpolation(x, np.sin(x), derivative=-1)
print(i_itp(1.0))                                       # ≈ 1 − cos(1) = 0.459698

# 2D: one knot array per axis, and data whose axis d runs along knots[d]
y = np.linspace(0.0, 1.0, 30)                           # knots of the second axis
data = np.sin(x)[:, None] * np.exp(y)[None, :]          # sin(x)·exp(y) on the 50 × 30 grid
itp2 = convolution_interpolation((x, y), data)          # the 2D interpolant
print(itp2(1.0, 0.5))                                   # ≈ sin(1)·exp(0.5) = 1.387351

# a mixed derivative, with an order per axis: ∂²/∂x∂y
dxy = convolution_interpolation((x, y), data, derivative=(1, 1))
print(dxy(1.0, 0.5))                                    # ≈ cos(1)·exp(0.5) = 0.890808

# arrays of points broadcast like NumPy arrays: here a 3 × 4 table of values
xs = np.array([[0.5], [1.0], [1.5]])                    # a column of x coordinates
ys = np.array([[0.1, 0.2, 0.3, 0.4]])                   # a row of y coordinates
print(itp2(xs, ys).shape)                               # (3, 4)

Kernels

kernel="auto" (the default) chooses by the number of dimensions: "b7" in 1D and 2D, "b5" in 3D, and narrower kernels beyond. You can choose any of:

kernel order of accuracy highest derivative highest integral
"a0" nearest neighbour none 2
"a1" linear none 2
"a3", "a4", "a5", "a7" cubic and higher 1 4
"b5", "b7", "b9", "b11", "b13" high order 3 to 7 6 to 8

Boundary conditions

The data are extended beyond each boundary by extrapolation: bc="detect" (the default) uses polynomial extrapolation where the data near the boundary allow it and linear otherwise. You can also choose "poly", "linear" or "quadratic", separately for each side and each axis.

Citing

If you use convinterp in your work, please cite it: doi.org/10.5281/zenodo.22972816 (always the latest version). A BibTeX entry is on the About page.

Declaration of AI Assistance

The Rust core and much of the Python code of convinterp were written with substantial assistance from Claude (Anthropic). The mathematical methods, the kernels and the reference implementation come from the author's Julia package ConvolutionInterpolations.jl, and the port is validated against it: the test suite compares convinterp with the Julia package across kernels, boundary conditions, derivative and integral orders and dimensions, with the boundary coefficients agreeing bit for bit. The author has reviewed and is responsible for all code.

License

MIT

Metadata

Release files for convinterp 0.2.0

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Table of built distributions (wheels) for convinterp 0.2.0
File
convinterp-0.2.0-pp311-pypy311_pp73-musllinux_1_2_x86_64.whl PyPy 3.11 PyPy 3.11 7.3 Linux musl 1.2+ x86-64 Details
convinterp-0.2.0-pp311-pypy311_pp73-musllinux_1_2_aarch64.whl PyPy 3.11 PyPy 3.11 7.3 Linux musl 1.2+ ARM64 Details
convinterp-0.2.0-pp311-pypy311_pp73-manylinux_2_17_x86_64.manylinux2014_x86_64.whl PyPy 3.11 PyPy 3.11 7.3 Linux glibc 2.17+ x86-64 Details
convinterp-0.2.0-pp311-pypy311_pp73-manylinux_2_17_aarch64.manylinux2014_aarch64.whl PyPy 3.11 PyPy 3.11 7.3 Linux glibc 2.17+ ARM64 Details
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convinterp-0.2.0-cp315-cp315-manylinux_2_17_x86_64.manylinux2014_x86_64.whl CPython 3.15 CPython 3.15 Linux glibc 2.17+ x86-64 Details
convinterp-0.2.0-cp314-cp314t-musllinux_1_2_x86_64.whl CPython 3.14 CPython 3.14 free-threading Linux musl 1.2+ x86-64 Details
convinterp-0.2.0-cp314-cp314t-musllinux_1_2_aarch64.whl CPython 3.14 CPython 3.14 free-threading Linux musl 1.2+ ARM64 Details
convinterp-0.2.0-cp314-cp314t-manylinux_2_17_x86_64.manylinux2014_x86_64.whl CPython 3.14 CPython 3.14 free-threading Linux glibc 2.17+ x86-64 Details
convinterp-0.2.0-cp314-cp314t-manylinux_2_17_aarch64.manylinux2014_aarch64.whl CPython 3.14 CPython 3.14 free-threading Linux glibc 2.17+ ARM64 Details
convinterp-0.2.0-cp314-cp314-win_arm64.whl CPython 3.14 CPython 3.14 Windows ARM64 Details
convinterp-0.2.0-cp314-cp314-win_amd64.whl CPython 3.14 CPython 3.14 Windows x86-64 Details
convinterp-0.2.0-cp314-cp314-musllinux_1_2_x86_64.whl CPython 3.14 CPython 3.14 Linux musl 1.2+ x86-64 Details
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convinterp-0.2.0-cp314-cp314-macosx_11_0_arm64.whl CPython 3.14 CPython 3.14 macOS 11.0+ ARM64 Details
convinterp-0.2.0-cp314-cp314-macosx_10_12_x86_64.whl CPython 3.14 CPython 3.14 macOS 10.12+ x86-64 Details
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convinterp-0.2.0-cp313-cp313-musllinux_1_2_x86_64.whl CPython 3.13 CPython 3.13 Linux musl 1.2+ x86-64 Details
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convinterp-0.2.0-cp313-cp313-manylinux_2_17_x86_64.manylinux2014_x86_64.whl CPython 3.13 CPython 3.13 Linux glibc 2.17+ x86-64 Details
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convinterp-0.2.0-cp313-cp313-macosx_10_12_x86_64.whl CPython 3.13 CPython 3.13 macOS 10.12+ x86-64 Details
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convinterp-0.2.0-cp312-cp312-musllinux_1_2_x86_64.whl CPython 3.12 CPython 3.12 Linux musl 1.2+ x86-64 Details
convinterp-0.2.0-cp312-cp312-musllinux_1_2_aarch64.whl CPython 3.12 CPython 3.12 Linux musl 1.2+ ARM64 Details
convinterp-0.2.0-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl CPython 3.12 CPython 3.12 Linux glibc 2.17+ x86-64 Details
convinterp-0.2.0-cp312-cp312-manylinux_2_17_aarch64.manylinux2014_aarch64.whl CPython 3.12 CPython 3.12 Linux glibc 2.17+ ARM64 Details
convinterp-0.2.0-cp312-cp312-macosx_11_0_arm64.whl CPython 3.12 CPython 3.12 macOS 11.0+ ARM64 Details
convinterp-0.2.0-cp312-cp312-macosx_10_12_x86_64.whl CPython 3.12 CPython 3.12 macOS 10.12+ x86-64 Details
convinterp-0.2.0-cp311-cp311-win_amd64.whl CPython 3.11 CPython 3.11 Windows x86-64 Details
convinterp-0.2.0-cp311-cp311-musllinux_1_2_x86_64.whl CPython 3.11 CPython 3.11 Linux musl 1.2+ x86-64 Details
convinterp-0.2.0-cp311-cp311-musllinux_1_2_aarch64.whl CPython 3.11 CPython 3.11 Linux musl 1.2+ ARM64 Details
convinterp-0.2.0-cp311-cp311-manylinux_2_17_x86_64.manylinux2014_x86_64.whl CPython 3.11 CPython 3.11 Linux glibc 2.17+ x86-64 Details
convinterp-0.2.0-cp311-cp311-manylinux_2_17_aarch64.manylinux2014_aarch64.whl CPython 3.11 CPython 3.11 Linux glibc 2.17+ ARM64 Details
convinterp-0.2.0-cp311-cp311-macosx_11_0_arm64.whl CPython 3.11 CPython 3.11 macOS 11.0+ ARM64 Details
convinterp-0.2.0-cp311-cp311-macosx_10_12_x86_64.whl CPython 3.11 CPython 3.11 macOS 10.12+ x86-64 Details
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convinterp-0.2.0-cp310-cp310-musllinux_1_2_x86_64.whl CPython 3.10 CPython 3.10 Linux musl 1.2+ x86-64 Details
convinterp-0.2.0-cp310-cp310-musllinux_1_2_aarch64.whl CPython 3.10 CPython 3.10 Linux musl 1.2+ ARM64 Details
convinterp-0.2.0-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl CPython 3.10 CPython 3.10 Linux glibc 2.17+ x86-64 Details
convinterp-0.2.0-cp310-cp310-manylinux_2_17_aarch64.manylinux2014_aarch64.whl CPython 3.10 CPython 3.10 Linux glibc 2.17+ ARM64 Details
convinterp-0.2.0-cp39-cp39-musllinux_1_2_x86_64.whl CPython 3.9 CPython 3.9 Linux musl 1.2+ x86-64 Details
convinterp-0.2.0-cp39-cp39-musllinux_1_2_aarch64.whl CPython 3.9 CPython 3.9 Linux musl 1.2+ ARM64 Details
convinterp-0.2.0-cp39-cp39-manylinux_2_17_x86_64.manylinux2014_x86_64.whl CPython 3.9 CPython 3.9 Linux glibc 2.17+ x86-64 Details
convinterp-0.2.0-cp39-cp39-manylinux_2_17_aarch64.manylinux2014_aarch64.whl CPython 3.9 CPython 3.9 Linux glibc 2.17+ ARM64 Details
convinterp-0.2.0-cp39-cp39-macosx_11_0_arm64.whl CPython 3.9 CPython 3.9 macOS 11.0+ ARM64 Details
convinterp-0.2.0-cp39-cp39-macosx_10_12_x86_64.whl CPython 3.9 CPython 3.9 macOS 10.12+ x86-64 Details

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Release files / convinterp-0.2.0-cp314-cp314-musllinux_1_2_x86_64.whl

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Release files / convinterp-0.2.0-cp314-cp314-musllinux_1_2_aarch64.whl

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Release files / convinterp-0.2.0-cp314-cp314-manylinux_2_17_x86_64.manylinux2014_x86_64.whl

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Release files / convinterp-0.2.0-cp314-cp314-manylinux_2_17_aarch64.manylinux2014_aarch64.whl

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Release files / convinterp-0.2.0-cp314-cp314-macosx_11_0_arm64.whl

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Release files / convinterp-0.2.0-cp314-cp314-macosx_10_12_x86_64.whl

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Release files / convinterp-0.2.0-cp313-cp313-win_arm64.whl

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Release files / convinterp-0.2.0-cp313-cp313-musllinux_1_2_x86_64.whl

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Release files / convinterp-0.2.0-cp313-cp313-musllinux_1_2_aarch64.whl

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Release files / convinterp-0.2.0-cp313-cp313-manylinux_2_17_x86_64.manylinux2014_x86_64.whl

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Release files / convinterp-0.2.0-cp313-cp313-macosx_11_0_arm64.whl

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Release files / convinterp-0.2.0-cp313-cp313-macosx_10_12_x86_64.whl

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Release files / convinterp-0.2.0-cp312-cp312-win_arm64.whl

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Release files / convinterp-0.2.0-cp312-cp312-win_amd64.whl

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Release files / convinterp-0.2.0-cp312-cp312-musllinux_1_2_x86_64.whl

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Release files / convinterp-0.2.0-cp312-cp312-musllinux_1_2_aarch64.whl

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Release files / convinterp-0.2.0-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl

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Release files / convinterp-0.2.0-cp312-cp312-manylinux_2_17_aarch64.manylinux2014_aarch64.whl

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Release files / convinterp-0.2.0-cp312-cp312-macosx_11_0_arm64.whl

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Release files / convinterp-0.2.0-cp312-cp312-macosx_10_12_x86_64.whl

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Release files / convinterp-0.2.0-cp311-cp311-manylinux_2_17_x86_64.manylinux2014_x86_64.whl

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Release files / convinterp-0.2.0-cp311-cp311-manylinux_2_17_aarch64.manylinux2014_aarch64.whl

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Release files / convinterp-0.2.0-cp310-cp310-musllinux_1_2_x86_64.whl

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Release files / convinterp-0.2.0-cp310-cp310-musllinux_1_2_aarch64.whl

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Release files / convinterp-0.2.0-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl

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Release files / convinterp-0.2.0-cp39-cp39-musllinux_1_2_x86_64.whl

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Release files / convinterp-0.2.0-cp39-cp39-musllinux_1_2_aarch64.whl

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Release files / convinterp-0.2.0-cp39-cp39-manylinux_2_17_x86_64.manylinux2014_x86_64.whl

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Release files / convinterp-0.2.0-cp39-cp39-macosx_11_0_arm64.whl

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Release files / convinterp-0.2.0-cp39-cp39-macosx_10_12_x86_64.whl

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